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Doctoral Thesis

Personalized drug dosing through modeling and feedback

Author(s): Caruso, Antonello L. G.

Publication Date: 2009

Permanent Link: https://doi.org/10.3929/ethz-a-006005960

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Diss. ETH No. 18819

Personalized drug dosingthrough modeling and feedback

A dissertation submitted to

ETH ZURICH

for the degree of

DOCTOR OF SCIENCES

presented by

ANTONELLO L. G. CARUSO

M.Eng. Biomedical Engineering

Politecnico di Milano

born 25.04.1981

citizen of Italy

accepted on the recommendation of

Prof. Dr. Manfred Morari, examiner

Priv.-Doz. Thomas Bouillon, co-examiner

Zurich 2009

© 2009

Antonello Caruso

All rights reserved

ISBN 978-3-909386-30-7

Da chimico un giorno avevo il potere

di sposare gli elementi e farli reagire,

ma gli uomini mai mi riuscı di capire

perche si combinassero attraverso l’amore

affidando ad un gioco la gioia e il dolore.

Fabrizio De Andre

Un chimico

Non al denaro, non all’amore ne al cielo (1971)

6

Acknowledgements

A most sincere thank you to Prof. Manfred Morari for giving me the opportunity to

join his group and for his continued support throughout my Master’s thesis project,

Ph.D. and Post-doc. His leadership and charisma have been a great example and

influence.

Thank you to Priv.-Doz. Thomas Bouillon for being a trusted and enlightening

research partner. Thank you for having almost always an answer and very often a

question.

Thank you to all the people I collaborated with at the University Hospital Bern,

SenTec AG, the Medical University of Vienna, and the SMS Lab at D-MAVT:

Peter, Martin, Michele, Gorazd, Volker, Pascal, Andreas, Urs, Jurg, Gisela, Daniel

and Alexander. I share with them the success of this work.

Thank you to the undergraduate students who I worked with and supervised

during my Ph.D.: Philip, Urs, Stephanie and Arthur. The projects were improbable

and refreshing and fun!

I am extremely grateful to the superb institution that is the ETH for all the

opportunities it has offered me. It’s been a great ride and I am proud to become

an ETH Alumnus. Thank you to the administrative staff at IfA: Martine, Alice,

Martha, Katerina, Esther, and Danielle for their precious support during my stay

at IfA.

Thank you to all the people I met at IfA and in general during my work at the

ETH. I learnt a lot from you and I am happy we shared a number of experiences.

Thanks to Eleonora and Valentina for paving the way and for always answering

my questions. Thanks to Frank for being my Virgil in Zurich. Thanks to Colin

for the good times we shared at work and at home. Cristian: han pasado cuatro

anos y estamos en la recta final. I will always treasure the memories. Eres un

amigazo, te mereces... 5000 Superpunkte! Thanks to everybody for the friendship,

the uncountable coffee breaks and the discussions that usually ensued.

Grazie a Papa, Mamma ed Elisabetta per essere la mia famiglia, per esserci stati

e per esserci. Rivolgo un pensiero particolare ai nostri Nonni, purtroppo ci hanno

lasciato troppo presto. Gli sforzi per portare a termine questo lavoro sono dedicati

a loro.

i

ii

Abstract

The research work presented in this thesis discusses innovative strategies for the

delivery of personalized pharmacologic therapy through modeling and feedback

control. The objective is to enable medical practitioners to deliver drug therapies

with a higher standard of care, better outcomes and improved patient well being.

Individualizing dosing to the specific needs of each patient allows to adequately fulfil

the therapeutic requirements of the individual and prevent the risks and inefficacy

associated with over- and under-dosing.

In Chapter 1, the topic of personalized drug dosing is introduced in relation to

two clinical problems that are addressed in this thesis: the delivery of sedation and

the administration of antiplatelet therapy. Also, the structure of this document is

outlined.

Chapter 2 discusses the terminology and basic pharmacology concepts that are

extensively used throughout the thesis. The goal is to acquaint the reader with the

phenomena involved with drug disposition and action on the human body and the

mathematical models that have been proposed to describe them.

In Chapter 3, the problem of anesthetic dosing for the delivery of sedation and

analgesia is addressed. The pronounced interindividual variability in drug sensitiv-

ity and the changing surgical stimulus require to continuously evaluate the pharma-

cologic effects and personalize anesthetic delivery. Titration to effect is used in the

clinical practice to optimize the desired effects (analgesia, sedation and anxiolisys)

and minimize the extent of the adverse effects (cardiorespiratory depression). In

this thesis, a novel dosing paradigm for the safe and effective delivery of personal-

ized sedation is proposed. A respiratory model is used as a patient simulator for

the design of the feedback control dosing strategy and to test the feasibility of the

proposed anesthetic paradigm.

Chapter 4 is focused on antiplatelet therapy and the modeling of anticoagulant

effects. Optimal platelet inhibition is based on maximizing antithrombotic proper-

ties while minimizing bleeding risk, and it is critically dependent on the assessment

of the individual sensitivity to the drugs. The objective of the work is to provide

a quantitative description of anticoagulant effects and to formulate dosing recom-

mendations in the individual. The study also yields experimental validation for

iii

iv

a novel model of pharmacodynamic interactions that combines therapeutic and

adverse effects into a comprehensive framework for analysis of drug usefulness.

The main achievements of the research work discussed in this thesis are sum-

marized in Chapter 5, as well as the potential areas for improvement and further

investigation.

In Appendices A, B, and C three clinical study protocols addressing further

instances of therapy individualization are included. These clinical trials have been

planned, prepared, and initiated, however final results are regrettably not available

at the time of writing. The aim is to provide the reader with a more comprehensive

insight into the range of projects directed at personalizing drug delivery that were

undertaken within the scope of the PhD work.

Sommario

In questa tesi vengono presentate e discusse nuove strategie volte alla somminis-

trazione di terapie farmacologiche personalizzate attraverso l’utilizzo di tecniche

di modellazione e di controllo automatico in retroazione. L’obiettivo e quello di

fornire agli operatori medici strumenti innovativi per formulare terapie farmaco-

logiche caratterizzate da migliori risultati clinici e aumento del benessere dei pazi-

enti. La personalizzazione del dosaggio in base alle specifiche caratteristiche di ogni

paziente consente di rispondere alle necessita terapeutiche individuali e di prevenire

i rischi e l’inefficacia associati a casi di sovra- e sottodosaggio.

Nel Capitolo 1, il tema del dosaggio farmacologico personalizzato e introdotto in

relazione a due problemi clinici affrontati in questa tesi: la somministrazione della

sedazione cosciente e la somministrazione di terapie anticoagulative. Viene inoltre

illustrata la struttura di questo documento.

Nel Capitolo 2 si discute la terminologia ed i concetti farmacologici chiave che

sono utilizzati nella tesi. Lo scopo e quello di familiarizzare il lettore con i fenomeni

di distribuzione ed azione dei farmaci sul corpo umano, e con i modelli matematici

che sono stati proposti nella letteratura per descriverli.

Nel Capitolo 3 si affronta il problema del dosaggio di anestetici per la sommin-

istrazione della sedazione cosciente. La notevole variabilita interindividuale nella

sensibilita ai farmaci, nonche i continui cambiamenti della stimolazione intraopera-

toria, richiedono di valutare continuamente gli effetti farmacologici e di adeguare il

dosaggio dell’anestetico. Tale regolazione del dosaggio viene effettuata nella prat-

ica clinica per ottimizzare gli effetti terapeutici desiderati (analgesia, sedazione

ed ansiolisi) e minimizzare gli effetti indesiderati (depressione cardiorespiratoria).

In questa tesi viene presentato un nuovo paradigma di dosaggio per la somminis-

trazione personalizzata della sedazione in maniera sicura ed efficace. Un modello

respiratorio e utilizzato come simulatore per la progettazione della strategia di con-

trollo in retroazione utilizzata per regolare il dosaggio, e per testare la validita del

paradigma anestetico qui proposto.

Il Capitolo 4 e focalizzato sulla terapia anticoagulativa e sulla modellazione degli

effetti farmacologici degli anticoagulanti. L’inibizione piastrinica ottimale si basa

sulla massimizzazione delle proprieta antitrombotiche e sulla contemporanea min-

v

vi

imizzazione del rischio emorragico. Essa dipende in maniera cruciale dalla valu-

tazione della sensibilita individuale ai farmaci. L’obiettivo di questo lavoro e quello

di fornire una descrizione quantitativa degli effetti degli anticoagulanti e di per-

mettere la formulazione di raccomandazioni per il dosaggio individualizzato. Lo

studio costituisce anche una validazione sperimentale di un modello innovativo di

interazione farmacodinamica che unifica gli effetti farmacologi desiderati e quelli in-

desiderati in un’unica piattaforma per l’analisi dell’efficacia ed utilita del farmaco.

I principali contributi del lavoro di ricerca discusso in questa tesi sono riassunti

nel Capitolo 5, in cui si commenta inoltre sulle potenziali future aree di ricerca e

sperimentazione.

Nelle Appendici A, B e C sono riportati tre protocolli di studi clinici che af-

frontano ulteriori problemi di personalizzazione di terapie mediche. Tali studi clinici

sono stati ideati, preparati ed iniziati nel corso del dottorato, tuttavia alla stesura

di questo documento i risultati finali non sono purtroppo disponibili. L’obiettivo

e quello di fornire al lettore una visione piu completa dei progetti che sono stati

svolti nel corso del dottorato, aventi in comune l’obiettivo di consentire e facilitare

l’individualizzazione delle terapie farmacologiche.

Contents

1 Introduction 1

1.1 Personalized drug therapy . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Feedback control of sedation . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Pharmacodynamic modeling for antiplatelet therapy . . . . . . . . . 6

1.4 Further research projects . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 Concepts and methods 9

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2 Pharmacokinetic modeling . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.1 Compartmental models . . . . . . . . . . . . . . . . . . . . . . . 11

2.2.2 Physiology based models . . . . . . . . . . . . . . . . . . . . . . 13

2.3 Pharmacodynamic modeling . . . . . . . . . . . . . . . . . . . . . . . . 17

2.3.1 The relationship between plasma concentration and pharma-

cological effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.3.2 The effect compartment . . . . . . . . . . . . . . . . . . . . . . 19

2.3.3 Pharmacodynamic variability . . . . . . . . . . . . . . . . . . . 23

3 Feedback control of sedation 25

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.1.1 Anesthesia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.1.2 Conscious sedation . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.1.3 Automatic control in anesthesia . . . . . . . . . . . . . . . . . 30

3.1.4 Problem formulation . . . . . . . . . . . . . . . . . . . . . . . . 32

3.1.5 Aim of the work . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.1.6 Chapter content . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.2.1 Ventilatory regulation in the human body . . . . . . . . . . . 34

3.2.2 State of the art in respiratory modeling . . . . . . . . . . . . . 37

3.3 Respiratory model structure . . . . . . . . . . . . . . . . . . . . . . . . 38

3.3.1 Compartmental gas exchange system . . . . . . . . . . . . . . 38

3.3.2 Cardiovascular regulation . . . . . . . . . . . . . . . . . . . . . 43

vii

viii Contents

3.3.3 Ventilatory regulation . . . . . . . . . . . . . . . . . . . . . . . 46

3.3.4 Ventilatory regulation in the presence of an opioid . . . . . . 52

3.4 Model analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.4.1 Assessment of the gas exchange system . . . . . . . . . . . . . 58

3.4.2 Response of the ventilatory control system in the absence of

drug . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.4.3 Ventilatory depressant effect of the opioid . . . . . . . . . . . 70

3.5 Proposed model improvements . . . . . . . . . . . . . . . . . . . . . . . 74

3.5.1 Blood dissociation curves . . . . . . . . . . . . . . . . . . . . . 75

3.5.2 Transcutaneous PCO2 sensing . . . . . . . . . . . . . . . . . . 76

3.5.3 Drug naıve ventilatory regulation . . . . . . . . . . . . . . . . . 76

3.5.4 Pharmacodynamic modeling . . . . . . . . . . . . . . . . . . . . 81

3.5.5 Opioid induced respiratory depression . . . . . . . . . . . . . . 83

3.5.6 Results discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 88

3.6 Proportional-integral control for remifentanil sedation . . . . . . . . . 89

3.6.1 Control design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

3.6.2 State estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

3.6.3 Closed loop delivery of remifentanil sedation . . . . . . . . . . 90


3.7 Parsimonious modeling of ventilatory regulation . . . . . . . . . . . . 93

3.7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

3.7.2 Model of the controlled system . . . . . . . . . . . . . . . . . . 94

3.7.3 Ventilatory response to O2 and CO2 . . . . . . . . . . . . . . . 96


3.7.5 Opioid induced ventilatory depression . . . . . . . . . . . . . . 99


3.8 Parsimonious modeling of the metabolic system . . . . . . . . . . . . 103

3.8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

3.8.2 Model of the controlled system . . . . . . . . . . . . . . . . . . 105

3.8.3 Ventilatory response to O2 and CO2 . . . . . . . . . . . . . . . 106

3.8.4 Pharmacokinetic analysis . . . . . . . . . . . . . . . . . . . . . 106

3.8.5 Effect compartment modeling . . . . . . . . . . . . . . . . . . . 109


3.8.7 Alfentanil induced ventilatory depression . . . . . . . . . . . . 110


3.9 Model predictive control for propofol sedation . . . . . . . . . . . . . 112

3.9.1 Control design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

3.9.2 Closed loop delivery of propofol sedation . . . . . . . . . . . . 116

Contents ix


3.10 Clinical investigation: respiratory depression during propofol seda-

tion in colonoscopy patients . . . . . . . . . . . . . . . . . . . . . . . . 117

3.10.1 Study investigators . . . . . . . . . . . . . . . . . . . . . . . . . 117

3.10.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

3.10.3 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

3.10.4 Study methodology . . . . . . . . . . . . . . . . . . . . . . . . . 120

3.11 Sedation delivery system prototype . . . . . . . . . . . . . . . . . . . . 122

3.11.1 System setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

3.11.2 Device drivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

3.11.3 Supervisory module . . . . . . . . . . . . . . . . . . . . . . . . . 126

3.11.4 Graphical user interfaces . . . . . . . . . . . . . . . . . . . . . . 145

3.12 Preliminary clinical study results . . . . . . . . . . . . . . . . . . . . . 145

3.12.1 Experimental findings . . . . . . . . . . . . . . . . . . . . . . . . 145

3.12.2 Preliminary results discussion . . . . . . . . . . . . . . . . . . . 146

4 Pharmacodynamic modeling for antiplatelet therapy 149

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

4.1.1 Antiplatelet therapy . . . . . . . . . . . . . . . . . . . . . . . . 150

4.1.2 Problem formulation . . . . . . . . . . . . . . . . . . . . . . . . 150

4.1.3 Aim of the work . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

4.1.4 Chapter content . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

4.2 Pharmacodynamic interaction and global outcome model . . . . . . . 152

4.3 Clinical investigation: anticoagulant pharmacodynamic interaction

modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

4.3.1 Study investigators . . . . . . . . . . . . . . . . . . . . . . . . . 155

4.3.2 Study methodology . . . . . . . . . . . . . . . . . . . . . . . . . 155

4.4 Parameter estimation for antiplatelet therapy data . . . . . . . . . . 158

4.5 Experimental results and model estimation . . . . . . . . . . . . . . . 159

4.6 Results discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

5 Main achievements and outlook 175

5.1 Feedback control of sedation . . . . . . . . . . . . . . . . . . . . . . . . 176

5.2 Pharmacodynamic modeling for antiplatelet therapy . . . . . . . . . 178

A Clinical investigation: antagonism of remifentanil induced respi-

ratory depression by postoperative pain 181

A.1 Study investigators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

A.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

x Contents

A.3 Study aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

A.4 Study design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

A.5 Study methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

A.5.1 Patient population . . . . . . . . . . . . . . . . . . . . . . . . . 184

A.5.2 Study plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

A.5.3 Model building . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

A.5.4 Measurement of remifentanil plasma concentrations . . . . . . 191

A.5.5 Sample size calculation and statistics . . . . . . . . . . . . . . 191

A.6 Ethical aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

B Clinical investigation: determining the optimal drug regimen in

individual patients with chronic pain 195

B.1 Study investigators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

B.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

B.3 Study design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

B.4 Study methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198

B.4.1 Drugs used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198

B.4.2 Patient population . . . . . . . . . . . . . . . . . . . . . . . . . 199

B.4.3 Study plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199

B.4.4 Optimization procedure . . . . . . . . . . . . . . . . . . . . . . 200

B.4.5 Data collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

B.4.6 Sample size calculation and statistics . . . . . . . . . . . . . . 201

B.5 Ethical aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

B.6 Expected benefits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

B.7 Subprotocol: Time profile of side effects caused by oxycodone, pre-

gabalin and amitriptyline . . . . . . . . . . . . . . . . . . . . . . . . . . 203

B.7.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203

B.7.2 Study aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203

B.7.3 Study methodology . . . . . . . . . . . . . . . . . . . . . . . . . 203

C Clinical investigation: a novel procedure for provocation discogra-

phy 207

C.1 Study investigators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

C.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

C.3 Study aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210

C.4 Market background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

C.5 Solution proposal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

C.6 Bench testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212

Contents xi

C.7 Study design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212

C.8 Study methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212

C.8.1 Patient population . . . . . . . . . . . . . . . . . . . . . . . . . 212

C.8.2 Study plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212

C.8.3 Feasibility and applicability of the automatic system . . . . . 214

C.8.4 Pressure pain threshold . . . . . . . . . . . . . . . . . . . . . . . 215

C.8.5 Further assessments . . . . . . . . . . . . . . . . . . . . . . . . . 216

C.9 Time schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216

C.10 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216

C.10.1 Main aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216

C.10.2 Secondary aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

C.11 Ethical aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218

C.12 Expected benefits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218

Bibliography 219

Curriculum Vitae 239

xii Contents

1

Introduction

2 1 Introduction

1.1 Personalized drug therapy

The quantitative analysis of the interactions between drugs and biological sys-

tems has received considerable attention over the last decades. The biomedical

community at large and medical researchers in particular, the medical technology

and pharmaceutical industry have devoted substantial resources to investigate this

topic. The rationale is that quantifying drug, physiology, disease, and trial infor-

mation is believed to determine improvements in clinical outcomes and support

efficient drug development and regulatory decisions. The use of modeling, iden-

tification, optimization, and automatic control methods and tools is increasingly

permeating the process of drug development as well as clinical practice. Individ-

ualizing drug therapy is one of the most exciting and promising outcomes that

researchers are striving to achieve in a vast number of applications.

Over the past 15 years, the Automatic Control Laboratory at the ETH Zurich

(Prof. Manfred Morari, D-ITET) has been an active player in this field with the

collaboration of several industrial and academic research partners: the University

Hospital Bern, the Vienna Medical University, Drager Medical AG, and SenTec

AG, amongst others.

Successful research work performed at the Institute include the following projects.

Gentilini and coworkers in 2001 proposed an automatic control scheme based on

the Bispectral Index (BIS, Aspect Medical Systems, MA, USA) for the delivery

of hypnosis with isoflurane. In 2003, Stadler and collaborators designed a model-

based closed-loop controller performing neuromuscular blockade with mivacurium.

In 2006 Zanderigo, Sartori and coworkers proposed a novel drug interaction model

combining positive and negative effects into a general drug utility framework.

This doctoral thesis continues and expands the work in the research areas of

pharmacological modeling and control with the objective to propose novel tech-

niques for achieving personalized drug dosing. In the following chapters we will

focus on two main research topics: the application of automatic control techniques

for the delivery of sedation and the clinical validation of novel pharmacodynamic

interaction models for antithrombotic therapy.

1.2 Feedback control of sedation

Sedation techniques are used to provide analgesia and reduce anxiety during diag-

nostic and minor surgical procedures such as endoscopy, bronchoscopy, extracor-

poreal shockwave lithotripsy and wounds/burns debridement [163]. Sedation and

analgesia is defined as a medically controlled state of depressed consciousness that

1.2 Feedback control of sedation 3

allows protective reflexes (cardiorespiratory control) to be maintained. The mod-

erate depression of consciousness is intended to facilitate the performance of the

medical procedure while ensuring patient comfort and cooperation. The sedated

patient retains the ability to breathe autonomously and to protect his airways; de-

pending on the depth of sedation, he can respond to verbal commands and tactile

stimulation with different degrees of purposefulness [84].

Drugs used for sedation are propofol, benzodiazepines or opioids, all of which

are respiratory depressants. The magnitude of this effect depends on dosing his-

tory (rate of administration, cumulation, coadministration of other drugs) and in-

dividual sensitivity to the drug(s). Drug combinations, high doses and/or rapid

administration rates can dangerously blunt the respiratory drive and lead to seri-

ous cardiorespiratory depression in both adults and children [7, 48, 90]. Hypoxia,

potentially progressing towards cardiocirculatory arrest is the most feared conse-

quence. Oxygenation is usually supported via provision of supplemental oxygen.

However, sufficient oxygenation does not imply adequate ventilation and therefore

hypercarbia and respiratory acidosis may still develop.

Serious injuries and cardiorespiratory events associated with drug overdosing dur-

ing sedation have significant social and economic repercussions. A recent survey

of surgical anesthesia malpractice claims over the years 1990-2002 concluded that

monitored anesthesia care has the highest proportion of claims for death/permanent

brain damage (sedation: 41%; general anesthesia: 37%; regional anesthesia: 21%)

and the highest median payment to the plaintiff (sedation: 159 kUSD; GA: 140

kUSD; RA: 127 kUSD) [19]. The survey identified oversedation leading to respi-

ratory depression as the main mechanism of patient injuries during sedation and

suggested improved monitoring through capnography and vigilance to reduce mor-

bidity.

The pronounced interindividual variability of drug sensitivity and the changing

surgical stimulus mandate the continuous evaluation of the pharmacologic effects

and the individualization of drug delivery. The goal is to optimize the desired effects

(i.e., analgesia, sedation and reduction of anxiety and agitation) while minimizing

the occurrence of adverse effects (cardiorespiratory depression) [42]. Titration to

effect is compounded by the lack of a preemptive indicator of analgesia and seda-

tion. In fact, the therapeutic effects are difficult to quantify; analgesia, for instance,

can only be assessed after the patient has been exposed to a noxious stimulus. It

has been suggested to use EEG-derived indicators such as the BIS to provide a

continuous measurement of the desired effects, however, EEG-derived parameters

display pronounced fluctuations in moderately sedated patients and are insensitive

to opioids in the therapeutic concentration range [62, 106, 118]. Clinical sedation

4 1 Introduction

scales (e.g. the VAS scale, the OASS scale) are user-dependent classifications and

are not automated. End-expiratory capnography delivers false low readings during

shallow breathing and partial airway obstruction and it is difficult to assess without

a tight fitting, low dead-space mask. A simple, objective and robust measure of

the therapeutic effects is therefore not available [189]. Titration to side effect as an

alternative dosing paradigm so far suffered from the lack of a fast and artifact re-

sistant sensor for respiratory depression. Apnea is not rapidly detected by sedation

providers without continuous monitoring of CO2 [175]. Recognition of apnea or

hypoventilation in patients who receive supplemental oxygen may also be delayed

if oxygen saturation (SpO2) alone is monitored [61].

In Chapter 3 we will advocate the combined use of transcutaneous CO2 tension

(PtcCO2) and SpO2 for respiratory monitoring during sedation. The reliability

of PtcCO2 readings is independent of airway status and pulse oximetry provides

information on the adequacy of peripheral oxygenation. A device combining tran-

scutaneous CO2 and SpO2 sensing has been recently introduced into anesthetic

practice. Its favorable dynamic properties (time constant of PtcCO2 sensor =

0.67 min) enable it to detect the onset of apnea significantly faster than pulse

oximetry alone [94, 170, 113, 141]. Beyond serving as a monitor for patient safety,

such a device could also provide an objective, continuously accessible and ther-

apeutically meaningful surrogate endpoint for the automatic titration of opioids

and propofol during sedation. In fact, the desired and undesired effects are medi-

ated by the same receptors, therefore drug induced respiratory depression always

correlates with analgosedation, and viceversa [137] (with the exception of opioid

tolerant subjects, for whom this remains to be established). Mu receptors in the

brainstem and the thalamus mediate both the analgesic and the respiratory depres-

sant effect of highly potent opioids [53,153] so that the two effects share important

pharmacodynamic characteristics [56] and exhibit similar plasma-effect site equili-

bration properties [85,10]. Benzodiazepines and propofol exert their sedative effect

at gamma-aminobutyric acid (GABA) receptors, that have also been shown to in-

duce respiratory inhibition [153]. Since the concentration-effect relationships for

the desired and undesired effect are similar, we believe that deliberately targeting

moderate levels of hypercapnia is a viable approach for sedation. The degree of hy-

percapnia can be selected by the care provider within a safe range (45-60 mmHg)

and serves as the setpoint of a feedback infusion system. Such a system would both

simplify the titration task and protect against lapses caused by lack of vigilance in

a highly dynamic environment.

This novel dosing paradigm for delivery of sedation is discussed further in Chap-

ter 3. The aim of the project is to implement the proposed paradigm into a feedback


control system, that is, to design a system for the automatic delivery of monitored

anesthesia care based on transcutaneous SpO2 and CO2 monitoring. The system

should achieve and maintain drug concentrations corresponding to adequate seda-

tion and analgesia, avoiding marked respiratory depression. The project is based

on the completion of the following tasks:

a. Develop a comprehensive model of human respiratory control that can repli-

cate experimental ventilatory responses to O2 and CO2 challenges.

b. Integrate the ventilatory model with the pharmacokinetics (PK) and pharma-

codynamics (PD) of the drug, specifically to achieve a suitable quantitative

description of the respiratory depressant effect of the anesthetic (= virtual

patient).

c. Design a control strategy for the automatic performance of sedation that

individualizes drug delivery, manages surgical stimulation, and prevents the

occurrence of severe respiratory depression.

d. Analyze the performance of the system adopting the virtual patient as a

substrate for simulations.

e. Implement the proposed paradigm into a control software system interfaced

to the commercially available PtcCO2 sensor and syringe pump for real time

sensing and calculation of dosing in human subjects.

f. Plan and perform clinical experiments at the University Hospital in Bern

to validate the dosing paradigm and test the feedback control drug delivery

system.

Chapter 3 is largely based on:

[36] A. Caruso, T. Bouillon, P.M. Schumacher, E. Zanderigo and M. Morari:

Control of drug administration during Monitored Anesthesia Care. IEEE

Transactions on Automation Science and Engineering 2006, Special Issue on

Drug Delivery Automation, 6:256-264.

[37] A. Caruso, and M. Morari: Model predictive control for propofol sedation.

Proceedings of the World Congress on Medical Physics and Biomedical En-

gineering, Munich, Germany, 2009.

6 1 Introduction

[94] V. Hartwich, P. M. Schumacher, A. Caruso and M. Luginbuhl: Dynamical

properties of a new transcutaneous carbon dioxide sensor. Proceedings of the

American Society of Anesthesiologists Annual Meeting, New Orleans, LA,

USA, 2009.

[35] A. Caruso, T. Bouillon, P.M. Schumacher and M. Morari: On the modeling

of drug induced respiratory depression in the non-steady-state. Proceedings of

the IEEE Engineering in Medicine and Biology Society Annual International

Conference, Vancouver, Canada, 2008.

[34] A. Caruso, T. Bouillon, P.M. Schumacher, M. Luginbuhl and M. Morari:

Drug-induced respiratory depression: an integrated model of drug effects on

the hypercapnic and hypoxic drive. Proceedings of the IEEE Engineering in

Medicine and Biology Society Annual International Conference, Lyon, France,

2007.

[208] E. Zanderigo, A. Caruso, T. Bouillon, M. Luginbuhl and M. Morari: Phar-

macodynamic modeling of drug-induced ventilatory depression and automatic

drug dosing in conscious sedation. Proceedings of the IEEE Engineering in

Medicine and Biology Society Annual International Conference, New York

City, NY, USA, 2006.

[29] T. Bouillon, A. Caruso, M. Luginbuhl, M. Morari, P.M. Schumacher and E.

Zanderigo: A system for controlling administration of anaesthesia. Patent

granted, 2006. Assignee: Universitat Bern and ETH Zurich. Priority date:

2006-06-21 (EP 20060102702). Publication number: WO 2007147505.

1.3 Pharmacodynamic modeling for antiplatelet

therapy

Platelet activation and aggregation play a pivotal role in cardiovascular disease,

triggering adverse events such as acute coronary syndrome and stroke. Inhibition

of platelet aggregation is therefore a primary therapeutic objective [58].

The goals of antiplatelet therapy are to attenuate platelet activation and ag-

gregation, prevent occlusive thrombus formation, arrest procoagulant activity and

inflammation, promote platelet disaggregation, and facilitate perfusion. Optimal

platelet inhibition is based on maximizing antithrombotic properties while minimiz-

ing bleeding risk, and it is critically dependent on the assessment of individual pa-

tient risk [24]. However, current practice guidelines are based mainly on large-scale

1.3 Pharmacodynamic modeling for antiplatelet therapy 7

trials that have been conducted without an evaluation of the antiplatelet response

in individual patients [110, 156]. The data available from translational research

studies strongly indicate that the present “one-size-fits-all” antiplatelet strategy is

flawed [91, 130]. At one end of the spectrum, selected patients with excessively

low platelet reactivity may bleed, whereas patients with high platelet reactivity

may have ischemic events. Determining a therapeutic target of optimal platelet

reactivity associated with reduced thrombotic risk and bleeding events remains an

elusive goal [91]. In the future, it is foreseeable that optimal antiplatelet therapy

will involve an objective assessment of the individual thrombotic potential based

on the measurement of platelet function. Subsequent treatment of each patient

will be directed by laboratory measurements to ensure an appropriate therapeutic

response.

In Chapter 4 we will characterize the concentration-effect surface for the combi-

nation of two anticoagulants (iloprost and MeSAMP) in vitro. A model recently

proposed by two Institute alumni will be used to investigate the global effect of

therapeutic regimens on the patient’s well being [208]. Said model combines de-

sired effects (such as the inhibition of platelet aggregation) and undesired effects

(like the risk of bleeding) into one comprehensive framework for analysis of drug

usefulness.

The aim of the project is twofold. First, we want to validate the novel global

outcome model mentioned above through application to a relevant clinical question.

Second, we want to achieve recommendations for personalized antiplatelet therapy

based on the objective assessment of the individual thrombotic potential through

measurements of platelet function.

The project is based on the completion of the tasks listed below:

a. Investigate the dose-response relationship of two selected antiplatelet drugs

through laboratory measurements of platelet reactivity performed at the Med-

ical University of Vienna in a population of 15 human volunteers

b. Determine the type (additivity, synergism, or infra-additivity/antagonism)

and extent of pharmacodynamic interactions

c. Take both positive (therapeutic) pharmacologic effects and negative (unde-

sired) effects into account and combine them into a global framework evalu-

ating drug usefulness and drug regimen desirability

d. Find the optimal drug regimen in the individual

Chapter 4 is based on the following publications:

8 1 Introduction

[181] G. Sveticic, A. Caruso, G. Scharbert, M. Curatolo, S.A. Kozek-Langenecker

and M. Morari: Determining optimal drug regimen for antiplatelet therapy

using a novel drug interaction model. In preparation, to be submitted to

Anesthesiology, 2009.

[39] A. Caruso, G. Sveticic, G. Scharbert, S.A. Kozek-Langenecker, M. Curatolo

and M. Morari: Pharmacodynamic interaction modeling for optimal drug dos-

ing in antithrombotic therapy. Proceedings of the International Conference

on Drug Discovery and Therapy, Dubai, UAE, 2010.

[38] A. Caruso, G. Sveticic, G. Scharbert, S.A. Kozek-Langenecker, M. Curatolo

and M. Morari: Pharmacodynamic modeling and optimal drug regimen for

antiplatelet therapy. Proceedings of the International Society for Anaesthetic

Pharmacology Annual Meeting, New Orleans, LA, USA, 2009.

1.4 Further research projects

Biomedical research is an exciting frontier of human knowledge and desire for

progress. Regrettably, researchers in this area often have to face significant hurdles

in carrying out the experimental part of their work. Amongst the reasons imposing

such constraints we can mention the following: limited or insufficient resources in

terms of project funding, project support by the management, human skills, or

human time; low prevalence of the condition under investigation (which limits the

possibility to carry out experimental work and the general interest in the matter);

ethical issues restricting the type or extent of the experiments.

As a biomedical researcher, I have come to realize that the time necessary to

design, plan, perform, and report a clinical study is often comparable to the dura-

tion of a PhD program. Despite having been fortunate enough during my PhD to

meet and collaborate with brilliant and motivated scientists, several of the projects

I contributed to are not completed at the time of writing. The lack of final results

to be presented here, however, does not do justice to the amount of work and the

efforts that have been devoted to the realization of those projects. Therefore in

Appendices A, B, and C I include the study protocols of three incomplete clini-

cal trials I participated in the design of. The aim is to provide the reader with

a more comprehensive insight into the range of projects directed at personalizing

drug delivery that I have undertaken during my work at IfA.

2

Concepts and methods

10 2 Concepts and methods

2.1 Introduction

The aim of this chapter is to acquaint the reader with the terminology and basic

concepts of pharmacology that will be used in this thesis. An overview of the most

widespread modeling methodologies for drug distribution and action is provided.

The chapter deals primarily with pharmacokinetics and pharmacodynamics. Phar-

macokinetics characterizes the distribution and elimination of drugs by the body,

in particular the relationship between drug concentration and time. Pharmacody-

namics, on the other hand, describes the relationship between concentration and

response (or effect): it explains how the drug affects the body.

2.2 Pharmacokinetic modeling

Pharmacokinetics (PK) are identified on the basis of observed input-output data

sequences. A drug bolus is administered and the concentration time course is

measured by blood sampling. The infusion time of the bolus is usually neglected,

therefore the response of the physiological system can be regarded as an approx-

imation of the system impulse response [178]. For many drugs the time course

of plasma concentration following an intravenous bolus can be described (using

non-linear regression) by a n-exponential equation, as depicted in Figure 2.1. The

mathematical representation of the pharmacokinetic model is then a sum of ex-

ponentials [173]. Best-fit estimation of the equation constants provides a suitable

solution for pharmacokinetics.

This approach to the PK problem has its grounds in linear system theory, where

the input-output relationship of a linear, time-invariant system is wholly defined by

its impulse response. Therefore the underlying assumption is that the dose-plasma

drug concentration relationship is linear and time-invariant. In broad terms it im-

plies that the parameters of the PK model are constant. This is clearly not a fully

satisfactory representation of the phenomena that take place in a complex biolog-

ical system undergoing a major external influence, such as anesthesia in humans.

However, for modeling purposes this approach is fully adequate and justifiable.

The time course of drug disposition in the body can be described through a num-

ber of approaches. Figure 2.2 portrays a classification of pharmacokinetic models.

Three widespread approaches characterize drug distribution and elimination via:

- empirical models;

- compartmental mammillary models;

2.2 Pharmacokinetic modeling 11

C(t) = A ⋅ eα⋅t +B ⋅ eβ⋅t +C ⋅ eγ⋅t

Cp

Time after bolus

Figure 2.1: Plasma concentration following a drug bolus

- physiologically based models.

Empirical models are black box models relating input and output by means of an

analytical expression, such as the n-exponential function discussed above. Com-

partmental models are formulated on the basis of the minimum number of com-

partments that adequately fits the observed data. Physiologically based models

are the most realistic representation of drug kinetics, because the parameters relate

directly to physiology, to anatomy and to biochemistry [178]. Mammillary and

physiologically based models are further discussed in the following.

2.2.1 Compartmental models

Compartmental models represent a customary solution for pharmacokinetic mod-

eling. They are based on the assumption that different regions of the body can

be represented by virtual compartments disregarding the physical properties of the

described tissues. For the sake of example, a hypothetical three-compartment mam-

millary model is shown in Figure 2.3, where a central compartment is connected to

two peripheral compartments.

As mentioned above, the plasma concentration time course following a drug bo-

lus can be fitted by a n-exponential function. The pharmacokinetics problem then

commonly reduces to finding the constants of the exponentials with a curve-fitting


Models

Linear Non-linear

Time-variant Time-invariant

Empirical

Compartmental

Physiological

Figure 2.2: Taxonomy of pharmacokinetic models. Adapted from the literature

[193].

procedure. In the case of mammillary models, drug distribution to and from each

PK model compartment is usually considered a first order process [3, 173]. There-

fore, the solution consists in the identification of compartmental volumes and first

order rate constants. Estimating the parameters of a sufficient number of compart-

ments allows for the fitting of experimental data. The major advantage of mam-

millary models is that an adequate description of the concentration time course can

be achieved with a low level of complexity [178].

Strictly speaking, the compartments have no physiological meaning [178]. In

clinical literature the central compartment is often identified as the “plasma” com-

partment, given that the compartmental concentration is the plasma concentration,

Cp. However, the exponential equation should be regarded as the solution of the

differential equation describing the central compartment drug concentration that

results from a bolus injection into the n-compartment model. The central com-

partment concentration is calculated from the intake rate, the elimination rate,

the inflow and outflow compartmental rates, which are assigned to fit experimen-

tal observations. Therefore the identification of a compartment as a well-defined


V1

V2V3

k13

k31 k21

k12

Bolus

k10

Figure 2.3: Diagram of a 3-compartment mammillary model. Vi is the volume of

the i-th compartment (i = 1,2,3); kij the drug distribution rate from

compartment i to compartment j (i, j = 1,2,3); k10 the drug elimination

rate from the central compartment.

physiological region represents a misconception of the problem.

2.2.2 Physiology based models

Physiology based pharmacokinetic models use actual physiological parameters such

as breathing rates, blood flow rates and tissue volumes to describe the pharmacoki-

netic process. These parameters are coupled with chemical-specific parameters like

blood/gas partition coefficients, tissue/blood partition coefficients and metabolic

constants to predict the dynamics of compound distribution in the physiological

system. An advantage of such models is that by simply using appropriate physio-

logical and biochemical parameters, the same model can be employed to describe

the dynamics of different drugs in different species [96].

The greatest potential of physiology based modeling is that it offers the possi-

bility of predicting physiological phenomena. A suitable pharmacodynamic model

can be coupled to the physiologically based pharmacokinetic model. The modeled


pharmacological effect can then influence drug pharmacokinetics via physiological

homeostatic mechanisms. This would be particularly useful for drugs that influence

cardiac output and regional blood flows, which in turn can affect drug distribution

and elimination [126].

Another advantage of physiology based over mammillary models is that elimi-

nation can be modeled as occurring in the tissue where it actually takes place in

the body [178]. Given that a mammillary model compartment does not represent a

clearly defined physiological region, it is not possible to model explicitly the renal

or hepatic clearance, for example.

On the other hand, a serious disadvantage of whole-body physiology based PK

models is their extensive dimensionality and complexity. Such drawbacks have

limited their use to date. Compromising between model descriptive properties

and computational complexity is a critical issue in physiologically based model

development. This approach should only be applied to cases where the potential

benefits justify the time and cost associated with its implementation [43].

A common approach to decrease the complexity of physiologically based pharma-

cokinetics is lumping suitable tissues within the structure of the model. Lumping

can be defined as a structural transformation of a complex physiological model to

obtain a simpler model with identical kinetic behavior. Proper lumping should

guarantee that no useful information about the kinetics of the underlying process

are lost [147].

Lumping of the whole-body model is an iterative procedure and is usually per-

formed in two ways:

- combining parallel tissues with identical specification and occupying identical

positions in the system so to form an aggregate tissue, in case they have

similar time constants (i.e., if they show similar kinetics);

- adjoining a serially connected tissue either to the compartment at its input

or to that at its output, or to both if they have small time constant (that is,

drug equilibration is rapid). See Figure 2.5 for an example of physiologically

based model lumping.

To date, mass transfer at the capillaries and mass diffusion within cells and inter-

stitial fluid are physical phenomena which are yet to be exhaustively appreciated.

Measured data are usually explained in terms of membrane permeability. Moreover,

there are two factors which can increase the modeling effort:

- active transport of solutes through biological membranes;


Lungs

Heart

Brain

Muscles

Fat

Bone

Skin

Stomach

Pancreas

Spleen

Gut

Liver

Kidneys

Hepatic clearance

Renal clearance

Pulmonary shunt

Ven

ous

circ

ula

tion

Arterial

circulation

Figure 2.4: A possible whole-body physiologically based PK model. Adapted from

the literature [147].

- bulk fluid flow in the capillaries.

Both can be neglected for our purposes [20].

Modeling complexity for each tissue varies depending on the assumptions. Each

modeled tissue can have:

- a perfusion-limited representation;

- a diffusion-limited representation.


Lungs

Heart

Brain

Muscles

Fat

Liver

Splanchnic

Kidneys

Hepatic Clearance

Renal Clearance

Pulmonary shunt

Ven

ous

circ

ula

tion

Arterial

circulation

Figure 2.5: Possible physiologically based model lumping. Adapted from the liter-

ature [147].

Capillary

Interstitial fluid

Tissue

Tissue

Vei

n

Vei

n

Art

ery

Art

ery

Figure 2.6: Local tissue models. To the left, a diffusion-limited representation; to

the right, a perfusion-limited representation. Adapted from the litera-

ture [20].

2.3 Pharmacodynamic modeling 17

In perfusion-limited PK representations, the drug entering a tissue from the capil-

lary bed is assumed to distribute instantaneously over the entire tissular volume.

The tissue is referred to as a “well-stirred tank” where mass distribution is imme-

diate. Movement of drug to and from the tissue is considered a first order process,

therefore a single-compartment model is employed. Diffusion-limited representa-

tions, on the other hand, make use of two or three-compartment models in order to

describe mass distribution from the capillary to the tissue, thorough the interstitial

fluid. See Figure 2.6 for an example of tissular representation.

Perfusion-limited pharmacokinetics constitute a convenient simplification of diffusion-

limited ones. However, the existence of diffusion barriers to fentanyl and alfentanil

in several organs and tissues has been determined in rats [21]. The early uptake of

the drugs resulted to be much lower than predicted. Even diffusion-limited tissular

representations fail to predict the initial distribution of fentanyl. A comparative

study of flow-limited and diffusion-limited physiologically based models for fentanyl

concluded that the two approaches show differences mainly in the first minute of

distribution, but that curve trends do not differ considerably.

In common physiologically based PK models, cardiac output and tissular blood

flows are constant during the uptake of the anesthetic, while clinical practice shows

that cardiac output and ventilation depend on the level of anesthesia. Nevertheless,

simulation results demonstrate that a change in cardiac output has little effect on

the initial distribution of the anesthetic [205].

2.3 Pharmacodynamic modeling

While pharmacokinetic models allow for the assessment of drug distribution and

elimination, the clinical and therapeutic value of a drug depends upon its dynamic

effect. Pharmacodynamics (PD) describes the relationship between drug mass and

pharmacological effect. PD modeling implies making the following fundamental

assumption: that the effect can be associated with the amount of drug measured

or computed in plasma (or another body fluid or tissue) [173].

Wagner [199] proposed to use the well-known Hill equation to relate effect inten-

sity with drug amount in a body fluid:

E = Aeγ

Aeγ +A50e

γ (2.1)

where E is the intensity of the pharmacological effect expressed as a fraction of

maximal effect, Ae is a pharmacokinetic quantity to which effect is related (usually

drug mass or concentration), A50e is a constant giving the value of Ae at 50% effect,


and γ is a parameter that alters the sigmoidicity of the Ae-to-effect relationship

[173]. Refer to Figure 2.7 for a graphical representation of the proposed sigmoid

pharmacodynamic model.

In Equation 2.1 the term E signifies the magnitude of the pharmacological effect

expressed as a fraction of the maximal effect. It is worth mentioning that in the

literature the effect is usually not normalized. The maximal effect Emax is included

in the equation for pharmacodynamics, yielding the following equation:

E = Emax ⋅ Aeγ

Aeγ +A50e

γ (2.2)

where E is the absolute intensity of pharmacological effect.

Equation 2.2 represents the most common pharmacodynamic effect equation; it

is referred to as the Emax pharmacodynamic model.

Finally, it is relevant to mention that the pharmacodynamic model varies signif-

icantly with the effect of interest. This implies that the pharmacodynamic model

parameters have to be re-estimated when considering a different pharmacological

effect or a different set of experimental conditions (i.e., different FIO2, breathing

apparatus, and the like).

2.3.1 The relationship between plasma concentration and

pharmacological effect

Traditional pharmacokinetic models are concerned with the disposition of drug

masses in the body: any site which receives small amounts of drug is disregarded.

Relatively to the pharmacological active site, there is no reason a priori to assume

that it corresponds with a region receiving large amounts of the compound. A way

to envision the problem is considering that the effect site of the drug is most likely a

small area in the central nervous system; for example, a receptor or a neural centre.

In general, it should be expected that drug kinetics in plasma are different than

that at the site of action [3,173]. Indeed, several authors report clinical observations

that support this hypothesis. Nowadays it is generally acknowledged that a given

plasma concentration exhibits a temporally varying relationship to drug effect [121].

The typical Cp versus effect curve drawn from experimental observations exhibits

hysteresis. The fact that plasma concentration does not always correlate with the

clinical effect is apparent above all during induction and emergence from anesthesia.

Moreover, the most relevant effects of anesthetic agents are patient sedation and

hypnosis. The site where the drug exerts these effects (termed the biophase or

effect site) is the cerebral tissue. Clearly, it is not feasible to measure the actual


0

0.5

1

E

Ae

E = Aeγ

Aeγ+A50e

γ

Figure 2.7: Sigmoid pharmacodynamic function associating Ae to E. Ae represents

the amount of drug resulting from the pharmacokinetic model, E the

fraction of maximal response.

cerebral concentration of the drug. Even if direct measurements were possible, it

would be necessary to determine the concentration at the receptors where the drug

exerts its effect, in order to successfully relate concentration to effect [3].

2.3.2 The effect compartment

At steady state no disequilibrium between the various sites or compartments is

possible, and a constant proportionality between plasma and effect site concentra-

tion is achieved. Hence it would be possible to relate drug effect with steady state

plasma concentration in order to describe the sensitivity of an individual to a drug.

However, this is not sufficient to fully describe pharmacodynamics, since temporal

characteristics must be modeled as well [173].

The temporal aspects of pharmacodynamics are described by postulating a hy-

pothetical “effect” compartment in the PK model. The kinetics of such effect

compartment are defined as to match the time dependence of the pharmacologi-

cal effect, in order to obtain a hysteresis-free relationship between concentration

and effect. The response of the body to the drug has a time dependence which


relies on physical and physiological processes that relate drug in blood to drug at

its site of action: perfusion, diffusion, partition, drug-receptor interaction and the

relationship between receptor occupancy and effect.

Sheiner and coworkers [173] proposed the use of Equation 2.1 to relate drug

effect to the hypothetical amount of drug in the effect compartment. Plasma con-

centration is modeled by whatever pharmacokinetic model is necessary to fit the

experimental drug concentration data. As stated above, the mathematical repre-

sentation of a PK model is usually a sum of exponentials, often arising from a

mammillary compartmental model. Under this interpretation of the pharmacoki-

netic problem, the effect compartment is modeled as an additional compartment

linked to the central compartment by a first order process. It is thought to receive

a negligible amount of drug, therefore its exponential does not enter into the PK

solution for mass drug disposition in the body [173]. Id est, the effect compartment

does not enter the mass balance equations of the PK model. See Figure 2.8 for a

representation of the pharmacokinetic model including an effect compartment.

The effect compartment is shown connected to the central compartment by a

first order rate constant, k1e, while drug dissipation from the effect compartment

occurs via another first order rate constant, ke0. Mass transfer to the effect com-

partment can be neglected if k1e is assumed to be small relatively to the magnitude

of the smallest rate constant of the PK model. Once this assumption is made,

the exact value of k1e is unimportant, as will be shown below. Conversely, the

rate constant for drug removal from the effect compartment, ke0, characterizes the

temporal aspects of equilibration between Cp and pharmacological effect.

The following differential equation determines the amount of drug in the effect

compartment:dAe

dt= k1eA1 − ke0Ae (2.3)

where Ae is the hypothetical drug amount in the effect compartment, A1 the drug

amount in the central compartment, k1e and ke0 as defined above. If the analytical

solution for drug in the central compartment after a bolus is:

A1 = D ⋅ N

∑i=1Aie

−αit (2.4)

where D is the dose, Ai and αi are constants (being i = 1,2 . . . N), then the solution

to Equation 2.3 is:

Ae(t) = k1e ⋅N

∑i=1

Ai(ke0 −αi)(e−αit − e−ke0t) (2.5)


V1

V2

V3

VN

Effect

compartment

k31

k21

k12

k10

k13

k1e

ke0

Bolus

k1N

kN1

Figure 2.8: N-compartment mammillary model. The effect compartment is added

to obtain a hysteresis-free relationship between drug concentration and

pharmacological effect [121]. Adapted from the literature [173].

Conversely for an intravenous infusion at rate R into the central compartment,

the solution to Equation 2.3 during the infusion is:

Ae(t) = k1eR ⋅N

∑i=1[ Ai

αike0

(1 − e−ke0t) − Ai

αi(ke0 − αi)(e−αit − e−ke0t)] (2.6)

The solution for time t > T , where T is the infusion end time, is:

Ae(t) = k1e [R ⋅ N

∑i=1 Ai

αi(ke0 − αi)(1 − e−αiT )(e−αit′

− e−ke0t′) + AeT

k1e

e−ke0t′] (2.7)

where t′ = t − T and AeT corresponds to Equation 2.6 evaluated at time t = T . Thus

Equations 2.5 to 2.7 provide values for Ae, the amount of drug in the effect com-

partment [173].

Given that drug concentration in plasma is a feasible measurement, it is more

meaningful to associate the pharmacological effect with drug in plasma rather than


with drug in a hypothetical effect compartment. To do so, one has to consider that

at steady state there is a steady state plasma concentration (Cp, ss) and a unique

corresponding steady state Ae. The task consists in expressing the pharmacody-

namic model in terms of the Cp, ss that gives rise to a certain Ae, rather than in

terms of Ae itself.

For any compartment (including the effect compartment) to reach steady state,

its exit rate must be greater than zero. It is assumed that ke0 obeys this constraint.

At steady state no net mass transfer into or out of any compartment occurs, so

thatdAe

dt= 0 (2.8)

Thus, from Equation 2.3

k1e ⋅A1, ss = ke0 ⋅Ae, ss ⇒ A1, ss = Ae, ss ⋅ke0

k1e

(2.9)

Given the definition of drug plasma concentration

Cp = A1

V1

(2.10)

where V1 is the volume of the central compartment, from Equation 2.9 it results

Cp, ss = Ae, ss ⋅ke0/k1e

V1

(2.11)

The term Ae(t) can be substituted in this last equation using Equation 2.5, 2.6,

or 2.7. The choice of the equation to be used for substituting depends on central

compartment drug intake. For all equations, replacing Ae gives

Cp, ss = ke0

k1e

⋅ k1e ⋅Z

V1

= ke0 ⋅Z

V1

(2.12)

where Z stands for the right hand side of Equation 2.5, 2.6, or 2.7, except for k1e.

As k1e cancels out of Equation 2.12, its exact value is of little relevance, as long

as we assume it to be small enough that it can be ignored in the PK solution for

Cp [173]. The Cp, ss determined by Equation 2.12 may be used in Equation 2.2 to

give

E = Emax ⋅(ke0 ⋅ Z

V1)γ

(ke0 ⋅ ZV1)γ +C50p, ss

γ(2.13)

where all the parameters relative to the PK model can be estimated. The new

parameters introduced for the modeling of pharmacodynamic are γ, Emax and


C50p, ss. The latter is the Cp, ss causing 50% maximal effect; in the following it

shall be referred to as C50 (effective concentration 50), in accordance with the

clinical literature. Equation 2.13 determines the magnitude of drug effect in terms

of steady state plasma concentration, while the kinetics of the effect are quantified

by the parameter ke0 [3, 173].

Using the model, the effect data can be fitted to Equation 2.13 with input infor-

mation being:

- the observed effect at time t;

- the estimated pharmacokinetic constants Ai and αi (for i = 1,2 . . . N) that

determine Cp at time t.

Hence the pharmacodynamic parameters γ, Emax and C50, as well as ke0, can be

estimated.

When ke0 takes on a large value compared to other exponential coefficients of

the model, the kinetics of the effect compartment parallel those of the driving

compartment [173]. If a mammillary model is considered, it means that the effect

compartment concentration is uniformly proportional to Cp over time.

2.3.3 Pharmacodynamic variability

Inter- and intra-individual pharmacodynamic variability is intrinsic to the nature

of biological systems. Sensitivity to a drug therapy can vary greatly between sub-

jects or even within the same subject at different time points or under different

conditions. For this reason, drug dosing must often be adjusted for the specific

individual based on the observed type and extent of pharmacological effects.

In the following we shall exemplify the clinical problem posed by pharmacody-

namic variability by discussing some of the factors that influence patient sensitivity

to anesthetics.

Age

Aging has been shown to reduce the C50 for propofol, implying increased sensitivity

of the elderly to the action of the anesthetic. Greater hemodynamic effects are

displayed, although the time to maximal effect can be delayed. The equilibration

rate between central and effect site compartment has been reported not to be altered

by age [3].

Similarly, remifentanil C50 is reduced with age. However, the clinical data show

that remifentanil equilibration between plasma and effect site is slower in the el-

derly [3]. These properties suggest that induction in elderly patients should be


achieved with lower plasma concentrations than in younger adults. It is worth

mentioning that the anesthetic should also be titrated more slowly to avoid emer-

gence of side effects.

Systemic diseases

To date, extensive research has been carried out on the influence of systemic dis-

eases, such as renal and hepatic diseases, on the pharmacokinetics of intravenous

hypnotics and opioids. However, little work was performed to examine their rel-

ative potency in patients with a systemic disease. In clinical practice it is often

assumed that patients in significantly pathologic conditions require less anesthetic.

Lower dosing could result from an increased central nervous system sensitivity to

the drug (a pharmacodynamic change) or a lessened fraction of drug molecules

subject to plasma protein binding (a subtle pharmacokinetic change) [3]. However,

no increased clinical effect for a specific blood concentration has been assessed in

pathologic subjects. In fact, patients with hepatic cirrhosis have been shown to

remain alert at the same propofol plasma concentration as healthy controls. Fur-

thermore little difference in propofol binding to plasma proteins has been found in

patients with hepatic and renal pathologies [3].

Titrating anesthesia to stimulus

Despite the fact that C50s have not clearly been shown to change in pathologic

conditions, there is significant patient variability to pharmacodynamic effects. Ob-

viously, the likelihood of patient response to a stimulus depends on the depth of

anesthesia, the effect site concentration and the degree of surgical stimulation. For

example, opioid dosing during intubation has to be higher than during skin inci-

sion to prevent the patient from experiencing pain [200]. Therefore the depth of

sedation should be tailored continuously to the sensitivity of the patient and the

extent of surgical stimulation by titrating drug concentration.

3

Feedback control of sedation

26 3 Feedback control of sedation

3.1 Introduction

3.1.1 Anesthesia

Anesthesia refers to a condition of reduced sensibility in the body. The term comes

from the Greek word aesthesia, which means “ability to sense”. The prefix a- (an-,

in the presence of a vowel) is used for negation. Therefore anesthesia stands for

“inability to sense” and it indicates a “condition of deprived sensibility”.

Anesthesia is a reversible pharmacological state induced by the administration

of anesthetic drugs. Delivery of adequate anesthesia during medical treatments

ensures patient hypnosis, analgesia and muscle relaxation.

Hypnosis describes a state of unconsciousness and the absence of post-operative

recall. A patient undergoing a surgical procedure might feel pain and is generally

in a position of great discomfort and anxiety. If the patient is not properly sedated,

the awareness of the events taking place in the operating room can be a traumatic

experience. It is therefore important to make sure that the patient is amnesic, i.e.

that the patient will retain no explicit memory of the events occurring during the

surgery.

Analgesia is associated with the relief of painful stimuli. The stress produced

by surgical pain triggers different autonomic responses that have an influence on

metabolism, immune function and the cardiovascular system [66]. Diverse reac-

tions to surgical stimulation can be observed, from rapid hemodynamic changes to

awakening. A stable analgesic state is necessary for the achievement of a steady

level of hypnosis, and vice versa. However, difficulties in quantifying both painful

stimulation and patient sensitivity make it troublesome to guarantee a stable anal-

gesic state. Analgesia is provided with the administration of analgesic drugs, such

as opioids (fentanyl, alfentanil, sufentanil, and remifentanil, amongst others). At

present there is no specific measure, parameter or sensor to evaluate analgesia in-

traoperatively. The concept of pain perception in the unconscious is actually still

debated and questioned [83]. Another source of complexity results from the fact

that clinical signs that could indicate the perception of pain by the patient, such

as tearing, pupil reactivity, eye moving and grimacing, are partially suppressed by

muscle relaxants, vasodilators and vasopressors.

Skeletal muscle relaxation is induced to facilitate tracheal intubation and the

access to internal organs. It also depresses movement responses to surgical stimu-

lation that could represent a health threat for the patient. Relaxation is achieved

via neuromuscular blocking agents and it can be assessed by the muscular response

to electrical stimulation. For example, it can evaluated by measuring the force of

3.1 Introduction 27

thumb adduction during ulnar nerve stimulation [83].

According to the International Association for the Study of Pain (IASP), regu-

lar re-evaluation of drug dosing during medical and surgical treatments is required.

Pronounced individual variability in the response to the drug and to surgical stimuli,

combined with changes in responsiveness over time, requires the individualization

of drug delivery. Tailoring the administration profile to a patient is based on a con-

tinuing process of effect appraisal and dose titration. The objective is to optimize

the desired effects (e.g. analgesia, anxiolysis and sedation) while minimizing the

undesired effects [42]. The work described in this chapter provides a method to

effectively address these issues.

There are several forms of anesthesia. Arguably the simplest classification is:

- general anesthesia;

- local or regional anesthesia;

- monitored anesthesia care (MAC), or (conscious) sedation.

In modern clinical practice, general anesthesia is provided only when strictly

necessary in order to reduce the invasiveness of the procedure. Hypnosis is delivered

via the administration of a hypnotic, which can be a volatile (e.g. isoflurane) or

an intravenous agent (e.g. propofol). Until recently no direct measure of hypnosis

under general anesthesia was available; arterial blood pressure was often used as

an indirect indicator. Nowadays the electroencephalogram is considered as the

major source of information to assess the level of hypnosis [83]. EEG patterns

show gradual modifications as the drug concentration increases in the body. In

1996 Aspect Medical Systems (MA, USA) proposed the Bispectral Index (BIS),

an EEG derived parameter which adequately evaluates the hypnotic component of

anesthesia.

Most surgeries are performed with local/regional anesthesia or monitored anes-

thesia care. The former (spinal, lumbar epidural, caudal anesthesia are examples)

requires small amounts of anesthetic and it is usually well tolerated by the body.

Emergence of the anesthetized is often rapid and unproblematic. The latter entails

the simultaneous practice of regional anesthesia and patient sedation, according to

the American Society of Anesthesiologists (ASA) [84].

Conscious sedation is defined as a medically controlled state of depressed con-

sciousness that allows protective reflexes to be maintained. The sedated patient

retains the ability to breathe autonomously and to protect the airways. Depending

on the depth of sedation, the patient can respond to verbal commands and tactile

stimulation with different degrees of purposefulness [152]. This procedure, usually


termed conscious sedation or sedation and analgesia, represents the field of interest

of the present work. In the following, conscious sedation and its implications on

ventilatory regulation are discussed with detail.

3.1.2 Conscious sedation

Conscious sedation is a widespread procedure providing analgesia and relieving

the stress, the anxiety and the discomfort often associated with medical proce-

dures [84, 168]. Although the drugs employed for sedation do not produce deep

unconsciousness, the patient is usually left with little or no memory of the surgical

treatment.

At present, conscious sedation is a well-established procedure carried out in hos-

pitals all around the world. It is employed in the clinical practice for a wide range

of medical treatments. The procedure is routinely performed during the following

surgical interventions:

- endoscopy (mainly gastroscopy and colonoscopy);

- evacuation of chronic epidural hematoma;

- superficial cleansing of wounds, abscess drainage;

- bronchoscopy or fiber optic intubation;

- virtual probe plastic surgery;

- ESWL (Extracorporeal ShockWave Lithotripsy);

- cystoscopy;

- ovocyte harvest for artificial fertilization;

- dental surgical interventions.

Several factors make sedation attractive compared to general anesthesia. Low

drug and equipment costs, the lack of prolonged monitoring following the proce-

dure, the short duration of patient recovery keep clinical costs at a moderate level.

Conversely, general anesthesia and the subsequent postanesthesia care have a sig-

nificant impact on clinical costs in terms of equipment, medications and human

resources. Moreover, the induction of a prolonged state of unconsciousness in the

patient affects adversely the duration and quality of recovery. Patients treated with

sedation are usually dehospitalized faster than those undergoing general anesthesia.

3.1 Introduction 29

On the other hand, conscious sedation is not suitable for all surgical treatments.

Markedly invasive surgeries, for example, usually require the provision of general

anesthesia and delay patient home readiness.

During sedation the patient is constantly observed. Blood pressure and oxygena-

tion, the heart rate and the ECG are monitored to determine the health conditions

of the patient. The electrical activity of the cardiac muscle is recorded by elec-

trocardiographic means, usually with a three-lead setup. The inspection of the

electrocardiogram is fundamental to assess the patient’s well-being. However, the

ECG is not able to provide by itself complete information on the cardiovascular

system. In fact the evidence of cardiac electrical activity alone does not reassure

the physician on the adequacy of peripheral perfusion. For such reason, electrocar-

diography is coupled with pulse oximetry. A pulse oximeter provides a continuous

measurement of arterial oxygen saturation [% SpO2] and pulse rate [beats min−1].

The measurements are performed via an IR sensor attached to the patient’s finger

or ear lobe. The probe can determine the actual presence of blood flow in the

periphery and detect hypoxia before the patient becomes clinically cyanosed.

Blood pressure, on the other hand, is measured with a plethysmograph unit

which comprises a tourniquet placed at the patient’s arm. The apparatus provides

a measurement every three to five minutes. Hence the information coming from

the plethysmograph is highly discontinuous and sporadic.

Although ventilation is impaired by the analgesic, the patient is able to breath

autonomously. The fact that mechanical ventilation is unnecessary decreases to

some extent the invasiveness of the procedure. The patient breathes room air, i.e.

the fraction of inspired oxygen is equal to 0.21. Usually such FIO2 is not sufficient

to maintain an adequate saturation in the blood. Extra oxygen is therefore provided

to the patient via a nasal cannula or a non-rebreather face mask. Typical oxygen

flows delivered during conscious sedation amount to 2-4 l/min.

Presently, ventilation is not monitored during patient sedation in the operating

theater. However, different factors hint at the necessity for a ventilatory mea-

surement - above all, the fact that the analgesic depresses ventilation. To date,

the death of the sedated patient can still occur due to respiration-related causes.

It is believed that pathologic conditions make the patient more sensitive to the

drug-induced ventilatory decline [3]. The monitoring of ventilation could assist the

anesthetist in tailoring drug infusion to the patient and the surgical situation. To

record ventilation several methods are available, including those listed below:

- visual inspection of the thorax;

- detection of thoracic electrical impedance changes;


- capnographic appraisal of end-tidal PCO2.

The simplest way of monitoring ventilation consists in the visual inspection of

the thorax. In the absence of any other respiratory measurement, it represents

the method anesthetists rely on to verify whether the patient is apnoeic. Clearly,

this method performs very poorly in terms of reliability, precision, repeatability,

automatization.

The second method is based on the positioning of electrodes on the thorax and

allows for the determination of tidal volumes. In fact, thoracic electrical impedance

changes in accord with changes in thoracic volume [158]. The method is very artifact

prone; movements of the patient and of the cables reduce the SNR of the detected

signal.

Finally, capnographic systems provide continuous monitoring of the respiratory

rate and end-tidal PCO2 (PetCO2). The apparatus employs a nasal cannula for

exhaled breath sampling. The cannula, 3 to 5 cm in length, does not impair sponta-

neous ventilation, however it yields incorrect measurements if the patient breathes

through the mouth. Another sampling setup makes use of a facial mask. The

deadspace of the tubes and of the mask itself reduces the reliability of the PetCO2

measurements, therefore only the respiratory rate data are usually considered. Both

setups are sensitive to shallow breathing and airway obstruction.

The adequacy of ventilation can be indirectly determined by measuring tran-

scutaneous CO2 tension (PtcCO2) and oxygen saturation. The measurement of

transcutaneous carbon dioxide pressure is not yet a routinary procedure in the

clinical practice. However, innovative sensors have been released that could en-

hance the monitoring of PtcCO2 for a noninvasive assessment of ventilation. These

devices combine pulse oximetry and PtcCO2 detection, therefore they record the

pulse rate, SpO2 and PtcCO2. Currently three manufacturers commercialize sen-

sors with equivalent characteristics. The manufacturers are: SenTec AG (Therwil,

Switzerland); Linde Medical Sensors (Basel, Switzerland); Radiometer A/S (Copen-

hagen, Denmark). Results of the recent clinical studies evaluating these devices can

be found in [94, 18, 97, 113, 192].

3.1.3 Automatic control in anesthesia

Anesthetists take care of patient’s well-being long before and after the surgical pro-

cedure. Before the surgery starts, they assess the health conditions of the patient

and select the type of anesthesia that should be induced. During the operation, they

confer with the surgical team, provide pain relief to the patient and support the

vital functions. At the end of the surgical treatment, they supervise the emergence

3.1 Introduction 31

hypnotics

analgesics

muscle relaxants

ventilation

surgical stimuli

blood loss

hypnosis

muscle relaxation

analgesia

EEG patterns

heart rate

blood pressure

expired CO2

⋮

⋮

unmeasurable

outputs

outputs

measurable

variablesmanipulated

disturbances

Figure 3.1: Schematic MIMO representation of the anesthesia problem. Adapted

from the literature [79].

from anesthesia and relieve pain, if necessary [178]. It becomes clear that anesthe-

sia is a complex, multifaceted problem, entailing the simultaneous supervision of

several variables. From an engineering point of view, anesthesia can be modeled as

an input-output system with manipulated variables, disturbances, measurable and

unmeasurable outputs. A multiple-input, multiple-output (MIMO) representation

of the anesthesia problem is depicted in Figure 3.8.1. The three components of

anesthesia are labelled “unmeasurable” in the figure since they cannot be directly

evaluated. Their appraisal is based on the available physiological measurements,

as discussed in the previous section.

In the operating theater anesthetists supply drugs and adjust several medical

devices to achieve analgesia, muscle relaxation, hypnosis and to compensate for the

effect of surgical disturbances. Throughout the entire process it is fundamental to

maintain the vital functions of the patient. The physician modifies the manipu-

lated variables of Figure 3.8.1 based on specific target values (such as plasma drug

concentration) and on monitor readings. Thus the role of the anesthetist resembles

that of a feedback controller, to a certain extent. It is straightforward to speculate

whether automatic controllers could manage and improve specific aspects of such

complex and delicate decision making process.

Several authors have recognized the advantages associated with the use of auto-

matic control in anesthesia [83, 178]. For example if automatic controllers would

carry out the most routinary aspects of the procedure, anesthetists would be able

to focus on those tasks that are most critical for the health of the patient [59]. Au-

tomatic control can plan and deliver drug administration profiles which, together

with accurate infusion devices, would avoid the risks associated with drug misdos-


ing. It is obvious what the disadvantages of drug overdosing are. However, it is

worth mentioning that drug underdosing should be also be prevented when possi-

ble. Underdosing can induce a state of inadequate anesthesia, which in turn makes

the patient experience pain and reduces the inhibition of movement responses to

surgical stimuli. The attempt to avoid occurrence of inadequate anesthesia in the

clinical practice results in an increased risk of overdosing. Therefore, automatic

systems can reduce the risks and costs related to drug consumption. Moreover,

reduced dosage shortens the time needed to the patient for emergence and, in turn,

the duration of his/her stay in the post-anesthesia care unit. Controllers should

also be able to compensate for interindividual variability and tailor drug adminis-

tration to the specific stimuli occurring during the surgical procedure [83]. Finally,

an automatic controller could play the role of a “reference” anesthetist to be used

in research during clinical studies.

To date, extensive research has been carried out on the application of automatic

control theory to the anesthetic practice, mainly general anesthesia. Automatic

systems have been developed, validated and tested on humans to control target

levels of hypnosis and muscle relaxation [83, 178].

3.1.4 Problem formulation

Anesthetics administered to deliver patient sedation have a significant inhibitory

influence on ventilation. Propofol and potent opioids, such as remifentanil, alfen-

tanil and fentanyl, have a dose-dependent respiratory depressant effect that can

ultimately lead to apnea and pose a death risk.

Drug-induced respiratory inhibition becomes dramatically of interest for surgical

procedures where the use of anesthesia is not coupled with artificial ventilation.

This is the case when conscious sedation is performed. As mentioned above, a

sedated patient retains the ability of breathing autonomously. If the ventilatory

decline induced by the anesthetic becomes significant, the anesthetist can supply an

extra flow of oxygen via a nasal cannula or a non-rebreather face mask. Adequate

levels of oxygen in the body are established as a result. On the contrary, no

reassurance relative to the CO2 levels can comfort the anesthetist. If the respiratory

decline is pronounced, an acidic state sets up in the body due to the excessive

amount of CO2. This phenomenon is referred to as respiratory acidosis; equivalent

terms are hypercapnic acidosis and carbon dioxide acidosis.

Although conscious sedation is a well-established, widespread clinical procedure,

it is far from being unproblematic. Clinical experience emphasizes the need for a

better understanding and management of respiratory-related events taking place

3.1 Introduction 33

during conscious sedation. It calls for the application of engineering and automatic

control concepts and methods in order to tailor drug administration profiles, shrink

the risk of opioid misdosing and ultimately reduce the mortality and morbidity of

the procedure.

3.1.5 Aim of the work

The present study aims at contributing to the improvement of conscious sedation

anesthetic care. The most difficult task anesthetists have to face when delivering

conscious sedation is handling drug administration and dosing. Extreme patient

inter- and intra-individual variability in sedative pharmacodynamics and the ven-

tilatory response to the drug makes anesthetic dosing for conscious sedation a

complex and delicate task. Drug dosing based solely on clinical experience is not

entirely satisfactory and can cause the onset of significant pharmacological side

effects during the procedure.

Objective of the work is to design an automatic feedback controller capable of

driving anesthetic infusion for sedation based on indicators of the patient’s ventila-

tory state. The recent commercialization of innovative, noninvasive PCO2 sensors

makes it feasible to routinely monitor tissular CO2 levels in the operating the-

ater. Optimizing the administration profile is expected to minimize the ventilatory

impairment and prevent the occurrence of adverse respiratory events, therefore

minimizing the risks associated with the anesthetic procedure.

3.1.6 Chapter content

This chapter is structured as follows. In Section 3.2 the reader is introduced to

the physiological systems that contribute to ventilatory regulation in the human

body. A brief review of the mathematical models proposed in the literature to

describe human respiratory control is also provided. Section 3.3 presents a com-

prehensive mathematical model of human ventilatory regulation and anesthetic

induced respiratory depression. The response of the model under different ventila-

tory conditions is analyzed in Section 3.4 (both drug naıve and after exposure to

respiratory depressants). Based on those results, proposed model changes and re-

finements are discussed in Section 3.5. With the model developed in these sections,

a proportional-integral control strategy for the delivery of personalized remifentanil

sedation is designed in Section 3.6.

In order to overcome the limitations of the model described in Section 3.3 in

terms of complexity and agreement with experimental results, a new model of


human ventilatory regulation is proposed in this thesis. In Section 3.7 a parsimo-

nious mathematical description of respiratory control and pharmacological effects

of ventilatory depressants is presented. In Section 3.8 a simplified model for the

controlled physiological metabolic plant is discussed and validated with simulation

results of drug induced respiratory depression in the non-steady state. This parsi-

monious model is then used as a physiological platform to design and test a model

predictive controller delivering propofol sedation (Section 3.9).

Finally, the clinical validation of the sedation paradigm is discussed. In Section

3.10 the protocol of the clinical study aimed at investigating respiratory depression

during sedation is described. Section 3.11 deals with the design and implementation

of a system for the delivery of personalized sedation. This platform is currently in

use to perform the clinical trials in gastroenterology patients. It also constitutes

the proof-of-concept prototype for a prospective commercial device delivering auto-

matic sedation. The preliminary clinical results collected through November 2009

are presented and discussed in Section 3.12.

3.2 Background

3.2.1 Ventilatory regulation in the human body

Human ventilatory response and control is a central issue of this work. Acquain-

tance with the regulatory systems that contribute to modulating ventilation is es-

sential for the understanding of ventilation related issues in the field of anesthesia.

Especially of interest is the pharmacological effect of anesthetic drugs on ventila-

tory neural centres and reflexes. This section intends to provide an overview of

the physiological mechanisms that control ventilation in the human body. Most of

the regulatory mechanisms illustrated below are included in the physiology-based

model described in Section 3.3.

Central respiratory centres

Spontaneous ventilation is the result of rhythmic neural activity in respiratory cen-

tres within the brainstem. Two medullary neural centres can be recognized: a

dorsal respiratory group, active primarily during inspiration, and a ventral respi-

ratory group, which is active during expiration. Although not firmly established,

the origin of the basic respiratory rhythm is due to either a spontaneous discharge

activity in the dorsal group or a reciprocating activity between the dorsal and ven-

tral groups. The close association of the dorsal respiratory group with the tractus

3.2 Background 35

solitarius may explain reflex changes in ventilation resulting from vagal or glos-

sopharyngeal nerve stimulation [144].

Two pontine areas influence the dorsal (inspiratory) medullary centre. A lower

pontine (apneustic) centre is excitatory, while an upper pontine (pneumotaxic)

centre is inhibitory. The pontine centres seem to fine-tune the respiratory rate.

Central sensors

The most important central sensors are the chemoreceptors that respond to changes

in hydrogen ion concentration. Central chemoreceptors are believed to lie on the an-

terolateral surface of the medulla and respond primarily to changes in cerebrospinal

fluid [H+]. This mechanism is effective in regulating arterial CO2 partial pressure

because the blood-brain barrier is permeable to dissolved carbon dioxide but not

to bicarbonate ions. Acute changes in PaCO2 are reflected in the cerebrospinal

fluid (CSF), but not those in arterial [HCO3−]. Thus a change in CO2 results in

a change of [H+]:CO2 +H2O H+ +HCO3

− (3.1)

Over the course of a few days, cerebrospinal fluid [HCO3−] can compensate to

match the changes in arterial [HCO3−] [144].

Increases in PaCO2 elevate CSF hydrogen ion concentration and activate the chemore-

ceptors. Brain hypoxia, on the other hand, depresses central chemoreceptive activ-

ity.

Peripheral sensors

Peripheral sensors are classified into peripheral chemoreceptors and lung receptors,

according to their position.

Peripheral chemoreceptors include the carotid bodies at the bifurcation of the

common carotid arteries and the aortic bodies surrounding the aortic arch [92].

The carotid bodies are the principal peripheral chemoreceptors in humans and are

sensitive to changes in PaO2, PaCO2, pH and arterial perfusion pressure. They

interact with central respiratory centres via the glossopharyngeal nerves, producing

reflex increases in alveolar ventilation in response to reductions in PaO2 and arterial

perfusion or increases in [H+] and PaCO2 [92].

Action potentials from these receptors are carried centrally by the vagus nerve.

Stretch receptors are distributed in the smooth muscle of airways. They are respon-

sible for inhibition of inspiration when the lung is inflated to excessive volumes (the

Hering-Breuer inflation reflex) and shortening of exhalation when the lung is de-

flated (the deflation reflex). Stretch receptors normally play a minor role in humans.


PaCO2 [mmHg]

Alv

eola

rve

nti

lati

on[l

min−1]

metabolic acidosishypoxia (adult)

awake

asleep

narcoticschronic airway obstruction

hypoxia (neonate)removal of carotid bodies

deep anesthesia

Figure 3.2: CO2 response curve under different conditions.

In fact, bilateral vagal nerve blocks have a minimal effect on the normal respiratory

pattern.

Irritant receptors in the tracheobronchial mucosa react to noxious gases, smoke,

dust and cold gases. Their activation produces reflex increases in respiratory rate,

bronchoconstriction and coughing [144].

Effects of anesthesia on respiratory control

The most important pharmacological effect of anesthetic drugs on breathing is a

general tendency to promote hypoventilation. The mechanism is probably twofold:

a central inhibition of chemoreceptors is coupled with a depression of external inter-

costal muscle activity. The anesthetic also inhibits the genioglossus, the geniohyoid

and other pharyngeal dilator muscles. The magnitude of the hypoventilating effect

is generally proportional to the depth of anesthesia. With increasing drug concen-

tration, a depression of the slope and a rightward shift can be observed in the CO2

response curve (refer to Figure 3.2). This effect is partially reversed by surgical

3.2 Background 37

stimulation.

Under anesthesia, a decline in functional residual capacity (FRC) can be ob-

served. Declines amount to 10-25% in healthy adults (independently of muscle

relaxants dosage) and to 35-45% in 6 to 18 year-old subjects. In young infants

under general anesthesia the FRC may be reduced to 10-15% of the basal value,

especially if the anesthetic is combined with muscle relaxants. FRC impairment

may lead to small airway closure, atelectasis, V /Q mismatch, declining SpO2.

3.2.2 State of the art in respiratory modeling

Mathematical modeling of the respiratory system dates back to the mid-1950s with

the pioneering works by Grodins and coworkers [88, 89]. The structure of those

early models is very comprehensive. They include a formulation of physiological

regulatory mechanisms, gas transport and chemical buffering in the human body.

Most of the models published in recent times, on the other hand, focus on spe-

cific regulatory aspects rather than on describing the behavior of the system as a

whole. For example, some studies [119, 186] explain thoroughly the dynamics of

regulation to analyze the transition to instability, but do not incorporate chemical

variables. Others [124] report exhaustive descriptions of acid-base equilibrium and

blood dissociation curves, but do not address the control of respiration.

In 1997 Chiari and colleagues [44] proposed a comprehensive model of the human

respiratory system that describes both ventilatory and cardiovascular regulation

and includes aspects of physiological gas transport and chemical buffering. At

the time the model was innovative in that it was the first one to merge different

regulatory features into a single theoretical framework. Four years later, Ursino

et al. [195] published a development of the work by Chiari. The mathematical

model was improved in the description of the regulatory mechanisms controlling

ventilation. The representation by Ursino comprises the modeling of peripheral

and central chemoreceptors and the central inhibitory regulation induced by brain

hypoxia.

In 2004 Magosso and coworkers [129] proposed a further development of the model

that takes into account the influence exerted on ventilation by fentanyl, an opioid

drug. More precisely, the model by Magosso yields a quantitative description of

the effect of fentanyl on the ventilatory control system and on respiratory volumes.

Therefore it enables the assessment of the respiratory inhibition caused by the

opioid and it provides a meaningful tool for the design of analgesia and sedation

controllers.

In the initial part of this study, we use a model derived from the work by Magosso


and colleagues [129] to simulate the effect of anesthetic drugs on the human body.

The Magosso model was initially considered because it is one of the most complete

representations of the ventilatory control system to date, as mentioned above.

Nevertheless, simulation results provided by the model are not entirely satisfac-

tory. Model behavior under determined conditions does not match what can be

inferred from the clinical practice. Thus the initial part of our study is focused on

further developing the original model. The following sections provide a detailed

description of the original model, the simulation results, and the proposed changes.

3.3 Respiratory model structure

The structure of the model proposed by Ursino and coworkers [195] is depicted in

Figure 3.3, 3.4, and 3.5. The model includes three compartments for gas storage

and exchange, namely the lung, the brain and the tissular compartment (see Figure

3.3). The brain is modeled as a stand-alone compartment because it is the site

where central respiratory nuclei and chemoreceptors are found. Local O2 and CO2

concentrations have a relevant influence on ventilation, therefore the gas exchanges

taking place in the brain are to be modeled separately.

A blood flow controller and a ventilation controller act as cardiorespiratory reg-

ulatory mechanisms in the model. They mimic the action of different physiological

feedback components, such as the central and peripheral chemoreceptors, that will

be discussed in the coming paragraphs.

3.3.1 Compartmental gas exchange system

Tissular mass balance equations

In each compartment, O2 and CO2 mass changes occur over time resulting from

mass transport, exchange, production and consumption. In the lungs, mass ex-

change takes place between alveolar air and pulmonary capillaries. In the tissues,

mass changes refer to metabolic CO2 production and O2 consumption. To take

into account mass variations per unit time, mass balance equations are written for

each state variable. The state variables are:

- O2 and CO2 partial pressures in the alveoli;

- O2 and CO2 concentrations in the brain and the tissue compartments.

Equations 3.2-3.6 are the mass balance equations for the lung, brain and tissue

compartments [195, 129]. In these mathematical equations, subscripts are used

3.3 Respiratory model structure 39

to identify the different compartments. The subscript A is employed for terms

referring to the alveoli, b for the brain tissue, t for body tissues. The subscript

a is used to refer to arterial variables (partial pressure or concentration). Labels

relative to venous terms are slightly more elaborate. The subscript v is used for

mixed-blood venous quantities, while vb, e, and vt refer to blood flowing out of the

brain, lung and tissular compartment, respectively.

VA ⋅dPA,j

dt= VA (PI,j −PA,j) + λQ (1 − s)(cv,j − ce,j) (3.2)

Vi ⋅dci,j

dt= Qi (ca,j − cvi,j) −Mi,j (3.3)

where

i = b, t (3.4)

j = O2,CO2 (3.5)

Mi,O2= ⎧⎪⎪⎨⎪⎪⎩

Mi,O20 if Pi,O2 > 6 mmHg

16Pi,O2

Mi,O2if Pi,O2 < 6 mmHg

(3.6)

In the above VA denotes alveolar ventilation, Q is the cardiac output, Qi the

blood flow through compartment i, and s the pulmonary shunt. Mi,j represents

the metabolic rate of the specific compartment; it is a positive quantity when re-

ferred to CO2 (implying production) and negative when relative to O2 (entailing

consumption). λ is a coefficient to convert blood concentrations at standard tem-

perature and pressure (dry) into alveolar partial pressures at body pressure and

temperature (saturated). Finally, PI,j is the gas pressure in the inspired air, being

j either O2 or CO2.

The values of all the parameters that appear in the equations are summarized in

Table 3.1.

Gas pressures and concentrations in blood

Respiratory gases do not exhibit a linear relationship between blood concentration

and partial pressure due to the presence of hemoglobin. When a mass exchange

takes place, O2 and CO2 blood content has to be taken into account. Therefore,

knowledge of the respiratory gas concentration in the blood flowing into and out

of the compartment is necessary to compute the mass balance equation. To that

purpose, the following steps are taken:


- blood flowing into a compartment is considered to be arterial blood while

blood flowing out of a compartment is regarded as venous;

- Henry’s law is used to compute gas partial pressures from blood concentra-

tions in the brain and tissue compartments;

- partial pressures in the blood outflowing from a compartment are assumed

equal to pressures in the tissue (i.e., Pvi,j = Pi,j and Pe,j = PA,j where i = b, tand j = O2,CO2);

- gas dissociation curves are used to determine venous blood concentrations

from O2 and CO2 partial pressures;

- gas dissociation curves are inverted to obtain arterial blood partial pressures

from gas concentrations;

- mixed venous blood concentrations are computed from brain and tissular

venous concentrations;

- arterial blood concentrations are determined taking into account the pul-

monary shunt (which, in the model, accounts for 2.4% of the overall cardiac

output).

Concerning the blood dissociation curves, Magosso and collaborators relied on

the work by Spencer and coworkers [176] who proposed a set of mathematical

equations to relate O2 and CO2 blood concentration to partial pressure. These

equations account for both the Bohr and the Haldane effect in order to account.

They are also invertible, so that it is possible to calculate the gas partial pressure

in the blood as a function of concentration. Both direct and inverse forms of the

mathematical equations are available in the original paper and are not rewritten

here for the sake of conciseness.

With respect to the computation of oxygen and carbon dioxide concentration in

mixed venous and arterial blood, the following equations are employed:

ca,j = (1 − s) ce,j + scv,j (3.7)

cv,j = Qb ⋅ cvb,j +Qt ⋅ cvt,j

Qb +Qt

(3.8)

j = O2,CO2

In 3.7, the mixing of blood flow from the alveoli and that from the pulmonary

shunt determines the O2 and CO2 arterial concentration. Similarly, the venous

concentration in 3.8 is obtained via weighted averaging of the concentration in

cerebral and tissular venous flows.


LungsVA, PA

BrainVb, Cb

TissuesVt, Ct

Lung Shunt

Qb, Cvb

Qt, Cvt

Qb, Cab

Qt, Cat

Q, Ca

Q, Cv

PA, V PI , V

Q ⋅ (1 − s)

Q ⋅ s Ce, Q ⋅ (1 − s)

Figure 3.3: Three-compartment gas exchange system.

CO2 tissular concentration

It was mentioned above that the CO2 partial pressure in the tissues is computed

via Henry’s law from the blood concentration of the species. However, CO2 trans-

port in blood occurs via three distinct mechanisms. Less than 10% of total carbon

dioxide is dissolved in the plasma, while approximately 20% chemically binds to

hemoglobin. The remaining 70% is converted into carbonic acid by carbonic anhy-

drase, an enzyme that catalyzes the hydration of carbon dioxide:

CO2 +H2O H2CO3 (3.9)

Carbonic acid then dissociates to form bicarbonate ions:

H2CO3 H+ +HCO3− (3.10)

Given that hemoglobin is confined within red blood cells, carbon dioxide in the

tissues is either dissolved or in the form of bicarbonate ions. Henry’s law applies

to dissolved species only, therefore it is necessary to distinguish between total and

dissolved tissular CO2. Chiari and colleagues [44] express total compartmental

CO2 as follows:

[CO2]toti = [CO2]dissolvedi+ [HCO3

−]i (3.11)


Mass balance in the alveoli

VA = 3.28 l s = 0.024

PI,O2= 149 mmHg PI,CO2

= 0 mmHg

Mass balance in the tissues

Vb = 1.32 l Vt = 38.68 l

[HCO3−]b = 26 mEq

l[HCO3

−]t = 26 mEql

Mb,O2= 0.05

l (STDP )min

Mt,O2= 0.2

l (STDP )min

Mb,CO2= 0.04

l (STDP )min

Mt,CO2= 0.16

l (STDP )min

Henry’s law

αO2= 3.17⋅10−5 l (STDP )

l mmHg

αCO2= 6.67⋅10−4

l (STDP )l mmHg

Conversion factors

λ = 863 mmHg

Table 3.1: Parameter values for compartmental mass balance equations and Henry’s

law.

= αi,CO2⋅ Pi,CO2

+ [HCO3−]i (3.12)

i = b, t

where αi,CO2is the solubility coefficient of the species and i = t, b, e. Reshuffling the

terms, we obtain the following equation for dissolved tissular carbon dioxide:

[CO2]dissolvedi= [CO2]toti − [HCO3

−]i (3.13)

Bicarbonate ion content in the tissues is assumed to remain constant since only a

negligible part is involved in acid-base reactions. CO2 partial pressure can then be

computed as

Pi,CO2= [CO2]dissolvedi

αi,CO2

(3.14)


3.3.2 Cardiovascular regulation

The model describes cardiac output regulation and it is capable of predicting tissu-

lar and cerebral blood flow based on O2 and CO2 blood content. In the human body

cardiovascular regulation takes place due to the action of multiple control mecha-

nisms. Such mechanisms can induce vasodilation, vasoconstriction, and changes in

cardiac output and systemic arterial pressure.

The model determines cardiac output as the sum of the cerebral blood flow Qb

and the tissular blood flow Qt. The basal cardiac output is assumed to be 5 l min−1

and basal cerebral perfusion is 0.75 l min−1. Local regulation of cerebral blood flow

is dependent on O2 and CO2 arterial content. Qt, on the other hand, is dependent

on arterial O2 only. In fact, different authors report that carbon dioxide partial

pressure has a scarce influence on noncerebral tissular blood flow [129, 195, 196].

The mathematical description of cardiovascular regulation in the model is:

ψO2(Pa,O2

) = c1 [e−Pa,O2

c2 − e−Pa,O20

c2 ] (3.15)

dyO2

dt= 1

τO2

⋅ (ψO2− yO2

) (3.16)

ψCO2(Pa,CO2

) = A +B/(1 +CeD log(Pa,CO2))

A +B/(1 +CeD log(Pa,CO20)) − 1 (3.17)

dyCO2

dt= 1

τCO2

⋅ (ψCO2− yCO2

) (3.18)

Qb = Qb0 (1 + yO2+ yCO2

) (3.19)

Qt = Qt0 (1 + ρ ⋅ yO2) (3.20)

Q = Qt +Qb (3.21)

Equations 3.16 and 3.18 represent the mechanism dynamics for O2 and CO2 regu-

lation, respectively. The value of yO2and yCO2

is zero in basal conditions, i.e. when

Pa,O2= Pa,O20 = 95 mmHg and Pa,CO2

= Pa,CO20 = 40 mmHg.

As it can be inferred from Equation 3.19, the O2 and CO2 regulatory mecha-

nisms interact linearly to determine cerebral blood flow. On the contrary, tissular

circulation depends solely on arterial O2 blood content. Parameter ρ in Equation

3.20 is the fraction of tissular blood flow which is subject to oxygen local regulation.

This ratio is smaller than 1 due to the existence of the splanchnic circulation and

other vascular beds which are scarcely affected by arterial O2 changes. In Equation

3.21, the cardiac output Q is computed as the sum of cerebral and tissular blood

flow.


+

VA

Brain

VE

Central Chem.

deadspace

∆VEP

∆VEC

CVD

Pb,CO2 Pb,O2

Lungs

QbQb

cvb,O2cvb,CO2

Mb,O2

Peripheral Chem.

Q

Mb,CO2

sQsQ

QtQt

Shunt

Blood

diss. curve

(1 − s)Q(1 − s)Q

VE0

Blood flow

Blood flow

regulation

regulation

cvt,O2cvt,CO2

ct,O2

ct,CO2

Tissues

Mt,CO2Mt,O2

ca,CO2

ca,O2

cv,O2cv,CO2

ce,CO2

ce,O2

cv,O2

cv,CO2

PI,O2 PI,CO2

Pa,O2

Pa,CO2

Figure 3.4: Block diagram representation of the model. The figure illustrates the

compartments and the physiological quantities discussed in the text.

The meaning of symbols and subscripts is: PA,j, PI,j (j = O2, CO2):

alveolar partial pressure and gas pressure in inspired air, respectively;

s: pulmonary shunt fraction; Q: cardiac output; ce,j, cv,j , ca,j : gas con-

centration in blood outflowing from the alveoli, in mixed venous blood,

in arterial blood; cvt,j , cvb,j : gas concentration in blood outflowing from

tissues and brain; ct,j , cb,j : tissular and cerebral gas concentration; Pb,j,

Pa,j : gas partial pressure in brain and in arterial blood; Mi,O2, Mi,CO2

(i = t, b): O2 consumption and CO2 production rate in the compart-

ment; Qi: compartmental perfusion; ∆VE0, ∆VEP , ∆VEP : basal venti-

lation and chemoreceptive ventilatory regulation; VE, VA: minute and

alveolar ventilation. Adapted from the literature [196].


+

×

VA

CVD

deadspace

VE0

Central Chem.

∆VEP

∆VEC

Peripheral Chem.

Lungs

Brain

Tissues

Mt,CO2, Mb,CO2

Mt,O2, Mb,O2

PI,O2 PI,CO2

VE

Blood flow

regulation

Pb,CO2

Pb,O2

Pa,O2

Pa,CO2

Pt,CO2

Pt,O2

Figure 3.5: Alternative structural representation of the model. The figure empha-

sizes the reciprocal relationships between model components. Variables

involved in regulation are displayed. Adapted from the literature [129].


Ventilatory regulation

VE0 = 6.62 l (BTPS)min

k = 0.333 Pa,O2c = 45 mmHg

K = 1.738 Bp = 18 mmHg kpc = 29.27 mmHg

τp = 7 s fpcmax = 12.3 spikess

kDp = 0.588 l

τc = 60 s fpcmin = 0.8352 spikess

kDc = 0.9239 l

Gp = 2.5l/min

spikes/s Gc,high = 2l/min

mmHg

Gc,low = 0.12l/min

mmHg

Central ventilatory decline

τα = 300 s Gα = 10 Pb,O20 = 32 mmHg

θmax = 35 mmHg θmin = 29.8 mmHg

Cardiovascular regulation

c1 = 17 c2 = 11 mmHg

A = 20.9 B = 92.8 C = 10570

D = -5.251

τO2= 10 s τCO2

= 20 s

Pa,O20 = 95 mmHg Pa,CO20 = 40 mmHg

Qb0 = 0.75 lmin

Qb0 = 0.75 lmin

ρ = 0.32

Table 3.2: Parameter values for regulatory mechanisms.

Parameter values are estimated to reproduce cardiovascular regulation experi-

mental data (Figure 3.6). The values are reported in Table 3.2. Parametric assign-

ment and estimation are discussed in [129, 195, 196] and are not reported here for

the sake of brevity.

3.3.3 Ventilatory regulation

In the model, ventilatory regulation is performed by three different mechanisms.

They mimic physiological respiratory control by inducing changes in minute venti-

lation based on blood O2 and CO2 content. The three regulatory systems are the


20 40 60 80 100

1

1.5

2

2.5

Arterial PO2 [mmHg]

Nor

mal

ized

car

diac

out

put [

−]

Model Koehler et al.

20 40 60 80 100

1

1.5

2

2.5

3

3.5

4

Arterial PO2 [mmHg]

Nor

mal

ized

cer

ebra

l blo

od fl

ow [−

]

Model McPherson et al., 1987 McPherson et al., 1994 Ulatowski et al.

Figure 3.6: Dependence of normalized cardiac output and cerebral perfusion on

arterial O2 pressure at basal PCO2 pressure. Solid lines: model simu-

lation results. Symbols: experimental data are taken from Koehler and

coworkers in dogs [114], McPherson and coworkers in dogs [133, 134]

and Ulatowski and collaborators in cats [194]. Adapted from the liter-

ature [195].


peripheral chemoreceptors, the central chemoreceptors and the central ventilatory

depression (CVD).

According to the literature, chemoreceptive stimulation exerts an additive effect

on ventilation; the interaction between peripheral and central chemoreceptors does

not show significant non-linearities [195]. The CVD mechanism, on the other hand,

acts as an inhibitory gain on the peripheral chemoreceptive system in case of brain

tissue hypoxia [129]. Total minute ventilation is then computed via the following

equation:

VE = (VE0 + α ⋅∆VEP +∆VEC) ⋅H(VE0 + α ⋅∆VEP +∆VEC) (3.22)

where VE0 is the value of ventilation in basal conditions, and ∆VEP and ∆VEC rep-

resent the changes in ventilation produced by the peripheral and central chemore-

ceptive activity, respectively. The multiplicative term α refers to the hypoxic

ventilatory depression and it is equal to 1 in basal conditions. Finally, H() de-

notes the Heaviside function which prevents ventilation from taking on negative

values. Given that ∆VEP and ∆VEC can be either positive or negative quantities, a

strong inhibitory chemoreceptive stimulation could in fact produce negative values

of minute ventilation.

Alveolar ventilation is determined from minute ventilation. The lung dead space

is assumed to be a constant fraction of minute ventilation [195], therefore it is

possible to calculate alveolar ventilation as

VA = VE (1 − k) (3.23)

where k is a constant parameter < 1 related to the dead space.

A more detailed description of the ventilation regulatory systems is given below.

Peripheral Chemoreceptors

In the model, the discharge frequency of peripheral chemoreceptors is described as

a function of the arterial O2 and CO2 pressure. The discharge frequency represents

a way to quantify the chemoreceptive activity that is afferent to the central nervous

system. It is determined as the number of action potentials occurring per second

(spikes s−1). Experimental data recorded in cats by Fitzgerald and coworkers [76]

were considered to determine the relationship between oxygen and carbon dioxide

partial pressure and the discharge activity of the peripheral chemoreceptors. From

the data it can be inferred that the relationship between discharge frequency and


oxygen pressure at constant PaCO2 can be described as a sigmoidal curve [76,195].

The following equation is used to compute peripheral chemoreceptive activity:

fpc =K ln(Pa,CO2

Bp

)fpcmax + fpcmin ⋅ exp [(Pa,O2−Pa,O2c)kpc

]1 + exp [(Pa,O2

−Pa,O2c)kpc

] (3.24)

where the PaO2-dependent term translates the sigmoidal interrelation of chemore-

ceptive activity and oxygen pressure. K, Bp, fpcmax, fpcmin, Pa,O2c, kpc are constant

parameters and their value is assigned to reproduce experimental findings (see Fig-

ure 3.7). fpc stands for the action potential frequency in the chemoreceptive affer-

ent fibres, while fpcmax and fpcmin represent its upper and lower saturation levels.

Their value is 12.3 spikes s−1 and 0.8352 spikes s−1, respectively. Pa,O2c is a constant

parameter equal to 45 mmHg. According to Ursino and colleagues, it represents

the “arterial oxygen pressure at the central point of the sigmoid” [195]. However,

no experimental data supporting such values could be found in the literature, nor

any reference to a point on the sigmoid function holding physiological significance.

The values were determined solely with the aim of reproducing experimental find-

ings. Therefore in what follows Pa,O2c, fpcmax and fpcmin are considered as constant

parameters with no apparent physiological meaning.

Chemoreceptive discharge activity affects minute ventilation by producing the

ventilation change ∆VEP appearing in Equation 3.46. The ventilation response to

peripheral chemoreceptive stimulation is modeled via a first order low-pass dynam-

ics with time constant τp and static gain Gp. The time constant τp of chemoreceptor

dynamics was given the value of 7 s according to the data reported in the litera-

ture [195]. Chemoreceptor activity is further described by a time delay Dp which is

inversely proportional to cardiac output Q and mimics the time required for blood

transport to the receptor [44]. The equation regulating the changes in ventilation

due to the arousal of peripheral chemoreceptors is:

d∆VEP (t)dt

= 1

τp−∆VEP +Gp ⋅ [fpc(t −Dp)] − fpc0 (3.25)

being

Dp = kDp

Q(3.26)

fpc0 is the basal value of the activity in the peripheral chemoreceptive afferent

fibres, meaning the discharge frequency value for PaO2= 95 mmHg and PaCO2=

40 mmHg. kDp, on the other hand, is a constant parameter assigned to produce

a time delay equal to 7 s in basal cardiac output conditions (Q = 5 l min−1), as

reported in the literature [195].

503

Feed

back

contro

lofsed

atio

n

Figure 3.7: Discharge frequency of peripheral chemoreceptors as a function of arterial CO2 partial pressure. Receptor

activity is evaluated at different levels of arterial O2 pressure (ranging from hypoxia to hyperoxia). Solid

lines: model simulation results. Symbols: experimental data recorded in cats by Fitzgerald and coworkers

[76]. Adapted from the literature [195].


Central Chemoreceptors

In the human body, central chemoreceptors play the role of a carbon dioxide sensor

that detects PCO2 changes in the medulla. According to the literature the receptors

are insensitive to changes of oxygen content in the blood [153]. Therefore in the

model central chemoreceptive activity depends on brain tissue PCO2.

Similarly as for the peripheral receptors, the ventilatory response to central

chemoreceptive stimulation is described by first order low-pass dynamics. The time

constant τc of the system is equal to 60 s in accordance with the literature [195].

The equation for computing ventilatory changes driven by central chemoreceptive

stimulation is:

d∆VEC(t)dt

= 1

τc⋅ −∆VEC +Gc ⋅ [Pb,CO2

(t −Dc)] − Pb,CO20 (3.27)

where

Dc = kDc

Q(3.28)

In Equation 3.27, Pb,CO20 stands for brain tissue CO2 pressure in basal conditions.

The gain Gc of the mechanism is not a constant parameter. Varying the mecha-

nism’s gain on ventilation reflects the existence of a breakpoint in the ventilatory

CO2 response curve [129]. Depending whether Pb,CO2> Pb,CO20 or Pb,CO2

< Pb,CO20,

Gc assumes the value of 2 or 0.12 (l/min)(mmHg)−1, respectively. Finally, as in the

case of peripheral chemoreceptors kDc is a constant parameter which determines

the time delay of the mechanism. For basal cardiac output conditions, the delay is

equal to 11 s [195].

Central Ventilatory Depression

In the model, ventilation is regulated by the central and peripheral chemorecep-

tors together with the depressant effect of hypoxia. From this point onwards we

shall refer to the latter mechanism as the central ventilatory depression (CVD).

The CVD describes the inhibition of the ventilatory response occurring during sus-

tained cerebral hypoxia. Inhibition of respiratory neurons due to hypoxia causes a

decline of ventilation. More precisely, brain hypoxia diminishes the CNS ventilatory

response to peripheral stimulation. Evidence of such effect in the human body is

reported in the literature [129]. In accordance to such findings, the CVD is modeled

as a varying gain on the peripheral chemoreceptive response [see Equation 3.46].

The gain is equal to 1 when O2 pressure in the brain is at its basal level, i.e. for


Pb,O20 = 32 mmHg. For other O2 values the gain varies linearly between an upper

and lower bound. At both thresholds the mechanism effect saturates and does not

exhibit further changes. The following equations describe the central ventilatory

depression effect:

αb,O2 =⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩

1 +Gα(θmin−Pb,O20)

Pb,O20

if Pb,O2 < θmin

1 +Gα(Pb,O2

−Pb,O20)Pb,O20

if θmax > Pb,O2 > θmin

1 +Gα(θmax−Pb,O20)

Pb,O20

if Pb,O2 > θmax

(3.29)

dα

dt= 1

τα⋅ (α − αb,O2) (3.30)

where θmax and θmin are the upper and lower Pb,O2thresholds, respectively. τα

describes the mechanism time constant. Equation (3.30) computes the variable α:

it represents the hypoxic ventilatory gain on peripheral chemoreceptive response.

3.3.4 Ventilatory regulation in the presence of an opioid

In 2004 the model described so far was extended by Magosso and collaborators [129]

to reproduce the effect of opioids on the ventilatory system. Fentanyl and other

opioids have a dose dependent depressant effect on ventilation. The extended model

takes into account the plasma concentration of the drug to quantify its effect on

the respiratory system. Minute ventilation is determined based on the O2- and

CO2-dependent regulatory mechanisms described in the above, and by the opioid

concentration in blood. Drug effects on ventilation include the inhibition of the

chemoreceptive response and the decline of respiratory neural activity.

A comprehensive description of drug effect modeling is provided in the following

paragraphs. See Figure 3.8 for a block-diagram representation of the extended

model as proposed by Magosso and colleagues [129].

Opioid effect on chemoreceptors

In the model it is assumed that fentanyl acts on chemoreceptive ventilatory regu-

lation by reducing the mechanism gain. The attenuation is a nonlinear function of

opioid plasma concentration. The higher drug content in blood, the stronger the

effect on ventilation. Moreover, drug effects are modeled in such a way that the

opioid exerts the same attenuation on both the peripheral and the central chemore-

flex response. This assumption is based on the hypothesis that fentanyl acts on

the respiratory neurons in the medulla rather than at a chemoreceptive level. The


information coming from peripheral and central chemoreceptors is processed in the

medulla. Therefore a depression of medullary neural activity results in the inhi-

bition of chemoreflex sensitivities. Evidence that opioid drugs act via a unique

mechanism on the same central site can be found in the literature [129]. Neverthe-

less, it is worth mentioning that other authors report different theories. Sarton and

coworkers, for instance, proposed the idea that drug mechanism and site of action

are receptor-specific [167]. Is such case the effect of the drug on the central and

peripheral chemoreceptive sensitivity would differ.

As mentioned above, the model makes use of a single attenuating factor to mimic

the influence of fentanyl on both chemoreceptive drives. Equations 3.25 and 3.27

are modified as follows:

d∆VEP (t)dt

= 1

τp⋅ −∆VEP +A(Cf) ⋅Gp ⋅ [fpc(t −Dp) − fpc0] (3.31)

d∆VEC(t)dt

= 1

τc⋅ −∆VEC +A(Cf) ⋅Gc ⋅ [Pb,CO2

(t −Dc) − Pb,CO20] (3.32)

where Cf stands for fentanyl blood concentration andA(Cf) represents the concentration-

dependent attenuation factor. The dependence of the attenuating factor on Cf is

described by the following equations:

Astatic = A0 ⋅ [1 − 1

2⋅ ( Cf

C50)γA] ⋅H A0 ⋅ [1 − 1

2⋅ ( Cf

C50)γA] (3.33)

dA

dt= 1

τf⋅ [−A +Astatic(Cf)] (3.34)

Astatic is the steady state drug concentration-effect relationship, which is expressed

in the form of a power model. Some authors report that the power model is more

accurate than the commonly used Emax model in reproducing physiological re-

sults [55]. Therefore a power function is used here for pharmacodynamic modeling.

Nevertheless, other studies showed that the power model performs relatively poorly

in describing the observations when compared to a sigmoidal Emax function [25].

Such divergent conclusions demonstrate the importance of evaluating different mod-

els in pharmacodynamic research.

In Equation 3.33 the term A0 is a constant parameter that represents the value

of the attenuating factor in the absence of drug. A0 is defined equal to 1 so that for

Cf = 0, Astatic = A0 = 1. Hence in steady state conditions the attenuation factor

A(Cf) assumes a unitary value and chemoreceptive sensitivities remain unaltered.

C50 and γA are constant parameters. The C50 (effective concentration 50) is

the fentanyl concentration level that produces an effect of 50%, that is, the blood


concentration causing a 50% decline in ventilation. γA is the power coefficient of

the pharmacodynamic model. C50 and γA were given values that could reproduce

clinical results in terms of CO2 response curve changes. As mentioned in Section

3.2.1, a depression of the slope and a rightward shift can be observed in the CO2 re-

sponse curve after administration of anesthetic (Figure 3.2). The values assigned to

C50 and γA allow for the reproduction of measured changes in CO2 responsiveness

(Figure 3.9).

Finally, H() stands for the Heaviside function which prevents chemoreceptor

gains from taking on negative values when Cf ≥ 21/γA ⋅C50.

In Equation 3.34, τf is the mechanism time constant. It takes into account

the time required to achieve equilibration between plasma concentration and effect

site concentration (medullary concentration). τf in the model was assigned the

value of 4 min; such value was chosen in accordance with the findings reported in

physiological literature [129].

Equation 3.33 and 3.34 show that the dependence of the attenuating factor on Cf

includes a non-linear static function and a first order low pass dynamics. The reason

A(Cf) has such mathematical description is discussed in the following. Magosso

and colleagues [129] did not include an effect compartment in their extended model.

The pharmacodynamic power model receives as an input the plasma concentration

rather than the effect compartment concentration. As explained in Section 2.3.2,

the plasma concentration does not always correlate with the clinical effects of anes-

thetic drugs [200]. To obtain a hysteresis-free relationship between drug concentra-

tion and pharmacological effect, an effect site compartment is added to the standard

three-compartment pharmacokinetic model [121]. The effect compartment per def-

inition does not take part in drug mass exchanges. Movement of the drug between

the central compartment and the effect site compartment is considered to be a first

order process with a specific time constant [3]. Hence the effect site concentration

is computed from plasma concentration via a first order dynamics. The pharma-

codynamic model then evaluates the magnitude of the effect through a nonlinear

static function. The mechanism that determines A(Cf) in the model has to mimic

the role of the effect compartment. This is the reason why the attenuation term

depends on Cf via a non-linear static function and a first order dynamics.

Opioid effect on respiratory neurons

In the model the effect of fentanyl includes a direct inhibition of the spontaneous

respiratory activity. Several experimental findings support the existence of a central

depressant mechanism of the drug, besides the influence on chemoreflex gains [129].


The equation for minute ventilation (Equation 3.46) is modified as follows:

VE = (VE0 −K(Cf) +α ⋅∆VEP +∆VEC) ⋅H(VE0 −K(Cf) + α ⋅∆VEP +∆VEC) (3.35)

to add the term K(Cf) which mimics the drug inhibitory influence on the res-

piratory neural centers. ∆VEP and ∆VEC result from Equation 3.31 and 3.32,

respectively.

The inhibitory term depends on the fentanyl plasma concentration. The mech-

anism effect is evaluated through a static relationship and a first order dynamics,

like the chemoreceptive attenuation term A(Cf) discussed in the above. The static

relationship Kstatic is a power function of fentanyl concentration Cf . It exhibits an

upper saturation to prevent the occurrence of apnea after a bolus injection. Opioid

boluses produce temporarily an extremely high plasma concentration of the drug,

but clinical experience shows that patients do no become apneic. The mathematical

description of the mechanism is:

Kstatic =⎧⎪⎪⎨⎪⎪⎩K0 ⋅C

γK

f for Cf ≤ Cf

K0 ⋅Cf

γKfor Cf > Cf

(3.36)

dK

dt= 1

τf⋅ [−K +Kstatic(Cf)] (3.37)

where τf is the same time constant appearing in Equation 3.34. The same equi-

libration rate is used for both mechanisms because the basic respiratory rhythm

originates in the medulla, where chemoreflex stimuli are processed. Therefore the

two regulatory systems have the same site of action [129].

K0, γK , Cf are constant parameters; their values are listed in Table 3.3. Para-

metric estimation was carried out in order to achieve model results consistent with

the literature. Clinical data considered for parameter selection was measured by

Mildh and coworkers in healthy volunteers at increasing steady state plasma concen-

trations [137]. The data comprise minute ventilation, arterial O2 partial pressure

and arterial CO2 partial pressure recordings at different levels of fentanyl plasma

concentration.

Simulation-based results provided by the model are presented in the following

section.


+

×

×

×

VA

CVD

deadspace

−

VE0

K(Cf)Central Chem.

∆VEP

∆VEC

A(Cf)

A(Cf)Peripheral Chem.

Lungs

Brain

Tissues

Mt,CO2, Mb,CO2

Mt,O2, Mb,O2

PI,O2PI,CO2

VE

Blood flow

regulation

Pb,CO2

Pb,O2

Pa,O2

Pa,CO2

Pt,CO2

Pt,O2

Figure 3.8: Block diagram representation of the extended model. Shaded blocks

denote the effects of the opioid on the respiratory system. Cf : fentanyl

plasma concentration; A(Cf): fentanyl attenuation of peripheral and

central chemoreceptive response; K(Cf): fentanyl direct inhibition of

the respiratory activity. Adapted from the literature [129].


Figure 3.9: Opioid induced changes in CO2 sensitivity. Experimental results re-

ported in the literature are compared to model simulations performed

at four different steady state levels of fentanyl plasma concentration

(Cf = 1, 2, 3, 4 ng ml−1). In vivo sensitivities are measured with the re-

breathing technique. The experimental conditions are reproduced in the

simulation environment at each concentration level. This is achieved by

linearly increasing PACO2 by 20 mmHg over 4 minutes (starting from

baseline) and evaluating ventilation at the beginning and at the end of

each interval. Adapted from the literature [129].

Ventilatory regulation in the presence of fentanyl

A0 = 1 γA = 0.5457 C50 = 2.571 ng/ml

K0 = 10 (l/min)(ng/ml)−1 γK = 0.5 Cf = 4 ng/ml

τf = 4 min

Table 3.3: Parameter values for drug-induced ventilatory depression.


3.4 Model analysis

In this section we shall analyze the response of the model under different condi-

tions. Simulated results will be compared to experimental observations in order to

determine whether the model provides an adequate description of the respiratory

control system. Section 3.4.1 evaluates model behavior by means of the alveolar

alveolar gas equation, a mathematical tool well known to respiratory physiologists.

Ventilatory system response in the absence of drug is assessed in Section 3.4.2. Of

particular interest for our purposes is the ventilatory response in the presence of

drug, discussed in Section 3.4.3.

3.4.1 Assessment of the gas exchange system

A method to evaluate model adequacy in describing gas exchange phenomena be-

tween tissular compartments relies on use of the alveolar gas equation. In the

medical field, this equation is frequently employed to estimate O2 alveolar pres-

sure from CO2 arterial pressure. We now describe how the alveolar gas equation is

derived, and the way it is used to assess model performance.

Metabolism refers to the chemical processes occurring within a living organism

in order to maintain life. Such processes consume oxygen and produce carbon

dioxide as a by-product. The ratio of produced CO2 to consumed O2 is called

respiratory quotient (RQ). The respiratory quotient depends on the metabolic

substrates supplied for energy production. If carbohydrates are the substrate, RQ

= 1; if proteins, RQ = 0.8; if lipids, RQ= 0.7. Cells, however, do not rely on a

single substrate so that on average RQ amounts to 0.8 circa.

Oxygen and carbon dioxide are exchanged between the alveoli and the pulmonary

capillaries. The ratio VCO2/VO2 (V being the exchanged volume) is called res-

piratory ratio (R). In steady state R = RQ, but they can differ during tran-

sients. For example, when a person hyperventilates RQ remains approximately

constant while R rises. The volume of exchanged carbon dioxide increases as more

CO2 is eliminated from blood during hyperventilation. Oxygen uptake, however,

changes slightly because of hemoglobin saturation and low physical solubility of

O2 in plasma. Therefore, the overall result is that the ratio VCO2/VO2 increases

during periods of hyperventilation.

The level of alveolar oxygen is the result of a balance between O2 delivery to the

alveoli and O2 uptake by the perfusing blood. Oxygen delivery depends on alveolar

ventilation and the level of O2 in the inspired air, whereas O2 uptake by the blood

depends on tissular oxygen consumption. Therefore:

3.4 Model analysis 59

VO2= VA ⋅ (FI,O2

−FA,O2) (3.38)

FI,O2− FA,O2

= VO2

VA

(3.39)

Given that

PI,O2−PA,O2

= (FI,O2− FA,O2

) ⋅ (Patmospheric − PH2O vapor) (3.40)

we have

PI,O2−PA,O2

= VO2

VA

⋅ (P atmospheric − P H2O vapor) (3.41)

= VO2

VA

⋅ (P atmospheric − 47)Moveover,

if R = 1 Ô⇒ PI,O2− PA,O2

= PA,CO2(3.42)

if R ≠ 1 Ô⇒ PI,O2− PA,O2

= PA,CO2

R(3.43)

In an ideal lung PACO2 = PaCO2, so that (for R = 0.8)

PI,O2− PA,O2

= Pa,CO2

R(3.44)

This mathematical equation is termed alveolar gas equation, and it is valid under

steady state conditions. Filley [153] proposed an alternative equation which is

applicable also to non-steady state cases:

PI,O2− PA,O2

= Pa,CO2

R⋅ [1 − FI,O2

(1 −R)] (3.45)

We now make use of Equation 3.45 to determine whether the model is able to predict

correct alveolar PO2 results. To this purpose, the simulation of a fentanyl bolus

injection (0.5 mg) is performed. We consider the case of a drug bolus because

it induces a strong and rapid respiratory decline. Therefore PAO2 is expected

to undergo major changes, enabling the appraisal of model performance through

the alveolar gas equation. Drug infusion and opioid effect on ventilation will be

extensively covered in Section 3.4.3.

Amongst model outputs, PAO2 and PaCO2 time courses are taken into consider-

ation. The former illustrates model response to the bolus, while the latter enables


0 2 4 6 8 1020

30

40

50

60

70

80

90

100

110

Alv

eola

r P

O2 [m

mH

g]

time [min]

0 2 4 6 8 1020

30

40

50

60

70

80

90

100

110

Alv

eola

r P

O2 [m

mH

g]

time [min]

Figure 3.10: Alveolar PO2 changes in response to a fentanyl bolus (0.5 mg). Bolus

administration occurs at time t = 0 [min]. Input drug plasma con-

centration coincides with the first 10 minutes of Figure 3.18 Cf time

course. Top: alveolar oxygen pressure resulting from model simula-

tion. Bottom: alveolar oxygen pressure computed via the alveolar gas

equation (Equation 3.45). The equation is computed for FIO2 = 0.21,

PIO2 = 149 mmHg, R = 0.8. PaCO2 values considered for equation

solving result from model simulation. The agreement between simu-

lated and computed PAO2 is fully satisfactory.


us to solve the alveolar gas equation. Figure 3.10 displays both the simulated and

the computed PAO2 curve. The match between the two is fully satisfactory. We

can conclude that the system is able to model adequately the relationship between

alveolar O2 and arterial CO2 partial pressure.

3.4.2 Response of the ventilatory control system in the

absence of drug

Ursino and coworkers [195] tested the response of the model to stepwise changes

in alveolar PCO2 at different O2 levels and compared the results to experimental

data reported in the literature. The results are reported in Figure 3.11. It may be

concluded that:

- model response under normoxia is fully adequate;

- model behavior under hypoxia yields correct results at steady state, however

the dynamics of the response to hypercapnic stimulation are slower than in

the human body;

- model results under hyperoxia do not match experimental observations.

In the following, drug naıve hypercapnic results presented by Ursino and cowork-

ers [195] are described more in detail. Moreover a comprehensive analysis of model

behavior under hyperoxia is provided. In addition, though not of critical interest

for the case of sedation, hypoxic conditions mimicking the effect of high altitude

are investigated.

Model response to hypercapnic stimulation

Figure 3.11 shows the ventilatory response to a square wave change in alveolar

PCO2, performed at different constant levels of alveolar PO2. Carbon dioxide

alveolar pressure is constrained in the simulation environment to match the time

course of experimental PCO2. Under basal conditions, PACO2 = 39 mmHg. Hy-

percapnic PACO2 is equal to 6.5 kPa = 48.75 mmHg under hyperoxia and to 48

mmHg under normoxia and hypoxia. Each simulation starts at time t = -5 min to

reach steady state conditions at the beginning of the hypercapnic stimulus.

In Section 3.3.3 it was discussed that total minute ventilation is calculated from

basal ventilation and the ventilatory response to chemoreceptive stimulation. Equa-

tion 3.46 is rewritten here for the sake of clarity:


0 5 10 15 20

0

10

20

30

40

Time [min]

Ven

tilat

ion

[l m

in−

1 ]

20

25

30

35

40

45

50

55

PA

CO

2 [mm

Hg]

Hypercapnia during hyperoxia

0 2 4 6 8 10 12

35

40

45

50

55

Time [min]

PA

CO

2 [mm

Hg]

11

22

33

44

55

Ven

tilat

ion

[l m

in−

1 ]

Hypercapnia during normoxia

0 2 4 6 8 10 12

35

40

45

50

Time [min]

PA

CO

2 [mm

Hg]

11

22

33

44

55

Ven

tilat

ion

[l m

in−

1 ]

Hypercapnia during hypoxia

Figure 3.11: Left: experimental data reported in the literature [54, 12]: minute

ventilation time courses observed in healthy volunteers. Right: sim-

ulated time course of minute ventilation (blue line) in response to a

square change in alveolar PCO2 (red line). Hypercapnic stimulation

is performed under hyperoxia (top), normoxia (middle) and hypoxia

(bottom). Adapted from the literature [195].


VE = (VE0 + α ⋅∆VEP +∆VEC) ⋅H(VE0 +α ⋅∆VEP +∆VEC) (3.46)

where VE0 is the value of minute ventilation under basal conditions and ∆VEP

and ∆VEC represent the changes in ventilation produced by the peripheral and

central chemoreceptive activity, respectively. The multiplicative term α refers to

the hypoxic ventilatory inhibition (CVD) described in (3.3.3).

The agreement between model results and clinical observations is partially sat-

isfactory. The figure shows that the model is able to correctly predict the respi-

ratory sensitivity to CO2 changes under normoxia (Figure 3.11, middle diagrams).

Under hypoxia steady state results exhibit good agreement with experimental ob-

servations, however model dynamics in response to the hypercapnic stimulation

is slower than that of the human body (Figure 3.11, lower panels). Finally, the

top diagrams of Figure 3.11 display the time course of minute ventilation under

hyperoxic conditions. The disagreement between results cannot be neglected. The

model predicts a strong depressant effect of hyperoxia on ventilation leading to

apnea which is not supported by clinical evidence. Minute ventilation is equal to 0

l min−1 in basal PACO2 conditions; it rises to positive values (approximately 12.5

l min−1) only at the onset of the hypercapnic stimulus. Simulated results can be

explained as follows. The excess of oxygen in the alveolar compartment causes pe-

ripheral chemoreceptors to exert an inhibitory effect on ventilation (∆VEP = -10 l

min−1 circa). Central chemoreceptors work as a carbon dioxide sensor, therefore in

basal PACO2 conditions their ventilatory stimulation is null. The outcome is that

simulated minute ventilation drops to zero. Conversely, apnoea does not occur in

healthy volunteers exposed to a slight increase in FIO2, such as the one determining

a PAO2 of 200 mmHg. Spontaneous ventilation in the human body results from the

rhythmic activity of respiratory centres in the brainstem. The breathing stimulus

is fundamental for survival, therefore inhibition by respiratory gases is limited and

cannot induce apnoea.

Individual contributions of central and peripheral chemoreceptors to minute ven-

tilation are purposely not displayed in Figure 3.11. Such results are in fact difficult

to interpret. No experimental data regarding the quantitative effect of chemore-

ceptive activity on ventilation are reported in the literature. Simulated results are

therefore of mere speculative nature. Nevertheless, in Ursino and coworkers [195]

the interested reader can find a discussion on the response of the regulatory system

in terms of chemoreceptive components ∆VEP and ∆VEC .


Model response under hyperoxia

Exposure to hyperoxia is investigated further to better characterize model behavior

and performance under such condition.

Ventilatory regulation in the model is performed by chemoreceptors and the

central ventilatory depression. These mechanisms exert their action on minute

ventilation depending on arterial O2 and CO2 content. It is of interest for our

investigation to evaluate how increased fractions of inspired oxygen reflect on the

compartmental gas exchange system. We turn to clinical expertise to determine

what the expected behavior is.

In the medical practice the pulmonary shunt fraction is estimated through the

following procedure. The patient is provided with 100% oxygen to breathe (FIO2 =

1). At sea level, the alveolar O2 partial pressure is:

PA,O2= P atmospheric − P H2O vapor − PA,CO2

= (3.47)

= 760 − 47 − 40 = 673 [mmHg]

where P atmospheric is the barometric pressure, P H2O vapor is the vapor pressure of

water when air is saturated, and PACO2 is the alveolar carbon dioxide pressure

under basal conditions. The pulmonary shunt is the mixing of deoxygenated blood

from pulmonary veins with oxygenated blood coming from pulmonary capillaries.

Therefore mixed blood has a lower oxygen content than the blood in pulmonary

capillaries. The shunt fraction can be estimated by measuring arterial PO2 and

comparing it to the alveolar pressure determined above (Equation 3.48). This

method only works for FIO2 = 1. In fact, ventilation and perfusion heterogeneity

can produce a reduction in arterial PO2 which cannot be distinguished from the

effect of a shunt unless FIO2 = 1. Clinical observations suggest that, when 100%

oxygen is administered, the arterial partial pressure has a value in the range 450-500

mmHg. Refer to Figure 3.12 for a graphical representation of these phenomena.

Simulating the effect of exposure to 100% O2 in the model yields results that

do not entirely agree with clinical experience. For FIO2 = 1, the model quite

correctly predicts that PAO2 = 655 mmHg, while PaO2 results to be equal to 190

mmHg. The reason for the mismatch between simulated and experimental arterial

partial pressure can be explained as follows. Blood storage of respiratory gases

in the model is described by a set of equations proposed by Spencer et al. [176].

The validity of the fit provided by the equations is stated to be in the range of

0-120 mmHg of oxygen partial pressure and 0-80 mmHg of carbon dioxide partial

pressure [176]. Agreement between experimental observations and results provided

by the equations is not assured for pressure levels outside the specified ranges.


Figure 3.12: Oxygen dissociation curve. O2 content in blood is associated with

oxygen partial pressure. The diagram illustrates the O2 content in

pulmonary capillaries and in mixed blood, and the relative alveolar-

arterial PO2 difference.

0 100 200 300 400 500 600 7000

4

8

12

16

20

24

P O2 [mmHg]

O2 c

onte

nt [v

ol %

]

Figure 3.13: The oxygen dissociation curve employed in [195] for gas exchange mod-

eling. Blood O2 content in basal PaCO2 conditions is shown. The

agreement with experimental data is satisfactory only over the PaO2

range of 0-120 mmHg.


It results that under hyperoxia the equations provide an imprecise description of

oxygen content in blood. In fact:

- at high O2 pressure, the curve predicts an oxygen content which is lower than

physiological values;

- above PO2 = 200 mmHg, the curve becomes horizontal predicting saturation

of oxygen content in blood.

In the model the mixing of oxygenated blood from the alveolar compartment

with shunted venous blood produces a correct, moderate reduction in blood O2

content. However, such small decrease in content produces a substantial change

in partial pressure due to the flatness of the curve at high PO2. This is the rea-

son why exposure to hyperoxic FIO2 produces a mismatch between simulated and

experimental arterial PO2.

Improving the description of blood gas storage would require the definition of

a different set of equations relating PaO2, PaCO2 to ca,O2, ca,CO2

, and vice versa.

This issue will be addressed in Section 3.5.1.

Model response under hypoxia

Further investigation of model behavior under hypoxia is carried out. The objective

is to determine whether ventilatory regulation is described accurately over a wide

range of hypoxic conditions. To this purpose, we study the respiratory response to

stepwise, acute exposure to simulated altitude (3000 and 6000 m above sea level).

It is well known that barometric pressure decreases with altitude. A reduction of

atmospheric pressure determines a proportional decrease in oxygen partial pressure.

For example, at 3000 m barometric pressure decreases to 523 mmHg and oxygen

partial pressure to 110 mmHg. Although the fraction of inspired oxygen is un-

changed compared to sea level (FIO2 = 0.21), we are under hypoxic conditions. A

non-acclimatized subject breathing atmospheric air at high altitude hyperventilates

in order to compensate for the decreased inspiratory PO2.

To reproduce acute exposure to hypoxia, we study the response of the model to

negative square changes in inspired O2 partial pressure. During 30-minute intervals,

PIO2 is kept constant at 100 mmHg and at 73 mmHg to simulate oxygen pressure

in air at 3000 m and 6000 m, respectively. PAO2 and PACO2 model results are

displayed in Table 3.4, together with clinical observations reported in the literature

[92]. Simulation results and experimental data are in excellent agreement at 3000 m

altitude. The match is not as adequate at a simulated altitude of 6000 m. Reported


Exposure to altitude

Altitude Barometric PO2 PAO2 PACO2

[m] pressure [mmHg] [mmHg] [mmHg] [mmHg]

0 760 159 104 40

3000 523 110 67 (67) 36 (35)

6000 349 73 40 (34) 24 (34)

Table 3.4: Atmospheric, oxygen, and alveolar O2 and CO2 pressure at different

altitudes above sea level. Physiological observations are compared to

model results (shown in brackets). Clinical data are reported in [92].

observations illustrate that at this altitude, physiological PAO2 and PACO2 are

respectively higher and lower than model predictions. However, those experimental

observations may be be explained as resulting from a state of depressed metabolism

in the subjects monitored during the study.

Guyton and coworkers [92] report that exposure to low-pressure air at very high

altitude causes an increase in ventilation at rest of maximum 65%. Cardiac output

is reported to increase by approximately 30%. These physiological responses occur

immediately after exposure and compensate for the reduced availability of oxygen

in inspired air. Figure 3.14 displays simulation results in terms of minute ventila-

tion and cardiac output. As expected, the model counteracts the decrease in PIO2

by increasing ventilation. The match between model results and experimental ob-

servations is satisfactory. For example, at 6000 m the model predicts a steady state

increase in cardiac output of 30%. The increase in ventilation amounts to 27%.

To determine the influence of cardiovascular regulation on the ventilatory re-

sponse of the model, the simulations described above are repeated neglecting the

effect cardiac output changes. That is, Equation 3.16 and 3.18 are manipulated so

that

⎧⎪⎪⎨⎪⎪⎩dyO2/dt = 0

dyCO2/dt = 0

Ô⇒

⎧⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎩

Qb(t) = Qb0

Qt(t) = Qt0

Q(t) = Qb0 +Qt0 = 5 l min−1

(3.48)

All other simulation conditions are identical. Model results are displayed in Figure

3.14 together with the ventilation time course for unconstrained Q. Given that


4.5

5

5.5

6

6.5

7

Q[l

min−

1]

0 30 60 90 120 150

149

73

110

PIO

2[m

mH

g]

Time [min]

6000 maltitude

3000 maltitude

6

8

10

12

14

VA

[lm

in−

1]

0 30 60 90 120 150

149

73

110P

IO2

[mm

Hg]

Time [min]

6000 maltitude

3000 maltitude

Figure 3.14: Circulatory and respiratory response to simulated altitude. Exposure

to low-pressure air occurs stepwise. Each step lasts for 30 min, starting

at time t = 30 min (3000 m altitude) and t = 90 min (6000 m altitude).

Top: cardiac output in response to altitude (blue line). To evaluate the

effect of cardiovascular regulation on the ventilatory response, a second

simulation was performed constraining cardiac output to its baseline

value (Q = 5 l min−1) (red dashed line). Bottom: ventilatory response

to simulated altitude. The ventilation time course for unconstrained

Q (blue line) is compared with the response obtained for constant

Q = 5 l min−1 (red dashed line). The discrepancy between the two

results is very small. At 6000 m altitude, VE changes from 8.31 l

min−1 (unconstrained Q) to 8.42 l min−1 (constant Q).


the dynamics of cardiovascular regulation are slower than those of ventilation, an

appreciable difference between the two cases is obtained only at steady state. How-

ever, the discrepancy is very small. For example, at 6000 m altitude the difference

in minute ventilation at steady state between the two cases is of about 1.5%. The

divergence in cardiac output, however, amounts to 30%, given that Q is constrained

to the constant value of 5 l min−1.

What can be inferred about this model is that small changes in ventilation can

compensate for relatively large adjustments in cardiac output. Indeed, such premise

is confirmed under several simulated conditions. In principle, it could be justifi-

able to eliminate the systems regulating cardiac output in order to attain a simpler

mathematical representation of the ventilatory system. This would lead to a reduc-

tion in model complexity, number of parameters and variables, and computational

time.

Summary of drug naıve model results

We can summarize the results discussed so far as follows:

- under normoxia, the model response is in good agreement with experimental

data;

- under hypoxia, simulations match experimental results under steady state

but not during transients;

- under hyperoxia, the model predicts a strong depressant effect of oxygen on

ventilation which is not supported by the literature.

Figure 3.15 and 3.16 recapitulate these results. The two diagrams display model

outcomes relating alveolar ventilation to arterial partial pressure. The results il-

lustrate the ventilatory response of the model under exposure to a wide range of

alveolar O2 and CO2 levels. In the simulations, alveolar oxygen partial pressure

is kept constant while stepwise changes in PACO2 are performed to evaluate the

ventilatory response of the model. Simulated alveolar O2 pressure values range

from hypoxia to hyperoxia (40, 60, 100, 300, 700 mmHg). Similarly, alveolar CO2

changes range from hypocapnia to hypercapnia (5-mmHg step increases from 30 to

60 mmHg). The two representations are helpful in emphasizing different aspects of

model behavior. Figure 3.15 highlights how hyperoxia produces ventilatory inhibi-

tion leading to apnea in basal PACO2 conditions. Figure 3.16 highlights that under

hyperoxic conditions the model predicts PaO2 values below 200 mmHg, which do

not match clinical observations.


30 35 40 45 50 55 60

0

10

20

30

40

50

60

PaCO2 [mmHg]

Alv

eola

r ve

ntila

tion

[l m

in−

1 ]40 mmHg

100mmHg

700 mmHg

300 mmHg

PAO2 = 60 mmHg

Figure 3.15: CO2 response curves for different PAO2 levels. Stepwise changes in

PACO2 are performed at constant alveolar O2 pressure. Under hyper-

oxia (PAO2 = 300, 700 mmHg) the model predicts a strong ventilatory

decline.

3.4.3 Ventilatory depressant effect of the opioid

Intravenous anesthesia is delivered with the injection of anesthetic drugs into the

bloodstream. When the rate of administration is very high and the duration is in the

order of a few seconds, we speak of a bolus injection. When drug administration

takes place over the course of minutes, we speak of drug infusion. Anesthetists

use a combination of boluses and infusions to deliver anesthesia. Therefore both

administration profiles are to be considered to assess the adequacy of the model in

describing the pharmacological effects on ventilation. Figure 3.17 and 3.18 display

model results following a constant infusion and a bolus administration, as reported

by Magosso and coworkers [129].

Figure 3.17 shows the response of the model to increasing steady state plasma

concentration levels. Results of interest for the purposes of this work are minute

ventilation, arterial O2 and CO2 partial pressure. Simulation results are compared


20 40 60 80 100 120 140 160 180 200 220

2030

4050

6070

0

10

20

30

40

50

60

PaO2 [mmHg]PaCO2 [mmHg]

Alv

eola

r ve

ntila

tion

[l m

in−

1 ]

Figure 3.16: O2-CO2 response surface. Under hyperoxia PaO2 takes on values that

are lower than physiologically expected. Line color code: colored lines

refer to the same PAO2 values as in Figure 3.15. Green line: alveolar

ventilation simulation results under baseline PACO2 conditions.

to experimental observations recorded in healthy volunteers by Mildh and cowork-

ers [137]. Simulation results provide an acceptable fit to experimental findings,

therefore we may conclude the model is able to predict the pharmacological effect

of fentanyl on ventilation during drug infusion.

Figure 3.18 displays the response of the model to a fentanyl bolus (0.5 mg).

Simulated observations are compared with clinical data reported by Stoeckel and

coworkers [129]. Fentanyl plasma concentrations measured in vivo after drug ad-

ministration are used to compute model plasma concentration, Cf . The response of

the model to drug infusion is reported here in terms of minute ventilation and arte-

rial PO2 and PCO2. Results are in fair accord with the experimental observations,

as can be inferred from Figure 3.18. The model is able to reasonably simulate the

time course of respiratory inhibition caused by a drug bolus.

However, it does not capture the rapid onset of fentanyl-induced ventilatory


0.1 0.16 0.25 0.4 0.630

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Fentanyl plasma concentration [ng/ml]

Nor

mal

ized

min

ute

vent

ilatio

n [−

]

0.1 0.16 2.5 0.63 1 1.6 2.5 4 6.3 100.4

0.6

0.8

1

1.2

1.4


Nor

mal

ized

PaO

2 [−

]

0.1 0.16 0.25 0.4 0.63 1 1.6 2.5 4 6.30.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8


Nor

mal

ized

PaC

O2

[−]

Figure 3.17: Simulated minute ventilation, PaO2 and PaCO2 (continuous lines)

under steady state conditions for increasing levels of fentanyl plasma

concentration. Model results are compared to experimental data ob-

served by Mildh and coworkers in healthy volunteers under steady state

conditions [137]. All results are normalized with respect to the basal

value, i.e. to the value for Cf = 0 ng/ml.


0 50 100 150 200 250

1

2

5

10

20

50

Time [min]

Fen

tany

l pla

sma

conc

entr

atio

n [n

g m

l−1 ]

0 50 100 150 200 2500

0.2

0.4

0.6

0.8

1

1.2

1.4

Time [min]N

orm

aliz

ed m

inut

e ve

ntila

tion

[−]

0 50 100 150 200 2500

0.2

0.4

0.6

0.8

1

1.2

Time [min]

Nor

mal

ized

PaO

2 [−

]

0 50 100 150 200 2500.8

1

1.2

1.4

1.6

1.8

Time [min]

Nor

mal

ized

PaC

O2

[−]

Figure 3.18: Ventilatory response to a fentanyl bolus (0.5 mg). Top left diagram:

in vivo time course of fentanyl plasma concentration is approximated

with a biexponential function to determine model input Cf . Other di-

agrams: simulated minute ventilation, PaO2 and PaCO2 (continuous

lines) are compared to clinical observations reported by Stoeckel and

coworkers [129] (bullets, mean ± SD).


decline. Minute ventilation shows a decrease which starts immediately after bo-

lus administration but reaches a minimum in approximately 7 minutes. It is not

known when the experimental minimum takes place because clinical data are sparse.

However, physiological observations exhibit a strong ventilatory inhibition after less

than 3 minutes, illustrating the fast onset of the pharmacological effect in the body.

Although the model provides a fairly satisfactory match of the experimental data

considered so far, the description of pharmacological effects proposed by Magosso

and coworkers presents the following drawbacks:

- drug effects on the regulatory mechanisms that control ventilation in the

human body are not wholly understood. Particularly, the quantitative as-

sessment of pharmacological effects on isolated regulatory mechanisms (as

attempted with the terms A(Cf),K(Cf)) is not supported by sound experi-

mental evidence in the literature;

- the pharmacodynamic description used in this model involves 7 parameters

(see Table 3.3). As the parameter estimation requires a considerable amount

of costly experimental data, it is difficult to apply this model to other drugs.

For instance, it is not possible to employ the C50 potency values reported

in the literature because the pharmacodynamic model does not consider this

parameter.

Therefore, we suggest to substitute the pharmacodynamic description proposed

by Magosso and coworkers [129] with the Emax sigmoid model discussed in Section

2.3. The proposal will be covered with detail in Section 3.5.4.

3.5 Proposed model improvements

The discussion in Section 3.4 was helpful to identify the aspects of ventilatory

regulation that the model is not able to describe satisfactorily. In the following

a few model changes are proposed with the objective to improve the agreement

between model results and physiological observations and to adapt the model to

the requirements of the research project.

Section ??n Section 3.5.3 we suggest a possible solution for the modeling of

minute ventilation under hyperoxia. Section 3.5.4 proposes the use of a different

PD representation for the modeling of pharmacological effect on ventilation.

3.5 Proposed model improvements 75

Oxygen blood dissociation curve

a = 3.22 ⋅10−2 mmHg−1 b = 8.153 ⋅10−3 mmHg−1 c = 2.646

= 0.2415 kPa−1 = 6.12 ⋅10−2 kPa−1

αO2= 1.32 µmol(mmHg l)−1 K = 14.74 mmHg CO2

= 8.848 mmol/l

= 9.9 µmol(kPa l)−1 = 1.965 kPa

Table 3.5: Parameter values for the modified oxygen dissociation curve.

3.5.1 Blood dissociation curves

As discussed in Section 3.3.1, oxygen and carbon dioxide transport in blood is

described with mathematical equations modeling O2 and CO2 dissociation and

accounting for the Bohr and Haldane effects [176]. The agreement with experimen-

tal data measured in whole blood (hemoglobin content = 15 g/dl, base excess =

0 mEq/l at 37 C) is adequate in the range 0-120 mmHg for PO2 and 0-80 mmHg

for PCO2. However, these dissociation curve equations disregard the amount of

oxygen carried in dissolved form. This term becomes significant when breathing

oxygen-enriched air, a condition that is relevant to this study. Therefore we modify

the original equation describing O2 molar concentration in blood as a function of

PO2 and PCO2 (Equation 4 in [176]) as follows:

CO2= CO2

[PO2

1+bP CO2

K(1+aP CO2)]

c

1 + [PO2

1+bP CO2

K(1+aP CO2)]

c +αO2PO2

(3.49)

where αO2is the Henry constant (solubility coefficient) of oxygen in blood and

the term αO2PO2

is the contribution of dissolved oxygen to total blood content, in

accord with Henry’s law. Linear least squares fit values of Equation 3.49 parameters

are listed in Table 3.5. CO2holds physiological significance since it corresponds to

the oxygen molar concentration in blood for 100% saturated hemoglobin. Because

the maximum O2 capacity of human hemoglobin is 1.34 ml/g = 0.059 mmol/g and

the average hemoglobin content in blood is 150 g/l, CO2is assigned a value of 8.848

mmol/l. The modified dissociation curve equation matches well the experimental

data over the entire PO2 range that is meaningful for the present investigation

(maximum FIO2 = 1 at room temperature and pressure).


3.5.2 Transcutaneous PCO2 sensing

The dosing paradigm for personalized sedation proposed in this thesis entails titra-

tion of anesthetic delivery based on PtcCO2 measurements. Therefore, the physi-

ological model must incorporate a mathematical description of the transcutaneous

PCO2 signal. In two studies performed in collaboration with the University Hospi-

tal Bern, the dynamic properties of the SenTec V-Sign sensor (SenTec AG, Therwil,

Switzerland) were evaluated through volunteer rebreathing experiments [94, 170].

This sensor is a Severinghaus-type device for the transcutaneous monitoring of the

partial pressure of carbon dioxide (PtcCO2). The studies concluded that the sen-

sor PtcCO2 can be related to end-tidal PCO2 (PetCO2) with a two compartment

model. Assuming that PetCO2 = PACO2, we can describe the model with the

following equation:

dPtcCO2(t)

dt= −k12PtcCO2

(t) + k21

V2

V1

(PACO2(t − Tlag) − Pss) (3.50)

with intercompartmental rate constant k12 = k21V2

V1= 1.27 min−1 and a time delay

Tlag of 25 s. The steady state PtcCO2-PeCO2 offset is 0.66 mmHg. This PtcCO2

model is included into the respiratory simulator to test the feasibility of the pro-

posed anesthetic paradigm.

3.5.3 Drug naıve ventilatory regulation

Model inadequacy in the description of ventilation under hyperoxia was discussed

with detail in Section 3.4.2. We now aim to improve the modeling of ventilatory

control in order to achieve a better agreement with physiological observations.

Of the three systems that regulate ventilation in the model, only peripheral

chemoreceptors are to be considered for amendment. The central ventilatory de-

pression (CVD) is a mechanism that acts upon the onset of brain hypoxia, therefore

it does not modify ventilation under hyperoxic conditions. Central chemoreceptors,

on the other hand, measure arterial CO2 pressure and affect ventilation accordingly.

Therefore the modeling efforts described in this section are focused on peripheral

chemoreceptors only.

The equations describing peripheral chemoreceptive activity are rewritten below

for the sake of clarity:

Dp = kDp

Q(3.51)


20 40 60 80 100

1

2

3

4

5

6

7

8

PaCO2 [mmHg]

Che

mor

ecep

tive

activ

ity [s

pike

s s−

1 ]

200

300 700

PaO2 = 100 mmHg

150

Figure 3.19: Activity in chemoreceptive afferent fibers versus arterial CO2 pressure

at different levels of arterial O2 (ranging from normoxia to hyperoxia).

fpc =K ln(Pa,CO2

Bp

)fpcmax + fpcmin ⋅ exp [(Pa,O2−Pa,O2c)kpc

]1 + exp [(Pa,O2

−Pa,O2c)kpc

] (3.52)

d∆VEP (t)dt

= 1

τp−∆VEP +Gp ⋅ [fpc(t −Dp)] − fpc0 (3.53)

where Dp is the lung-receptor transit time (mechanism time delay), fpc stands for

the discharge frequency of the receptors, and ∆VEP is the change in ventilation due

to peripheral chemoreceptive stimulation. The meaning of all other terms in these

equations is discussed in Section 3.3.3.

Equation 3.52 and 3.53 indicate that the ventilatory response to peripheral

stimulation depends on both oxygen and carbon dioxide arterial partial pressure.

Chemoreceptive discharge frequency over a wide range of PaO2 and PaCO2 levels

is depicted in Figure 3.19, which summarizes the results reported in Figure 3.7.

A possible solution to model inadequacy under hyperoxia is a new parametric

assignment. The goal is to ensure that the peripheral discharge activity fpc yields

correct ventilatory results under hyperoxia while remaining unchanged under hy-

poxia and normoxia. Parameters liable to change are those included in the PaO2

dependent part of Equation 3.52. Thus, a new parameter estimation is performed

for fpcmax, fpcmin, kpc, and PaO2c.


fpcmax = 8.73 spikes s−1 kpc = 15.08 mmHg

fpcmin = 2.23 spikes s−1 Pa,O2c = 56.67 mmHg

Table 3.6: Estimated parameter values to describe peripheral chemoreceptive ac-

tivity.

According to Ursino and coworkers [195], fpcmax and fpcmin (in spikes s−1) hold a

well defined physiological meaning. They represent the upper and lower saturation

levels of peripheral discharge frequency in afferent fibres, respectively. Ursino and

colleagues cite the work by Fitzgerald and coworkers [76] to support their state-

ment. Fitzgerald reports experimental observations concerning peripheral receptors

activity in cats subject to different levels of inspired O2 and CO2 [76]. However,

the results by Fitzgerald and colleagues are not expressed in spikes s−1, but as a

percentage of the maximum response to asphyxia, % MAR. Therefore we are free to

change the value of the parameters with no risk of overlooking any physiologically

significant issue.

The parameter estimation is performed with the objective to improve the agree-

ment with clinical observations under hyperoxia. Model behavior under normoxia

and hypoxia is to remain unchanged. The experimental data considered for param-

eter estimation were recorded by Dahan and collaborators in healthy volunteers

under hyperoxic conditions [54]. Least square parameter estimates are listed in

Table 3.6. Figure 3.20 displays the relationship between fpc and PaCO2 under hy-

peroxia with the original and the newly estimated set of parameters. Simulation

results are compared to experimental observations reported by Fitzgerald and col-

laborators [76]. Figure 3.21 reproduces the ventilatory results displayed in Figure

3.11 and shown here a second time with regard to the updated parameter values.

Both figures indicate that the newly estimated parameters improve the agreement

between model results and experimental observations under hyperoxia, while main-

taining unaltered the behavior of the model under normoxia and hypoxia.

With the objective of mimicking the effects of intraoperative noxious stimula-

tion, we incorporate a description of human ventilatory response to pain into the

physiological model. The effect of painful stimulation is modeled as a respiratory

tonic drive producing a 15% increase in minute ventilation baseline, in agreement

with the experimental observations reported in the literature [69, 86, 166].


0 20 40 60 80 100

5

10

15

20

25

30

PaCO2 [mmHg]

Che

mor

ecep

tive

activ

ity [s

pike

s s−

1 ]

PaO2 = 500 mmHg

Figure 3.20: Discharge frequency of peripheral chemoreceptors as a function of ar-

terial CO2 partial pressure under hyperoxic conditions. Top: fpc curve

computed with original parametric values. Simulated data (continuous

line) are compared with experimental observations (symbols) recorded

in cats by Fitzgerald and coworkers [76]. Adapted from the liter-

ature [195]. Bottom: fpc curve computed a second time with the

updated parameter values. Newly estimated parameters improve the

agreement between model results and experimental observations.


0 5 10 15 20

0

10

20

30

40

Time [min]

Ven

tilat

ion

[l m

in−

1 ]

20

25

30

35

40

45

50

55

PA

CO

2 [mm

Hg]

Hypercapnia during hyperoxia

0 2 4 6 8 10 12

35

40

45

50

55

Time [min]

PA

CO

2 [mm

Hg]

11

22

33

44

55

Ven

tilat

ion

[l m

in−

1 ]

Hypercapnia during normoxia

0 2 4 6 8 10 12

35

40

45

50

Time [min]

PA

CO

2 [mm

Hg]

11

22

33

44

55

Ven

tilat

ion

[l m

in−

1 ]

Hypercapnia during hypoxia

Figure 3.21: Ventilatory regulation response to hypercapnic stimulation under hy-

peroxia, normoxia, hypoxia with the newly estimated parametric val-

ues. Experimental protocols are discussed in Section 3.4.2. Compared

to Figure 3.11, the agreement with the experimental observations is

greatly enhanced under hyperoxia.


3.5.4 Pharmacodynamic modeling

In [129] Magosso and coworkers simulate the ventilatory response to the opioid

fentanyl and propose a detailed description of drug effects on the different mecha-

nisms that regulate ventilation. Their description of anesthetic pharmacodynamics

was discussed in Section 3.3.4. Arguably, modeling drug effects with this level of

detail is not sufficiently supported by the literature. The reason is that it is nearly

impossible to design an experimental protocol geared towards simultaneously deter-

mining O2 and CO2 regulatory dynamics as well as drug effects on each regulatory

subsystem in a human subject.

In the following we propose to consider a pharmacodynamic model with a more

parsimonious structure. We suggest to describe pharmacological respiratory effects

as a concentration-dependent inhibition of minute ventilation. Pharmacodynamic

modeling is performed using the inhibitory fractional sigmoid Emax model for

drug effects on minute ventilation (see Section 2.3). The choice of the Emax

model over other commonly used pharmacodynamic models (such as the power

model) is justified by its widespread use and accuracy in reproducing experimental

results [25]. Effect quantitation is achieved with the following equation:

E = 1 −Emax ⋅Cγ

e

Cγe +C50γ (3.54)

where E is the pharmacological effect (minute ventilation inhibition) as a function

of the drug concentration, Emax the maximal effect, C50 the drug concentration

causing 50% depression of minute ventilation under isohypercapnia, and γ is the

sigmoidicity (Hill) factor. Assuming the drug is a full agonist (that is, Emax =1), the dynamic effect of the drug can be determined with a minimal number of

parameters. The effect E takes on values ranging from 1 (no depressant effect for

Ce = 0) to 0 (total ventilatory inhibition for Ce → ∞). Figure 3.28 illustrates the

structure of the modified model.

We shall now test the pharmacodynamic model discussed in the above. Results

in terms of fentanyl induced ventilatory depression obtained with the Emax model

will be compared with those reported by Magosso and coworkers [129]. In order

to achieve adequate model validation we shall take into account two additional

opioids: alfentanil and remifentanil.


Ventilatory Regulation

PeripheralChemoreceptors

ChemoreceptorsCentral

Lungs

Brain

Tissues

Gas ExchangePI,CO2

PI,O2

Cardiovascular Regulation

Q

VA

VE

VE0

Pb,CO2

Pb,O2

Pa,CO2

Pa,O2

Pt,CO2

Pt,O2

Dead Space

Link Model

Ce

PD Model

I

Cp

PK Model

Ptc,CO2

E

Figure 3.22: The metabolic model and its relationship to the ventilatory and car-

diovascular control systems (CVD not shown). Model inputs are the

metabolic rates of oxygen consumption/carbon dioxide production

(not shown) and the partial pressures of the respiratory gases in in-

spired air (PI,O2, PI,CO2

). Pi,CO2, i = a, b, t, tc: arterial, cerebral, tissue,

transcutaneous partial pressure of carbon dioxide (equivalent nota-

tion for oxygen). Shaded blocks depict the structure of the anesthetic

pharmacokinetic-dynamic model. I, Cp, and Ce are the infusion rate,

plasma and effect site concentration of the anesthetic, respectively. E:

pharmacological depressant effect on ventilation; VE0: baseline venti-

lation; VE: minute ventilation; VA: alveolar ventilation; Q: cardiac

output. The dead space indicates the fraction of minute ventilation

that does not participate in gas exchange (VA = 23⋅ VE).


3.5.5 Opioid induced respiratory depression

Ventilatory results in the presence of fentanyl

The goal is to reproduce the ventilatory results recorded during fentanyl infusion

that were presented in Section 3.4.3 with the physiological model modified according

to Sections 3.5.1-3.5.4. Emax pharmacodynamic parameters are estimated via least

squares fitting to reproduce experimental observations of respiratory depression

following a fentanyl bolus (0.5 mg) in volunteers reported by Stoeckel and colleagues

[180]. The time course of drug plasma concentration (Cf) that is input to the model

is depicted in Figure 3.18 (first panel).

Estimated pharmacodynamic parameters are listed in Table 3.7. The results in

terms of model ventilatory response to the bolus are shown in Figure 3.23. Minute

ventilation is computed both with the original pharmacodynamic description by

Magosso and coworkers [129] and with the Emax model discussed in Section 3.5.4.

The figure shows clearly that Emax pharmacodynamics enhances the agreement

of model behavior with clinical observations. Moreover, the sigmoid pharmacody-

namic function enables the model to capture the fast onset of the pharmacological

effect. A minimum in the ventilatory response is reached within 1 minute after

bolus administration. The original pharmacodynamic model takes about 7 minutes

to reach the minimum, therefore missing the initial fast decline in ventilation that

is recognizable from the clinical data displayed in the figure.

Ventilatory results in the presence of alfentanil

In order to provide further validation for model behavior, another opioid is taken

into consideration: alfentanil. Use of alfentanil in anesthesia care units to provide

conscious sedation is widespread. Therefore it is meaningful to investigate whether

the model is capable of reproducing experimental observations recorded during

alfentanil infusion.

Emax pharmacodynamic parameters are estimated via least squares fitting in

order to match the ventilatory response of the model to clinical observations. Pa-

rameter values are listed in 3.7. The experimental data used for parametric as-

signment were provided by the Anesthesia Department of the University Hospital

Bern. The experimental protocol used for collecting the data will be discussed in

Section 3.8.7.

Figure 3.24 shows the results in terms of the Cp and ventilation time course

following an alfentanil bolus injection. The plasma concentration, Cp, that is in-

put to the model is calculated by fitting experimental blood concentration data.


0 50 100 150 2000

0.2

0.4

0.6

0.8

1

1.2

1.4

Time [min]

Nor

mal

ized

min

ute

vent

ilatio

n [−

]

Figure 3.23: Ventilatory response to a fentanyl bolus (0.5 mg). Simulated minute

ventilation obtained with the original pharmacodynamic model by

Magosso and coworkers [129] (purple line) and with the proposed

Emax model are compared to clinical observations reported by

Stoeckel and coworkers [180] (bullets, mean ± SD). Emax pharma-

codynamics improve the agreement between model and experimental

results, particularly it enables the model to match the experimental

rapid onset of the pharmacological effect.

The figure shows a good agreement between model ventilatory results and clinical

observations.

PaCO2 results in the presence of remifentanil

The last sedative drug to be taken into account is remifentanil, a highly potent

opioid. Remifentanil is often employed to provide sedation and at high doses it can

be used to induce general anesthesia. The use in the clinical practice is widespread

and well established. The main advantages of remifentanil over other opioids are:

- remifentanil is susceptible to rapid ester hydrolysis by nonspecific esterases in

blood and tissue. Biotransformation is so fast that the duration of a remifen-

tanil infusion has little influence on wake-up time. Its context-sensitive half-

time (that is, the time required for plasma drug concentration to decline by

50% after discontinuing the infusion) is approximately 3 minutes, regardless


0 10 20 300

50

100

150

200

250

Time [min]

Alfe

ntan

il C

p [ng

ml−

1 ]

0 10 20 300

0.2

0.4

0.6

0.8

1

1.2

1.4

Time [min]

Nor

mal

ized

min

ute

vent

ilatio

n [−

]

Figure 3.24: Ventilatory response to an alfentanil bolus. Bullets (mean ± SD):

experimental data provided by the University Hospital Bern. Top:

alfentanil plasma concentration time course. Experimental results are

fitted to determine model input Cp (continuous purple line). Bottom:

ventilatory results of the model (continuous blue line) are compared

to in vivo observations. The agreement between simulated ventilation

and experimental observations is satisfactory.


0 20 40 60 80 100 120 140 1600

2

4

6

8

10

12

time [min]

Rem

ifent

anil

plas

ma

conc

entr

atio

n [n

g m

l−1 ]

0 50 100 15035

40

45

50

55

60

65

70

75

Time [min]

PaC

O2

[mm

Hg]

Figure 3.25: Arterial PCO2 response to a remifentanil infusion in one study sub-

ject. Experimental data are provided by the University Hospital Bern.

Top: remifentanil plasma concentration time course calculated by a

TCI infusion pump. The concentration profile is used as an input to

the model. Bottom: PaCO2 model results (continuous blue line) are

compared to in vivo observations (red dashed line).


Fentanyl

Emax = 1 C50 = 1.04 ng ml−1 γ = 1.27 ke0 = 0.18 min−1

Alfentanil


Remifentanil


Table 3.7: Estimated parameters for opioid pharmacodynamics of respiratory de-

pression.

of the duration of infusion [144];

- extrahepatic hydrolysis implies the absence of metabolite toxicity in patients

with hepatic dysfunction;

- patients with pseudocholinesterase deficiency have a normal response to remifen-

tanil [144].

Lack of drug accumulation following repeated boluses or prolonged infusions differs

from other currently available opioids. This feature makes remifentanil particu-

larly suitable for use in conscious sedation since time for emergence is short and

independent from the duration of the surgical procedure [144].

For such reasons, remifentanil is the drug of choice for the design of the PtcCO2-

based controller for delivery of sedation. We are therefore interested in identifying

the pharmacodynamic model that is going to be used for evaluating the pharma-

cological effect on minute ventilation.

Clinical data employed to perform Emax model parameter estimation were

recorded at the University Hospital Bern. In vivo remifentanil drug plasma concen-

tration was calculated by a target controlled infusion (TCI) pump. The resulting Cp

profile is used as an input to the model. Least squares fitting estimated parameters

are listed in Table 3.7.

PaCO2 simulated results are displayed in Figure 3.25 and compared to experi-

mental observations in one study subject. The agreement between model results

and experimental findings is satisfactory.

In Section 3.6 the Emax pharmacodynamic model describing remifentanil effects

on minute ventilation will be employed in the design of a feedback controller for

the delivery of sedation.


3.5.6 Results discussion

The physiological model presented in the above combines several isolated phar-

macological and physiological aspects of respiratory regulation and drug induced

respiratory depression under various conditions. Several studies in the literature

address the effect of chemical stimuli and anesthetics on specific respiratory and

metabolic subsystems. Our work provides a unified picture of respiratory regu-

lation and drug effects on breathing under different clinically relevant conditions.

The model serves as a simulator/test bed for both drug tolerability and control

issues under non-steady state conditions.

The patient simulator expresses drug induced respiratory depression as a concen-

tration dependent effect on minute ventilation. It does not describe the pharmaco-

logical effects on tidal volume and respiratory rate separately, although it has been

shown that their dynamics are different [5]. Modeling these two ventilatory com-

ponents may improve the capability to predict apneic events and could therefore

be of interest to the anesthetic practice.

This study modeled the effects of remifentanil on breathing and did not consider

coadministration of other drugs. Polypharmacy of sedative/analgesic drugs can

cause severe respiratory effects due to the pharmacological interaction of the drugs.

However, coadministration of another respiratory depressant would lead to more

pronounced hypercapnia and therefore reduce administration of the automatically

administered drug, thereby protecting the patient. This hypothesis should be tested

in the clinical environment with sedation trials based on multiple drug protocols.

Despite the modeling efforts described in Sections 3.5.1-3.5.5, the agreement be-

tween model simulation results and experimental data of ventilatory regulation

and drug induced respiratory depression is not entirely satisfactory. Moreover, the

model proposed by Magosso and collaborators [129] provides a level of physiolog-

ical detail that may not be required to address the problem of sedation. That

translates into substantial model complexity and a large number of parameters to

be estimated if the model is to be adapted to the individual. For the purposes of

our work, a more parsimonious model structure is desirable. The objective is to

achieve a mathematical representation of human breathing and respiratory depres-

sion pharmacodynamics that can be easily adjusted to different anesthetic agents

and adapted to the individual by estimating a limited number of parameters. To

this purpose, a simplified model of human ventilatory regulation is proposed in Sec-

tion 3.7. A parsimonious description of the controlled metabolic system is discussed

in Section 3.8.

3.6 Proportional-integral control for remifentanil sedation 89

Controller

Override

I

I

SpO2

Windup

Anti-on/off

PI

Safety

Patient

Simulator

PKPD

Vent.

System

error

PtcCO2

PtcCO2

P tcCO2 Kalman

Filter

Figure 3.26: Configuration for the closed-loop control of sedation delivery. I: drug

infusion rate; PtcCO2: sensor measurement of transcutaneous CO2

partial pressure; P tcCO2: estimated measurement; PtcCO2: control

setpoint. The override system enforces the SpO2, Cp, and Ce thresh-

olds in order to maximize the safety of opioid administration.

3.6 Proportional-integral control for remifentanil

sedation

3.6.1 Control design

Using the respiratory model developed in the previous sections as a test bed, we

design a feedback control strategy for the delivery of personalized remifentanil se-

dation. The aim of the control algorithm is to manage drug administration for

induction of sedation and maintenance of the PtcCO2 setpoint defined by the anes-

thesiologist. Adequate management of intraoperative painful stimuli, surgical dis-

turbances and inter-patient variability is required. An endpoint of 50 mmHg is

selected for paradigm validation because in volunteers it corresponds to mild res-

piratory depression and plasma concentrations well in the analgesic range [127].

The control algorithm must fulfil the following conservative constraints to ensure

patient safety: SpO2 > 93%, remifentanil Cp and Ce < 4 ng/ml. In case the thresh-

olds are exceeded (e.g. for exceptional drug sensitivity), a safety override stops the

automatic infusion and reverts the responsibility of dosing to the care provider.


In the region of interest for application to sedation, the PtcCO2 response of

the model to stepwise changes in Ce is approximately linear and of first order, so

the requirements in terms of controller sophistication are limited [9]. Therefore,

a proportional-integral (PI) control strategy is selected. A two-degree-of-freedom

control structure is employed to improve tracking performance while ensuring rapid

suppression of disturbance effects.

3.6.2 State estimation

A state observer is included in the sedation system to perform estimation of the

PtcCO2 signal. As observer the Kalman filter is selected because we do not rule

out the presence of stochastic noise in the PtcCO2 signal. The positioning of the

Kalman filter within the control loop and the configuration of the sedation delivery

system are depicted in Figure 3.26.

The use of Kalman PtcCO2 estimates is also intended to assist in the detection

of sensor failure or disconnection [77]. For instance, during the medical procedure

it may happen that the sensing element is displaced from its measurement site on

the patient. The PtcCO2 measurements would then rapidly approach a value of

zero because the CO2 content in atmospheric air is equal to 0.04%. In the sedation

system, a substantial mismatch between the measured and estimated PtcCO2 is

interpreted as being indicative of a fault. We define that the system detects a sensor

failure/disconnection if the sensor output undershoots the Kalman estimate by 7

mmHg or more. Following the detection of a fault, the system rejects the sensor

output. The prediction at each time step is then based on the previous estimate

and the current control command only. In the clinical implementation a warning

message would be issued at this stage, drawing the attention of the care provider.

The system does not discard measurement information when the sensor reading is

higher than the estimated value, since false high readings revert the virtual patient

to a safe state by decreasing the infusion rate.

3.6.3 Closed loop delivery of remifentanil sedation

In order to validate the proposed dosing paradigm for sedation, we simulated titra-

tion to and maintenance of a target PtcCO2 using the physiological model described

in the above as a virtual patient. Closed-loop results for a PtcCO2 target of 50

mmHg and FIO2 = 33% in three virtual patients are displayed in Figure 3.27. The

three patients are differently sensitive to the respiratory depressant (high, average,

low sensitivity). To mimic the nuisance phenomena that often occur in the oper-

3.6 Proportional-integral control for remifentanil sedation 91

ating theater during sedation delivery, the following disturbances were reproduced

in the simulation studies:

i a painful stimulus at t = 90 min;

ii a generic surgical disturbance at t = 160 min that causes an abrupt increase

of 4 mmHg in arterial PCO2 (to mimic for instance the effect of tourniquet

release);

iii the disconnection of the sensor at t = 230 min.

The Cp versus time diagram in Figure 3.27 shows that the control algorithm adjusts

drug dosing to track the reference signal, reject the disturbances and individualize

drug delivery depending on the specific sensitivity of the virtual patient. Remifen-

tanil plasma concentrations delivered by the controller (between 1 ng/ml and 2.5

ng/ml at steady state) lie within the analgesic and therapeutic range for seda-

tion [127]. When sensor disconnection occurs, the PtcCO2 signal quickly drops to

zero; thereafter at each time step the Kalman filter outputs a PtcCO2 estimate

based on the previous estimate and the current control command only (no estimate

update with measurement information since the sensor is detached) as discussed in

Section 3.6.2. Minute ventilation is displayed as another indicator of drug induced

respiratory depression. Ventilation remains at safe levels, both transiently and

at steady state. Throughout the entire simulated procedure the hypoxic override

remains inactive since blood oxygenation stays always above the 93% threshold.


The ability of opioids to provide adequate analgesia is limited by the ventilatory

depression associated with overdosing in spontaneously breathing patients. There-

fore, quantitation of drug induced ventilatory depression is a pharmacokinetic-

pharmacodynamic problem relevant to the practice of anesthesia and in particular

to the delivery of monitored anesthesia care.

The goal of the work discussed in this chapter is to address the problem of drug

delivery in the spontaneously breathing patient and to provide a solution that en-

hances safety in clinical practice. Dosing during sedation is critical because there

is no direct, objective measurement of the therapeutic effect and the drug induced

adverse effects are life threatening. We proposed an innovative dosing strategy

that entails the measurement of the pharmacological side effect rather than the

evaluation of the therapeutic effect to provide guidance for the automatic control


0 50 100 150 200 25040

45

50

55

est.

Ptc

CO

2[m

mH

g]

reference C50 = 0.7 [ng/ml] C50 = 1 [ng/ml] C50 = 1.3 [ng/ml]

40

45

50

55

mea

s. P

tcC

O2

[mm

Hg]

0 50 100 150 200 2500

5

0 50 100 150 200 2500

1

2

3

Cp [n

g/m

l]

0 50 100 150 200 2500.6

0.7

0.8

0.9

1

Time [min]

Ven

tilat

ion

[−]

Figure 3.27: Simulated closed-loop induction and maintenance of sedation (FIO2 =

0.33). Model results in terms of estimated PtcCO2, measured PtcCO2,

remifentanil plasma concentration and normalized minute ventilation

are displayed. The reference PtcCO2 signal is changed from baseline

to 50 mmHg at time t = 20 min, thereby activating the controller and

initiating drug infusion. A painful stimulation and a generic surgical

disturbance occur for 10 minutes at time t = 90 min and t = 160 min

respectively. At t = 230 min PtcCO2 signal loss occurs (reproducing

for instance the detachment of the sensor). The sequence of events is

simulated for three different levels of drug sensitivity: high sensitivity

(C50 = 0.7 ng/ml, dotted line), average sensitivity (C50 = 1 ng/ml,

solid line), low sensitivity (C50 = 1.3 ng/ml, dash-dotted line).

3.7 Parsimonious modeling of ventilatory regulation 93

of drug delivery (surrogate endpoint based dosing paradigm). More specifically, we

suggested titrating the administration of sedatives and analgesics to the individ-

ual sensitivity based on transcutaneous measurements of PCO2. In the following

we validate the dosing paradigm by means of computer simulations. The results in

Figure 3.27 show that the control algorithm individualizes drug infusion, titrates in-

fusion to effect and delivers concentrations within the analgesic range. Closed-loop

control may also be effective and robust to intraoperative disturbances, individual

drug sensitivity, and sensor disconnection.

Improved safety, reliable and adequate therapy, workload reduction for the care

providers, cost saving in terms of drugs and manpower would be the most prominent

benefits of implementing the proposed dosing paradigm into a therapeutic device

for use during sedation. The system may fulfil the clinical demand for improved

sedation care and has therefore the potential to be converted into a commercial

healthcare device. Moreover the technology of the single components (sensor, actu-

ator, processing and control unit) is available and relatively inexpensive compared

to anesthesia workstations. However a second, independent sensor (e.g. a nasal

thermistor) may be necessary to detect ongoing breathing and identify possible

single fault conditions.

It is relevant to mention that the dosing paradigm was exemplified here with the

choice of remifentanil as anesthetic drug. Nevertheless, in principle the paradigm

can be applied to other sedative/analgesic drugs with respiratory depressant side

effects (for instance, other opioids such as fentanyl and alfentanil; propofol; combi-

nations of drugs). Indeed, in Section 3.9 we shall design a control strategy for the

delivery of propofol sedation.

3.7 Parsimonious modeling of ventilatory

regulation

3.7.1 Introduction

As discussed in Section 3.5.6, it is desirable to simplify the physiological model of

ventilatory control in order to deal with a more parsimonious set of parameters. In

the following we address an alternative description of the mechanisms regulating

ventilation based on oxygen and carbon dioxide blood content.

Multiple studies have investigated the response of the human (cardio)respiratory

system to chemical stimuli both in the presence and absence of ventilatory depres-

sant drugs. More specifically, experimental results are reported in the literature de-


scribing: the effect of oxygen on the hypercarbic respiratory drive [54,123]; the effect

of carbon dioxide on the acute hypoxic respiratory drive [203, 160, 111]; the effect

of respiratory depressant anesthetics on the hypercarbic drive [137, 206, 30, 25, 26];

the effect of drugs on the acute hypoxic drive [112, 187, 72, 149]. Unfortunately,

most of them are not suitable for simulation, inter/extrapolation and dose find-

ing, the reason being that the experimental paradigms are geared towards isolating

specific physiological phenomena rather than providing a unified description of the

respiratory system behavior.

The aim of the work described in this section is to integrate the available knowl-

edge into a parsimonious mathematical ventilatory model describing the synergistic

interaction between the hypoxic and the hypercarbic respiratory drive and the ef-

fects of anesthetic drugs on the control of breathing. The following criteria were

defined prior to model building:

i The model must provide an adequate description of the hypercarbic respira-

tory drive, the acute hypoxic respiratory drive and their interaction in the

absence of drug;

ii The model must reproduce the inhibitory effects of major anesthetic drugs

on both the O2 and CO2 ventilatory response;

iii The model must be parameterized completely with published parameters

and/or parameters from published data.

In the following a concise presentation of the proposed model for ventilatory reg-

ulation is provided (Section 3.7.3 and 3.7.4). The descriptive power of the model

is evaluated through simulations performed in the Matlab/Simulink software envi-

ronment (The MathWorks, Natick, MA, U.S.). Simulation results are compared to

published experimental data and critically discussed (Section 3.7.5 and 3.7.6).

3.7.2 Model of the controlled system

To characterize ventilatory regulation (both in presence and absence of respiratory

depressant drugs) a controlled plant representing physiological metabolism and gas

exchange is required. We shall adopt the model of respiratory gas exchange and

metabolism discussed in Sections 3.3-3.5. For the sake of clarity, the main charac-

teristics of the metabolic system are summarized below.

The model describes oxygen and carbon dioxide disposition in the body in terms

of O2 and CO2 metabolism, transport in blood and exchange within tissues [44,195].


Ventilatory Regulation

AHORD

HCRD

Lungs

Brain

Tissues

Gas ExchangePICO2

PIO2

Cardiovascular Regulation

Q

VA

VE

VE0

PbCO2

PbO2

PaCO2

PaO2

PtCO2

PtO2

Dead Space

Figure 3.28: The gas exchange system and its relationships to the ventilatory and

cardiovascular control mechanisms are displayed. The inputs to the

system are the partial pressures of the respiratory gases in inspired air

(PIO2, PICO2

) and the metabolic rates of oxygen consumption/carbon

dioxide production (not shown). PiCO2, i = a, b, t: arterial, cere-

bral, tissular partial pressure of carbon dioxide (equivalent notation

for oxygen). HCRD: hypercarbic respiratory drive; AHORD: acute

hypoxic respiratory drive; VE0: baseline ventilation; VE: minute ven-

tilation; VA: alveolar ventilation; Q: cardiac output. The dead space

indicates the fraction of minute ventilation that does not participate

in gas exchange (VA = 23VE).

It comprises a compartment for the lungs and one for the brain; all other tissues

are lumped together into a third compartment. The inputs to the model are the

inspiratory PO2 and PCO2 and the rate of metabolic CO2 production and O2

consumption in the tissues. The content of oxygen and carbon dioxide in each

compartment is determined through mass balance equations that take into account

tissular exchange with blood and consumption/production within the tissue. Re-

gional blood flow is controlled by a cardiovascular regulatory system that operates

to maintain tissular PO2 and PCO2 close to baseline. Figure 3.28 displays the

interconnections between the metabolic plant and the regulatory mechanisms of

regional blood flow and respiration.


3.7.3 Ventilatory response to O2 and CO2

The control of breathing in man acts to achieve respiratory homeostasis in response

to oxygen and carbon dioxide challenges. In the following we shall focus on ven-

tilatory regulation in the absence of drug. We shall first describe the respiratory

effects of O2 and CO2 separately; we will then integrate the two mechanisms into

a synergistic model of respiratory control.

Carbon dioxide is a powerful stimulant of breathing. The ventilatory response to

CO2 under isooxic conditions has been frequently described as a linear relationship

between minute ventilation and carbon dioxide partial pressure and the existence

of a CO2 apneic threshold has been postulated by extrapolation [54,12]. At present

there is however no consensus on whether the CO2 ventilatory sensitivity is inde-

pendent of PCO2. In fact, an abrupt change in slope has been observed in the

hypocapnic region of the human CO2 ventilatory response curve [148]. Different

studies have concluded that the ventilatory response to PCO2 in the hypocapnic

range is nonlinear and the responsiveness to carbon dioxide extends well below eu-

pneic levels [17, 155]. Moreover, experimental evidence of resting ventilation fully

supported by a wakefulness or neural (non-chemoreceptive) drive contradicts the

notion of an apneic PCO2 threshold [142]. To account for these findings we model

the ventilatory response to carbon dioxide with the following (steady state) expres-

sion that predicts a non-linear decrease of ventilation under progressive hypocapnia

and that has been validated in the hypercapnic range through rebreathing experi-

ments in humans [25, 26]:

VE(ss)VE0

= [PaCO2(ss)

PaCO20

]F

(3.55)

where VE(ss)VE0

is the fractional (i.e. normalized) minute ventilation; PaCO2(ss) and

PaCO20 are the steady state and baseline arterial partial pressure of carbon dioxide,

respectively; F denotes the carbon dioxide responsiveness of the specific individual

[25, 26, 30].

The influence of oxygen on respiratory control under isocapnia has been suitably

described in the literature both in terms of a VE − PO2hyperbolic relationship

[123, 203] and a VE-SatO2 linear dependence [160, 111]:

VE(ss)VE0

= C + kO2

PaO2(ss) −A (3.56)

= 1 + n [SatO20 − SatO2(ss) ] (3.57)


where PaO2(ss) and SatO2(ss) are the arterial partial pressure and saturation of

oxygen at steady state; kO2is the shape parameter of the hyperbolic function

and represents the degree of hypoxic responsiveness; parameter C is the fractional

ventilation during isocapnic hyperoxia; parameter A describes the location of the

vertical asymptote of the hypoxic ventilatory drive [203,111]; SatO20 is the oxygen

saturation at baseline and n the slope of the acute hypoxic respiratory drive [160].

These relationships carry identical information on the effect of oxygen on ventilatory

regulation, therefore they can be used interchangeably after transformation of PO2

into SatO2 (or vice versa).

Although the relationships in Equations 3.56, 3.57 provide an equivalent descrip-

tion of the hypoxic respiratory drive, the VE - SatO2 expression might be preferred

because: i) there is evidence that the stimulus to the peripheral chemoreceptors is

O2 saturation or content, not PO2 [203]; ii) oxygen saturation can be measured

easily in the clinical practice via pulse oximetry; iii) a linear relationship might

be a more convenient tool for care providers (e.g. anesthesiologists) to predict

ventilatory changes during medical procedures.

The CO2- and O2-dependent regulatory terms presented in the above ought to be

merged into a single mechanism to provide an integrated description of respiratory

control in man (in the absence of drugs). Several authors reported the existence of

a positive interaction between the ventilatory effects of carbon dioxide and oxygen

[123, 12, 54, 201]. A simple and effective way to express the synergism between

the hypercarbic and the hypoxic drive is the multiplication of the respective terms

[195,184]. Assuming that both respiratory drives exhibit first-order dynamics [185,

54, 195, 44], we can express the integrated model of ventilatory regulation in the

non-steady state as follows:

VE = VE0 ⋅ VCO2(t) ⋅ VO2

(t) (3.58)

being

τCO2

dVCO2(t)

dt+ VCO2

(t) = [PaCO2(t − TCO2

)PaCO20

]F

(3.59)

τO2

dVO2(t)

dt+ VO2

(t) = C + kO2

PaO2(t − TO2

) −A (3.60)

= 1 + n [SatO20 − SatO2 (t − TO2) ] (3.61)

where τCO2, τO2

and TCO2, TO2

are the time constants and time delays (lung-receptor

transit times) of the CO2- and O2-dependent mechanisms, respectively.


The model is parameterized entirely with published parameters and/or parame-

ters extrapolated from published data in order to achieve a satisfactory agreement

with experimental ventilatory results in the non-steady state (see Figure 3.30): F =

4.0 [30, 25, 26]; C = 0.6, kO2= 24.3 mmHg [203,111]; A = 32 mmHg [203,111,47];

n = 0.1 [203]; τO2= 9.8 s, TO2

= 9.3 s, τCO2= 45 s and TCO2

= 10.5 s [54, 186].


The pharmacodynamics of drug-induced respiratory depression are described by

means of the well-established inhibitory sigmoid Emax model. Multiple studies

provide evidence that drug effects on the acute hypoxic and the hypercarbic respi-

ratory drive are different [31,187,149,206]. Therefore the pharmacologic effects on

the CO2 and the O2 response terms (Equations 3.59, 3.61) are modeled separately

as follows:

τCO2

dVCO2(t)

dt+ VCO2

(t) = [PaCO2(t − TCO2

)PaCO20

]F

⋅

⎡⎢⎢⎢⎢⎢⎣1 −

(Ce(t)C50a)γ

1 + (Ce(t)C50a)γ⎤⎥⎥⎥⎥⎥⎦

(3.62)

τO2

dVO2(t)

dt+ VO2

(t) = 1 + n [SatO20 − SatO2 (t − TO2) ] ⋅⎡⎢⎢⎢⎢⎢⎣1 −

(Ce(t)C50b)

1 + (Ce(t)C50b)⎤⎥⎥⎥⎥⎥⎦

(3.63)

where Ce is the effect compartment (or biophase) drug concentration; C50a (C50b)

represents the drug concentration determining a 50% decrease in the hypercarbic

(acute hypoxic) respiratory drive, for unchanged PaCO2 (SatO2); Emax = 1; γ is

the sigmoidicity (Hill) factor [137].

To yield a unified and comprehensive picture of respiratory pharmacodynam-

ics we examine the influence of anesthetics on O2 and CO2 metabolism. As

hypnotics and sedatives inhibit oxygen and carbon dioxide metabolic consump-

tion/production up to 30% of their basal value [157], a correction for the reduced

CO2 production is introduced using an inhibitory Emax model [26]:

MPCO2(t) =MPCO20 ⋅

⎡⎢⎢⎢⎢⎢⎢⎣1 − (1 −MP CO2min) ⋅ (

Ce(t)C50c)δ

1 + (Ce(t)C50c)δ⎤⎥⎥⎥⎥⎥⎥⎦

(3.64)

being MPCO20 the baseline metabolic production of carbon dioxide and MPCO2min

the minimal fractional CO2 production under anesthesia. Because carbon dioxide

excretion equals production only at steady state, it is not possible to determine


40 60 80 100 120 140 1600

1

2

3

4

5

6

7

PetO2 [mmHg]

Nor

mal

ized

min

ute

vent

ilatio

n [−

]

PetCO2 = 51.3 mmHg

PetCO2 = 46.2 mmHg

PetCO20 = 41.5 mmHg

Figure 3.29: The ventilatory response to hypoxia at different end-tidal PCO2 levels

ranging from normocapnia to hypercapnia in one subject. Symbols:

steady state experimental measurements of minute ventilation in re-

sponse to the hypoxic challenge (subject 4 in [123]). Lines: minute

ventilation resulting from model simulations that replicate the exper-

imental conditions (individual parameter values determined via least

squares fitting: kO2= 15.0 mmHg; C = 0.8; A = 30 mmHg; F = 7;

PaCO20 = 41.5 mmHg).

experimentally the inhibitory effect of the drug on the CO2 metabolic production

in the non-steady state, nor to differentiate it from the effects on the hypercarbic

response. Consequently, we employ single set of pharmacodynamic parameters to

express both effects; that is, C50a = C50c and γ = δ.

3.7.5 Opioid induced ventilatory depression

The model adequately describes experimental data published in the literature rel-

ative to the interaction between the hypercarbic and the acute hypoxic respiratory

drive in the absence of drug. The model was tested against several hypoxic response


experiments measured in healthy volunteers at different isocapnic levels (ranging

from normocapnia to hypercapnia) reported in [123]. Figure 3.29 shows the steady

state ventilatory response curve to progressive hypoxia under normocapnia and the

synergistic effect of hypercarbia on the hypoxic respiratory drive for one represen-

tative subject; the experimental observations are compared to the corresponding

model simulations. Due to the pronounced interindividual variability, predictions

based on population parameters do not adequately describe the data for all the sub-

jects. However individualization of the parameters leads to a satisfactory fit, there-

fore the model structure is acceptable. The dynamic behavior of the respiratory

model was tested against experimental CO2 step challenges performed in healthy

subjects under hyperoxic, euoxic and hypoxic conditions (see Figure 3.30) [54, 12].

Further simulations were carried out to evaluate the performance of the model

in the presence of drug. The predicted pharmacologic effect on the hypercarbic

respiratory drive was judged against experimental data recorded during infusions of

fentanyl and alfentanil [137]. Minute ventilation versus plasma concentration results

measured in healthy volunteers breathing room air (FIO2 = 0.21) are displayed in

Figure 3.31 and compared to model simulations. With respect to drug effects on

the hypoxic response, the model matches published results on isoflurane-induced

hypoxic drive depression at different arterial PCO2 levels (C50b = 0.1 MAC) [112,

187,72].


The work discussed in the previous sections proposes a parsimonious mathemat-

ical model integrating several isolated physiological and pharmacological aspects

of acute drug-induced respiratory depression under various conditions. Our work

does not aim at extending the physiological knowledge on a singular regulatory

mechanism; rather, it constitutes an original effort to combine multiple features of

human ventilatory control into a single theoretical framework. The model fulfils the

stated specifications and adequately describes published data on the hypercarbic

and hypoxic drive interaction and the global effect of drugs on respiration.

Several authors have described the ventilatory response to carbon dioxide in

terms of a central (slower) and a peripheral (faster) mechanism with different

gains [54, 184, 12, 195]. Such a model has been extensively discussed in Sections

3.3-3.5. However, the relative contribution of the chemoreflexes in determining

ventilation is unclear under many circumstances. It appears that only under deep

anesthesia and non-rapid eye movement (NREM) sleep are the chemoreceptors the

sole determinants of respiration [201]. The contribution of a wakefulness drive may


0

10

20

30

40

50

Time [min]

Ven

tilat

ion

[l m

in−1

]

0 5 10 15 20

35

40

45

50

55

Pet

CO

2 [mm

Hg]

Hypercapnia under hyperoxia

0 2 4 6 8 10 1230

35

40

45

50

55

Ven

tilat

ion

[l m

in−1

]

0

11

22

33

44

55

Time [min]

Pet

CO

2 [mm

Hg]

Hypercapnia under normoxia

0 2 4 6 8 10 1230

35

40

45

50

55

Ven

tilat

ion

[l m

in−1

]0

11

22

33

44

55

Time [min]

Pet

CO

2 [mm

Hg]

Hypercapnia under hypoxia

Figure 3.30: Left diagrams: the ventilatory response to a hypercapnic challenge is

measured in healthy volunteers under hyperoxia, euoxia and hypoxia

(PetO2 = 200, 100, and 53 mmHg respectively). The experimental

measurements are reported in [54] (upper panel) and in [12] (middle

and bottom). Right diagrams: simulated response of the ventilatory

control system to a square change in PCO2. The simulations replicate

the experimental conditions in terms of PetO2 and PetCO2 with null

pulmonary shunt fraction. Baseline minute ventilation is 12 l/min

under hyperoxia, 8.7 l/min under normoxia and hypoxia.


0 0.5 1 1.5 2 2.5 3 3.5 40.4

0.6

0.8

1

1.2

1.4

Nor

mal

ized

min

ute

vent

ilatio

n [−

]

0 25 50 75 100 125 150 175 2000.4

0.6

0.8

1

1.2

Targeted concentration [ng/ml]

Fentanyl Alfentanil

Figure 3.31: Minute ventilation at different steady state plasma concentrations of

fentanyl (top diagram) and alfentanil (bottom), FIO2=0.21. Sym-

bols (mean ± SD): experimental observations in healthy subjects re-

ported in [137]. Lines: fractional minute ventilation resulting from

model simulations. The pharmacodynamic Emax model describing

the inhibitory effect of the drug on the carbon dioxide response is

parameterized with published isohypercapnic pharmacodynamic pa-

rameters [206, 30].

be required to explain ventilation at rest in the awake [142]. Because the role played

by the chemoreflexes in determining respiration is subject to controversy, a lumped

CO2-dependent regulatory mechanism with first-order dynamics (Equation 3.59)

was proposed, thereby fulfilling the specification of a parsimonious description of

ventilatory control. Model predictions are in good agreement with experimental

non-steady state measurements of the hypercarbic response in healthy volunteers

under different isooxic conditions (Figure 3.30).

For the sake of structural simplicity the model presented in the above describes

ventilatory control in terms of changes in minute ventilation. The regulation of

tidal volume and respiratory rate (or breathing interval) was not investigated de-

3.8 Parsimonious modeling of the metabolic system 103

spite experimental evidence that respiratory depressant anesthetics may have un-

equal effects on those components of breathing [5]. Differentiating between the

contribution of tidal volume and respiratory rate to minute ventilation during drug

delivery may be of interest for the anesthetic practice and specifically the delivery

of sedation.

The coadministration of sedatives and analgesics is often employed in the clinical

theater and can lead to severe cardiorespiratory depression due to the synergistic

interaction of the drugs. This modeling approach however does not examine the

influence of anesthetic polypharmacy on breathing. The expressions in Equations

3.62-3.64 describe the effect of a single respiratory depressant on the control of

breathing and carbon dioxide metabolism, and we caution the reader not to ex-

trapolate the pharmacodynamics of respiratory depression for drug combinations.

Modeling the ventilatory effects of anesthetic polypharmacy would represent a phys-

iologically meaningful and clinically relevant development of the respiratory model.

The model presented here describes several isolated physiological and pharma-

cological aspects of breathing regulation and drug-induced respiratory depression

under various conditions. Pharmacologic respiratory effects on the isohypercapnic

hypoxic drive and the isooxic hypercarbic drive, including their interaction, are

combined into a single framework with substantial predictive capability in the clin-

ical situation. The model can also serve as a patient simulator to investigate issues

of drug tolerability, automatic control of drug delivery and individualization of drug

dosing under non-steady state conditions. Moreover, the hypoxic respiratory drive

has little influence on ventilation at PaO2 > 80 mmHg even under severe hyper-

capnia. Drug effects on the hypoxic response are therefore of minor significance

compared to the inhibitory effects on the hypercapnic drive in the clinical setting,

where oxygenation is usually supported via the provision of O2-enriched air to the

patient. This aspect is further discussed in Section 3.8.3.

3.8 Parsimonious modeling of the metabolic

system

3.8.1 Introduction

The goal of the work presented in this section is to implement a parsimonious model

of physiological gas exchange, metabolism and disposition in the human body.

After integration with the ventilatory regulation model proposed in Section 3.7,

we achieve a parsimonious mathematical model describing the ventilatory response


Figure 3.32: The controlled metabolic plant and its relationship to the ventila-

tory regulation mechanisms. HCRD: hypercarbic respiratory drive;

AHORD: acute hypoxic respiratory drive. Neglecting PO2 dynamics

as described in Section 3.8.3, the gas exchange system can be simpli-

fied to a one-compartment model for CO2 disposition as discussed in

Section 3.8.2. Dead space is assumed to be equal to 30% of minute

ventilation, that is, VA = 0.7 VE .

to hypercarbia and the effects of anesthetic drugs on the control of breathing.

An integrated description of drug induced ventilatory depression in the non-

steady state with parameters identifiable from clinically accessible data is not avail-

able so far. Several studies describe the effect of respiratory depressant drugs on iso-

lated endpoints: minute ventilation under isohypercapnic and pseudo-steady state

conditions, minute ventilation under isohypercapnic conditions, partial pressure of

carbon dioxide (arterial, PaCO2, or end-expiratory, PetCO2) under pseudo- and

non-steady state conditions. Nevertheless, concomitant modeling of minute venti-

lation and PCO2 changes in the non-steady state has not yet been undertaken.

In the following we propose a model describing simultaneously measured minute

ventilation and PaCO2 changes after administration of a fast-onset respiratory de-

pressant agent. The model is validated with experimental data regarding the ad-

ministration of a highly potent anesthetic agent, alfentanil. All parameters, includ-

ing CO2 sensitivity, are identified from measured PaCO2 and minute ventilation

experimental data.


3.8.2 Model of the controlled system

Possibly the simplest model of carbon dioxide disposition in the human body is

a one-compartment model characterized by a constant rate of CO2 production

(representing baseline metabolic production in the absence of drug) and a rate of

CO2 elimination that is a function of ventilation [30, 25, 26]. We can approximate

the physical behavior of carbon dioxide in the compartment to that of an ideal gas

stored in a well-mixed tank. Assuming constant temperature and compartmental

volume, changes in CO2 amount over time can then be equivalently described with

balance equations employing CO2 mass, amount of substance or partial pressure

as the dependent variable. Changes of CO2 partial pressure in the compartment

over time can then be expressed as:

dPaCO2(t)

dt= kin − kout(t) (3.65)

where PaCO2(t) is the arterial partial pressure of carbon dioxide, kin is the baseline

(constant) rate of CO2 production, and kout(t) is the rate of elimination. We can

express kout(t) as the product of the current elimination rate constant of carbon

dioxide, kel, and PaCO2(t):dPaCO2

(t)dt

= kin − kel(t)PaCO2(t) (3.66)

= kin −VA(t)VdCO2

PaCO2(t) (3.67)

being VA(t) the alveolar ventilation, and VdCO2the apparent volume of carbon diox-

ide distribution in the body. Under the assumption that carbon dioxide production

is constant in the absence of drug, and assuming the system to be at steady state

at t = 0, the following expression for kin is derived:

dPaCO2(t)

dt∣t=0= 0 ⇒ kin = VA0

VdCO2

PaCO20 (3.68)

where VA0 and PaCO20 are the baseline alveolar ventilation and arterial CO2 partial

pressure, respectively. The change of PaCO2 in the compartment over time can in

conclusion be described as follows:

dPaCO2(t)

dt= VA0

VdCO2

PaCO20 −VA(t)VdCO2

PaCO2(t) (3.69)

The metabolic system described in the above and the ventilatory regulation

model discussed in the next section are depicted in Figure 3.32.


Parameter Mean SE SD

VdCO2[l] 36.03 3.38 10.68

F [−] 4.01 0.16 0.51

MPCO2min [−] 0.67 0.04 0.13

ke0MV [min−1] 0.78 0.15 0.46

ke0CO2[min−1] 0.55 0.08 0.25

C50 [ng/ml] 65.34 1.82 5.76

γ [−] 1.81 0.10 0.32

Table 3.8: Estimated population values of respiratory model parameters: bolus ad-

ministration data (SE: standard error; SD: standard deviation).

3.8.3 Ventilatory response to O2 and CO2

In Section 3.7.3 the ventilatory regulation model was parameterized entirely with

published parameters and/or parameters extrapolated from published data in or-

der to achieve adequate agreement with drug-naıve experimental ventilatory re-

sults. In the work discussed here, however, the carbon dioxide sensitivity, F , and

the pharmacodynamic parameters are estimated in each study subject from mea-

sured PaCO2 and minute ventilation values after administration of a fast acting

mu agonist, alfentanil.

Simulation case studies using a sophisticated model of respiratory and metabolic

physiology [195] demonstrate that, despite sustained hypoventilation (precisely, forVE(ss)

VE0

= 0.5), arterial blood is fully saturated (SatO2 ≈ 100%) when breathing

oxygen-enriched air (FIO2 ≥ 0.5). This is in agreement with what was concluded

in Section 3.7.6. Therefore the modeled oxygen dependent term of ventilatory

regulation, VO2, can be simplified to a constant factor. In the following we shall

assume VO2(t) = 0.8, ∀ t.

3.8.4 Pharmacokinetic analysis

To describe drug distribution kinetics we opt for a compartmental mammillary

modeling approach. This customary class of pharmacokinetic models is based on

the following simplifying assumptions:

- different regions of the body can be represented by virtual compartments

disregarding the physical properties of the described tissues;

- intravenously administered drugs mix instantaneously and completely within

an initial distribution volume, termed the central compartment (i.e., the cen-


0

200

400

500

100

300

Alfe

ntan

il C

p[n

g/m

l]

30

40

50

60

70

PaC

O2

[mm

Hg]

0 10 20 30 405 15 25 35 450

0.2

1

1.41.2

0.80.60.4N

orm

aliz

edm

inut

e ve

ntila

tion

[−]

Time [min]

Figure 3.33: The alfentanil plasma concentration, arterial CO2 partial pressure and

fractional minute ventilation time course after administration of 1 mg

alfentanil intravenous bolus. Bullets: experimental observations in 10

healthy volunteers. Dash-dotted lines: respiratory model simulation

results (individual fits). Continuous lines: simulation results achieved

with population respiratory model parameters (see Table 3.8).


0 100 200 300 4000

100

200

300

400

Measured Cp [ng/ml]

Sim

ulat

ed C

p[n

g/m

l]

30 40 50 60 70 8030

40

50

60

70

80

Measured PaCO2 [mmHg]

Sim

ulat

ed P

aCO

2[m

mH

g]

0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

1

1.2

Measured normalized minute ventilation [−]

Sim

ulat

ed n

orm

.m

inut

e ve

ntila

tion

[−]

Figure 3.34: Goodness-of-fit diagnostic plot for the ventilatory control model.

Model predictions of alfentanil plasma concentration, PaCO2, and

fractional minute ventilation based on individual parameter values are

plotted against measurements taken in 14 ASA status I-II patients

during intravenous constant infusion of alfentanil.


tral compartment to which drugs are input exhibits well-mixed tank behav-

ior);

- the dose-drug concentration relationship is linear and time-invariant.

A two-compartment mammillary model is fitted to each individual plasma con-

centration versus time course, Cp(t). The mass balance equations for the two

compartments are:

dC1(t)dt

= −(k10 + k12)C1(t) + k21C2(t) + I(t)V1

(3.70)

dC2(t)dt

= k12C1(t) − k21C2(t) (3.71)

Cp(t) = C1(t) (3.72)

where I(t) is the drug infusion rate, V1 and V2 the volumes of distribution, k10 the

central elimination rate constant, k12 and k21 the intercompartmental (distribution)

rate constants.

3.8.5 Effect compartment modeling

We hypothesize the existence of distinct sites of pharmacologic action for the drug

dependent decrease of minute ventilation and metabolic CO2 production. A central

link model [173] is therefore introduced for each of the effects, according to the

following equations:

dCeMV (t)dt

= ke0MV [Cp(t) −CeMV (t)] (3.73)

dCeCO2(t)

dt= ke0CO2

[Cp(t) −CeCO2(t)] (3.74)

where Cp(t) is the drug concentration in plasma calculated from the individual

dosing history and pharmacokinetic parameters (Equations 3.70-3.72); Ce(t) is the

drug concentration in the effect compartment; ke0 is the first-order rate constant

governing the transfer of drug from the central to the effect compartment, and vice

versa. The subscripts MV and CO2 indicate whether the quantities refer to the

pharmacologic effect on minute ventilation or CO2 production, respectively.


To describe drug effects on ventilatory regulation, the pharmacodynamic model

presented in Section 3.7.4 is considered. Assuming the administration of oxygen-

enriched air, we can neglect the hypoxic respiratory drive as well as drug effects on


Parameter Mean SE SD

VdCO2[l] 41.82 3.46 12.95

F [−] 4.27 0.17 0.65

MPCO2min [−] 0.78 0.03 0.11

ke0MV [min−1] 1.25 0.11 0.41

ke0CO2[min−1] 0.71 0.06 0.21

C50 [ng/ml] 71.66 3.33 12.45

γ [−] 1.77 0.08 0.30

Table 3.9: Estimated population values of respiratory model parameters: constant

infusion data.

the O2 response (see Section 3.8.3). Therefore the pharmacodynamic model can be

simplified and reduced to the following equations:

VE(t) = VE(0) ⋅ VCO2(t) ⋅ VO2

(t) ⋅⎡⎢⎢⎢⎢⎢⎣1 −

(Ce(t)C50)γ

1 + (Ce(t)C50)γ⎤⎥⎥⎥⎥⎥⎦

(3.75)

MP CO2(t) =MPCO20 ⋅

⎡⎢⎢⎢⎢⎢⎣1 − (1 −MPCO2min) ⋅ (

Ce(t)C50)γ

1 + (Ce(t)C50)γ⎤⎥⎥⎥⎥⎥⎦

(3.76)

3.8.7 Alfentanil induced ventilatory depression

The descriptive performance of the model is evaluated through simulations aimed

at reproducing experimental results of drug effects on ventilatory regulation after

administration of a fast-onset mu agonist. The experimental data was provided by

our collaborators at the University Hospital Bern. The clinical protocol employed

to collect the experimental measurements is described in the following.

After obtaining institutional review board approval and written informed consent,

we enroled 24 subjects for administration of a fast-onset, highly potent mu agonist,

alfentanil.

Amongst the study subjects, 14 men classified as American Society of Anesthe-

siologists (ASA) physical status I or II were scheduled for major urologic surgery.

The unpremedicated patients were studied before anesthesia was induced. A 2.3

µg (kg min)−1 intravenous infusion of alfentanil was started while the patients

were breathing oxygen-enriched air (FIO2 = 0.5) over a tightly fitting face mask.

This enabled recording of the respiratory rate, approximate minute ventilation, and

end-expiratory partial pressure of carbon dioxide using the standard monitors of


an anesthesia workstation (Cicero; Drager, Lubeck, Germany). Minute ventilation

was averaged per minute from single breath values. The infusion was discontinued

when a cumulative dose of 70 µg/kg had been administered, the end-expired partial

pressure of carbon dioxide exceeded 65 mmHg, or apneic periods lasting more than

60 s occurred. Arterial blood samples were drawn before and 3, 6, 9, 12, 15, 20,

25, 30, 35, 40, 45, 50, and 60 min after the start of the infusion for alfentanil assay

and determination of PaCO2.

The second group of study subjects constituted of 10 volunteers that received

1 mg alfentanil i.v. bolus while breathing pure oxygen (FIO2 = 1). PaCO2 was

sampled at 0, 1, 2, 3, 4, 5, 7.5, 10, 12.5, 15, 20, 30, 45 minutes.

The simulated ventilatory response achieved with least-squares estimates of the

individual parameters and the experimental data measured after administration

of 1 mg alfentanil bolus are displayed in Figure 3.33. Model predictions of arte-

rial PCO2 and fractional minute ventilation based on individual parameters are

plotted in Figure 3.34 against measured data in constant infusion study subjects.

The proposed model adequately describes the experimental data under both drug

administration conditions.

Ventilatory and pharmacodynamic parameters for the population are naıvely

derived by averaging the individual parameter values, according to the experimental

dosing regimen. The estimated population parameters are summarized in Table 3.8

and 3.9 for the bolus administration and the constant infusion group, respectively.


The model of respiratory regulation has a parsimonious yet comprehensive struc-

ture with substantial predictive capability in the non-steady state. It was shown

in Section 3.7 that the ventilatory model provides an adequate description of the

hypercarbic respiratory drive, the acute hypoxic respiratory drive and their inter-

action in the absence of drug. Here, we establish that the proposed model can

describe clinical experimental results of drug induced respiratory depression under

non-steady state conditions for diverse dosing regimens of a fast-acting and potent

anesthetic agent. The estimated population parameters are in good agreement with

results published in the literature [30, 25]. Interestingly, CO2 sensitivity could be

estimated without performing drug naıve CO2 response curves.

Introduction of a single hypothetical effect compartment for the drug dependent

decrease of minute ventilation and CO2 production was attempted but it performed

relatively poorly describing the observations when compared to the model discussed

here, demonstrating the importance of evaluating multiple models in pharmacody-


namic research.

Besides providing clinically relevant predictions of respiratory depression, the

model can also serve as a test bed to investigate issues of drug tolerability and dose

finding/control under non-steady state conditions. In the next section we shall

employ it as a virtual patient for the design and test of a model-based feedback

control strategy aimed at delivering propofol sedation.

3.9 Model predictive control for propofol

sedation

In order to investigate the applicability of the proposed sedation paradigm to clin-

ical practice we undertake further testing in a simulation environment.

The use of propofol in gastroenterology practice has been steadily increasing

over the last decade [99] because of its favorable pharmacokinetics/dynamics and

side effect profile. With prospective application to colonoscopy patients at the

University Hospital Bern, in the next sections we investigate the problem of propofol

administration for delivery of sedation.

The unified framework of ventilatory physiology and respiratory drug effects pro-

posed in Section 3.8 is employed in the following to design and test a feedback con-

troller for the administration of sedation. As control strategy, we choose a model

predictive control (MPC) algorithm in order to take advantage of the capabilities

inherent to this method of predicting future plant behavior and fulfilling problem

constraints. The design of the MPC controller for the automatic delivery of sedation

is described in the next section.

3.9.1 Control design

In the following we discuss a reference tracking problem for a linear constrained

system in the presence of disturbances and plant-model mismatch. The objective

is to achieve offset free performance and apply such control law to the delivery of

propofol sedation.

Model linearization

Because we consider linear MPC, we linearize the nonlinear plant described in

Section 3.8 (virtual patient) around the operating point PtcCO2 = 52 mmHg, Ce =2.9 µg/ml, which according to clinical experience corresponds to moderate/deep

sedation [26, 27].

3.9 Model predictive control for propofol sedation 113

Preliminaries

For control design we consider a linear, time invariant discrete system:

xk+1 = Axk +Buk (3.77)

yk = Cxk (3.78)

in which xk ∈ Rnx, uk ∈ Rnu , yk ∈ Rny , A ∈ Rnx×nx , B ∈ Rnx×nu , C ∈ Rny×nx . We

assume (A,B) stabilizable and (C,A) detectable with C full row rank (i.e. the

output variables must be independent of each other). We define the controlled

variables as z =Hy, where z ∈ Rnz , H ∈ Rnz×ny , with H full row rank and nu ≥ nz.

We consider the following receding horizon optimal control problem with quadratic

objective function:

J∗(xk) ∶= minu0,...,uN−1

N−1

∑i=0(xT

i Qxi + uTi Rui) + xT

NQNxN (3.79)

s.t. xi ∈ X ⊆ Rnx, ui−1 ∈ U ⊆ R

nu , ∀ i ∈ 1, . . . ,NxN ∈ Txi+1 = Axi +Bui

R ≻ 0, Q ⪰ 0, QN ⪰ 0

The optimization problem is defined by the plant model matrices (A,B), the

prediction horizon N , the current state vector x0, the objective function cost ma-

trices Q and R, the terminal set T and terminal cost QN . At every time step k the

optimal input sequence is computed as the solution of the optimization problem

above for x0 = xk. Of the computed optimal open-loop control sequence, the input

uk = u∗0 is applied to the plant and the rest of the input sequence (u∗1, . . . , uN−1) is

discarded [154,128].

We assume the state vector is not directly measurable, therefore the states are

estimated from the plant measurements by means of a Kalman state observer with

filter gain L. At each time step k, the state vector is estimated as:

xk+1∣k = (A −LC)xk∣k−1 +Buk +Lyk (3.80)

1143

Feed

back

contro

lofsed

atio

n

0 500 1000 150035

40

45

50

55

Time (s)

Ptc

CO

2 (m

mH

g)

0 500 1000 1500−1

0

1

2

3

4

Time (s)

Ce (

µg/m

l)

C50 = 1.2 C50population

0 500 1000 15000

50

100

150

200

250

300

Time (s)

Infu

sion

rat

e 1%

pro

pofo

l (m

l/h)

0 500 1000 15000

50

100

150

200

250

Time (s)

Cum

ulat

ive

prop

ofol

dos

e (m

g)

0 500 1000 150035

40

45

50

55

Time (s)

Ptc

CO

2 (m

mH

g)

0 500 1000 15000

1

2

3

4

Time (s)

Ce (

µg/m

l)

C50 = C50population

0 500 1000 15000

50

100

150

200

250

300

Time (s)

Infu

sion

rat

e 1%

pro

pofo

l (m

l/h)

0 500 1000 15000

50

100

150

200

250

Time (s)

Cum

ulat

ive

prop

ofol

dos

e (m

g)

0 500 1000 150035

40

45

50

55

Time (s)

Ptc

CO

2 (m

mH

g)

0 500 1000 15000

1

2

3

4

Time (s)

Ce (

µg/m

l)

C50 = 0.8 C50population

0 500 1000 15000

50

100

150

200

250

300

Time (s)In

fusi

on r

ate

1% p

ropo

fol (

ml/h

)0 500 1000 1500

0

50

100

150

200

250

Time (s)

Cum

ulat

ive

prop

ofol

dos

e (m

g)

Figure 3.35: Simulation results of the MPC propofol sedation problem.

3.9 Model predictive control for propofol sedation 115

Disturbance model

In order to achieve offset-free performance, we augment the system state with an

additional integrating disturbance vector [154, 128]. As mentioned in the above,

the state vector is repeatedly estimated from the plant measurements by using a

Kalman estimator designed for the following augmented system:

[ xk+1

dk+1

] = [ A Bd

0 I] [ xk

dk

] + [ B0]uk +wk (3.81)

yk = [ C Cd ] [ xk

dk

] + vk (3.82)

where dk ∈ Rnd, Bd ∈ Rnx×nd, Cd ∈ Rny×nd. The vectors wk ∈ Rnx+nd and vk ∈ Rny

are the process and measurement zero-mean white-noise disturbances, respectively.

The estimator gain matrix for the augmented model is:

L = [ Lx

Ld

] (3.83)

being Lx ∈ Rnx×ny and Ld ∈ Rnd×ny the matrices for the augmented state and the

disturbance, respectively. The Kalman estimate is therefore:

[ xk+1∣k

dk+1∣k] = [ A Bd

0 I] [ xk∣k−1

dk∣k−1] + [ B

0]uk+

+ [ Lx

Ld

] (yk −Cxk∣k−1 −Cddk∣k−1) (3.84)

MPC controller

We employ a steady state target calculator to compute the steady state target

xss(rss, dss) and uss(rss, dss) for a given reference rss and disturbance dss, as de-

scribed in [146, 154]:

[ I −A −BHC 0

] [ xss

uss

] = [ Bd

−HCd

]dss + [ 0

I] rss (3.85)

A solution exists for any rss, dss if:

rank [ I −A −BHC 0

] = nx + nz (3.86)


The objective is to asymptotically eliminate the error in the control sequence, given

a constant reference signal r∞ and assuming constant, non-decaying disturbances

and plant-model mismatch and stability of the closed loop, that is:

z(k) → r∞ for k →∞ (3.87)

Let the solution to Equation 3.86 exist; we modify the MPC problem according

to the target variables xss, uss:

J∗(xk) ∶= minu0,...,uN−1

N−1

∑i=0(xi − xss)TQ(xi − xss)+

+ (xN − xss)TQN(xN − xss)+ (ui − uss)TR(ui − uss) (3.88)

s.t. xi ∈ X ⊆ Rnx , ui−1 ∈ U ⊆ R

nu , ∀ i ∈ 1, . . . ,NxN ∈ T (xss, uss)xi+1 = Axi +Bui

R ≻ 0, Q ⪰ 0, QN ⪰ 0

3.9.2 Closed loop delivery of propofol sedation

We apply the control strategy outlined in the above to the administration of propo-

fol for the delivery of sedation. We assume the use of 1% propofol emulsion (10

mg/ml). The prediction horizon is chosen to be N = 50 with a sampling time

Ts = 10 s, which accounts for the relatively slow dynamics of the physiological CO2

response. The following constraints on the input and the outputs are defined in

agreement with clinical recommendations for sedation [98]:

0 ml/h < u < 270 ml/h

40 mmHg < PtcCO2 < 60 mmHg

0 µg/ml < Ce < 4 µg/ml

(3.89)

In Figure 3.35 we depict the results of a representative simulated sedation case

that includes an initial induction phase and a subsequent maintenance phase. At

time t = 0− s the system is drug-naıve and in steady state at baseline (PtcCO2 =

40 mmHg, Ce = 0 µg/ml). At t = 0 s the setpoints for control are set to the

following values: PtcCO2 = 50 mmHg, Ce = 2.5 µg/ml. The results are shown

in terms of PtcCO2, Ce, rate of delivered infusion, and cumulative dose for three

3.10 Respiratory depression during propofol sedation in colonoscopy patients 117

different virtual patients: one subject with normal sensitivity to the drug (i.e. C50

= C50population = 1.33 µg/ml [26]), and two subjects with significant variability

in drug sensitivity (± 20% of C50population). The controller successfully manages

the physiological variability and achieves the PtcCO2 and Ce setpoints despite the

plant-model mismatch with satisfactory timing. Similar results can be obtained

with other setpoints, provided they satisfy the constraints stated in Equation 3.89.


The physiological model derived in Section 3.8 allowed us to investigate efficiently

the use of a model based controller to deliver propofol sedation. The MPC controller

adjusts drug delivery and achieves the target PtcCO2 and Ce setpoints despite sig-

nificant pharmacodynamic variability. Employing the model based control strategy

presented in this section is advantageous compared to the less sophisticated design

that was considered in Section 3.6 because it optimizes future control moves based

on the predicted evolution of the system and it offers the possibility to handle

constraints on the input and outputs.

The proposed dosing paradigm is currently being investigated in gastroenterology

patients at the University Hospital Bern, our clinical partner institution. In the

next section the study methods are discussed. Preliminary results of the feasibility

study are presented in Section 3.12.

3.10 Clinical investigation: respiratory

depression during propofol sedation in

colonoscopy patients

3.10.1 Study investigators

Investigators:

M. Eng. Antonello Caruso, Automatic Control Lab, ETH Zurich, Switzerland

Prof. Manfred Morari, Automatic Control Lab, ETH Zurich, Switzerland

Priv.-Doz. Dr. med. Martin Luginbuhl, Department of Anesthesiology and

Pain Therapy, University Hospital Bern, Switzerland

Dr. sc. tech. Peter Schumacher, Head R&D, SenTec AG, Therwil, Switzer-

land


Dr. med. Pascal Vuilleumier, Department of Anesthesiology and Pain Ther-

apy, University Hospital Bern, Switzerland

CRNA Volker Hartwich, Department of Anesthesiology and Pain Therapy,

University Hospital Bern, Switzerland

3.10.2 Introduction

The proposed dosing paradigm for the automatic delivery of sedation is lacking

in vivo validation. Therefore during my time at IfA we planned an observational

clinical study to validate the sedation paradigm in patients. The study was designed

and prepared in collaboration with our research partners at the Inselspital (see

below for a complete list of clinical investigators). Because of the widespread use of

sedation for gastroenterologic procedures, we identified colonoscopy (the endoscopic

examination of the colon) as a suitable clinical application. The study is currently

being completed at the Inselspital. Regrettably, final results are not yet available

for presentation and discussion at the time of writing.

In the following we will provide a description of the study plan and methods. In

Section 3.11 we shall describe the most significant features of the clinical prototype

that was designed and is currently being used to perform the clinical study. The

prototype was conceived and implemented by myself and the D-MAVT Bachelor

student Philip Jonas at IfA and by Dr. Peter Schumacher at the Inselspital in

several stages between March 2008 and April 2009. Finally, in Section 3.12 we will

provide the preliminary clinical findings from the first batch of colonoscopy patients

we investigated as of November 2009.

3.10.3 Background

Propofol administration performed by non anesthesiologists is increasingly frequent,

especially for gastroenterologic procedures [99]. Data on safety have been published

mainly in the non anesthesiologic literature [102, 101]. In Switzerland but not in

other European countries the sedation rate is high and the vast majority of patients

are monitored via pulse oximetry [99,117]. Gastroenterologists administer propofol

mostly by boluses of 10-20 mg i.v. and titrate to effect, resulting in total doses of

1.5-2.4 mg/kg for esophago-gastro-duodenoscopies and colonoscopies, respectively

[100]. The rate of side effects reported in the gastroenterologic literature is as

follows:

- Decrease of mean arterial pressure greater than 25% in 32%


- systolic arterial pressure < 90 mmHg in 15

- bradycardia < 50 min−1 in 3.7%

- SpO2 below 90% in 1.6% with oxygen administration of at least 2 l/min

nasally.

Higher incidences were reported in ASA 3 and 4 patients [100].

Although these data show that the incidence of severe side effects is low there are

several concerns. Propofol induces hypoventilation and upper airway obstruction

already in the concentration range of 2.5 mcg/ml plasma concentration [26, 68].

Oxygen administration masks the decrease of the respiratory volume. Oxygen de-

saturation to SpO2 90% occurs only 8 min after start of apnea in pre-oxygenated

adults [14], whereas it occurs after 1 min in a non pre-oxygenated adult of normal

weight [63]. With a transcutaneous carbon dioxide monitor (V-Sign, SenTec AG,

Therwil, Switzerland), detection of hypoventilation in sedated patients undergoing

colonoscopies was more rapid, and a 7.6 mmHg increase in transcutaneous carbon

dioxide partial pressure was recorded [97]. The sedative and respiratory depressant

effect of propofol occurs in the same concentration range in unstimulated patients.

Measurement of the sedation level by means of processed EEG parameters, such

as the Bispectral Index, or the state or response entropy, is unreliable because of

artifacts [78,190]. Respiratory depression can be easily measured with a transcuta-

neous carbon dioxide monitor and may therefore represent a promising alternative.

Titration of a sedative drug to a safe level of respiratory depression with a closed

loop control system may facilitate propofol sedation, particularly when provided

by non anesthesiologists.

The purpose of this observational study is:

1. to compare the respiratory depression effect of propofol in terms of the in-

crease of transcutaneous PCO2 in patients undergoing elective colonoscopy

before and during the exam

2. to determine the transcutaneous PCO2 associated with adequate sedation

during colonoscopy

3. to design a controller algorithm according to these findings

4. prospectively, to test said controller in a group of patients.


3.10.4 Study methodology

Study design

Observational, single center study, setting: University Hospital Bern

Study population

50 patients of American Society of Anesthesiologists (ASA) physical status I-III

scheduled for colonoscopy under conscious sedation will be enrolled.

The exclusion criteria are:

- chronic treatment with CNS active drugs or opioids or chronic alcohol con-

sumption of more than 20 g daily

- symptomatic neurologic (including epilepsy) or psychiatric disease

- history of severe cardiovascular, pulmonary, renal and liver disease

- difficult airway (more than one of the criteria predicting difficult intubation,

Mallampati score > 2, retrognathy, mouth opening less than 4 cm, short neck

and limited cervical spine reclination)

- obstructive sleep apnea.

Because it is an observational study no control group and no randomization is

necessary. A randomized controlled study is planned as follow-up study.

Study plan

Upon arrival in the endoscopy suite the unpremedicated patients are connected

to a Datex AS3 compact monitor (GE Healthcare, Helsinki, Finland) for ECG,

SpO2, end-expiratory CO2 and NIBP, and a venous line is placed in an antecu-

bital vein. After calibration a transcutaneous sensor (V-Sign, SenTec AG, Therwil,

Switzerland) for measuring transcutaneous carbon dioxide and oxygen saturation

is attached to the earlobe. The data from both monitors is recorded on a computer

hard disc. The V-Sign (CO2) monitor is connected to a laptop computer which

drives an ASENA GH infusion pump (Cardinal Health, Baesweiler, Germany) used

for infusing propofol (Disoprivan, Astra-Zeneca, Grafenau, Switzerland). Addition-

ally respiratory rate is monitored with the end-expiratory CO2 curve.

Before starting the propofol infusion, nasal prongs are attached and connected

to the AS3 monitor CO2 sampling tube. Oxygen 6 l/min is administered via face

mask.


Variable Minimum value Maximum value Remarks

RR 5 min−1 - Indicative of severe

respiratory depression

SpO2 90% - Indicates hypoventilation

(signal may be subject to artifacts)

HR 50 min−1 100 min−1 May indicate relevant

hemodynamic instability

MAP 60 mmHg 110 mmHg May indicate relevant

hemodynamic instability

Table 3.10: Safety alerts

Upon equilibration of the transcutaneous CO2 to baseline, the propofol infusion

will be started with an initial target effect site propofol concentration between 2

and 4 µg/ml and the endoscopy is started. During endoscopy the target propofol

concentration can be adjusted according to the requirement of the patient.

Measurements

The following time stamps are recorded: start of data acquisition, start of pa-

tient monitoring, end of sensor calibration, start of propofol infusion, insertion of

endoscope, reach of coecum, endoscope removal The observer assessment of alert-

ness/sedation score (OAAS/S) is recorded before and 5 minutes after the start of

the propofol infusion, every five minutes during the infusion and before the infusion

is stopped.

After stopping the infusion the patient’s response to verbal command is tested

every 30 seconds and the time the patient opens his eyes on verbal command as

well as the time of orientation (prename, date of birth) is recorded.

Immediately after the colonoscopy the gastroenterologist assesses the quality of

the examination conditions by a short questionnaire. Before discharge also the

patient evaluates the quality of sedation by means of a short questionnaire.

Safety

The system displays a safety alert in case the values in Table 3.10 are exceeded.


3.11 Sedation delivery system prototype

In this section the platform currently in use to perform the sedation clinical study

is described. The system enables the control and operation of a syringe pump for

anesthetic delivery in real time; it gathers sensor data and embodies a number of

sensor checks and alarms; it provides past and predicted PCO2 and drug concentra-

tion values; it allows the storage of clinical data for later access and analysis. This

platform was specifically designed for the sedation trials and implemented jointly

at IfA and the Inselspital between March 2008 and April 2009. It comprises of both

hardware and software elements which are described in the following.

3.11.1 System setup

Hardware configuration

The hardware configuration of the clinical prototype built to perform PCO2 based

sedation is depicted in Figure 3.36. Two computers constitute the backbone of

the system: a host PC running a graphical user interface (GUI) and managing all

interactions with the end-user, and an embedded real time platform connected to

the system’s actuator and sensors. As real time device we use a xPC TargetBox

(The MathWorks Inc, Natick, MA, USA), a product purposely designed for rapid

prototyping applications. The two computers are Ethernet connected.

The SenTec V-Sign sensor (SenTec AG, Therwil, Switzerland) provides accu-

rate, continuous real time monitoring of patient ventilation and oxygenation. For

backup and validation purposes we also use the Nico monitor (Philips Respironics,

Murrysville, PA, USA) that infers cardiac output based on changes in respiratory

carbon dioxide concentration. A Alaris GH Syringe Pump is employed for drug

delivery to the patient. All three devices are connected with the xPC TargetBox

via a serial connection.

Software configuration

The anesthetic platform is implemented in two different software environments, as

shown in Figure 3.37. The pharmacokinetic/dynamic patient model and the drivers

for actuator and sensors are implemented in the Matlab/Simulink environment

running on the host PC. The graphical user interfaces are also executed on the host

machine, enabling the care provider to monitor and operate the sedation system.

The Simulink and Stateflow models of the Matlab/Simulink environment are then

deployed into the xPC Target environment on the xPC TargetBox for real time

3.11 Sedation delivery system prototype 123

Figure 3.36: Hardware setup of the sedation system prototype.

Figure 3.37: Software setup of the anesthetic application showing the two software

environments discussed in Section 3.11.1.


execution.

3.11.2 Device drivers

In the following individual features of actuator/sensor drivers are identified.

Pump driver

The sedation system enables the end user to perform the following tasks on the

syringe pump:

- enable/disable the pump driver for device control via GUI or manual

- remotely switch on/off the pump

- start/pause/stop the infusion

- set the infusion rate

Figure 3.38 illustrates the pump control hierarchy. The user can only control

the device when the driver is enabled, otherwise the pump responds exclusively to

commands set on its physical interface. To verify correct connection between the

device and the xPC TargetBox, the pump driver confirms every two seconds its

functionality. When this signal is lost the pump device alerts the system user with

a RS232 timeout warning.

The actuator driver provides information about the current status of the pump.

The device updates and outputs every second the following signals:

- actual infusion rate [ml/h]

- total infused volume [ml]

- time to infusion end due to empty syringe [s]

SenTec sensor driver

Every second the sensor driver provides the following signals:

- transcutaneous CO2 partial pressure [mmHg]

- oxygen saturation [%]

- sensor status information (status flags)


Figure 3.38: Actuator control hierarchy.

The PCO2 signal provides a measurement of carbon dioxide in the blood. The

SpO2 signal quantifies blood oxygen saturation. Sensor flags detect the following

conditions:

- sensor resting in docking station

- digital monitor failure

- unit ready

- movement artefact in measurements

- movement and low signal

- CO2 stabilization

- sensor detached from patient, signal lost

- sensor calibration

- excess ambient light


Figure 3.39: Schematic illustration of the anesthetic platform architecture. Blue

ovals: signals transferred between system elements. Yellow rectangles:

anesthesia system components deployed into the real time environ-

ment. Green rectangle: graphical user interfaces running on the host

computer.

- sensor failure

Nico sensor driver

The following sensor signals are provided by the driver:

- respiratory rate [min−1]

- device internal time [s]

Contrary to the SenTec sensor, the Nico monitor updates the output signals at

the end of each respiratory cycle. The internal time signal is used to ensure that

connection to the monitor is not lost during system operation, in case the device

output is not updated because of patient apnea.

3.11.3 Supervisory module

Clinical and technical requirements as well as safety concerns mandate the use of

a supervisory module within the sedation system. Its purpose is to handle the

interactions between the user via the GUIs and the device drivers. It also manages


Figure 3.40: The top layer of the supervisory module chart.

system initialization and shutdown as well as data storage, transfer and recovery.

Moreover, during system operation the supervisory module continuously monitors

the actuator and sensor signals to detect crossing of potentially dangerous pre-

defined thresholds. When a violation occurs, the supervisory module prompts the

user for action. Figure 3.39 outlines the location and connections of the supervisory

module within the sedation system architecture.

The supervisory module is implemented as a Stateflow chart. As discussed in

the above, the module acts as a control unit for the sedation system with the main

task to operate the pump, manage the sensor signals and handle user-system in-

teractions. The sedation system can be in four states as illustrated in Figure 3.40.

At startup the system is in a state labeled initialization mode. During normal exe-

cution the system switches to the operating mode. At shutdown the system enters

the stop mode. In case of an emergency the system is forced into the emergency

mode. The conditions to switch from one state to another are listed beside the

corresponding arrow. Text shaded in yellow symbolizes a button in the main sys-

tem GUI (see Section 3.11.4) that must be pressed to induce the state transition.

The tasks performed by the system during normal execution (operating mode) are

shown in Figure 3.41.


Figure 3.41: Hierarchy of the state operating mode.

Figure 3.42: Configuration Gui. The input fields refer to the parameters of the

automatic controller, the patient metrics and the PK model.

3.1

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Figure 3.43: Main Gui. As an example, the therapy is running in closed loop with a PtcCO2 setpoint of 55 mmHg. The

SenTec and Nico sensor signals are displayed numerical and also plotted in the right pane of the interface.

Additionally, the pharmacokinetic model predictions for the plasma and effect propofol concentration are

shown from 15 minutes into the past to 10 minutes into the future.

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90

10095

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2 [%

]

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e

Patient 6

propofol setpoint fentanyl C

e [ng/ml]

propofol Ce [µg/ml]

PtcCO2 [mmHg] endoscope in−to coecum from coecum−out pain intraop. event

Figure 3.44: Intraoperative measurements for Patient 6 (see Section 3.12.1 for a detailed explanation of figure content).

3.1

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36 38 40 42 44 46 4840

60

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IS [−

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Patient 6

Pearson ρ = −0.86392Spearman ρ = −0.85433

0 500 1000 1500 2000 2500 3000 3500 4000 450035

40

45

50P

tcC

O2

[mm

Hg]

Time [s]

0 500 1000 1500 2000 2500 3000 3500 4000 450040

60

80

100

BIS

[−]

Time [s]

pre−op post−op intra−op linear fit

Figure 3.45: Top: BIS measurements vs. transcutaneous CO2 partial pressure readings in Patients 6. The clinical data

is presented as raw measurements before, during and after the colonoscopy (red, blue, and green circles,

respectively), and the linear fit for all measurements (blue line). Center and bottom: transcutaneous CO2

partial pressure and BIS measurements (color coded as in top panel).

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34 36 38 40 42 44 46 48 50 52 5460

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Hg]

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Patient 8

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IS [−

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pre−op post−op intra−op linear

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e [ng/ml]


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post−op intra−op linear fit

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Hg]

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BIS

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Patient 10

Pearson ρ = 0.075158Spearman ρ = 0.031871


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Patients 6−11

PtcCO2 [mmHg]

0.9 1 1.1 1.2 1.3 1.4 1.540

60

80

100

BIS

[−]

PtcCO2 [norm]


Figure 3.56: BIS measurements vs. CO2 partial pressure readings for patients 1-11 taken during the procedure. Top:

Raw measurements (blue circles) and linear fit (red line). Bottom: CO2 partial pressure measurements

are normalized to individual baseline.


0 1 2 3 4 525

30

35

40

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55

OASS [−]

PC

O2

[mm

Hg]

Patients 1−11

measurements linear fit

0 1 2 3 4 525

30

35

40

45

50

55

PC

O2

[mm

Hg]

Patients 1−11

OASS [−]

Figure 3.57: CO2 partial pressure measurements vs. OASS scores for patients 1-11

taken during the procedure. Top: Raw measurements (blue circles)

and linear fit (red line). Bottom: Measurements are depicted with

boxplots. The same linear fit is superimposed.


0 1 2 3 4 50.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

PC

O2

[−]

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Patients 1−11

measurements linear fit

0 1 2 3 4 50.9

1

1.1

1.2

1.3

1.4

1.5

1.6

PC

O2

[−]

Patients 1−11

OASS [−]

Figure 3.58: CO2 partial pressure measurements normalized to individual baseline

vs. OASS scores for patients 1-11 taken during the procedure. Top:

Normalized measurements (blue circles) and linear fit (red line). Bot-

tom: Measurements are depicted with boxplots. The same linear fit is

superimposed.

3.12 Preliminary clinical study results 145

3.11.4 Graphical user interfaces

With the configuration GUI shown in Figure 3.42, the sedation system user is able

to enter the initial platform configuration data. Patient information is used to

calculate the individual pharmacokinetic model with the possible choice between

the Schnider [169] or Marsh [132] model. In the event of new connection after a

host PC or network crash the system enables the recovery of data stored until the

crash.

The main system GUI, illustrated in Figure 3.43, serves as an operational inter-

face to the real time application running on the xPC TargetBox. Its design and

layout are tailored to the requirements of the clinical study and fulfil the clinical

recommendations of our research partners at the University Hospital Bern.

3.12 Preliminary clinical study results

3.12.1 Experimental findings

In this section the preliminary outcomes of the clinical study investigating respira-

tory depression during propofol sedation are presented. These findings are discussed

in Section 3.12.2.

To date, 11 colonoscopy patients have been enrolled in the study. Patient recruit-

ment at the University Hospital Bern is currently ongoing with the aim to complete

the target study population of 50 subjects as planned in the experimental protocol

(see Section 3.10).

The first 4 patients enrolled in the study were treated according to an exploratory

protocol that differs from the one described in this thesis. Moreover no BIS mea-

surements were recorded in these patients. For reasons of consistency, the time

courses of the intraoperative recordings for Patients 1-4 are not presented here.

Data regarding the relationship between respiratory depression and depth of seda-

tion in these and the other patients enrolled so far are presented in Figure 3.57 and

3.58.

Intraoperative recordings in Patient 5 are not shown here because the measure-

ment set is incomplete. The sedation system shut off briefly after the initiation of

propofol delivery. This incident was a case of operator error. The PCO2 sensor

cables were not connected to the study platform that correctly detected the fault

and shut itself off for safety reasons.

Figures 3.44-3.55 display the intraoperative recordings in individual subjects for

Patient 6 to 11.


The information shown in Figure 3.44 with regard to Patient 6 is explained here.

Top panel: propofol setpoint and calculated fentanyl and propofol effect site con-

centrations. Second panel: transcutaneous PCO2 measurements and intraoperative

time and event markers. Black line: duration of endoscope insertion (from begin-

ning to coecum); yellow line duration of endoscope removal (from coecum to exit);

red stars: time stamp for evident painful stimulation; green triangles: time stamp

for intraoperative event that may create PtcCO2 measurement artifacts (e.g. pa-

tient talking or snoring, patient movement required by gastroenterologist, etc.);

numbers: time stamp and result of OASS measurement. Third and fourth pan-

els: oxygen saturation and respiratory rate measurements (quick drops in SpO2

are artifacts). Bottom panel: infusion rates requested by the system and actually

delivered by the pump, and cumulative drug infusion.

Figure 3.45 shows the time courses of BIS and PtcCO2 recordings in Patient 6

(center and bottom panel) and the correlation between the two signals (top panel,

including Pearson’s and Spearman’s correlation coefficient values).

Similarly, Figures 3.46-3.55 present the information described above with respect

to Patients 7-11.

Finally, Figures 3.56-3.58 display combined experimental data regarding the re-

lationship between respiratory depression (assessed via PtcCO2) and depth of se-

dation (Figure 3.56: BIS measurements in Patients 6-11; Figures 3.57 and 3.58:

OASS scores in Patients 1-11) in the population of study subjects investigated to

date.

3.12.2 Preliminary results discussion

The preliminary results in the first 11 patients of the study show that the ex-

tent of respiratory depression induced by propofol during colonoscopy (measured

as increase of transcutaneous PCO2) is lower than expected. According to our

observations, anxiety, discomfort and pain stimulation are the main causes of the

observed phenomenon. These outcomes suggest that the model of respiratory de-

pression discussed in the previous sections may not be entirely applicable to this

patient population.

Moreover, baseline PtcCO2 before initiation of drug delivery is significantly lower

than what is physiologically expected. The average baseline in the 11 subjects is

35.6 mmHg (standard deviation: 4.1 mmHg). Initial PtcCO2 is lower than 36

mmHg in 5 of the 11 patients. This phenomenon may be due to hyperventilation

stimulated by preoperative anxiety. Another potential factor is the respiratory com-

pensation of the metabolic acidosis induced by bowel cleansing. Little information

3.12 Preliminary clinical study results 147

on this topic is available in the literature because CO2 monitoring does not belong

to the standard clinical protocol for colonoscopy. However a study by Kim and

coworkers provides evidence supporting this hypothesis [109].

At the time of writing patient recruitment and investigation is ongoing. Regret-

tably, only preliminary outcomes are available for presentation in this thesis. In

light of these results, it can be inferred that mental stress and painful stimulation

may reduce the respiratory depressant effect of propofol. Moreover upon arrival in

the gastroenterology suite the patient is in a state of metabolic acidosis induced by

the bowel preparation that is required prior to the colonoscopy. This causes res-

piratory compensation through hyperventilation and likely determines an increase

in CO2 responsiveness (steeper CO2 response curve, see Figure 3.2) [64]. In con-

clusion, applicability of the proposed dosing paradigm for personalized sedation to

colonoscopy procedures is unclear at the time of writing.


4

Pharmacodynamic modeling

for antiplatelet therapy

150 4 Pharmacodynamic modeling for antiplatelet therapy

4.1 Introduction

4.1.1 Antiplatelet therapy

Platelet activation and aggregation play a pivotal role in cardiovascular disease.

Physiological procoagulant and anticoagulant mechanisms balance each other in a

refined and delicate equilibrium. Coagulation disorders trigger adverse events such

as acute coronary syndrome, stroke with ensuing ischemia, and thromboembolism.

Inhibition of platelet aggregation is therefore a primary therapeutic objective [58].

Antiplatelet therapy is intended to attenuate thrombocyte activation and ag-

gregation, prevent occlusive clot formation, arrest procoagulant activity, promote

thrombus disaggregation, and facilitate tissular perfusion. Optimal platelet inhibi-

tion is based on maximizing antithrombotic properties while minimizing bleeding

risk, and it is critically dependent on the assessment of individual patient risk [24].

4.1.2 Problem formulation

Abundant clinical and experimental evidence supports the notion that inhibiting

platelet reactivity is a viable and effective way to reduce thrombotic risks in pa-

tients with cardiovascular diseases [91] and prevent ischemic complications after

acute coronary syndromes and stenting [130]. Nonetheless, current anticoagulation

guidelines are based mostly on large-scale trials that have been conducted without

an evaluation of the antiplatelet response in individual patients [110,156]. The data

available from translational research studies strongly indicate that the present “one-

size-fits-all” antiplatelet strategy is flawed [91, 130]. At one end of the spectrum,

selected patients with excessively low platelet reactivity may bleed. Patients with

high platelet reactivity may on the other hand be subject to ischemic events. Deter-

mining a therapeutic target of optimal platelet reactivity associated with reduced

thrombotic risk and bleeding events remains an elusive goal [91]. In the future, it is

foreseeable that optimal antiplatelet therapy will involve an objective assessment of

the individual thrombotic potential based on the measurement of platelet function.

Subsequent treatment of each patient will be directed by laboratory measurements

to ensure an appropriate therapeutic response.

Drug combinations are frequently used in medical therapies because of the ex-

pected enhancement of the positive effect(s). Indeed, since different anticoagu-

lants inhibit platelet aggregation through different pathways, dual (or multiple)

antiplatelet therapy provides complementary and additive benefits compared with

single agents. However, side effects may also be potentiated through synergistic

pharmacodynamic interactions, possibly resulting in the reduced or limited clinical

4.1 Introduction 151

usefulness of the multiple drug regimen. A pharmacodynamic interaction model re-

cently proposed by two Institute alumni combines desired pharmacological effects

and undesired effects into one comprehensive framework for analysis of drug useful-

ness [208]. In the following said model is employed to investigate the global effect of

anticoagulation therapeutic regimens in relation to the observed magnitude of the

intended effect (inhibition of platelet aggregation) and the undesired effect (risk of

bleeding).

4.1.3 Aim of the work

This work aims at addressing several aspects of anticoagulant pharmacodynam-

ics for both single and multiple drug therapies. First, quantitation of iloprost

and MeSAMP anticoagulant potency has not yet been undertaken to the best of

our knowledge. Therefore we intend to investigate the dose-response relationship

of those antiplatelet drugs through laboratory measurements of platelet reactiv-

ity in a population of human volunteers. Second, we aim to determine the type

and extent of their pharmacodynamic interactions (additivity, synergism, or infra-

additivity/antagonism). We shall take both positive (therapeutic) pharmacologic

effects and negative (undesired) effects into account and combine them into a global

framework evaluating drug usefulness and drug regimen desirability. Thus we will

experimentally validate the theoretical global outcome model proposed in [208]

through its application to a relevant clinical question. Finally, we want to achieve

recommendations for personalized antiplatelet therapy based on the objective as-

sessment of the individual thrombotic potential through measurements of platelet

function.

4.1.4 Chapter content

This chapter is structured as follows. In Section 4.2 the global outcome model

mentioned in the above is presented with the prospective application to antiplatelet

therapy data. The protocol of the clinical study aimed at investigating iloprost and

MeSAMP anticoagulant effects in volunteers is described in Section 4.3. In Section

4.4 the parameter estimation methodology is discussed with respect to the specific

type of data at hand. Finally, the experimental measurements and modeling results

are presented and discussed in Sections 4.5-4.6.


4.2 Pharmacodynamic interaction and global

outcome model

As discussed in the above, drug combinations are administered in a wide range of

medical therapies in order to take advantage of the expected enhancement of the

desired effect(s). Pharmacodynamic interactions may however also occur for the

undesired effects. It is therefore desirable to design an integrated measure of drug

benefits and related risks, characterized over the entire dose or concentration range.

To address this question Zanderigo and Sartori, two former students at IfA, and

their collaborators proposed the “well being” parameter as a way to summarize

the pharmacological desired and undesired effects into a single index [208]. This

methodology can be applied to single drug therapies as well as to multiple drug

regimens. With the objective to achieve a general modeling framework of drug

interaction, effect, and utility, the mathematical description of pharmacodynamic

interactions proposed by Minto and coworkers [140] was extended in [208] to con-

sider the occurrence of the drugs’ negative effects. The Authors were then able to

define and quantify the global outcome of therapies relying on drug combinations

based on the administered drug amounts.

In the case of the simultaneous administration of two drugs, the global outcome

index can be graphically represented with a 3D surface, where the x and y axes de-

scribe the biophase concentrations of the two drugs and the z-axis the corresponding

value of global outcome.

An accurate mathematical description of the model can be found in the litera-

ture [208]. In the following, a summary of the model will be presented as a basis

for later discussion of antiplatelet therapy results. Without loss of generality, we

shall concentrate on the two-drug case because the antiplatelet therapy study plan

mandates investigation of iloprost-MeSAMP combinations.

Minto and coworkers proposed that when two drugs A and B are administered

simultaneously in a defined, fixed ratio θ, they can be thought as behaving as a new

pseudo-drug having its own specific concentration-effect relationship. In analogy to

the one drug case, we can then make the assumption that the pharmacodynamics of

each drug combination (characterized by a definite θ value) can be described with

a sigmoid function relating the drug effect to the drug combination concentration.

The latter is determined by adding quantities of the drugs A and B in the fixed θ

ratio characterizing the drug combination in question. In the following will shall

label drug quantities as U (e.g. UA and UB). In order to account for the difference

in potency between the two drugs, said quantities need to represent drug amounts

in terms of units of potency. After normalization of potency, quantities of different

4.2 Pharmacodynamic interaction and global outcome model 153

drugs can be compared and related directly to the pharmacological effect.

The mathematical equations describing what discussed so far are:

UA = CA

C50A

, UB = CB

C50B

(4.1)

and

θ = UB

UA +UB

, θ ∈ [0,1] (4.2)

Only drug A is present if θ = 0. Conversely, only drug B is present when θ = 1.

The model is therefore fully reversible to the single drug case.

The dose-response relationship for drug combinations is modeled as:

E(θ) = Emax(θ) ⋅ (UA+UB

U50(θ) )γ(θ)1 + (UA+UB

U50(θ) )γ(θ)(4.3)

U50(θ) represents the potency of the drug combination of ratio θ. Per definition,

U50(θ = 0) = U50A = 1 and U50(θ = 1) = U50B = 1. γ(θ) is the steepness of the sig-

moidal function. Emax(θ) is the maximal effect that the combination with ratio

θ can achieve. In case of partial agonism, Emax is going to be smaller than the

maximum possible effect. If UA or UB are zero, Equation 4.3 collapses to the classic

Emax model description of single drug pharmacodynamics.

The parameters Emax, U50, and γ can be expressed as functions of the drug

ratio θ by a generic polynomial of the form:

f(θ) = k

∑i=0βiθ

i, for θ ∈ [0,1] and f = U50, γ or Emax (4.4)

In this equation, k is the order of the polynomial. Considering the high interpatient

variability and the cost of every experimental data point, it may be not realistic to

estimate a large number of parameters. Moreover, it becomes difficult to clinically

interpret the coefficients when more than the second power is present. Therefore, for

simplicity, we consider the model restricted to the second order coefficients (k = 2),

as already implemented in the simulations by Minto and Zanderigo [140, 208]:

f(θ) = β0 + β1θ + β2θ2 (4.5)

Considering that

f(θ = 0) = β0 = fA (4.6)

f(θ = 1) = β0 + β1 + β2 = fB ⇒ β1 = fB − fA − β2, (4.7)


Equation 4.5 becomes:

f(θ) = fA + (fB − fA − βf) ⋅ θ + βf ⋅ θ2 (4.8)

where we have relabeled β2 as βf . Under the assumptions discussed in the above

and provided that single drug pharmacodynamic parameters are known, each com-

bination parameter f = U50, γ or Emax can therefore be expressed as a function

of θ following the estimation one single interaction parameter, βf .

In the case of U50, given that U50(θ = 0) = U50A = U50(θ = 1) = U50B = 1, Equa-

tion 4.8 further simplifies to

U50(θ) = 1 − βf ⋅ θ + βf ⋅ θ2 (4.9)

Extending the model presented so far to consider the occurrence of undesired

effects, in the case of administration of a two drug regimen the resulting negative

effect EN can be described as:

EN(θN) = EmaxN(θN) ⋅ (UA,N+UB,N

U50N (θN ))γN (θN )

1 + (UA,N+UB,N


(4.10)

where all the variables and parameters have the same meaning as described for the

positive effect. Analogously to Equation 4.8 and 4.9, EmaxN , γN and U50N are

represented as a function of the undesired effect pharmacodynamic parameters for

the single drugs composing the regimen (EmaxA,N , γA,N , U50A,N , EmaxB,N , γB,N ,

U50B,N), of their ratio θN , and of the interaction parameters for the negative effect

(βEmax,N , βγ,N , βU50,N).

According to the interaction model by Zanderigo and coworkers [208], the global

outcome W is calculated as the algebraic sum of the positive and the negative

effects as:

W = E(θ) − ω ⋅EN(θN) (4.11)

where ω represents the relative weight of the two effects. In the following we shall

consider ω = 1 for the sake of simplicity and the lack of specific clinical requirements.

Note that the presented model is a pharmacodynamic interaction model and no

assumptions on possible pharmacokinetic interactions are made.

4.3 Clinical investigation: anticoagulant pharmacodynamic interaction modeling 155

4.3 Clinical investigation: anticoagulant

pharmacodynamic interaction modeling

4.3.1 Study investigators

Investigators:



Dr. med. Gorazd Sveticic, Department of Anesthesiology and Intensive Care

Medicine, Medical University of Vienna, Austria

Dr. med. Gisela Scharbert, Department of Anesthesiology and Intensive Care

Medicine, Medical University of Vienna, Austria

Prof. Sybille Kozek-Langenecker, Department of Anesthesiology and Inten-

sive Care Medicine, Medical University of Vienna, Austria

Prof. Michele Curatolo, Department of Anesthesiology and Pain Therapy,


4.3.2 Study methodology

Study design

Observational, single center study, setting: Medical University of Vienna

Study population

After obtaining the written informed consent, blood from 15 healthy adult volun-

teers is investigated in vitro. Exclusion criteria include: known hematological or

other systemic disease, intake of any systemic medication within the previous 14

days or illicit drug or alcohol abuse.

Study plan

The study is conducted in the hemostasis laboratory to perform platelet function

tests immediately after sampling. On arrival in the laboratory, subjects are asked to

rest for 10 minutes before drawing blood samples. Blood for platelet aggregometry


is withdrawn into 13 3.0 ml DTI-tubes (direct thrombin inhibitor blood collec-

tion tube: hirudin 25 µg/ml; Dynabyte, Munich, Germany) from an antecubital

vein by venipuncture without stasis using a 21-gauge butterfly needle. The first 3

ml are discarded. Platelet aggregometry is then performed using the impedance

aggregometer Multiplate (Dynabyte, Munich, Germany).

Study drugs

The drugs selected to perform the study are iloprost and MeSAMP.

Adenosine diphosphate (ADP), released by activated platelets, is a potent platelet

aggregator that activates platelets by interacting with the P2Y1 and P2Y12 re-

ceptors. Iloprost, a chemically stable compound with prostacyclin PGI2 mimetic

activity, inhibits platelet aggregation by stimulating adenylyl cyclase. The P2Y12

receptor is in fact negatively coupled to adenylyl cyclase. Its inhibition further

exerts antithrombotic effects through the potentiation of prostacyclin antiplatelet

activity [41].

Methyl-S-adenosine monophosphate (MeSAMP) is a direct-acting, reversible and

short-acting inhibitor of the platelet P2Y12 receptor, preventing ADP-induced

platelet activation and subsequent aggregation [4,145,197]. Despite its widespread

use for laboratory experiments on platelet reactivity, to the best of our knowledge

MeSAMP is not commercially available for clinical use.

A more obvious selection of anticoagulant drugs would have included clopidogrel

and/or aspirin, being the two most common compounds used in antiplatelet ther-

apy. However clopidogrel is a prodrug, i.e. it necessitates conversion in vivo by

the hepatic CYP system to the active metabolite, which irreversibly binds to the

platelet P2Y12 receptor and inhibits platelet function for the life of the affected

platelet [74]. Clopidogrel could not therefore be used in an in vitro study. As-

pirin, on the other hand, has been shown not to affect the coagulative response to

TRAP [105]. We confirmed this behavior with preliminary tests at our hemostasis

laboratory.

Effects

In this work we shall consider drug effects on ADP-induced platelet reactivity as

the positive (therapeutic) effect, and effects on TRAP-induced platelet reactivity

as the negative (undesired) effect. The rationale for the choice of the positive effect

is that clinical data support the view that inhibiting platelet reactivity to ADP

determines a reduction in the incidence of ischemic events [91]. The choice of the

negative effect is explained in the next paragraph.

4.3 Clinical investigation: anticoagulant pharmacodynamic interaction modeling 157

Clinical and experimental evidence has indicated that ADP-mediated P2Y12 sig-

naling appears to play a prominent role in platelet activation. P2Y12 antagonists

(i.e. iloprost and MeSAMP) have a broad inhibitory profile and can inhibit platelet

aggregation in response to multiple agonists, such as thromboxane, collagen, and

thrombin [177]. On the other hand, bleeding is a significant complication of anti-

coagulant treatment. More intense anticoagulation has been reported to increase

the risk of major hemorrhage [188,120] and thrombin inhibition is associated with

spontaneous bleeding [125, 116]. We investigate drug concentrations that disrupt

the coagulative mechanisms mediated by thrombin, posing a threat of spontaneous

hemorrhage that is clinically undesirable. Hence, massive inhibition of TRAP-

induced aggregation is regarded as a negative pharmacologic effect.

Measurements

Whole blood aggregometry measures electrical impedance between electrodes im-

mersed in whole blood. Blood is stirred using an electromagnetic stirrer (800 rpm).

The attachment of platelet aggregates on the electrodes increases the impedance

between them. The impedance change is transformed to arbitrary aggregation units

by the system software and plotted against time. In contrast to optical aggregome-

try, the use of whole blood eliminates the need for centrifugation and tests platelet

function under more physiological conditions.

Impedance aggregometry was introduced by Cardinal and Flower in 1980 [32].

The Multiplate technique is an improvement of impedance aggregometry using a

computer-controlled 5-channel device and disposable test cells with a dual sensor

unit. With the use of disposable test cells there is no need to clean and ensure the

integrity of the electrodes after each test.

Platelet aggregation (drug naıve or in the presence of anticoagulants) is deter-

mined in response to ADP (12.8 µg M) and thrombin receptor activating peptide

(TRAP, 1 mM), using commercially available test reagents recommended for Mul-

tiplate analysis. Pipetting is performed using an electronic pipette connected to

the analyzer.

Safety

The risk of drawing blood from a healthy volunteer is negligible.


4.4 Parameter estimation for antiplatelet therapy

data

Without loss of generality, in the analysis of antiplatelet data we shall consider

an inhibitory sigmoid Emax model because the drugs under investigation exert

an inhibitory effect on platelet aggregation. Equation 4.3 and 4.10 are therefore

modified as follows:

E(θ) = E0 −Emax(θ) ⋅ (UA+UB

U50(θ) )γ(θ)1 + (UA+UB

U50(θ) )γ(θ)(4.12)

EN(θN) = E0 −EmaxN(θN) ⋅ (UA,N+UB,N


1 + (UA,N+UB,N


(4.13)

where E0 is the value of platelet reactivity at baseline (i.e. without exposure to the

drugs).

As discussed in Section 4.2, in order to calculate the global outcome response

surface for the combination of two drugs it is necessary to estimate from the exper-

imental data the pharmacodynamic parameters for the single drugs (EmaxA, γA,

C50A, EmaxB , γB, C50B, and the corresponding ones for the negative effect) as

well as the 6 interaction parameters for both positive and negative effects (βEmax,

βEmax,N , βγ, βγ,N , βU50,N , βU50). The E0s, i.e. the extent of platelet drug-naıve

aggregation in response to different activating reagents, must also estimated from

the experimental data.

Assuming that the probability distribution for the observations is Gaussian (more

precisely: that the experimental errors are independent and normally distributed

with constant standard deviation), the least squares and maximum likelihood esti-

mators coincide. Therefore all the parameters mentioned in the above are estimated

via least squares fitting using the impedance aggregometry results collected in the

study population of volunteers.

To assess the quality of the estimates we use two graphical tools: the Tukey-

Anscombe (TA) plot and the normal quantile-quantile (QQ) plot. The TA plot is

a qualitative test for the homogeneity of residual variance. The residuals (i.e. the

model errors in predicting the observations) are plotted against the fitted values

and in the ideal case vary randomly around the horizontal axis. When the TA

plot shows a trend, there is evidence that the estimated model parameters are not

appropriate (assuming the model structure is). In this case a data transformation

(logarithm, square root, reciprocal) is attempted for improvement.

4.5 Experimental results and model estimation 159

To identify outliers and test for normality of the residuals, their empirical quan-

tiles are plotted against the theoretical quantiles of a N (0,1) distribution. The re-

sulting plot is the so-called QQ plot. If the observations are normally distributed,

the QQ plot is linear.

Goodness-of-fit plots are also used here to identify patterns in the performance

of the model to predict experimental measurements. Predicted results are plotted

against the corresponding platelet aggregation data and theoretically the model

should not consistently under- or over-estimate the experimental results.

During the analysis it was observed that MeSAMP is a partial TRAP aggregation

antagonist, i.e. MeSAMP cannot completely inhibit platelet aggregation in response

to TRAP when administered alone. Therefore the MeSAMP Emax for TRAP is

smaller than E0 for almost all subjects taking part in the study. However small

relative amounts of iloprost, a full agonist, are sufficient to make the combination

exhibit a complete inhibitory effect (i.e. for θ values approaching 1, EmaxN = E0).

Because Equation 4.8 does not seem appropriate to describe TRAP pharmacody-

namics (more precisely, to capture the behavior of EmaxN as a function of θN ),

βEmax,N is determined minimizing the sum of squared residuals for a power function

of θN constrained to cross only the EmaxN(θN = 1) data point. Let us label θN′

the drug ratio value at which this function crosses the EmaxN = 1 horizontal line.

Then we define EmaxN(θN) as follows:

for θN ≤ θ′N EmaxN(θN) = 1

for θN > θ′N EmaxN(θN) = 1 − (θN − θ′N)βEmax,N (4.14)

4.5 Experimental results and model estimation

Complete estimation results for two of the fifteen subjects taking part in the study

are presented in this section. Subject A and Subject C were selected for presentation

here amongst study participants on the basis of experimental data availability. They

are in fact the subjects in which most drug combination ratios were investigated.

More precisely, seven ratios were studied in Subject A and nine ratios in Subject

C. Because Subject A and C are two of the clinical investigators involved in the

study, they were available for repeated blood withdrawals. Assessment of primary

hemostasis capacity through platelet aggregometry should be performed within the

first 2 hours after harvesting [107]. Large sets of data can therefore only be collected

with repeated sampling of blood. Depending on individual availability, a minimum

of five ratios was investigated in each subject, with the exception of two subjects

for which only three ratios were studied.

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0 0.2 0.80.4 0.6 10.4

0.6

0.8

1

1.2

θ [−]

U50

[−]

Subject A

0 0.40.2 0.6 0.8 10

1

2

3

4

θ [−]

γ [−

]

0 0.2 0.4 10.6 0.80.2

0.4

0.6

0.8

1

1.2

θ [−]

Em

ax [−

]

ADP TRAP f(θ)

ADP for f = U50, γ or Emax

f(θ)TRAP

for f = U50, γ or Emax

Figure 4.1: Experimental measurements (stars) and model fit (dashed lines) for parameters U50(θ), γ(θ), Emax(θ).The graphs show platelet aggregation data for Subject A in response to ADP (in red) and TRAP (in blue).

θ = 0 for pure iloprost, θ = 1 for pure MeSAMP. Emax is normalized to estimated E0.


0 0.2 0.4 0.6 0.8 1 1.20

0.2

0.4

0.6

0.8

1

1.2

Measured aggregation [AU⋅min]

Pre

dict

ed a

ggre

gatio

n [A

U⋅m

in]

ADP goodness−of−fit

0 0.2 0.4 0.6 0.8 1 1.20

0.2

0.4

0.6

0.8

1

1.2


Pre

dict

ed a

ggre

gatio

n [A

U⋅m

in]

Figure 4.2: Top: experimental measurements (symbols) and response surface model

of platelet aggregation in response to ADP in Subject A. White lines:

iso-effect curves. Red line: 50% iso-effect curve. These lines are also

projected onto the z = 0 plane and depicted as a contour plot. Red and

blue sigmoidal curves: model fit for pure iloprost (θ = 0) and MeSAMP

(θ = 1), respectively. Black sigmoidal curves: model fit for different

θ (i.e. drug ratio) values. The investigated ratios are shown in Fig-

ure 4.1. Bottom: goodness-of-fit plot relative to the response surface

shown above. The right panel shows the same data as the left panel,

differentiating the dots according to the θ value.


0 0.2 0.4 0.6 0.8 1 1.20

0.2

0.4

0.6

0.8

1

1.2


Pre

dict

ed a

ggre

gatio

n [A

U⋅m

in]

TRAP goodness−of−fit

0 0.2 0.4 0.6 0.8 1 1.20

0.2

0.4

0.6

0.8

1

1.2


Pre

dict

ed a

ggre

gatio

n [A

U⋅m

in]


of platelet aggregation in response to TRAP in Subject A. White lines:










0 200 400 600 800 1000 12000

10

20

30

40

50

60

70

Iloprost [pg/ml]

Subject A: Global outcome response surface

MeS

AM

P [µ

g/m

l]

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Figure 4.4: Top: global outcome response surface for Subject A, obtained from

the ADP- and TRAP-induced platelet aggregation response surfaces

(Figure 4.2 and 4.3). Bottom: concentration map of the global outcome

surface shown above. Potentially optimal drug regimens that maximize

the global outcome are located in the region adjacent to the combination

Ciloprost = 278 pg/ml, CMeSAMP = 6.6 µg/ml (corresponding to W =80%). Similar global outcomes can be obtained with single drugs (in the

region centered at Ciloprost = 535 pg/ml with W = 80%, or at CMeSAMP =45.2 µg/ml with W = 83%).

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0 0.2 0.80.4 0.6 10

1

2

3

θ [−]

U50

[−]

Subject C

0 0.2 0.4 10.6 0.80.4

0.6

0.8

1

1.2

θ [−]

Em

ax [−

]

0 0.40.2 0.6 0.8 10

2

4

6

8

θ [−]

γ [−

]

ADP TRAP f(θ)

ADP for f = U50, γ or Emax

f(θ)TRAP

for f = U50, γ or Emax

Figure 4.5: Experimental measurements (stars) and model fit (dashed lines) for parameters U50(θ), γ(θ), Emax(θ).The graphs show platelet aggregation data for Subject C in response to ADP (in red) and TRAP (in blue).

θ = 0 for pure iloprost, θ = 1 for pure MeSAMP. Emax is normalized to estimated E0.


0 0.2 0.4 0.6 0.8 1 1.20

0.2

0.4

0.6

0.8

1

1.2


Pre

dict

ed a

ggre

gatio

n [A

U⋅m

in]

0 0.2 0.4 0.6 0.8 1 1.20

0.2

0.4

0.6

0.8

1

1.2


Pre

dict

ed a

ggre

gatio

n [A

U⋅m

in]

ADP goodness−of−fit


of platelet aggregation in response to ADP in Subject C. White lines:










0 0.2 0.4 0.6 0.8 1 1.20

0.2

0.4

0.6

0.8

1

1.2


Pre

dict

ed a

ggre

gatio

n [A

U⋅m

in]

0 0.2 0.4 0.6 0.8 1 1.20

0.2

0.4

0.6

0.8

1

1.2


Pre

dict

ed a

ggre

gatio

n [A

U⋅m

in]

TRAP goodness−of−fit


of platelet aggregation in response to TRAP in Subject C. White lines:










0 100 200 300 400 500 600 700 8000

5

10

15

20

25

30

35

40

45

50

Subject C: Global outcome response surface

Iloprost [pg/ml]

MeS

AM

P [µ

g/m

l]

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Figure 4.8: Top: global outcome response surface for Subject C, obtained from the

ADP- and TRAP-induced platelet aggregation response surfaces (Fig-

ure 4.6 and 4.7). Bottom: concentration map of the global outcome sur-

face show above. Potentially optimal drug combinations that maximize

the global outcome are located in the region centered at Ciloprost = 331

pg/ml, CMeSAMP = 15.0 µg/ml (corresponding to W = 81%).


0 1 2 3 4 5 60

20

40

60

80

100

120

Fitted equation : E = E0 −Emax ·

(UA+UB)γ

(UA+UB)γ+U50γ

Sum of error = 3541.3430,Emax = 78.9956,U50 = 0.6385, γ = 1.0931,E0 = 78.9956

UA + U

BA

DP

rea

ctiv

ity

10 20 30 40 50 60 70 800 90−40

−20

0

20

40

Predicted reactivity

Res

idua

ls

TA plot

−2.5 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5−40

−20

0

20

40

Standard normal quantiles

Qua

ntile

s of

in

put s

ampl

e

QQ plot

0 1 2 3 4 5 60

1

2

3

4

5


(UA+UB)γ

(UA+UB)γ+U50γ


UA + U

B

AD

P r

eact

ivity

1 1.5 2 2.5 3 3.5 4 4.5 5

−0.6

0

−0.3

0.3

0.6


Res

idua

ls

TA plot

−2.5 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5−1

−0.5

0

0.5

1


Qua

ntile

s of

inpu

t sam

ple

QQ plot

Figure 4.9: Top panels: the untransformed data clearly exhibit a funnelling trend in

the TA plot. Bottom panels: after a log-transformation, the trend dis-

appears. Normality of the residuals may arguably also have improved,

as shown in the QQ plot. Experimental data: Subject C, ADP-induced

coagulation data, θ = 0.8914.


0 0.5 1 1.5 2 2.5 30

20

40

60

80

100

120


(UA+UB)γ

(UA+UB)γ+U50γ


UA + U

B

TR

AP

rea

ctiv

ity

0 10 20 30 40 50 60 70 80 90 100−20

−10

0

10

20


Res

idua

ls

TA plot

−2 −1.5 −1 −0.5 0 0.5 1 1.5 2−20

−10

0

10

20


Qua

ntile

s of

inpu

t sam

ple

QQ plot

0 0.5 1 1.5 2 2.5 30

2

4

6


(UA+UB)γ

(UA+UB)γ+U50γ


UA + U

B

TR

AP

rea

ctiv

ity

−1 0 1 2 3 4 5 6−0.4

−0.2

0

0.2

0.4


Res

idua

ls

TA plot

−2 −1.5 −1 −0.5 0 0.5 1 1.5 2−0.4

−0.2

0

0.2

0.4


Qua

ntile

s of

inpu

t sam

ple

QQ plot

Figure 4.10: Top panels: the untransformed data clearly exhibit a funnelling trend

in the TA plot. Bottom panels: after a log-transformation, the trend

disappears. Experimental data: Subject I, TRAP-induced coagulation

data, θ = 0.6977.

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Subject C50iloprost,ADP C50MeSAMP,ADP βADP C50iloprost,TRAP C50MeSAMP,TRAP βTRAP

[pg/ml] [µg/ml] [-] pg/ml [µg/ml] [-]

A 192 14.1 1.5 1321 77.3 2.3

B 275 8.0 2.2 841 3 50.9 -0.3

C 286 17.4 1.4 517 31.3 -4.8

D 393 14.9 -0.3 2557 142.6 0.1

E 99 3.9 -1.1 1464 121.7 1.7

F 237 10.0 -4.9 1098 68.9 0.1

G 181 4.2 -11.7 1127 95.1 1.6

H 59 2.7 -3.6 755 81.6 0.5

I 199 8.7 1.7 1028 44.5 1.0

J 409 6.6 1.8 985 53.1 1.8

K 133 6.5 0.5 1035 40.7 -0.6

L 189 23.4 0.2 1295 22.7 -6.1

M 161 2.7 -11.1 1150 119.7 2.5

N 117 7.2 -6.2 816 120.5 1.3

O 85 2.6 -1.1 845 3.9 -11.0

average 201 8.9 -2.0 1122 71.6 -0.7

st. dev. 104 6.1 4.5 465 41.4 3.6

Table 4.1: C50 estimation results in the 15 volunteers and in the population (averaged values), for both iloprost and

MeSAMP, ADP- and TRAP-induced effects.

4.6 Results discussion 171

Pharmacodynamic interaction parameter plots are displayed in Figure 4.1 and

4.5 for Subject A and C, respectively. Figures 4.2-4.3 and 4.6-4.7 show the modeled

concentration-effect surface of platelet reactivity in response to ADP and TRAP

and the relative goodness-of-fit plots for the two subjects. Figure 4.4 and 4.8 show

the overall 3D global outcome response surface as well as the projection of said

surface on the z = 0 plane, in order to highlight the regions of maximal global

outcome.

Figure 4.9 and 4.10 show two examples of the improvement of residual variance

and residual normality that can be achieved through data transformation. Guidance

for data transformation is obtained by inspecting the TA and the QQ plots relative

to the untransformed data.

C50 estimation results for each individual and in the population are summarized

in Table 4.1, as well as the estimated C50 interaction parameters for ADP and

TRAP effects. Other parameter estimation results are not reported here for the

sake of conciseness and because of limited clinical usefulness.

4.6 Results discussion

The aim of this study was to apply the novel pharmacodynamic interaction model

proposed in [208] to a clinically relevant problem, specifically to the description

of the inhibitory effects produced by anticoagulants on platelet reactivity. We

tested hemostasis in response to ADP and TRAP with impedance aggregometry

in the presence of iloprost and MeSAMP. Through the use of least squares esti-

mation methods and residual analysis tools, pharmacodynamic response surfaces

were achieved that exhibit a good fit to the experimental data taken in the study

population of volunteers.

As discussed in Section 4.4, MeSAMP is a partial agonist for the inhibition

of platelet activation in response to TRAP. Iloprost is a full TRAP aggregation

antagonist. We observed experimentally that small relative amounts of iloprost

in iloprost-MeSAMP combinations would achieve maximal inhibition of platelet

response to TRAP. In this study, we proposed to model the behavior of EmaxN

as a function of θN according to Equation 4.14. Nonetheless, further investigation

is required to determine with higher confidence the exact relationship between

the maximum anticoagulant effect and the ratio of the two anticoagulants in the

combination.

Parameter estimation results for the study population are listed in Table 4.1.

They are adequately consistent in terms of drug C50s for ADP and TRAP ef-


fects. There are however outliers. Subject O, for instance, seems to be significantly

sensitive to the drugs, particularly to MeSAMP. Subject D, on the other hand,

appears to be rather insensitive, especially to iloprost. Whether these results are

accurate or rather influenced by experimental imprecision is unclear at the time

of writing. Because this is the first study addressing quantitation and modeling

of anticoagulant pharmacodynamics, there is no data available in the literature for

comparison of the estimates. Further investigation in at least these two subjects

may be necessary.

Another objective of this work was to determine the optimal combination of

iloprost and MeSAMP in the individual. Results for Subject A and C are dis-

played in Figure 4.4 and 4.8, respectively. Optimal dosing outcomes for all subjects

participating in the study are summarized in Table 4.2. Recommendations for

personalized dosing are listed in this table with the corresponding global outcome

index value, W .

Most subjects exhibit only a global maximum in the W surface (e.g. Subject

C, see Figure 4.4). The optimal combination is then simply defined as the con-

centration pair that maximizes W . Six subjects however exhibit one or two local

maxima besides the global maximum (e.g. Subject A, see Figure 4.4). This may

for instance occur when the therapeutic window of a single drug is very wide in

the specific individual. As the onset of the negative effect occurs at concentrations

that are considerably higher than those producing the positive effect, the outcome

parameter may reach values close to the global maximum.

From a clinical point of view, a small difference in W may not translate into a

visible improvement in patient well being. In the presence of local maxima, from a

clinical perspective it may be desirable to take into account other factors, beyond

the W value. For instance, it may be argued that the increment in W between

a local and a global maximum does not justify the higher dosage (if that’s the

case). A conservative criterion such as the following could then for instance be

defined. When the global and local maxima differ by less than 5% in W value, the

optimal combination is chosen amongst those pertaining to the (global and local)

maxima as the least potent one with respect to the negative effect. That is, as

the concentration pair that minimizesUiloprost,N+UMeSAMP,N

U50N (θN ). The results listed in

Table 4.2 are derived according to this criterion. Different criteria could similarly

be defined based on clinical requirements and recommendations.

The dose optimization results of Table 4.2 are in agreement with therapeutic

(i.e. effective) drug dosages suggested in the literature for single drugs [1,131]. No

information on dosing for the combination is available in the open literature at the

time of writing. As the experimental measurements this work is based on were

4.6 Results discussion 173

Subject Ciloprost CMeSAMP W

[pg/ml] [µg/ml] [%]

A 278 6.6 80

B 206 2.8 78

C 331 15.0 81

D 269 29.4 87

E 81 13.4 88

F 483 0.0 78

G 265 0.0 84

H 83 26.9 85

I 401 2.0 90

J 0 21.5 77

K 295 7.3 87

L 641 0.5 85

M 34 20.7 81

N 57 28.3 73

O 617 1.3 83

Table 4.2: Recommendations for personalized antiplatelet therapy in the study pop-

ulation. Optimal drug combinations are listed in the table with the

corresponding global outcome value, W .

taken in vitro, the clinical applicability of this dose optimization methodology still

remains to be investigated.


5

Main achievements and outlook

176 5 Main achievements and outlook

5.1 Feedback control of sedation

In this thesis we propose and discuss a novel anesthetic paradigm for the safe and

effective delivery of personalized sedation. The objective is to tailor drug admin-

istration to the needs of the specific patient while minimizing the risks associated

with anesthetic delivery. The dosing paradigm takes advantage of the similar phar-

macodynamics of drug induced ventilatory depression and sedation. We suggest to

purposely titrate drug dosing to a moderate extent of the undesired effect in order

to safely achieve an adequate level of the desired, therapeutic effect.

The rationale for the proposed methodology is that light sedation is difficult to

quantify, and drug overdosing leads to dangerous cardiorespiratory events. Markers

for the ventilatory state of the patient are readily available on the market and can

therefore be employed to increase the safety of anesthetic practice. Our preferred

indicator for ventilation is CO2 partial pressure, which can be obtained with a

noninvasive, continuous combined transcutaneous capnometry/pulse oximetry de-

vice such as the SenTec PtcCO2 monitor (SenTec AG, Therwil, Switzerland). As

discussed in Chapter 3, the PtcCO2 signal correlates well with the capnogram and

the sensing technology is not prone to respiratory and movement artifacts and does

not require access to the airways.

In order to protect the intellectual property related to the novel sedation paradigm,

in 2006 we filed an international patent application that was subsequently granted.

We envision the concept could be implemented into a commercial product provid-

ing computer assisted personalized sedation. In 2008 patent rights were licensed to

SenTec AG for product development and commercial use.

Chapter 3 of this thesis provides substantial contributions to support the sedation

protocol proposed in this thesis. Prior to the validation in the clinical environment,

we tested and refined the paradigm using a human physiology platform that we de-

veloped to that purpose. Respiratory metabolism and regulation, drug distribution

in the body, and dynamics of pharmacological effects were taken into consideration

and included in the human ventilatory model described in Section 3.5, 3.7, and 3.8.

The model underwent several refinements and simplifications in order to isolate

the respiratory mechanisms that have an impact on the problem at hand and to

reduce complexity. Achieving a comprehensive yet parsimonious model structure is

of uttermost significance. On the one hand, an incomplete model would not provide

meaningful or reliable predictions under specific conditions. On the other hand, an

overly complex model would not allow for estimation of individual parameters from

the little data that is available for a typical sedation patient.

The physiological model allowed us to investigate efficiently the use of several


different controller structures. The objective was to verify whether a feedback

controller targeting mild hypercapnia/hypoventilation (PtcCO2 between 45 and

60 mmHg) and anesthetic effect site concentrations corresponding to moderate to

deep sedation in the population would yield acceptable performance and safety.

Two of the control structures mentioned above are presented in this thesis. First,

a proportional-integral controller was tested on the respiratory platform to deliver

sedative concentrations of remifentanil (Section 3.6). Then we developed a model

based controller, specifically a model predictive control algorithm, to deliver propo-

fol sedation in a refined version of the respiratory platform (Section 3.9). Both

controllers successfully individualize drug delivery based on the feedback informa-

tion received from the physiological plant and achieve the target PtcCO2 and Ce

setpoints despite significant pharmacokinetic/dynamic variability.

The pharmacodynamic modeling and feedback control theoretical advances must

be matched with experimental work verifying our assumptions and validating our

concepts. To that purpose our collaboration with the Anesthesiology and Pain

Therapy Department at the University Hospital Bern is most valuable. Together

with our research partners in Bern, we designed, planned, and initiated two clinical

studies to provide evidence for the feasibility of the proposed paradigm.

A first study was designed with the objective to provide support for the correla-

tion between ventilation, and PCO2 as a ventilatory indicator, and the anesthetic

therapeutic endpoint. The clinical trial involves gastroenterology patients enrolled

at the University Hospital Bern, Switzerland. A prototype of the sedation deliv-

ery system was built in order to carry out the clinical experiments and administer

computer assisted anesthesia. Regrettably at the time of writing the study is incom-

plete and therefore final results cannot be discussed here. However as of November

2009, an initial batch of colonoscopy patients has already been investigated. These

preliminary experimental results are presented and discussed in Section 3.12.

In a second study, discussed in Appendix A, we investigate the effect of pain on

ventilatory regulation. Clinical experience and numerous studies reported in the

literature suggest that pain has an excitatory influence on ventilation and may an-

tagonize anesthetic induced respiratory depression. As we expect pain stimulation

to occur during the performance of the medical procedures sedation is used for,

we are testing the extent of pain antagonism of respiratory depression pharmaco-

dynamics. The results obtained through this study will be helpful to revise the

controller algorithm and improve its applicability and effectiveness in the clinical

environment.


5.2 Pharmacodynamic modeling for antiplatelet

therapy

In Chapter 4 we discussed a novel modeling platform to investigate drug interac-

tions and their optimal dosage. Originally proposed by two IfA alumni and cowork-

ers in [208], the model takes into account the pharmacodynamic interactions that

multidrug regimens may exhibit. It also combines positive and negative pharma-

cological effects into one comprehensive framework for analysis of drug usefulness.

This framework enables to assess efficiently global therapy outcomes and patient

well being by mapping drug concentrations to a single index describing therapy

quality.

In this thesis we sought to both validate experimentally the theoretical frame-

work and further fulfil the needs for personalized drug dosing in medical care. We

provided experimental support for the modeling platform through its application

to antiplatelet therapy, a clinical practice in which the demand for therapy indi-

vidualization is rapidly increasing. According to recent opinions reported in the

literature [91, 130], the “one-size-fits-all” antiplatelet strategy presently suggested

by practice guidelines has severe limitations. Patients with excessively low platelet

reactivity may bleed, whereas patients with high platelet reactivity may be subject

to ischemic events. Optimal antiplatelet therapy should involve an objective assess-

ment of the individual thrombotic potential based on the measurement of platelet

function. Individual treatment is critically dependent on the assessment of patient

risk and should be directed by laboratory measurements to ensure an appropriate

therapeutic response. In this thesis we focused on the anticoagulant properties

of two drugs, iloprost and MeSAMP, and described their pharmacological activity

through response surface modeling.

The work presented in Chapter 4 has multiple objectives. First, we intended to

investigate the concentration-effect relationship of the anticoagulants and provide a

quantitative description of their pharmacodynamics. Second, we studied iloprost-

MeSAMP pharmacodynamic interactions for both positive and negative effects.

Finally, we achieved suggestions of optimal drug dosing for antiplatelet therapy in

the individual.

The work provides experimental support for the applicability of the proposed

modeling framework in the clinical practice to evaluate drug usefulness and deliver

personalized therapy. It also yields clinically relevant information in terms of phar-

macodynamic parameters for the single drugs as well as drug interaction coefficients

for regimens employing iloprost-MeSAMP combinations.

Further research and experimental investigation is required to provide additional

5.2 Pharmacodynamic modeling for antiplatelet therapy 179

validation for the theoretical modeling framework discussed in the above. For in-

stance, in some clinical applications it may be desirable to take multiple positive

and/or negative pharmacological effects into account to achieve a global assess-

ment of therapy quality. The modeling platform could be expanded to fulfil this

requirement. Nevertheless, an important experimental limitation could arise in the

investigation of severe side effects in humans because of ethical reasons. Another

potential area of improvement is the lack of a pharmacokinetic model describing

drug distribution in the body. Combining drug kinetics and dynamics into the

framework would allow to associate drug dosing and therapy outcomes and directly

derive dosing recommendations for optimal therapy.

Regarding the results on antiplatelet therapy, our first successful experience with

iloprost and MeSAMP suggests in the future we should consider drugs of more

widespread use in the clinical practice. Moreover the study has been conducted in

vitro, therefore the clinical validity of the results still remains to be ascertained.


A

Clinical investigation:

antagonism of remifentanil

induced respiratory depression

by postoperative pain

182 A Antagonism of remifentanil induced respiratory depression by postoperative pain

A.1 Study investigators

Investigators:



Priv.-Doz. Dr. med. Martin Luginbuhl, Department of Anesthesiology and

Pain Therapy, University Hospital Bern, Switzerland

Dr. med. Dagmar Kaiser, Department of Anesthesiology and Pain Therapy,


Dr. sc. tech. Peter Schumacher, Department of Anesthesiology and Pain

Therapy, University Hospital Bern, Switzerland

Dr. med. Lorenz Theiler, Department of Anesthesiology and Pain Therapy,


A.2 Introduction

Opioids are frequently used for postoperative pain control and conscious seda-

tion. Respiratory depression is the most serious and potentially fatal side ef-

fect in intravenous patient controlled analgesia (IV PCA) with a frequency of

110% [172, 162, 40]. There remains a low but unpredictable risk of severe respi-

ratory depression even in young healthy patients because current monitoring tech-

niques and clinical practices are insufficiently reliable to detect opioids induced

respiratory depression (e.g. pulse oximetry in the presence of supplemental oxygen

administration [204]. In a recent closed claims study hypoxia due to respiratory

depression was the most frequent cause in cases with fatal outcome or permanent

brain damage in monitored anesthesia care [19]. Despite its favourable pharmacoki-

netic properties, respiratory depression during conscious sedation with remifentanil

was reported by several authors [103, 122, 171]. Bouillon and co-workers reported

a model for remifentanil induced respiratory depression in the non-steady state,

which can be used for dose finding [25]. In this model the effect of painful stim-

ulation is not included, however. The indirect response model accounts for the

respiratory stimulant effects of CO2, which invariably follows a drug-induced re-

duction of ventilation. The plasma remifentanil concentration inducing a reduction

of 50% in minute ventilation at constant PaCO2 is 0.92 ± 0.2 ng/mL according to

A.3 Study aims 183

this model. This concentration reduces alveolar ventilation to a reasonable 88% of

baseline in steady state, and compares well to the 50% minute ventilation reduction

found under iso-hypercapnic conditions in a previous study [150]. The non-steady

state indirect response model by Bouillon et al. describes drug effect and ventilation

changes at the same time and therefore better represents the clinical reality [25].

Experimental pain stimulation without analgesic drug administration was associ-

ated with increasing ventilation and decreasing end-tidal carbon dioxide concentra-

tion [166, 65]. Chronic intractable pain induced chronic hyperventilation [86] and

in patient under treatment with IV Morphine the sudden reduction of pain by a

peripheral nerve block is associated with an increased number of oxygen desatura-

tions [46]. Pain induced by diagnostic or therapeutic interventions such as percuta-

neous transhepatic cholangioplasty, shock wave lithotripsy in urology or postoper-

ative wound pain may therefore affect opioid induced respiratory depression. The

impact of pain on opioids respiratory depression has been poorly investigated so far.

Quantifying the impact of pain on opioid induced respiratory depression may help

to improve dosing guidelines and patient safety during postoperative pain treatment

and conscious sedation. The opioids most frequently used in anesthesia (fentanyl,

alfentanil, remifentanil and sufentanil) are pure receptor agonists. It can be as-

sumed that the analgesic effect is mediated by the same receptor as the respiratory

depressant effect. For alfentanil the C50 of respiratory depression in the absence of

painful stimulation (73 ng/ml) [30] is similar as the plasma alfentanil concentration

needed for postoperative analgesia (100 ng/ml) [104]. This suggests the analgesic

and respiratory depressant effect of opioids may be parallel. Recently a novel device

to measure transcutaneous CO2 has been validated (SenTec AG, Therwil, Switzer-

land) and a computer to measure alveolar ventilation (NICO monitor, Respironix

Inc. Pittsburg, PA, USA) is available. The respiratory effects of remifentanil and

painful stimulation will thus be directly measurable. The purpose of this open la-

bel observational cross-over study is to develop a model for remifentanil-induced

respiratory depression including a parameter for the presence or absence of painful

stimulation and to assess the analgesic effect of remifentanil titrated to moderate

respiratory depression (i.e. a transcutaneous PCO2 of 50 mmHg) on postoperative

wound pain. Further the previous clinical validation of the transcutaneous CO2

monitor shall be confirmed.

A.3 Study aims

The study aims at verifying the following hypotheses:


1. Postoperative pain will induce a significant respiratory stimulation and thus a

right-shift of the response curve of the remifentanil concentration on alveolar

ventilation or arterial PCO2. The inclusion of pain as a covariate will improve

the fit of the data on remifentanil induced respiratory depression measured

with PtcCO2 and alveolar ventilation (main hypothesis).

2. The PtcCO2 and the predicted plasma remifentanil equally predict the anal-

gesic effect of remifentanil.

3. Transcutaneous CO2 (PtcCO2) correlates closely with PaCO2 and PetCO2

in a dynamic situation.

4. PtcCO2 inversely correlates with the pain score (VAS 0-100)

A.4 Study design

Open label prospective observational study in a University Hospital (Inselspital).

A.5 Study methodology

A.5.1 Patient population

After approval by the ethics committee of the Canton of Bern and after obtaining

written informed consent 20 patients scheduled for major orthopedic surgery under

general anesthesia (with postoperative IV analgesia) with a planned duration of

surgery not exceeding 3 hours will be enrolled. Patients with ASA physical status

of III or higher will be excluded, i.e. patients with relevant neurologic, cardiac,

pulmonary, liver or kidney disease. Patients under analgesic treatment with opioids

or patients with alcohol or any drug abuse and patients under treatment with

central-nervous system affecting drugs (anti-depressants, sedatives, anti-epileptics)

will also be excluded.

A.5.2 Study plan

After a fasting period of 6 hours and without giving any sedative drug for pre-

medication the patients will be connected to a Datex AS3 anesthesia monitor (GE

Health Care, Helsinki, Finland) and to a SenTec transcutaneous PCO2 monitor

(SenTec single sensor monitoring, Therwil, Switzerland). A cannula is placed in

an antecubital vein for drug infusion. A continuous infusion of Ringer’s Lactate 2

A.5 Study methodology 185

Figure A.1: Study plan to evaluate the antagonism of opioid induced respiratory

depression exerted by postoperative pain. Preop test: first step-wise

increase of remifentanil to assess remifentanil induced ventilatory de-

pression without pain stimulation. Postop stabilization: first hour in

the PACU, titration of remifentanil to achieve VAS ≤ 30. Postop test:

second step-wise increase of remifentanil to assess remifentanil induced

respiratory depression with concomitant pain stimulation. Possibility

1: respiratory depression end-point with remifentanil concentration at

the end of postoperative stabilization not reached. Possibility 2: respi-

ratory depression end-point with remifentanil concentration at the end

of postoperative stabilization already reached.


ml/kg will be given and 2 mg of tropisetron (Navoban, Novartis, Basel, Switzerland)

will be injected i.v. A 20 G Flowswitch Viggo arterial catheter will be inserted after

local anesthesia into the radial artery of the non-dominant hand after confirming

patency of the ulnar artery with the Allen’s test [81]. A continuous positive airway

pressure mask will be placed and connected to a modified Mapleson D Bain Sys-

tem. At the y-piece of the breathing circuit a the NICO rebreathing system will

be inserted and connected to the NICO monitor (Respironix Inc. Pittsburg, PA,

USA). All data will be recorded on a laptop computer throughout the study using

Labview software (Labview version 5.0, National Instruments Corporation, Austin,

Texas USA). Heart rate, blood pressure, ventilatory rate, tidal volume, minute ven-

tilation, body temperature (esophageal probe) and inspiratory/expiratory oxygen

and carbon dioxide concentrations will be recorded from the Datex AS3 Monitor,

transcutaneous PCO2 and SpO2 from the Sentec Monitor and alveolar ventilation

will be computed by the NICO monitor based on CO2 production (ml/min) and

end-expiratory CO2 concentration. A graphical representation of the study plan is

presented in Figure A.1.

Part 1 (prior to surgery)

After recording baseline data for 10 minutes a target-controlled remifentanil in-

fusion will be started with an Alaris PK TCI syringe pump (Cardinal Health,

Basingstoke, Hampshire, UK) using the pharmacokinetic parameters by Minto and

co-workers [139]. Starting with 2 ng/ml the plasma target concentration will be

increased in steps of 2 (± 1) ng/ml until the respiratory rate falls below 5 min−1

for longer than 5 min. or until transcutaneous PCO2 is higher than 60 mmHg.

A 20 minutes equilibration period will be observed at each target concentration

(Figure A.2). When one of the endpoints of respiratory depression will be reached

the infusion will be stopped and the plasma remifentanil concentration be allowed

to passively decrease to zero. Arterial blood samples will be withdrawn at baseline,

2 min. before, and 2 min. after every increase of target concentration, as well as

immediately 2 min. before and 2, 5, 10 and 20 min. after stopping the infusion for

arterial blood gas analysis and measurement of plasma remifentanil concentrations

(12 samples).

Part 2 (during anesthesia and surgery)

Before induction the remifentanil target concentration will be increased to 4 ng/ml

and anesthesia will be induced with propofol (1.5 to 2.5 mg/kg). Tracheal in-


Figure A.2: Simulation of the ventilatory response to a remifentanil plasma con-

centration of 2 ng/ml according to Bouillon and coworkers [25]. Dot-

ted line: predicted plasma remifentanil concentration. Fine solid line:

predicted effect site remifentanil concentration. Dash-dotted line: pre-

dicted PaCO2. Thick solid line: predicted alveolar ventilation.

tubation will be facilitated with rocuronium (0.5 mg/kg). In cases operated in

prone position, 0.2 mg of glycopyrrolate will be given IV before turning the patient

from supine to prone position. Anesthesia will be maintained with desflurane in

80% oxygen, adjusted to keep the BIS between 40 and 60 and to maintain the

mean arterial pressure within ± 20% of baseline (= pre-induction value). During

surgery the remifentanil target concentration will be kept constant at 3 ng/ml in

order to avoid development of acute tolerance [2]. This concentration corresponds

to the plasma concentration, reached with a fixed infusion rate of 0.1 µg/kg min

which has been used by Guignard and co-workers [2] in a 40 year-old man with a

BMI of 27 (Simulation according to the pharmacokinetic parameters of Minto and


co-workers [139]). The patients that developed acute opioid tolerance received a

mean intraoperative remifentanil infusion rate of 0.3 µg/kg min [2], resulting in a

remifentanil plasma concentration of 8 ng/ml. During surgery tachycardia (heart

rate exceeding 100 min−1) not related to hypovolemia will be treated by boluses or

an infusion of esmolol, hypotension not due to hypovolemia with norepinephrine.

After surgery and postoperative x-ray control desflurane will be turned off, the

fresh gas flow will be increased to 10 l/min, residual neuromuscular blockade will be

antagonized with 2.5 mg of neostigmine and 0.5 mg of glycopyrrolate. The target

remifentanil concentration will be maintained at 3 ng/ml. If spontaneous respira-

tion does not start at this concentration, the target remifentanil concentrations will

be allowed to decrease in steps of 0.5-1 ng/ml until spontaneous respiration starts.

The patient will be extubated as soon as he/she responds to verbal command and

sufficient spontaneous respiration has resumed. 10 minutes after extubation the

pain score (VAS 0-100) will be assessed. If greater than 30 the remifentanil con-

centration will be increased in steps of 0.5-2 ng/ml until the pain score (VAS) is ≤30. Arterial blood samples for measurement of arterial blood gases and remifentanil

plasma concentrations will be withdrawn 15 minutes after skin incision and 10 min.

after extubation (2 samples).

Part 3 (PACU)

After transfer to the PACU the target remifentanil concentration will be adjusted

to maintain the VAS score ≤ 50 until one hour after PACU arrival. According to

the rapid elimination kinetics of desflurane [207] the end-expiratory concentration

one hour after extubation will be have been decreased to less than 10% of the value

before turning off the vaporizer before emergence (simulation based on the Yasuda

Model [207] assuming a duration of desflurane administration of 120 minutes).

Assuming an end-tidal desflurane concentration of 6 vol%, the concentration 1

hour after emergence will be around 0.5 vol%, which is even lower than the sub-

anesthetic concentration of desflurane (0.2 MAC) where van den Elsen and Dahan

did not find a significant effect on hypoxic or hypercapnic respiratory drive [73,57].

One hour after PACU arrival the patient will be asked to quantify the pain

intensity (VAS 0-100) and the actual target remifentanil plasma concentration will

be recorded. A tight fitting face mask is then attached and connected to the

modified Mapleson D Bain System. If the end-points of respiratory depression are

already reached at the target remifentanil concentration associated with a VAS ≤ 30

the remifentanil concentration will then be allowed to decrease in steps of 0.5 ng/mL


until the VAS score increases to 50. If the end-points of respiratory depression are

not reached the target remifentanil concentrations will be increased in steps of 0.5-2

ng/ml, until the end-points of respiratory depression are reached. An equilibration

period of 20 min. is observed at each target concentration unless pain intensity

is > VAS of 50. At each target plasma concentration the VAS score, the arterial,

end-expiratory and transcutaneous PCO2 will be recorded. After reaching the

maximal target remifentanil concentration the plasma remifentanil concentration

will be allowed to passively decrease to the mininal effective concentration or until

the VAS score is > 30. Data acquisition will be stopped 30 minutes later.

Arterial blood samples will be drawn on arrival in the PACU, at the minimal

effective concentration, 12 min. before and 2 min. after each change of the target

remifentanil concentration (during the upward titration) and 2 min. before and

2, 5, 10, 20, 40 and 60 minutes after reduction of the infusion rate for blood gas

analysis and measurement of plasma remifentanil concentrations (ca. 16 samples

depending on the number of titration steps).

The patients will be discharged to the ward according to clinical practice of the

department. During the decay of the remifentanil concentration fentanyl will be

given IV as soon as VAS is higher than 30 and a patient controlled analgesia with

fentanyl will be installed according to the clinical protocol of the department.

A.5.3 Model building

For the analysis we will make the following assumptions:

- The CO2-minute ventilation response curve in our patients is similar as in

the population investigated by Bouillon et al. [25].

- The postoperative wound pain between 1 and 2 hours after surgery will be

more or less constant.

- Potential acute opioids tolerance induced by remifentanil will similarly affect

analgesia and respiratory depression.

We will extend the models of the remifentanil induced respiratory depression

for steady state and non-steady state by Bouillon et al. [25] by a parameter for

pain stimulation. Under steady state conditions (stable CO2 and remifentanil) the

alveolar ventilation was estimated according to the following equation:

Valv(ss) = Valv(0) ⋅ (1 − Cp(ss)γC50γ +Cp(ss)γ )

1

F+1

(A.1)


where Valv(ss) and Valv(0) denote the alveolar ventilation at steady state and

at baseline, Cp(ss) the plasma remifentanil concentration at steady state, C50 the

plasma remifentanil concentration with 50% depression of alveolar ventilation and

F the gain of minute ventilation by increasing CO2 concentrations.

For the non-steady state they suggested the following model.

Valv(Cp, PecCO2) = Valv(0) ⋅ (1 − Cp(ss)γC50γ +Cp(ss)γ ) ⋅ (

PecCO2(t)PecCO2(0))

F

(A.2)

where Valv(Cp, PecCO2) denotes the alveolar ventilation at a given plasma con-

centration of remifentanil and a given effect site CO2 concentration, Valv(0) the

alveolar ventilation at baseline, Cp the plasma remifentanil concentration at time t,

C50 the plasma remifentanil concentration with 50% depression of alveolar ventila-

tion, PecCO2 the effect site CO2 concentration and F the gain of minute ventilation

by increasing CO2 concentrations. The effect site CO2 concentration was be com-

puted based on the parameters determined by Bouillon et al [25] according to the

following equation:

dPecCO2

dt= ke0 ⋅ (PetCO2(t) − PecCO2(t)) (A.3)

with PetCO2 denoting the end-expiratory CO2 concentration, and the ke0 the

end-expiratory-effect site equilibration constant for CO2. The same ke0 will be

used as determined previously [25].

We hypothesize that postoperative wound pain at a given effect remifentanil

concentration will increase alveolar ventilation. Repeated transcutaneous electri-

cal stimulation increased minute ventilation in volunteers breathing room air with

unclamped CO2 by 28%, i.e. Valv(stimulation) = 1.28 ⋅ Valv(baseline) [166]. Pain-

induced increase of baseline alveolar ventilation will be described as follows:

Valv pain(0) = Valv(0) ⋅ (1 +P ⋅K) (A.4)

where P denotes the presence or absence of pain stimulation (with P = 1 or

0) and K the increase of baseline alveolar ventilation during painful stimulation.

This equation will be applied in steady state as well as in non-steady state. Our

assumption is that pain will be constant during the second test period in the PACU,

implies that K is also constant during the test period.

Error models: proportional and exponential models will be used to describe the

interindividual variability of the parameters as appropriate:

θi = θTV ⋅ (1 − η(i)) (A.5)


or

θi = θTV ⋅ eη(i) (A.6)

where θi refers to the individual value of the respective parameter in the ith

individual and θTV is the typical value of the respective parameter in the population,

and η varies randomly between individuals with mean zero and variance Ω2. An

additive (constant SD) error model was chosen for residual variability:

DVobs =DVexp + ε (A.7)

DVobs refers to the observed value of the dependent variable DVexp refers to

the value predicted based on dose, time, and the individual pharmacokinetic and

pharmacodynamic parameters. ε is a normally distributed random variable with

mean zero and variance Ω2.

A.5.4 Measurement of remifentanil plasma concentrations

The arterial blood will be sampled in tubes previously prepared with citric acid

and centrifuged immediately after withdrawal. They will be frozen at −20 C

until analysis. The remifentanil plasma concentrations will be determined by gas

chromatography mass spectrometry as described previously [8].

A.5.5 Sample size calculation and statistics

In the previous study by Bouillon and co-workers 10 volunteer were tested [25].

In other previous pharmacokinetic-pharmacodynamic studies investigating a single

drug a sample size of 20 patients allowed to estimate the model parameters with

sufficient precision [71,70]. In interaction studies or in studies where more complex

models with a number of covariates were investigated a sample size of 40 to 60

patients have to be investigated [139,28].

The program system NONMEM, version V (GloboMax LLC, NONMEM Project

Team Hanover, MD, USA) will be used for all model fits and empirical Bayesian

estimation of the individual parameters. The population data of test 1 and test

2 (remifentanil ramp up with and without pain) will be fit for steady state and

non-steady state. The improvement of the fit by including pain as a covariate will

be tested using the log likelihood test, with a P < 0.01 considered significant.

The correlation of the transcutaneous, the end-tidal and the arterial PCO2 will

be tested with a Bland-Altman plot.

The correlation of the VAS score and the transcutaneous and the arterial PCO2

will be tested with a Spearman rank order correlation. The transcutaneous and the


arterial PCO2 and the predicted plasma remifentanil concentration associated with

a sufficient analgesia (VAS ≤ 30) will be determined in a receiver operator curve

plot.

The prediction probability (Pk) of the CO2 concentrations and the predicted

remifentanil concentrations to correctly predict sufficient analgesia will be deter-

mined according to Smith and co-workers [174].

A.6 Ethical aspects

Remifentanil is a short acting and easily titratable opioid, which is not routinely

used for postoperative analgesia in our department. It is regularly used, however,

for conscious sedation (e.g. for shock wave lithotripsy in urology). Opioid side

effects are of limited duration because of its rapid elimination by plasma esterases.

For study purposes an arterial cannula will be inserted and the patients will be

infused remifentanil before the induction of anesthesia for 45 minutes. The patients

have to tolerate a tight fitting face mask during the pre-operative and postoperative

testing of respiratory depression. The facemask is essential in order to measure

minute ventilation, tidal volumes and end-tidal carbon dioxide concentrations. The

patients will be informed about these points before enrollment.

The placement of an arterial line has a very low rate of serious complications,

provided a patent ulnar artery. Patency of the ulnar artery will be checked with

the Allen’s test before placement. Although the higher remifentanil concentrations

will decrease alveolar ventilation the patients will not become hypoxic because they

will breathe 100% oxygen. Hypercapnia will be limited to 60 mmHg. Because of

the rapid elimination of remifentanil a more serious respiratory depression would

be easily reversible after discontinuation of the remifentanil infusion. A short tem-

porary hypercapnia in the range of 60 mmHg is frequently observed immediately

after emergence of anesthesia and is well tolerated.

“Permissive” hypercapnia of even higher values is applied in patients with severe

ARDS.

Because of the rapid elimination of remifentanil with rapid decreases of effect site

concentrations a break through of pain is possible. In order to minimize this the

postoperative part of the study starts at an effect site remifentanil concentration

where the pain intensity is in the usual target level (VAS ≤ 30). The immediate

postoperative pain control will be similar as in routine cases since analgesic drugs

have often to be titrated in the first 3 hours after surgery. Pain scores of 50 or

higher are therefore not unusual in daily routine. The study will provide additional

A.6 Ethical aspects 193

basic data which may help to improve patient safety in postoperative analgesia with

opioids and during monitored anesthesia care.


B


determining the optimal drug

regimen in individual patients

with chronic pain

196 B Determining optimal drug regimen in individual patients with chronic pain

B.1 Study investigators

Investigators:





Dr. med. Urs Eichenberger, Department of Anesthesiology and Pain Therapy,


Dr. med. Jurg Schliessbach, Department of Anesthesiology and Pain Ther-

apy, University Hospital Bern, Switzerland

Dr. med. Andreas Siegenthaler, Department of Anesthesiology and Pain


Dr. med. Gorazd Sveticic, Department of Anesthesiology and Pain Therapy,


B.2 Introduction

In pain management, single drugs often do not provide satisfactory pain relief but

may at the same time cause unacceptable side effects. For example, adverse events

of opioids may restrict their use in non-cancer pain: substantial proportion of

patients on opioids (22%) withdraws from therapy because of adverse events [143].

Combining drugs that act at different receptors and on different pain mechanisms

may enhance pain relief and allow a reduction in the amount of single components.

In that way, the same analgesic effect with a lower incidence of side-effects may be

achieved.

Chronic neuropathic pain and musculoskeletal pain syndromes have enormous

medical, social and economic implications [87, 136, 60]. Even though various com-

binations of different drugs are commonly used in the therapy of these syndromes,

this practice is poorly supported by the published evidence [52]. There is very little

literature comparing a combination with a single-drug regimen. Furthermore, the

optimal doses of each combination regimen remain unknown.

In randomized controlled trials, two or more groups of different drug combina-

tions are usually investigated. However, when combining drugs at different doses,

B.3 Study design 197

hundreds of combinations are possible. For instance, if 5 different values for 3 drugs

are considered, 53 = 125 different combinations exist. Therefore, the optimal com-

bination is unlikely to be identified by randomized controlled studies, since a very

small proportion of all possible combinations are analyzed.

Further, even when a relevant randomized controlled trial generates a definite

answer, its result may not apply to an individual patient: regardless of the overall

trial result, some patients appear to benefit from the experimental therapy and

some do not. In addition, extrapolation may not be appropriate if the patient does

not meet eligibility criteria.

Double blind, randomized controlled trials of single subjects or individualized

medication effectiveness tests (n-of-1 trials or IMETs) have been developed to con-

firm or disprove the effectiveness of the treatment regimen in the individual patient6

and to provide useful information for clinical decisions [151]. A series of pair treat-

ment periods is used so that each patient randomly receives either active therapy

or placebo in crossover design manner.

No studies combining the n-of-1 paradigm with an optimization model to find an

optimal combination of drug regimen have been published so far.

In a previous study [51], we applied a model [16] to optimize drug combination for

thoracic epidural analgesia after major abdominal surgery. Later, we improved the

method and applied it to two additional studies: one on intravenous patient con-

trolled analgesia [182] and one on lumbar epidural analgesia after major orthopedic

surgery [183]. By using for the first time an optimization model in clinical inves-

tigations, these studies provided a new tool for optimizing clinical regimens [75].

Using this method, the optimum can be reached by investigating a limited number

of combinations [51, 16, 182, 183,75].

The aim of the present study is to find the optimal combination of different drug

regimes for individual patients with neuropathic or chronic musculoskeletal pain by

using a scientific method as an alternative to the empirical dose finding strategy

currently used.

The optimal combination is defined as the one producing the highest analgesic

effect with an acceptable incidence of side effects. To this purpose, we will develop

and apply for the first time a model of stepwise individual optimization of drug

combination.

B.3 Study design

Observational, single center study, setting: University Hospital Bern


B.4 Study methodology

B.4.1 Drugs used

Amitriptyline (Tryptizol)

Analgesic action of tricyclic antidepressants (TCAs) has been extensively studied

and proven [138]. Antidepressant drugs have been showed to be effective in variety

of neuropathic pains and are often the first choice treatment, the best evidence

available being for amitriptyline [164]. The use of anti-depressants in the treatment

of regional musculoskeletal pain conditions is only weakly supported by results from

controlled clinical trials [115].

Pregabalin (Lyrica)

Antiepileptic drugs are commonly used in the treatment of chronic neuropathic

pain. Results from clinical trials have been positive in the treatment of trigeminal

neuralgia, painful diabetic neuropathy (DPN) and postherpetic neuralgia (PHN)

[198, 179, 191]. The availability of newer anticonvulsants tested in higher qual-

ity clinical trials has marked a new era in the treatment of neuropathic pain.

Gabapentin has the most clearly demonstrated analgesic effect for the treatment

of neuropathic pain, specifically for treatment of painful diabetic neuropathy and

postherpetic neuralgia [191]. Efficacy, tolerability, and safety of pregabalin for

treatment of chronic neuropathic pain associated with DPN or PHN was demon-

strated in randomized controlled trial [80]. Pregabalin reduced symptoms of pain,

disturbed sleep, and fatigue compared with placebo in the treatment of fibromyal-

gia syndrome (FMS), characterized by widespread musculoskeletal pain and low-

ered pain threshold [49]. It was well tolerated and improved global measures and

health-related quality of life.

Oxycodone (Oxycontin)

Opioids are increasingly used in the treatment of chronic non-malignant pain. Effi-

cacy and safety of oxycodone in ambulatory patients with moderate to severe non-

cancer pain (low back pain, osteoarthritis pain, postherpetic neuralgia and painful

diabetic neuropathy) requiring opioid therapy was demonstrated in randomized-

controlled trials [93, 82, 108, 45].

B.4 Study methodology 199

Drug combinations

The combinations used for each study subject will be determined according to

previous medication or personal judgment of the practicing chronic pain specialist.

Possible drug combinations are:

1. Amitriptyline and pregabalin

2. Amitriptyline and oxycodone

3. Pregabalin and oxycodone

B.4.2 Patient population

Recruited at the Division of Pain Therapy, patients suffering from chronic neuro-

pathic and chronic musculoskeletal pain will be studied. A definite diagnosis of

neuropathic or chronic musculoskeletal pain will be made by an experienced, prac-

ticing chronic pain specialist, based on the history of daily pain lasting at least 6

months [135]. Written informed consent will be obtained by all patients.

Patients will have to complete at least 4 daily pain diaries during the 7 days

prior to randomization, using a visual analogue scale with 0 as ‘no pain’ and 10 as

‘worst possible pain’, with an average score ≥ 3 out of 10 over this period being an

inclusion criteria to participate in the study.

Exclusion criteria include: age < 18 yr, pregnancy, occurrence of unacceptable

side effects with drugs investigated, known renal impairment, epilepsy, clinically

significant hepatic disease, significant neurological or psychiatric disorders unrelated

to the chronic pain, other severe pain that might impair the assessment of the

investigated pain syndrome and illicit drug or alcohol abuse.

B.4.3 Study plan

Each combination will be given during 1 week without a washout period. The

initial complex will include 4 combinations at choice of the investigator, that are

expected to produce analgesia with no or minimal side effects. Thus the initial set

of combinations will be studied during a period of 4 weeks. Patient will get a set of

standard dose capsules to take every 12 hours during the week. Patients, physician

in charge, staff who informed patients and collected the data will not be aware of

the dosage of the drugs used at the particular optimization step.

The hospital pharmacy will take care of the correct dose and blinding, using

neutral looking capsules containing the investigated regimen defined by blinded

investigators for each optimization step.


B.4.4 Optimization procedure

The procedure is a modification of the novel optimization method previously applied

in a clinical study for post-operative pain management1. The aim of the procedure

is to optimize the analgesic effect, i.e. to minimize the pain score. To this purpose,

the optimal combination of drug A and drug B is sought. Constraint of the search

procedure is an unacceptable incidence of side effects. When a combination hits

the constraint, a regression algorithm is applied to bring the search back to the

therapeutic range.

The investigation consists of sequential optimization steps. The basic principle

is to utilize the results obtained by the analysis of a group of combinations to

create subsequent combinations in a stepwise manner, until optimal analgesia with

an acceptable incidence of side effects is reached. The group of 4 combinations

analyzed at each step is named a “complex”. The following procedure is used for

each complex.

1. Analysis of analgesia and side effects of the combinations included in the

complex studied.

2. Identification of the combination characterized by the worst analgesic effect

or associated with an unacceptable incidence of side effects. This combination

is not included in the subsequent complexes.

3. Creation of a new complex of combinations. This complex includes the best

3 combinations of the previous complex (best analgesia with acceptable in-

cidence of side effects) and the new combination generated from the results

obtained with the previous complex. This new combination is identified by

applying the novel optimization method presented in the recent work by Sveti-

cic and colleagues [183]. The new combination replaces the one mentioned in

point 2. The new combination is then administered to the patient.

4. Application of the procedure 1-3 to the new complex.

The optimization procedure is interrupted when no further improvement in the

mean pain score is achieved after three consecutive steps.

Rules of the search include: minimum and maximum value of variables, minimum

increase (lowest clinically relevant dose increment) and maximum increase (highest

safe dose increment) of variables, and constraints (Table B.1).

For oxycodone there is no upper limit, because for clinical use opioids are ad-

ministered according to analgesia and side effects without maximum dose levels.

B.4 Study methodology 201

Drug Minimum Maximum Minimum Maximum

value [mg/d] value [mg/d] increase [mg/d] increase [mg/d]

Pregabalin 50 600 50 150

Oxycodone 10 no maximum value 10 30

Amitriptyline 10 100 10 25

Table B.1: Drug doses and adjustments

B.4.5 Data collection

Each patient will be assessed as usual in our pain clinic. Demographic variables,

general medical status, social environment, pre-treatment and concomitant disease

will be noted.

The change in mean weekly pain diary score from baseline to average in last

4 days of each study week will be considered as the primary efficacy parameter.

Every 8 hours patients will assess the pain using the visual analogue scale with 0

as ‘no pain’ and 10 as ‘worst possible pain’. Baseline score is defined as a mean of

the last 7 pain diary entries preceding visit 1. The combination weekly mean pain

score (end point) is the mean pain score from the last 4 days preceding therapy

change visit.

Secondary parameters are the diary assessment drug specific side effects, quality

of life using the Short Form-36 (SF-36) Health Survey [202] and depression using

the Beck Depression Inventory [11].

Patients will be assessed every week at scheduled visits for reports of pain and

adverse events (elicited by non-specific questioning). Data for the SF-36 and Beck

Depression Inventory will be collected at baseline and at the end of the study.

B.4.6 Sample size calculation and statistics

For this kind of study, no power analysis can be made, since the data are not

analyzed for statistical significance [16, 15]. We believe that the model can be

reasonably evaluated by analyzing 15 patients per combination. Dropouts are not

considered.


B.5 Ethical aspects

Combining drugs for treatment of chronic pain is common practice. In our study,

we will use only already established drug combinations in the usual dosages, our

aim being the optimization of a therapy that would be implemented independent

of the participation in the study.

The basic optimization method has been used in 2 previous investigations on

epidural analgesia [51, 183] and in one on patient controlled analgesia [182]. This

model led to a progressive reduction in the incidence of side effects and to an

improvement in the quality of analgesia. No complications have been observed. In

the present study, we will use an improvement of the previously used optimization

models, based on a retrospective analysis of the data collected in the previous

investigations and adjusted for the use in individual patients.

We therefore do not expect additional hazards resulting from the study.

B.6 Expected benefits

For chronic pain patients, pain is one of the most important symptoms affecting

the quality of their life, social functioning and social costs. Pain treatment is one

of the most relevant aspects characterizing the quality of patient care. Providing

an optimal pain therapy is an ethical commitment.

The identification of the optimal combination can improve treatment of chronic

pain and reduce the incidence of side effects. This might improve the quality of life

and reduce the social costs.

There is a lack of published data on the use of drug combinations. Research

on drug combinations may offer a perspective of better treatment of these difficult

pain conditions.

Scientific based approach should be preferred to the purely empiric criteria usu-

ally employed to select the combinations analyzed in randomized controlled trials.

The presented novel model for optimizing therapy in individual patients can repre-

sent a useful tool in future clinical research, not only in the field of pain manage-

ment.

B.7 Subprotocol: Time profile of pharmacological side effects 203

B.7 Subprotocol: Time profile of side effects

caused by oxycodone, pregabalin and

amitriptyline

B.7.1 Background

It is known that all the three investigated drugs cause side effects mostly at the

beginning of the titration phase. These side effects may decrease or disappear

during treatment in part of the patients. However, there have been no studies

that formally addressed the issue of time course of side effects. This information

is important to establish a profile of the three drugs investigated before they are

combined for the optimization study. Furthermore, the results would be clinically

relevant, since better information of patients on the time profile of side effects could

increase compliance and adherence to treatment.

B.7.2 Study aims

To describe the time factor of side effects for oxycodone, pregabalin and amitripty-

line.

B.7.3 Study methodology

Patient population

All consecutive patients who are referred to our pain unit for ambulatory evaluation

will be potential participants. Additionally, patients will be recruited by advertise-

ment in local newspapers as for the optimization study. Patients will be included

in the study if one of the three drugs investigated will be clinically indicated.

Ongoing treatment with either an opioid, antiepileptic or antidepressant is an ex-

clusion criterion for recruiting patients in the oxycodone, pregabalin and amitripty-

line groups, respectively. Further exclusion criteria will be the same as for the main

study approved by the ethics committee: pain duration < 6 months, age < 18 yr,

pregnancy, occurrence of unacceptable side effects with drugs investigated, known

renal impairment, epilepsy, clinically significant hepatic disease, significant neuro-

logical or psychiatric disorders unrelated to the chronic pain, other severe pain that

might impair the assessment of the investigated pain syndrome and illicit drug or

alcohol abuse.


For this kind of study, no power analysis can be made, since the data are not

analyzed for statistical significance. We believe that the model can be reasonably

evaluated by analyzing 30 patients per drug.

Assessments

Each patient will be assessed as usual in our pain clinic. Routinely collected pa-

rameters include: demographic characteristics, pain intensity (BPI), work status,

interference of pain with daily activities (MPI), depression (BDI), catastrophizing

(CSQ-subscale), pressure algometry at 2nd toe and DNIC by ice water test.

Patients will be asked to fill daily a pain diary (Schmerztagesbuch) for one week

before start of the study medication and during the whole period of the study.

Patients will be assessed every week at scheduled consultations for reports of

pain and adverse events (nausea, dizziness, tiredness, and others to be defined by

the patient) as recorded by the pain diary. At the end of each dose step, overall

change compared with the previous dose step will be assessed by the Patient Global

Impression of Change Scale, whereby the change is rated as one of 7 categories, from

‘very much improved’ to ‘very much worse’ [67]

Medication

The choice of one of the three drugs will be left to the treating physician according

to the optimal treatment for the individual patient. Only one of the three drugs

is administered, i.e. no combination of the three drugs is prescribed. Concomitant

intake of other analgesics is at best avoided by stopping medication. However, if

the clinical indication is given, the intake of drugs of other classes is allowed, as

long as they are known not to cause any of the side effects listed above.

Patients and doctors will not be blinded to the study medication in order to

mimic clinical conditions as close as possible. The following titration schedules will

be used.

- Oxycodone slow-release (one dose every 12h): 5-5, 10-10, 20-20, 30-30, 40-40,

50-50.

- Pregabalin (one dose every 12h): 50-50, 100-100, 150-150, 150-150-150 (one

dose every 8h), 300-300 mg.

- Amitriptyline slow-release (one dose every 24h): 0-0-25, 0-0-50, 0-0-75, 0-0-

100 mg.

B.7 Subprotocol: Time profile of pharmacological side effects 205

The increase in dose will be made taking into consideration the pharmacoki-

netic characteristics of the drugs, in particular the time to reach a steady state.

These times are 24h [161], 24-48h [13] and 7-10 days for oxycodone, pregabalin

and amitriptyline (including the main metabolite nortriptilyne), respectively. We

therefore define the following minimal titration times for each dose:

- Oxycodone slow-release: 7 days;

- Pregabalin: 7 days;

- Amitriptyline: 14 days.

Side effects will not be treated pharmacologically. Whenever side effects are

observed, the following procedures will be adopted:

1. mild side effects with little or no impairment of daily life: increase the dose

as described above;

2. moderate side effects with significant impairment of daily life: no increase in

dose in the following week;

3. strong and intolerable side effects: reduction in dose to the previous step;

discontinuation of the treatment only if the patient is not willing to continue

or if clinically indicated.

Titration will be stopped when a reduction in pain intensity that is rated as

satisfactory by the patient is reached.

Analysis

The measurements on the time behavior of the side effects will be analyzed and

modeled in order to describe the transient overshoot in effect magnitude upon

increase of dosage. Possibly also the response to dosage decreases will be analyzed.

A mathematical model of pharmacodynamics will be proposed that captures the

transient and steady state behavior of the effects and that will necessarily deal

with issues of non-linearity and physiological variability. The characteristics of the

effect vs. time curve (amplitude, time constant of decay, time delay, etc.) will be

estimated from the data measured in patients.


Ethical aspects

The patients receive assessments and treatments according to the routine of our pain

unit. The drug is chosen based on the optimal treatment for the individual patient.

The protocol is a preparation for the study approved by the ethics committee, using

the same drugs according to the routine of the pain clinic. According to the rules

of the local ethics committee, no permission is required.

Expected benefits

There are no data on how fast and how often side effects decrease over time. This

represents a problem when these drugs are combined in the planed study on the

optimization procedure. Furthermore, this knowledge is important for better infor-

mation of patients on the expected resolution of side effects.

C


a novel procedure

for provocation discography

208 C A novel procedure for provocation discography

C.1 Study investigators

Investigators:





Dr. sc. tech. Peter Schumacher, Department of Anesthesiology and Pain


Prof. Paul Heini, Department of Orthopedic Surgery, University Hospital

Bern, Switzerland

Prof. Lars Arendt-Nielsen, Center for Sensory-Motor Interaction, University

of Aalborg, Denmark

C.2 Introduction

Chronic low back pain is a common medical problem. One of the possible causes

is a disruption in the annulus fibrosus of an intervertebral disc. Since the annulus

fibrosus, especially its outer third, is strongly innervated [23], degenerative changes

or internal tears can result in chronic nociceptive stimulation causing low back pain

as well as referred pain to the lower extremities. These internal disc disruptions

are radial fissures which extend to the inner (grade 1 of disruption), the middle

(grade 2), the outer third (grade 3) or even spread circumferentially (grade 4)

within the annulus [165]. They are predominantly located in the posterior part, i.e.

the area of innervation of the sinuvertebral nerve. Intradiscal lesions, however, are

hardly revealed by imaging techniques such as CT or MRI, so that the diagnosis of

discogenic pain is difficult to make in a first attempt by these means [22].

Provocation discography is generally accepted as the gold standard method for

the diagnosis of discogenic pain. A spinal needle is inserted into the nucleus pul-

posus of the suspected disc (as well as into two additional discs serving as negative

controls) under X-ray view. Contrast medium is then injected into the nucleus,

continuously augmenting intradiscal pressure. The pressure that is recorded at the

first appearance of the contrast medium is termed “opening pressure”. As pressure

rises proportionate to the amount of injected fluid, the patient is repeatedly asked

C.2 Introduction 209

whether he feels pain, and, if so, whether this pain is concordant (i.e. the same

pain, radiating to the same areas it usually does). The pain intensity is recorded

on a numeric rating scale (NRS), i.e. a scale on which the patient indicates his

actual pain intensity within an interval ranging from 0 (no pain) to 10 (strongest

pain imaginable). With the contrast medium still in the disc, a possible lesion

can be detected either by X-ray during discography, or on following CT. In case

of a positive result of discography, surgical fusion, disc prosthesis or intradiscal

electrothermal annuloplasty (IDET) can be therapeutic options.

The criteria according to which a disc is considered positive are defined by the

International Spine Intervention Society (ISIS). It is important to emphasize that

healthy discs usually do not hurt upon pressure application during discography

(hence the two negative controls), or, in few cases, only when pressure rises to high

levels. Because pressure levels are continuously monitored during the procedure,

it is possible not only to determine whether a disc is positive, but also to asses its

exact pain threshold.

The lower the pain threshold of the stimulated disc is, the stronger the evidence

that the disc is the source of pain. Conversely, the higher the threshold is, the more

probable a false-positive results. Such false-positive responses can be, for instance,

due to subjective components in pain perception or to altered pain processing re-

sulting from central sensitization. One possible hypothesis suggests that perpetual

nociceptive input from chronic painful processes in adjacent structures, e.g. the zy-

gapophysial joint, may lead to extension of the receptive field of sensory neurons to

the intervertebral disc and to lowering of the pain threshold when stimulating that

disc. In this case, the disc could be considered positive by discography, although

the true pathology lies in a different anatomical site [33].

There are a number of problems associated with the procedure that may seri-

ously impact the validity of the diagnostic information gained form it. First and

probably foremost is that the increase of intradiscal pressure is not standardized

and, depending on lesions and the morphology of the disc, cannot be properly con-

trolled by the performing physician. Especially if lesions are present the intradiscal

pressure increase will be linked by a non-linear and time variant relationship to

the amount of injected contrast medium. Secondly the pain intensity rating of the

patient during the procedure is by nature a subjective rating. It is additionally

influenced by the communication between physician and patient, e.g. the time in-

terval between questions and also possible misunderstandings between patient and

physician. Thirdly there is no blinding of the physician in regard to the investigated

disc, the physician knows whether he/she is examining the control or suspected disc

which in turn might influence his/her assessment. Without explicit evidence These


combined factors likely result in a high inter- and intraobserver variability which

make it difficult to arrive at diagnostic conclusions that are fully reproducible and

therefore meaningful.

C.3 Study aims

In this study we present a novel method to perform provocative discography that

addresses above mentioned problems of conventional discography. This method

has the potential to deliver more reliable and reproducible results for the diagnostic

assessment of discogenic pain. In a first phase we will develop the technical platform

to standardize the provocative discography procedure. In a second phase we will

perform an exploratory clinical proof of concept study to verify the feasibility of

the method and to investigate the benefits of the new procedure.

Properties of the new platform are defined as follows:

- the intradiscal pressure is increased continually, the physician can select an

increase rate, e.g. 10 PSI/minute

- the necessary flow of the contrast medium is automatically adjusted by the

system and also recoded together with the pressure for later review

- the patient gets a simple control panel with a button interface with the in-

struction to a) press the button as soon as he/she can feel the effect of injec-

tion of contrast medium and to b) press the button again if he/she is feeling

intolerable pain

- safety aspects:

◾ the system guarantees that the a maximum intradiscal pressure (i.e. 100

PSI according to the ISIS guidelines) or the preselected increase rate are

not exceeded and that the pressure is never negative

◾ the system does not inject more contrast medium per disc as has been

preselected; for routine cases, the maximum volume will be 3 ml accord-

ing to the ISIS guidelines

◾ at all times an emergency button assures the possibility that the system

returns to a safe state and that the case can be continued manually if

needed

◾ the relevant requirements as per RL-93-42-EWG have to be observed

C.4 Market background 211

The study aims in the second phase will be to show the a) feasibility of the pro-

posed measuring method and apparatus and b) the reproducibility of measurements

performed with the method. Our hypothesis is that a) the measuring method is

technically feasible and applicable in the clinical setting; b) the maximum tolerable

intradiscal pressure can be reproduced in multiple measurements with a standard

deviation that is on average less than 5 PSI.

C.4 Market background

No commercial system is available that has the required properties. A prototype

system has to be developed and built for this proof of concept study. Based on a

publication or patent submission an industrial partner can then be contacted for co-

operation and for further development of the technology and the method/procedure.

Two injection systems including pressure monitoring are currently commercially

available. Merit Medical (Merit Medical Systems, South Jordan, UT, USA) sells

the Intellisystem II monitor combined with the Intellisystem 25 syringe, originally

launched for angioplasty purposes allowing pressures up to 25 bar (approx. 350

PSI). Stryker (Stryker Corporation, Kalamazoo, MI, USA) has recently released

the Discmonitor device, a disposable syringe with integrated pressure and flow

monitor. The device was developed for provocative discography but is listed as

substantially equivalent to the Merit Medical system and is therefore also listed as

an angioplasty device.

C.5 Solution proposal

Ideally a prototype development would build on one of the commercially available

devices to avoid potential problems with the approval of the study. Those devices

have the proper mechanical structure, built in sensors and are approved for the

intended clinical procedure.

A prototype will therefore consist of a mechanical apparatus that accommodates

one of the commercial syringes. The apparatus will have a motor that can drive

the screw piston of the syringe. The motor will be controlled by an xPC real time

system running a control algorithm to precisely control the pressure measured via

the pressure sensor of the syringe. The real time system will furthermore read and

process the data from a simple control panel that records the patient reactions

to the induced pain. To complete the system a graphical user interface running

on a separate notebook computer will be provided that allows interaction with the


system. The control algorithms and the user interface will be developed and verified

with Matlab/Simulink (The MathWorks Inc, Natick, MA, USA).

C.6 Bench testing

During the development of the control algorithms a comprehensive model of a

disc will be tested in multiple configurations in software simulations to maximize

robustness of the algorithms. Before the system will be applied to patients it will

undergo extensive bench testing. To this end a laboratory model of a disc will

be built to actually test the behavior of a variety of possible morphologies and

flow/pressure relationships in the final configuration. Special attention will be

given to the safety functions of the system.

C.7 Study design

The study will be carried out at the University Hospital of Bern, Department of

Anesthesiology, Division of Pain Therapy. It is a prospective, observational clinical

trial.

C.8 Study methodology

C.8.1 Patient population

Ten patients with low back pain for at least 6 months will be studied. The patients

will be recruited at the Division of Pain Therapy by usual referral for evaluation

and treatment. Inclusion criteria: Patients scheduled for discography (independent

of the study), pain duration of at least 6 months. Sufficient knowledge of German,

French or Italian language. Exclusion criteria: Usual exclusion criteria for patients

undergoing discography in clinical setting. A written informed consent will be

obtained from all patients.

C.8.2 Study plan

Before the procedure, pain intensity using the visual analogue scale (VAS) will be

recorded (0 = no pain, 10 = worst pain imaginable). Furthermore, the patient will

draw on an anatomical map the area where pain is felt.

C.8 Study methodology 213

Figure C.1: Example of the intradiscal pressure time course during an experiment

in one disc.

Discography will be performed based on the ISIS practice standards for lumbar

disc stimulation and following the routine standards of our institution. The pressure

increase for pain provocation will not be done manually but with the automatic

system which guarantees a continuous increase of the intradiscal pressure at a

selectable rate.

All discs that can potentially be the cause of the patient’s clinical findings as well

as at least one unsuspicious control disc will be tested. The nucleus pulposus of the

discs will be injected with non-ionic contrast medium (Omnipaque 300) combined

with an antibiotic (Cefazoline 2 g or, if allergy is suspected, Clindamycine 600

mg) through a syringe with an integrated pressure transducer connected to the

automatic system as described above.

At first the intradiscal pressure increase rate is set to 5 PSI/minute. The opening

pressure (OP) is recorded by the physician via user interface. As soon as the patient

feels the injection pressure he/she presses the button on the user control panel. The

related pressure is recorded (P0) and the pressure increase is stopped; the system

will maintain a constant pressure. The physician then continues the procedure

via the user interface panel at a pressure increase rate of 20 PSI/minute up to a

maximum of 100 PSI. When the patient cannot tolerate the pain anymore he/she

again pushes the button. The related pressure is recorded (P1). Furthermore,

pain intensity by VAS is assessed and the patient draws he area of pain on an


anatomical map. The pressure is then reduced by 20 PSI and maintained constant.

If the pain is still not tolerated the pressure is manually decreased via user interface

until accepted by the patient. The patient will then be asked whether the pain

was discordant or concordant. After a waiting period of at least 2 minutes the

pressure increase procedure is repeated twice for pressures P2 and P3 for multiple

measurements per disc (Figure C.1). Pressure and flow will be recorded at least with

an interval of 1 second at all times during the procedure and stored electronically.

The procedure will be stopped when the defined maximum of contrast medium has

been injected or a pressure of 50 PSI above the opening pressure has been reached,

independent whether all measurements (P0-P3) have been collected or not. The

whole procedure is then repeated for preferably two but at least one control disc.

Modified ISIS criteria for categorizing a disc as probably positive are:

A. The patient feels the pain during pressure increase as intolerable and presses

the button.

B. The pain is concordant.

C. The pain intensity is at least 7/10 on the numerical rating scale (NRS, where

0 = no pain, 10 = worst pain imaginable).

D. The pain that is reproduced is produced at a pressure less than 50 PSI above

opening pressure.

E. Stimulation of adjacent discs provides controls such that

when only one adjacent disc can be stimulated,

1) that disc is painless, or

2) pain from that disc is not concordant and is produced at a pressure

grater than 50 PSI above opening pressure;

when two adjacent discs can be stimulated,

1) both discs are painless, or

2) one disc is painless and

3) if the other disc is painful, that pain is not concordant and is produced

at a pressure greater than 50 PSI above opening pressure.

C.8.3 Feasibility and applicability of the automatic system

To evaluate the performance of the novel automatic system the following data will

be analyzed:

C.8 Study methodology 215

Setpoint precision

The actual control precision of the preset pressure and pressure increase rate will

be calculated using the mean absolute deviation (MAD), defined as follows:

MADi = 1

Ni

Ni

∑j=1∣pmeasured(i, j) − preference(i, j)∣ (C.1)

being Ni = total number of measurements during observation period for subject

i.

Safety

Number of incidents will be counted that are relevant to the safety of the procedure:

- use of emergency button

- manual continuation of the procedure because of perceived unsafe or unsat-

isfactory performance (no emergencies)

- violation of pressure limits

Outcome

The capability to reproduce pain threshold measurements within a single disc will

be quantified by the average standard deviation of the P1, P2 and P3 pressure

levels found a) in the multiple discs assessed in one patient, b) in all suspected

discs of the study population, c) in all control discs of the study population and d)

in all discs.

C.8.4 Pressure pain threshold

We will assess the patient’s pain detection and pain tolerance threshold using a

pressure algometer, whose probe has a surface area of 1 cm2 (Somedic AB, Stock-

holm, Sweden). Pressure will be increased from 0 to max. 1200 kPa at a rate of

30 kPa/s. Pain detection threshold is defined as the pressure at which the sensa-

tion turns to pain. Pain tolerance threshold is defined as the point at which the

subject perceives the pain as intolerable. Before each session, the subjects will be

allowed to get accustomed to the procedure by performing several measurements

for training until they are familiar with it. The PPT will then be registered three

times at each site and the arithmetical means of these three measurements will be


used for data analysis. Three different sites will be measured: painful area of the

back, non-painful area of the back on the same side and the ipsilateral great toe.

C.8.5 Further assessments

All patients who are referred to our clinic, independent of the participation in a

study, are asked to fill in our standard questionnaires, the Beck Depression Inven-

tory BDI and the SF-36, before the first consultation. The BDI assesses possible

changes in mood and depressive tendencies associated with chronic pain, whereas

the SF-36 provides a more general insight in quality of life, considering basic activi-

ties of daily living, reductions in physical activities or restricted working capability.

Additionally, all patients are asked to draw the location of their pain on an anatom-

ical map, thereby indicating the “target pain” as well as radiating pain (if existent).

We will use this data for descriptive statistics in our study population.

C.9 Time schedule

The development and verification of the technology in the first phase of the study

will require a time period of 9 month. Estimated duration of phase two, clinical

experiments: 18 month. The procedure will be performed in one session. 1) Before

discography: collection of demographic and clinical data, BDI and SF-36 (as rou-

tinely performed), PPT test, assessment of pain area, VAS score. 2) Discography

with recordings of: pain quality, intensity on NRS, pressures OP, P0, P1, P2 and P3

and pain area on anatomical map for every painful disc separately. 3) 30 minutes

after discography: PPT test and VAS.

C.10 Data analysis

C.10.1 Main aim

The main goal of the study is to Demonstrate the feasibility and reproducibility

of the novel measuring procedure. Acceptable performance of the novel system

within the scope of this proof of concept will be based on the following minimum

requirements based on the inclusion of 10 patients:

C.10 Data analysis 217

Setpoint

- an average MAD of less than 5 PSI and not more than 10 PSI in one single

patient

Safety

- no use of the emergency button

- a maximum of two patients where the procedure has to be finished manually

(not counting those patients where the systems stops injecting because the

maximum amount of contrast medium has been reached)

- overall violation of pressure limits less than 30 seconds, but not more than 5

seconds in a single patient

Outcome

- the maximum tolerable intradiscal pressure can be reproduced in multiple

measurements with a standard deviation that is on average less than 5 PSI

As observational data we will present:

- the average of the P1-3 pressures will be correlated to the PPT findings

- the opening pressures (OP) and the P0 pressures will be correlated

C.10.2 Secondary aim

The secondary goal of the study is to determine the presence of central hypersen-

sitivity in patients. The patient’s PPT will be compared by the Student’s t-Test

to a historic control group from a previous study on healthy volunteers [50] which

showed a mean pressure pain tolerance threshold of 663 kPa and a standard devi-

ation of 149, measured at the foot. A recent study on whiplash patients [95] with

central sensitization showed mean values of 354 kPa and a standard deviation of

96, measured at the foot. Considering a difference of 300 kPa, assuming a standard

deviation of 150 and setting α = 0.05 and β = 0.8, a sample size of 6 subjects per

group would produce enough power to detect a difference between the groups, our

study is therefore powered enough to show this difference.


C.11 Ethical aspects

Patients would undergo discography anyway, independent of the participation in

the study. The use of the automatic injection system will not increase the risk

exposure, as the pressure increase will be smooth and controlled and less jerky as it

could be when performing the procedure manually. An emergency button and the

presence of additional personnel will guarantee a safe procedure at all times, even

when the system starts to malfunction. Pressure algometry has been widely used

by several research groups, including ours, e.g. [6, 50, 159]. No damage has been

observed yet, nor are we aware of any risk associated with this method.

C.12 Expected benefits

Chronic low back pain is an important medical and socio-economic problem, as it

causes huge suffering and costs to the society. The identification of the source of

pain remains an essential clinical problem, preventing the development of appro-

priate treatment modalities. If the hypotheses of this study are confirmed, a new

tool for the diagnosis of discogenic pain could be developed. Central hypersensi-

tivity is thought to be an important mechanism in chronic pain, but its role in

the determination of discogenic pain is still unknown. There is an urgent need to

clarify whether findings of animal research on central sensitization are applicable

in clinical pain conditions.

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Curriculum Vitae

Personal Data

Name Antonello Caruso

Date of Birth April 25, 1981

Place of Birth Milan, Italy

Nationality Italian

Marital Status Single

Education

1/2006 - 12/2009 PhD Student: Automatic Control Laboratory, ETH Zurich,

Switzerland.

Research areas: Modeling, control, and optimization for anes-

thesia pharmacology and personalized drug dosing.

Supervisor: Prof. Manfred Morari.

2005-2007 Postgraduate Diploma of Advanced Studies in Applied Statis-

tics, ETH Zurich, Switzerland.

2000-2005 Bachelor and Master in Biomedical Engineering: Politecnico di

Milano, Italy.

2003-2004 Visiting Erasmus student at Lulea University of Technology,

Sweden

1998-2000 International Baccalaureate Diploma Programme: United World

College of the Adriatic, Duino (TS), Italy.

1995-2008 High School: Liceo Scientifico Statale ”Vittorio Veneto”, Milan,

Italy.

Experience

1/2006 - 12/2009 ETH Zurich, Switzerland: Researcher at the Automatic

239

240 Curriculum Vitae

Control Laboratory: Creation of drug delivery technology IP

and commercialization via a licensing deal.

1/2006 - 12/2009 ETH Zurich, Switzerland: Teaching Assistant: Laboratory

experiments on control design, MatLab courses.

7/2002 - 9/2002 De Marchi Hospital, Milan, Italy: Internship at the Hos-

pital’s Biomedical Technology Laboratory.

Languages

Italian Native language

English International Baccalaureate (I.B.) bilingual diploma

Spanish Excellent

German Fair

Publications

Intellectual property

A. Caruso, T. Bouillon, M. Luginbuhl, M. Morari, P.M. Schumacher, E. Zan-

derigo, ”A system for controlling administration of anaesthesia,” Patent number:

WO 2007147505, Assignee: ETH Zurich and Bern University; June 2006.

Journal papers

A. Caruso, T. Bouillon, P.M. Schumacher, E. Zanderigo, M. Morari, ”Control

of drug administration during Monitored Anesthesia Care,” Special Issue on Drug

Delivery Automation, IEEE Transactions on Automation Science and Engineering

6(2), pp. 256-264, Apr 2009.

A. Konig, A. Caruso, M. Bolliger, L. Somaini, H. Vallery, M. Morari, R. Riener,

”Model-based heart rate control during Lokomat walking,” Special Issue on Reha-

bilitation via Bio-Cooperative Control of Biomechanics, Physiology and Presence,

241

IEEE Transactions on Neural Systems and Rehabilitation Engineering, submitted

for review.

G. Sveticic, A. Caruso, G. Scharbert, M. Curatolo, S.A. Kozek-Langenecker, M.

Morari, ”Pharmacodynamic interaction modelling and optimal drug regimen for

anticoagulation therapy,” Anesthesiology, in preparation.

International Conferences

A. Caruso, M. Morari, ”Model based closed-loop control of propofol sedation

using transcutaneous CO2 as target variable,”Anesthesiology 111:A1057; ASA An-

nual Meeting, New Orleans, Oct 2009.

V. Hartwich, P.M. Schumacher, A. Caruso, M. Luginbuhl, ”Dynamical properties

of a new transcutaneous carbon dioxide sensor,” Anesthesiology 111:A1469; ASA

Annual Meeting, New Orleans, Oct 2009.

A. Caruso, M. Morari, ”Model predictive control for propofol sedation,” IFMBE

Proceedings, vol. 25, pp. 923-926; World Congress on Medical Physics and Biomed-

ical Engineering, Munich, Sep 2009.

A. Caruso, P.M. Schumacher, M. Morari, T. Bouillon, ”Simultaneous modeling

of drug induced hypercarbia and hypoventilation in the nonsteady state,” Anesthe-

siology 109:A15; ASA Annual Meeting, Orlando, Oct 2008.

A. Caruso, P.M. Schumacher, M. Morari, ”A novel direct search method for

the optimization of multiple-drug regimens for pain treatment,” Anesthesiology

109:A1471; ASA Annual Meeting, Orlando, Oct 2008.

A. Caruso, T. Bouillon, P.M. Schumacher, M. Morari, ”On the modeling of drug

induced respiratory depression in the non-steady-state,” Conf Proc IEEE Eng Med

Biol Soc 2008, pp. 5564-5568; 30th IEEE EMBC, Vancouver, Aug 2008.

A. Caruso, P.M. Schumacher, M. Luginbuhl, M. Morari, T. Bouillon, ”A parsi-

monious model integrating drug effect on the hypercarbic and hypoxic ventilatory

drive,” Anesthesiology 107:A20; ASA Annual Meeting, San Francisco, Oct 2007.

D. Leibundgut, V. Hartwich, P.M. Schumacher, A. Caruso, G. Pestel, ”Inter ob-

242 Curriculum Vitae

server agreement of manually assessed differences in pulse pressure (dPP),” Anes-

thesiology 107:A455; ASA Annual Meeting, San Francisco, Oct 2007.

A. Caruso, M. Morari, T. Bouillon, M. Luginbuhl, P.M. Schumacher, ”TCI for

multiple drugs: the two dimensional user interface approach,” World Congress of

Total Intravenous Anaesthesia, Venice, Sep 2007.

A. Caruso, T. Bouillon, P.M. Schumacher, M. Luginbuhl, M. Morari, ”Drug-

induced respiratory depression: an integrated model of drug effects on the hyper-

capnic and hypoxic drive,” Conf Proc IEEE Eng Med Biol Soc 2007, pp. 4259-4263;

29th IEEE EMBS, Lyon, Aug 2007.

A. Caruso, T. Bouillon, E. Zanderigo, P.M. Schumacher, M. Luginbuhl, ”Closed

loop administration of remifentanil for monitored anesthesia care using PCO2 as

endpoint,” Anesthesiology 105: A1198; ASA Annual Meeting, Chicago, Oct 2006.

P.M. Schumacher, A. Caruso, V. Hartwich, M. Luginbuhl, T. Bouillon, ”Dy-

namic properties of a new transcutaneous CO2 sensor: fast enough for early de-

tection of apnea?,” Anesthesiology 105: A477; ASA Annual Meeting, Chicago, Oct

2006.

E. Zanderigo, A. Caruso, T. Bouillon, M. Luginbuhl, M. Morari, ”Pharmacody-

namic modelling of drug-induced ventilatory depression and automatic drug dosing

in conscious sedation,” Conf Proc IEEE Eng Med Biol Soc 2006, pp. 5029-5032;

28th IEEE EMBC, New York, Aug 2006.

Zurich, November 2009.

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