Physiologically Based

7/30/2019 Physiologically Based

1/33

Physiologically BasedPharmacokinetic Modeling:

An Introduction

Hugh A. Barton

US Environmental Protection Agency

National Center for Computational Toxicology

Research Triangle Park, [email protected]


2/33

Outline

What is pharmacokinetics (PK)?

Why PK?

PK Modeling Methods

PBPK Model Components PBPK Model Structures

This presentation does not represent official US

EPA policy.


3/33

AUC: area under the

concentration-time curve(mg/L*hr)

Cl or Cld: clearance (L/hr)

Cmax: maximumconcentration (mg/L or M)

ka: absorption rate constant(1/hr)

Km: Michaelis-Mentenconstant (M)

Vmax: maximal metabolismrate

Abbreviations PD: pharmacodynamics

PK: pharmacokinetic TD: toxicodynamics

TK: toxicokinetics

V or Vd: volume ofdistribution (L) or tissue (L)(conversion of volume tomass assumes 1 g/mL, the

density of water) Q: blood flow


4/33

What is Pharmacokinetics?

What the body does to a chemical

Absorption, Distribution, Metabolism,Excretion (ADME)

Kinetics: rates of change, PK: chemical concentrations as a function

of time

Pharmacokinetics = Toxicokinetics

Pharmacodynamics: What the chemical

does to the body (PD=TD)


5/33

Why Use PK-based Analyses? Improved candidate selection during chemical or drug

development Cross-species comparisons of metabolism or absorption Duration of action of different formulations

Improved toxicity study design Dose, species, dosing interval selection

Improved toxicity study interpretation Cross-species comparisons of metabolites or tissue

distribution Links to pharmacodynamics and effects

Improved risk and safety assessments

Understanding interspecies, dose, route-to-routeextrapolations Evaluating population variability

Modeling populations (e.g., polymorphisms) versus individuals Modeling life stages (e.g., children, elderly, ill)

Evaluating uncertainties


6/33

Dose-response AssessmentExposure:

externaldose/concentration

Pharmacokinetics:internal tissue dose

Pharmacodynamics:action on target tissue

Response:measured toxicity

Low Information Default


7/33

Which Pharmacokinetic Analysis

Method?

Classical Compartmental Models Noncompartmental Models

Population Pharmacokinetics

PBPK Models


8/33

Classical Compartmental

Fits equations to data to estimate PK parameters

Requires in vivo data in relevant species

Can be physiological, e.g., methanol distributes

with total body water, but not a requirement Limitations:

Used for nonvolatiles, though adaptable for volatiles

PK changes with exposure difficult to address

Limited tissue distribution characterization

CleV1

V2

Cld

ka

0.001

0.010

0.100

1.000

10.000

0 500 1000 1500 2000 2500

Time (hr)

Observed

PredictedPlasma(g/mL)


9/33

Noncompartmental/Regression

Analysis

Mathematical analysis

of plasma time coursedata: trapezoid rule,nonlinear regression Uses assumption of

linear terminal phase to

calculate AUC (zero toinfinty) from datacollected to final timepoint

No model structure

assumptions Requires in vivo

chemical concentrationdata in relevant species

Calculates

pharmacokineticoutputs such as AUC: area under curve CL: clearance Vss: steady state

volume of distribution Tmax: time of max.

concentration Cmax: max. conc.


10/33

Population Pharmacokinetics

Statistical analyses to characterizepharmacokinetic parameters forpopulations of people

Often focuses on issues of limited data(sparse data) for each individual withinthe population versus extensive time

course data for an individual


11/33

PBPK models describe the organism as a set of tissuecompartments interconnected by blood (plasma) flow

Systems of differential equations based upon massbalance

Physiologically Based

Pharmacokinetic (PBPK) Models


12/33

PBPK Analysis Captures biological processes and hypotheses

explicitly

Varying degrees of detail or biological realism Flexibility to reflect biology

Can incorporate changes in PK due to chemical (e.g.GSH depletion, protein induction), growth/aging

Facilitates analyses across species, doses and humanpopulation subgroups

Limitations: Greater requirements for in vitro or in vivo data

Statistical evaluation of uncertainty and variability morechallenging

Model development and implementation requires appropriateexpertise


13/33

PBPK Model Components

Model Purpose/Goal

Deterministic Model Biological Hypotheses

Exposure conditions

Desired outputs

Non-deterministic Model

Statistical model Data


14/33

Model Purpose: Basic QuestionsWhat do I need to know to carry out an analysis based upon

internal dosimetry (i.e., applying pharmacokinetics)?

What toxic effects at what life stages? (i.e., potential critical studies) What species (toxicity, PK, metabolism studies)?

Toxicity testing animals Humans

What is known about the mode of action for each toxicity of interest? Parent chemical and/or metabolite(s) (reactive or not?) Interactions with macromolecules, cells, tissues, systems? Critical for PK model structure and selection of dose metrics.

How will model be used in safety or risk assessment?

Route-to-route extrapolation (What routes?) Cross-species extrapolation Cross-chemical extrapolation


15/33

PBPK Model Components

Physiological/Anatomical Biochemical/Physicochemical

ADME

Tissue:blood partitioncoefficient

Blood:air partition coefficient

Enzymatic rate constants

Equilibriumor rate constantsfor protein binding

Transporter rate constants

Tissue volumes

Blood flow rates

Cardiac output

Glomerular filtration rate

Alveolar ventilation rate

Hematocrit

Glutathione concentration

DNA concentration


16/33

What Tissues (Compartments)? Absorption

Distribution Storage (e.g., fat, bone, serumprotein binding)

Distributional kinetics (e.g., totalbody water)

Clearance Metabolism Excretion (e.g., urine, bile, hair)

Target Tissues for Toxicity or

surrogate (often blood)


17/33

Description for a Single Well-mixed

Tissue CompartmentTERMS

Qt= tissue blood flow

Cvt= venous blood concentration

Pt= tissue blood partitioncoefficient

Vt = volume of tissue

At= amount of chemical in tissue

mass-balance equation:dA

dt V

dC

dt Q C Q C

t

t

t

t art t vt= =

venous equilibration assumption CC

Pvtt

t=

QtCartQtCvt

TISSUE

Vt; At; Pt

Cvt: free concentration in tissue available for clearance(s)


18/33

Diffusion Limited Distribution

TISSUE mass-balance equation:

( )tttbt

tt

t PCCPAdt

dCV

dt

dA/==

TISSUE

QtCvtQtCart

Vt; At; Pt

Vtb; Atb

PAT

TISSUE BLOOD

TISSUE BLOOD mass-balance equation:

( ) ( )bttttvtartt

tbtb

tb CPCPACCQ

dt

dCV

dt

dA+== /

permeability areacross-product for

tissue (L/hr)

PAT:

IntracellularFluid: 33 L

Capillary Wall

Blood:

2 L RBC3 L plasma

InterstitialFluid: 13 L


19/33

Liver Compartment

rate of change ofamount in liver rate of uptake inarterial blood rate of loss invenous blood rate of lossby metabolism= - -

( ) vlmvlm

vlal

l

CK

CV

CCQdt

dA

+

=

When Cvl


20/33

Chemical-Specific Data

In vivo PK: chemical levels over time and doses Single or repeated exposures

Exposure (dosing) regimens: intravenous bolus or infusion, oral

bolus, inhalation, dermal Serial determinations in multiple animals (e.g., tissue or blood

concentrations)

Repeated measures in same animal/human (e.g., serum, urine,feces, exhaled breath, closed chamber atmosphere)

In vitro or ex vivo Partition coefficients: analysis of equilibrium chemical distribution to

blood and tissues

Protein binding rate or equilibrium constants

In vitro metabolism (e.g., estimates of Km and Vmax)

Changes in biochemistry following exposure (e.g., GSH depletion)


21/33

Examples of PBPK Models

Pharmacological Agents

Volatile Organic Compounds

Mixtures

Vapors with Nasal Toxicity

Lifestages


22/33

PharmacologicalAgents:

All-TransRetinoic Acid

= submodel

Slowly Perfused

Fat

Placenta

Embryo

Liver

Intestine

Gut

Feces

CO2

13-CIS

4-OXO

Glucuronide

Qc

Qsk

Qr

Qs

Qf

Qpl

Ql

QgQg

kb

krko

Do

kctktckf

Vmx , kmx

kCO2

Vmg , kmg

kh

ke

kv

Stratum Corneum

Dv

Plasma

Richly Perfused

Dsk

Dsc

Formulation

Viable Epidermis

Clewell HJ 3rd, Andersen ME,Wills RJ , Latriano L.

A physiologically basedpharmacokinetic model forretinoic acid and its metabolites.

J Am Acad Dermatol. 1997Mar;36(3 Pt 2):S77-85.


23/33

Key Factors in Risk Assessmentfor all-trans-Retinoic Acid

Species differences in metabolism

rodents: oxidation to active form

primates: glucuronidation to inactive form

Exposure route differences in bioavailability

rapid oral uptake can exceed capacity ofglucuronidation pathway

slow topical uptake subject to high affinity clearance

Kinetic differences between isomers

all-trans: rapid glucuronidation/clearance

13-cis: slow oxidation/clearance


24/33

Water soluble model

for dichloroacetate(Barton et al., 1999)

Metabolism

Rest of Body(Volume of

Distribution)

CVL

QL

CVB

Liver

Urinary

Clearance

CL

GILumen

ka

drinking water

or gavage

Injection

Pharmacological Agents:

Dichloroacetate


25/33

Pharmacological Agents: Diazepam

MU

TE

AD

HT

SK

BR

LI

ST

SPL

LU

RE

KI

Venous

Blood

Arteria

lBlood

metab

Wide range of mathematicalanalyses:

Gueorguieva I, Nestorov IA, Rowland M. Fuzzy

simulation of pharmacokinetic models: casestudy of whole body physiologically basedmodel of diazepam. J PharmacokinetPharmacodyn. 2004 J un;31(3):185-213.

Gueorguieva I, Aarons L, Rowland M.

Diazepam pharamacokinetics from preclinical tophase I using a Bayesian populationphysiologically based pharmacokinetic modelwith informative prior distributions in WinBUGS.

J Pharmacokinet Pharmacodyn. 2006Oct;33(5):571-94.

Gueorguieva I, Nestorov IA, Rowland M.Reducing whole body physiologically basedpharmacokinetic models using global sensitivityanalysis: diazepam case study. JPharmacokinet Pharmacodyn. 2006

Feb;33(1):1-27.


26/33

Volatile OrganicCompounds:Vinyl Chloride

QFFat

CA

CVF

QRRich

CA

CVR

QS

Slow CACVS

QCLung

QPCI CX

QL

Liver CACVL

KZER

KA

KGSMCO2

KCO2

Reactive

Metabolites(RISK)

Glutathione

Conjugate(RISKG)

KFEEKGSM

Tissue / DNAAdducts(RISKM)

KB

KOKS

GSH

VMAX1KM1

VMAX2KM2

Clewell HJ , Gentry PR, GearhartJ M, Allen BC, Andersen ME.

Comparison of cancer riskestimates for vinyl chloride usinganimal and human data with aPBPK model.

Sci Total Environ. 2001 J ul

2;274(1-3):37-66.


27/33

Human risk estimates (per million) for lifetime exposure to

1 ppb vinyl chloride in air based on the incident of liver

angiosarcoma in animal bioassays

Animal Bioassay Study 95% UCL Risk/million/ppb

Males Females

Maltoni - mouse inhalation 1.52 3.27

Maltoni - rat inhalation 5.17 2.24Feron - rat diet 3.05 1.1

Maltoni - rat gavage 8.68 15.7

See Clewell et al 2001 and references therein.


28/33

Human risk estimates (per million) for lifetime inhalation

of 1 ppb vinyl chloride in air based on the incident of liver

angiosarcoma in human epidemiological studies

Epidemiological Study95% UCL

Risk/million/ppb

Fox & Collier 0.71 - 4.22

Jones et al. 0.97 - 3.60

Simonato et al. 0.40 - 0.79

See Clewell et al 2001 and references therein.


29/33

VOCs: Mixtures

Liver

PoorlyPerf.

Richly Perf.

Lung

Metab Gut

Liver

PoorlyPerf.

Richly Perf.

Lung

Metab Gut

( )vl

im

vlm

vlal

l

CKIK

CVCCQ

dt

dA

++

=

]/1[

Barton HA, Creech J R, Godin CS, Randall GM,Seckel CS. Chloroethylene mixtures:pharmacokinetic modeling and in vitrometabolism of vinyl chloride, trichloroethylene,and trans-1,2-dichloroethylene in rat. Toxicol

Appl Pharmacol. 1995 Feb;130(2):237-47


30/33

MS Bogdanffy, R Sarangapani,DR Plowchalk, A J arabek, andME Andersen A biologicallybased risk assessment for vinyl

acetate-induced cancer andnoncancer inhalation toxicityToxicol. Sci. 1999 51: 19-35

Nasal Toxicity: Vinyl Acetate


31/33

Life Stage & Species Extrapolations

Body

Liver

Brain

Metab

Placenta

Lung

Richly

Perf.

PoorlyPerf.

Mammary

Liver

Gut

Maternal ModelNeonatal Model

Embryo/Fetal Model

Liver

Poorly

Perfused

RichlyPerfused

Lung

MetabolismGut


32/33

Conclusion

Model purpose

Deterministic Biological Model PK Determinants (ADME)

Target Tissues

Exposure Routes

Non-deterministic Model

Often statistical (likelihood based) Describes relationship between data and

model


33/33

References ReviewsBarton HA. Computational pharmacokinetics during developmental windows

of susceptibility. J Toxicol Environ Health A. 2005 J un 11-25;68(11-12):889-900

Barton HA, Pastoor TP, Baetcke K, Chambers J E, Diliberto J , Doerrer NG,Driver J H, Hastings CE, Iyengar S, Krieger R, Stahl B, TimchalkC. Theacquisition and application of absorption, distribution, metabolism, andexcretion (ADME) data in agricultural chemical safety assessments. CritRev Toxicol. 2006 J an;36(1):9-35

Clewell HJ 3rd, Andersen ME, Barton HA. A consistent approach for theapplication of pharmacokinetic modeling in cancer and noncancer riskassessment. Environ Health Perspect. 2002 J an;110(1):85-93.

Himmelstein KJ and Lutz RJ (1979) A Review of the Applications ofPhysiologically Based Pharmacokinetic Modeling. J PharmacokinetBiopharm7(2):127-145.

Krishnan K and Andersen ME (2001) Physiologically Based PharmacokineticModeling in Toxicology. In Principles and Methods in Toxicology, 4th

Edition, A. Wallace Hayes (Ed), Taylor & Francis, Philadelphia. pp 193-241.

Documents

Physiologically Based