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CRISMA CenterUPMC Critical CareUPMC Critical Care
Exemplary Care Cutting-edge Research World-class Educationwww.ccm.pitt.edu
Medical decision making and model-based reasoning
2010 Winter School in Mathematical &2010 Winter School in Mathematical & Computational Biology
U i it f Q l d B i b
Gilles Clermont, MD
University of Queensland, Brisbane
CRISMA CenterCenter for Inflammation and Regenerative ModelingCritical Care Medicine, Mathematics, and Industrial EngineeringUniversity of Pittsburgh
Exemplary Care Cutting-edge Research World-class Education
Objectives
Medical decision making
Constructing clinical knowledgeConstructing clinical knowledge
Model-based diagnostics
Global patterns and individual variability
Quantitative approaches to variability
Bedside translationBedside translation
Exemplary Care Cutting-edge Research World-class Education
Objectives
Medical decision making
Constructing clinical knowledgeConstructing clinical knowledge
Model-based diagnostics
Global patterns and individual variability
Quantitative approaches to variability
Bedside translationBedside translation
Exemplary Care Cutting-edge Research World-class Education
Case presentation72 yo to hospital by ambulance with vomiting, abdominal pain for 24 hours
Past medical historyDiabetes, on oral hypoglycemic agent
Vital signsTemperature 37.8 CBlood pressure very low 72/40Heart rate high 120
Exemplary Care Cutting-edge Research World-class Education
The essence of clinical medicine
???
TherapeuticsTherapeutics
DiagnosticsTesting gTesting
Exemplary Care Cutting-edge Research World-class EducationObservables States
Information gathering
Exemplary Care Cutting-edge Research World-class Education
Medical decision makingI f di i ( t t ) f i l t i f tiInfer diagnosis (state) from incomplete information (observations)
Inverse probleme se p ob e
Several diagnoses may be compatible with observations at handobservations at hand
Ill-posed
Diagnostic evaluation to narrow diagnosticDiagnostic evaluation to narrow diagnostic possibilities
Gathering of addition informationPerturbation challenges (experiment)
Therapeutic actionp
IterationState is typically evolving
Exemplary Care Cutting-edge Research World-class Education
State is typically evolvingTitration of care
Clinicians and the inverse problem
Exemplary Care Cutting-edge Research World-class EducationZenker, Rubin, Clermont, PLoS Comp Bio 2008
Objectives
Medical decision making
Constructing clinical knowledgeConstructing clinical knowledge
Model-based diagnostics
Global patterns and individual variability
Quantitative approaches to variability
Bedside translationBedside translation
Exemplary Care Cutting-edge Research World-class Education
The drug pipelineLead/candidate identification - $
Pre-clinical work - $I it
DifficultCandidate identificationClinical trial logisticsIn vitro
Animal
Phase 0 Phase I clinical $
Clinical trial logistics
InefficientHeuristicPhase 0, Phase I clinical - $
Toxicity/Safety
Phase II clinical RCT - $$
Heuristic
Expensive$BPhase II clinical RCT $$
Dose rangingEfficacy – proxy outcomes
$B
Lengthy>12 years
Phase III clinical RCT - $$$EfficacyEffectiveness
>12 yearsFew exceptions
?RewardComparative outcomeRegistration
?RewardLimited exclusive rights
Exemplary Care Cutting-edge Research World-class Education
Phase IV –post marketing
The response to an inflammatory insult
Sepsis=i f ti i fl ti
Severe sepsis=i d f ti
Initiating EventInflammation
infection+inflammation sepsis+organ dysfunction
Initiating EventDamage/Dysfunction
Exemplary Care Cutting-edge Research World-class EducationAnti-inflammation
Hotchkiss and Karl NEJM 2003; 348:138-150
mm
ator
yIn
flam
ynf
lam
mat
ory
Ant
i-in
Exemplary Care Cutting-edge Research World-class Education
Clinical trials of immunomodulation
Acute Chronic
Sepsis
Acute pancreatitis
Inflammatory bowel disease
Acute pancreatitisAuto-immune diseases
Rhumatoid arthritisPsoriasis
Transplantation/rejectionTransplantation/rejection
Th h i thThe more chronic the process, the more successful we have been !
Exemplary Care Cutting-edge Research World-class Education
Clinical trials of immunomodulation in sepsis
>60 phase III clinical trials
>25,000 patients
>1.6 billion dollars
Exemplary Care Cutting-edge Research World-class Education
The strength of the Consensus – Then 2004
2553218
Quality {Strength {
Exemplary Care Cutting-edge Research World-class Education
{
The strength of the Consensus - 2008
2553218
Quality {Strength { 1. Strong –> do
2. Weak –> consider
Exemplary Care Cutting-edge Research World-class Education
{ ea co s de
Surviving sepsis - I
Exemplary Care Cutting-edge Research World-class Education
www.survivingsepsis.org
Surviving sepsis - II
Exemplary Care Cutting-edge Research World-class Education
Problems with RCTs in sepsis
Pre-clinical studies have high success but:Subjects have different degree of illness (30% vs 85%)
Studies in animal at low risk of deaths tell the same story as clinical trials (Eichacker et al. 2003)
Administration schedule is differentProblem of “attributable” mortality worse in humans
Phase II trials based on little dataPhase II trials based on little data
Design of Phase III trials is also poorly informed
Exemplary Care Cutting-edge Research World-class Education
More problems with sepsis trialsDoes the drug have the purported biological activity?
Is the burden of proof for efficacy relevant to the diseaseIs the burden of proof for efficacy relevant to the disease the drugs are intended to help?
Trials are limited by the nature of the study populationTrials are limited by the nature of the study populationHeterogeneousCo-morbidities
Exemplary Care Cutting-edge Research World-class Education
Redesigning clinical trials
Phase IIPlay the winner; drop the looser designsAdaptive seamless phase design
Use phase II patients as part of the phase II trialsTwo-stage designsTwo stage designs
Phase IIIG ti l d iGroup sequential design
Advanced adaptive schemespAdaptive randomizationSample-size reestimationBi k d tiBiomarker-adaptiveOthers
Treatment-switching
Exemplary Care Cutting-edge Research World-class Education
Treatment switchingHypothesis modification (superiority vs. non-inferiority)
But…
How does the result of an RCT apply to a particular patient?
Most proposed modifications to the canonical dogma run against the principle of personalized medicine.against the principle of personalized medicine.
ThThus
Growing malaise with the use of RCTs are the soleGrowing malaise with the use of RCTs are the sole method in discovering clinical “truths”
M d l b d th d h l i d i iModel-based method can help in redesigning some aspects of clinical trials, not all
Exemplary Care Cutting-edge Research World-class Education
Medical Decision Making - Treatment
Resuscitate with fluids
Give antibioticsGive antibiotics
Exemplary Care Cutting-edge Research World-class Education
Take care of the underlying cause
Objectives
Medical decision making
Constructing clinical knowledgeConstructing clinical knowledge
Model-based diagnostics and therapeutics
Global patterns and individual variability
Quantitative approaches to variability
Bedside translationBedside translation
Exemplary Care Cutting-edge Research World-class Education
Back to our problem
Can a mathematical model help?
Exemplary Care Cutting-edge Research World-class Education
Can a mathematical model help?
The response to an inflammatory insult
Severe sepsis=i d f ti
I f ti
Inflammationsepsis+organ dysfunction
InfectionDamage/Dysfunction
Exemplary Care Cutting-edge Research World-class EducationAnti-inflammation
A model of the inflammatory response
N* *N( )nau t+1 2
DP ( )cau t+
CA3
Exemplary Care Cutting-edge Research World-class Education
Several modes of death
Aseptic death Septic deathp p
Exemplary Care Cutting-edge Research World-class Education
Many asymptotic behaviors are possible
Exemplary Care Cutting-edge Research World-class Education
Predicting the response to treatment
Exemplary Care Cutting-edge Research World-class EducationOsuchowski, CCM 2009
Steroids
RationaleProfound anti-inflammatory effect
Decreases feverDecreases swellingPromotes apoptosis of immune cellsPromotes apoptosis of immune cells
Concept of relative adrenal insufficiency
Exemplary Care Cutting-edge Research World-class Education
Steroids (Ca) at high doses
Exemplary Care Cutting-edge Research World-class Education
Steroids at low dosesA handful of recent studies using smaller doses (200–300 mg/day hydrocortisone) for longer periods of time may have beneficial effectshave beneficial effects.
reversal of shocktrends toward decreased organ system dysfunctiondecreased mortality
Relative adrenal insufficiencyy
Yet, one large study (CORTICUS) failed to support this contentioncontention
Exemplary Care Cutting-edge Research World-class Education
A model-based intervention
Not good at all(N
*)
Not good
Very good
No change
Exemplary Care Cutting-edge Research World-class Education
Very good
CRISMA CenterUPMC Critical CareUPMC Critical Care
Exemplary Care Cutting-edge Research World-class Educationwww.ccm.pitt.edu
Objectives
Medical decision making
Constructing clinical knowledgeConstructing clinical knowledge
Model-based diagnostics
Global patterns and individual variability
Quantitative approaches to variability
Bedside translationBedside translation
Exemplary Care Cutting-edge Research World-class Education
An acute inflammatory perturbation
LPS 40ng/kg IVLPS (10ng/kg IV) LPS 40ng/kg IV
5000
6000#1
#7
LPS (10ng/kg IV)
250
300
#2
#5
3000
4000
5000 #9
#21
150
200
250
TNF
(pg/
ml)
#13
#14
0
1000
2000
0
50
100
seru
m T
00 1 2 3 4 5 6
Time (h)
00 1 2 3 4 5 6
Time (h)
Trajectories are consistent within individuals
Exemplary Care Cutting-edge Research World-class Education
“Shapes” are often consistent across individualsSuffredini et al. 1996
Genetic and Inflammatory Markersof Sepsis (GenIMS)of Sepsis (GenIMS)
NIGMS/NIH R01 2001 2005 (A K ll )NIGMS/NIH R01 y2001-2005 (Angus, Kellum)With additional support from GSK, OBI, DPC, Brahms
I ti h t t d f ti t ti t ED ith CAPInception cohort study of patients presenting to ED with CAPProposed N = 2,700 at 38 hospitals clustered in 4 regions
Pennsylvania (SW)y ( )ConnecticutMichigan (Detroit area)Tennessee (Memphis area)Tennessee (Memphis area)
Blood donor pools from same region(s) for population normsPowered for analyses in whites and blacks
Exemplary Care Cutting-edge Research World-class Education
All Inpatients with CAP (n = 1886)
4550
354045
IL6IL10
202530
pg/m
l IL10TNF
101520
05
1 2 3 4 5 6 71 2 3 4 5 6 7
Days
Exemplary Care Cutting-edge Research World-class Education
Cytokines by Outcome (60 days)
IL-6
120140 SSD
IL-10
10
12 SSD
406080
100120
pg/m
l
SSANSS
4
6
8
10
pg/m
l
SSANSS
020
1 2 3 4 5 6 7
Days
0
2
1 2 3 4 5 6 7
Days
TNF SSDSSA
4
6
8
10
pg/m
l
SSANSS
0
2
4
1 2 3 4 5 6 7
p
Exemplary Care Cutting-edge Research World-class Education
Days
Day 1 cytokine levels in patients with and without severe sepsis
2.3h 95
% C
I
TNF
h 95
% C
I
4.6
IL-6
2.1
1.9elin
e TN
F w
it
elin
e IL
6 w
ith
4.2
3.8
<0 00011.9
1.7
Base
Severe sepsis(n=715)
No SS(n=1073)
p<0.0001
Bas
Severe sepsis(n=715)
No SS(n=1073)
3.4
3.0
p<0.0001
CI IL-10
2.6
2 40 w
ith 9
5% C
2.4
2.2
2 0
Bas
elin
e IL
10
p<0.0001
Exemplary Care Cutting-edge Research World-class Education
2.0Severe sepsis(n=715)
No SS(n=1073)
Day 1 cytokine levels in non-septic patients for prediction of severe sepsis
CI 2.1
TNF
4.0CI
IL-6
e an
d 95
%
2.0
1 9
3.8
3 6e an
d 95
% C
at b
asel
ine 1.9
1.8p = 0.0087
3.6
3.4
at b
asel
ine
p = 0.0009
TNF
1.7
p
Severe sepsis(n=268)
No SS(n=1073)
3.2IL6
Severe sepsis(n=268)
No SS(n=1073)
Analysis restricted to day 1 levels of those patients who do NOT have severe sepsis on first day
Exemplary Care Cutting-edge Research World-class Education
who do NOT have severe sepsis on first day
IL-6, IL-10 patterns v. Outcomes
HMLIL6/IL10
2 95 43 2H
3.813.735.6M
1.47.926.1LOverall %Frequency
2.95.43.2H
HMLIL6/IL10
% S
72 261 447 5H
47.241.725.5M
26.927.518.7L% SevereSepsis
72.261.447.5H
84 693 696 4L
HMLIL6/IL1060 day %
56.174.390.0H
69.784.395.3M
84.693.696.4L60 day %Survival
Exemplary Care Cutting-edge Research World-class Education
Day 1 levels and survivalh
95%
CI
2.4 5.0
95%
CI TNF IL-6
line
TNF
with
2.2
2.0
4.6
4.2
3 8elin
e IL
6 w
ith
Dead(n=212)
Alive(n=1410)
Bas
e
1.8p<0.0001 3.8
3.4Dead(n=212)
Alive(n=1410)
Base p<0.0001
2 8% C
I IL-102.8
2.6
IL10
with
95%
2.4
2.2
DeadAlive
Bas
elin
e I
p<0.0001
Exemplary Care Cutting-edge Research World-class Education
Dead(n=212)
Alive(n=1410)
Day 1 cytokine levels in patients who develop ARF and those that do not
7
7.5TNF
ARF = RIFLE-I or F5.5
6
6.5
Pg/m
l ±SD
4
4.5
5P
ARFNo ARF
p<0.0001
(n=258)(n=1544)
IL-680IL-107.5
l ±SD
50
60
70
l ±SD 6
6.5
7P
g/m
p<0.0001
20
30
40
50
Pg/
m
p=0.0285
4
4.5
5
5.5
Exemplary Care Cutting-edge Research World-class Education
ARF(n=258)
No ARF(n=1544)
20ARF(n=258)
No ARF(n=1544)
4
The good news
Standard (although but no means elementary) statistical techniques identify “classes” of patients
PhysiologyOmics
Qualitative patterns, but not magnitude of response, often preserved across individuals
Within species
Exemplary Care Cutting-edge Research World-class Education
Objectives
Medical decision making
Constructing clinical knowledgeConstructing clinical knowledge
Model-based diagnostics
Global patterns and individual variability
Quantitative approaches to variability
Bedside translationBedside translation
Exemplary Care Cutting-edge Research World-class Education
CRISMA CenterUPMC Critical CareUPMC Critical Care
Exemplary Care Cutting-edge Research World-class Educationwww.ccm.pitt.edu
Variability and personalized medicine
2010 Winter School in Mathematical &2010 Winter School in Mathematical & Computational Biology
University of Queensland Brisbane
Gilles Clermont, MD
University of Queensland, Brisbane
CRISMA CenterCenter for Inflammation and Regenerative ModelingCritical Care Medicine, Mathematics, and Industrial EngineeringUniversity of Pittsburgh
Exemplary Care Cutting-edge Research World-class Education
The big picture
Exemplary Care Cutting-edge Research World-class Education
Sources of variability
Between-subject variability
Measurement variability (between occasion)Measurement variability (between-occasion)
Residual uncertainty
Exemplary Care Cutting-edge Research World-class Education
Naïve pooling
All data points are assumed to arise from a single individual
A single function is fit to the combination of all individuals
Ignores intra-individual variability as well as correlation in time within individuals
Variant: fitting the average/median curve (generated before the fit))
Exemplary Care Cutting-edge Research World-class Education
Mixed models for ODE - pharmacokinetics
Naïve pooling Average fitp g Average fit
Exemplary Care Cutting-edge Research World-class Education
One model – many patients
MM
Exemplary Care Cutting-edge Research World-class Education
Two-stage models
Standard TS
k k k kY X Eθ= +y
Iterative TS
g(x)( | , ) ( )( | )
k k k popk k k X Y mY X ρ ρ θθ
Exemplary Care Cutting-edge Research World-class Education
( | ) ( )( , | )( | , ) ( )
k
k k kk k k pop
Y
Y XX Y m
ρ ρρ θρ ρ θ
=∫
Linear mixed-effects modelsOne model one patientOne model – one patient
M
M
MExemplary Care Cutting-edge Research World-class Education
Linear mixed-effects model
yi i i i i
i i i i i
Y m X b EY mX m X b b E= + += + + + +
SSE
xm
Exemplary Care Cutting-edge Research World-class Education
x
The simplest viral model (v1.0)
λ
Healthycell d
β
Virus Targetcell a - where active cell killingk
is implicit in this death rate
u - virus deathor shedding
Killercell
or shedding
Exemplary Care Cutting-edge Research World-class Education
Reaction formulation
xλ
∗ →x: target cellsy: infected cells
i
k
x
y v
∗ →
→
v: virusr: killer cell
y v
v x yβ
→
+ →x vx dxλ β•
•
= − −•
d u a
v x y
x v y
+ →
→ ∗ → ∗ →∗
y vx ay
v ky uv vx
β
β
•
•
= −
=
y vx ay ryβ γ•
= − −
y r rγ
+ →
, ,x v y→ ∗ → ∗ →∗ v ky uv vxβ= − −
r c fr•
= −c
f
y
r∗ →
Exemplary Care Cutting-edge Research World-class Education
f
r → ∗Baccam et al, J Virol 2007
Mixed models for ODE
Exemplary Care Cutting-edge Research World-class EducationBaccam et al, J Virol 2007
Mixed-effects modelsOne model one patientOne model – one patient
MMMMM
Individual models vary in parameters? Alternative mathematical structures? Alternative mathematical structuresevaluated based on
Global error over the populationExemplary Care Cutting-edge Research World-class Education
Global error over the populationParsimony
Mixed-effects modelsMostly applied to
Generalized linear models“F i l ” ll d li bl“Fairly” well-posed non-linear problems
Frequent in population pharmacokinetics
Stochastic expression ofBetween subject variabilityj yRepeated measuresUnexplained residual error
Expressed as AlgebraicDiff ti l tiDifferential equations
NONMEMMonolix
Exemplary Care Cutting-edge Research World-class Education
What about the ill-posed problem?
The error model is important
Deviation between model predictions and data/heuristics
A few synonymsA few synonymsErrorObjective functionjCost function
Problem dependent functional formsProblem dependent functional forms Least squares - MLEMulti-objectivej
( ) ( ) 1 1( ) ( ) ( ( )) .....Td i i HE d m C d m b mθ θ θ= Γ − − +Γ − +∑( ) ( ) 1 1
, ,
( ) ( ) ( ( ))d i i Hs v t∑
Data Heuristics
Exemplary Care Cutting-edge Research World-class Education
Data
Non-linear problem may be very messy
ErrorWell-posed Ill-posed
??
?
?
?Which is the correct minimum?
??
?
Parameter axis
minimum?
Exemplary Care Cutting-edge Research World-class Education
Parameter axis
This is what clinicians do all the time !
The Ill-posed problemModel ensemble as a collection of “good” models
ErrorError
Probability(density)
Exemplary Care Cutting-edge Research World-class EducationParameter axis
Patient specific models and ill-posednessThe one-step processThe one step process
E(Mn)( n)
E(M ) ≡ P ti t ifi blE(Mn) ≡ Patient-specific ensemble
Exemplary Care Cutting-edge Research World-class Education
Naïve pooling and ill-posedness
E(Mn)( n)
E(M ) ≡ M t d l E blE(Mn) ≡ Metamodel or EnsembleMany many more models than individuals
Exemplary Care Cutting-edge Research World-class Education
Many many more models than individuals
Influenza virus biology
VaVa
VHVSAVIdtdV
V
VVVHVAV
2
1
1+−−−−= αγγγ
dH FHbVHRaRHDbdtdH
HFHVRHD −−++= γ)(
IaEIbVHdtdI
IIEHV −−= γ
dM
FaHFbIcMbdtdF
FFHFF −−+=
MaMVbDbdt
dMMMVMD −−+= )1)((
dt
RaFHbdtdR
RHF −=
)1( EaIEbMEbdtdE
EEIEM −+−=dt EEIEM
)1( PaMPbdtdP
PPM −+=
AaSAVPbdA−−= γ AaSAVPb
dt AAVA −−= γ
)1( SrPdtdS
−=
Exemplary Care Cutting-edge Research World-class Education
Hancioglu, Swigon ,Clermont, JTB 2008
Ensemble modelParallel computation environment
Known how to distribute chainschainsAdaptive load balance
6 “meta-chains”6 meta-chainsValidity unknown
e7 samplese7 samples
Several “clusters” of behavior compatible with datacompatible with data
Standard behaviorRelapsing behavior“S d ”“Superspreaders”
Exemplary Care Cutting-edge Research World-class Education
Parameter distributions
Exemplary Care Cutting-edge Research World-class Education
Probabilistic course of disease
Exemplary Care Cutting-edge Research World-class Education
Also compatible with the data
Exemplary Care Cutting-edge Research World-class Education
Treatment predictions
Not intuitive
Exemplary Care Cutting-edge Research World-class Education
Probabilistic ensembles for individuals
E(M)E(M)
pop iθ θ θ= +As a mixed-effect modelAs a mixed effect model,
Remains an open-problem
Exemplary Care Cutting-edge Research World-class Education
θ θi
Probabilistic ensembles – for subpopulations
E(M)E(M)
Sparsity -> pooling “similar” patients may be good enoughThe clinician does thisThe clinician does this
Exemplary Care Cutting-edge Research World-class Education
ConclusionsWe live in the ill-posed world
There are methods (early) of approachThere are methods (early) of approachLimited by paucity of data in any single individualLimited by incongruence between time of observation and di d idisease dynamics
Bayesian-methods may indicate a systematic approach to this problem
Computationally intensive for real-time acute care p yapplications
Exemplary Care Cutting-edge Research World-class Education
Objectives
Medical decision making
Constructing clinical knowledgeConstructing clinical knowledge
Model-based diagnostics
Global patterns and individual variability
Quantitative approaches to variability
Bedside translationBedside translation
Exemplary Care Cutting-edge Research World-class Education
Biomarker-guided therapy using model-predictive control
First attempts at applying engineering concept to guide treatment
Diabetes (Parker)Anti-coagulationDepth of anesthesia (Haddad Bailey)Depth of anesthesia (Haddad, Bailey)
Currently NO point-of-care measurements of biomarkers would allow the implementation of such techniques for acute inflammation
Not quite true!Not quite true!
Exemplary Care Cutting-edge Research World-class Education
Targeted Therapy - Model Predictive Control
“Base” SystemBase System• Real patient• Patient metamodelINPUT
•Actual dataOUTPUT•Actual dataActual data Actual data•Predicted data
Sensor• Error betweenActuator
Th d i d i “h l h”
Error betweenactual/desired
Actuator
Controller
• The desired output is “health” • The MPC method uses actual data and model simulations
to estimate output: the discrepancy is estimated (Sensor)
Exemplary Care Cutting-edge Research World-class Education
• The MPC method suggest an optimal intention strategy which is time dependent (Actuator)
Model Predictive ControlObjective: find the control strategy which minimizes the difference between the predicted trajectory and a reference goal over a finite horizon. (D=0, P=0)
X
g ( , )Predictions are calculated using a model of the process.
statespace o o
X
o
predicted trajectory
oo
o oo
current stateoo
reference trajectory
di ti h i
TK TK+1 TK+P
current stateoo
TK+P+1
prediction horizon
time
control
TK+C+1
control strategydose
Exemplary Care Cutting-edge Research World-class Education
control variable
control window
The model
minnau
na
na
na( )nau t+
maxnau dp ( )cau t+
ca
Exemplary Care Cutting-edge Research World-class Education
mincau max
cauDay, Rubin, Clermont, Math Biosc 2010
Titrated therapy (MPC)
Exemplary Care Cutting-edge Research World-class Education
Simulated clinical trial of a balanced treatmentControls vs. Static vs. Standard vs. Targeted therapy
Insult is Sepsis1000 patients are sim lated1000 patients are simulatedTreatment initiated based on levels of activated phagocytic cellsBoth anti and pro-inflammatory effectors are allowed to be either administered or removed
Static therapy: fixed dose of anti-inflammatory
Standard Therapy: titrated based on baseline data and an existing (meta) model
Targeted Therapy: is allowed to react to observations (biomarker data) which are different from model
Exemplary Care Cutting-edge Research World-class Education
predictions
Population heterogeneity creates mismatch
Exemplary Care Cutting-edge Research World-class Education
Targeted therapy is better, more forgiving
Exemplary Care Cutting-edge Research World-class Education
Titrated therapy – population variationsSuccess Failure
Exemplary Care Cutting-edge Research World-class Education
How complex should useful models be?It depends on the intent
DescriptionPredictionPrediction
Measureable read-outs
Compartmentalized
Design of a device to selectively g yadsorb septic blood
Exemplary Care Cutting-edge Research World-class Education
Knowledge and successful translation
EmpiricalEpicycles
Kepler/Newton Ellipses
GR - EinsteinPrecessing ellipses
QG - ??Black hole physicsEpicycles
- to XVII centuryEllipses Precessing ellipses Black hole physics
First interactionbetween a physical
Discrepancy betweenpredictions and
Discrepancy betweengravity and otherbetween a physical
law and empiricobservation
predictions and empiric observation
gravity and otherforces of nature
Exemplary Care Cutting-edge Research World-class EducationDepth of knowledge