Some principles of modeling and simulation in preclinical research - - PowerPoint PPT Presentation

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Some principles of modeling and simulation in preclinical research - - PowerPoint PPT Presentation

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Some principles of modeling and simulation in preclinical research and drug development Philippe Jacqmin Exprimo confidential Modelling and simulations throughout drug development: Objectives of M&S should focus on the next phase(s) of

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Exprimo confidential

Some principles of modeling and simulation in preclinical research and drug development

Philippe Jacqmin

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Modelling and simulations throughout drug development:

Pre-clinical Discovery Phase I Phase IIb Phase IIa Phase III Confirm Explore Explore Confirm Confirm Explore Candidate Selection Drug Evaluation Global Development

(Semi-)mechanistic PK/PD models Descriptive Drug & Disease models

Objectives of M&S should focus on the next phase(s)

  • f development to support decisions that need to be made
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Mechanistic versus descriptive (empirical) models: Mechanistic

  • Early stages of development
  • Good understanding of

system

  • Interpretable parameters
  • Interpolation and

extrapolation

  • May require less data

Descriptive

  • Late stages of development
  • Fair understanding of

system (grey box)

  • Less meaningful parameters
  • Interpolation
  • Usually requires a lot of

data

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M&S throughout Discovery and Pre-clinical:

Current phase

  • Feasibility assessment mechanism
  • f action
  • Define metrics candidate selection
  • Assess safety margin
  • Combined meta-analysis and objective

review of all discovery and pre-clinical data Next phase

  • Evaluation and selection appropriate

biomarker(s)

  • Optimize designs of early ph-I

studies with biomarkers Pre-clinical Discovery Phase-I Phase-IIb Phase-IIa Phase-III Confirmatory Explanatory Explanatory Confirmatory Confirmatory Explanatory Candidate Selection Early Development Late Development

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1.

The systems are complex

  • Nonlinearity and/or time dependency
  • Complex data (multiple sources, noisy, errors...)

2.

To integrate information

  • Across time, dose-levels, drugs and systems

3.

To predict and extrapolate

  • We are not only interested in the specific observation
  • We are often not primarily interested in the setting studied

4.

To optimize further studies

5.

The model can be used as a “knowledge repository”

  • Describe what is currently known about mechanism of action

and system

6.

The model might help to fill in the “gaps” in data

7.

The model can help us identify and quantify uncertainty

Why do we model in drug development?

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Components of drug models

e.g. Dose-Conc. relationship Conc.-Effect relationship Physiological mechanisms Maturation processes Inter-individual, inter-occasion and residual variabilities Uncertainty and correlation Relationships between parameters and compound/ system characteristics

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Pharmacokinetic-Pharmacodynamic modelling

Pharmacology Pharmacodynamics Effect Pharmacokinetics Dose Concentration Clinics Efficacy Pharmacotherapeutics Safety

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Pharmacokinetic models

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What happens when a drug is administered as an intravenous bolus?

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From ‘descriptive’ to ‘mechanistic’ model based on flow dynamic systems

Kidneys Liver Lungs GFR CYP Vmax/Km

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Model with oral absorption (first order)

Peripheral compartment k12 k21 G.I.

and peripheral compartment

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Physiologically-based pharmacokinetic model (PBPK)

Lung Adipose Skin Bone Heart Brain Muscle Liver Kidney Stomach Pancreas Spleen Gut

Venous blood Arterial blood

Heart Heart Clhepatic Clrenal QAdipose QAdipose QSkin QSkin QBone QBone QHeart QHeart QBrain QBrain QMuscle QMuscle QLiver QLiver QKidney QKidney QStomac QPancreas QSpleen QGut Clpulm

http://cdds.georgetown.edu/conferences/Theil.pdf

Qlung Qlung

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From in silico to in vivo

In Silico-based Molecular descriptors Software-based Ka, F Gastroplus Vss, Kp’s Vss-Predictor CL SimCyp Absorption Distribution Metabolism

GENERIC PBPK MODEL FRAMEWORK An integrated PBPK model of rat and human that can simulate the overall kinetics in plasma and several tissues prior to in vivo studies

http://cdds.georgetown.edu/conferences/Theil.pdf

In vitro-based Solubility Permeability Lipophilicity, pKa Plasma protein binding Hepatocyte clearance

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Pharmacodynamic models

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The receptor theory

First postulated by John Langley (1820-1878) Furthered by Paul Ehrlich (1854-1915)

“Corpora non agunt nisi fixata”

drug

http://www.med.nyu.edu/Pharm/Levy2003.ppt

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RT or BMAX = Total amount of receptor (binding sites/mg protein or nM) R = Free receptor (binding sites/mg protein or nM) D or Free = Free drug (nM) DR or Bound = complex drug-receptor (binding sites/mg protein or nM) K1 = association rate constant (min-1) K-1 = dissociation rate constant (min-1) KA = Association constant [ ] = concentration (nM)

Clark’s occupation theory

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Some graphical representations

BMAX = 8 nM KD = 2 nM BMAX = 8 nM KD = 2 nM BMAX = 8 nM KD = 2 nM

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From receptor occupancy to pharmacological effect A simple view: the EMAX model

This assumed that: The measured effect was linearly related to the number of receptor occupied by the drug Maximum effect was attained at maximum binding

EC50 EMAX

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log-linear effect concentration model

Some derived/simplified models

linear effect concentration model

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From receptor occupancy to pharmacological effect A more complete view

Ligand Receptor binding Generation

  • f second

messenger Change in cellular activity Affinity Intrinsic activity Effect Intrinsic efficacy Drug specific System/tissue specific Clark Ariëns Stefenson Furchgott KD

  • e and (S)

and [R]t and f(S)

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EMAX model and sigmoid EMAX model

=1 =2 =0.5 =1 =2 =0.5

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Operational model of agonism: effect of intrinsic activity (different drugs)

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Apparent dissociation between receptor occupancy and measured effect:

Production of glucose by -adrenoreceptor stimulation

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PK-PD models

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Concentration–effect–time relationship: direct response inhibition

Dose = 0.8 mg KA = 1 h-1 V = 80 L CL = 16 L.h-1 IC50 = 1.0 ng/mL n = 1.0 Imax = 1.0 BSL = 100

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The time delay between receptor occupancy and effect also depends on the second messenger mechanism

LEES, P., CUNNINGHAM, F. M. & ELLIOTT, J. Principles of pharmacodynamics and their applications in veterinary pharmacology. Journal of Veterinary Pharmacology & Therapeutics 27 (6), 397-414.

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Effect compartment (or Link) model

Dose = 0.8 mg KA = 1 h-1 V = 80 L CL = 16 L.h-1 IC50 = 1.0 ng/mL n = 1.0 Imax = 1.0 BSL = 100 Ke0 = 0.2 h-1

Plasma Biophase Biophase Biophase

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Concentration–effect–time relationship for an indirect response model with inhibition of build-up

R

Kin Kout R

Inhibition of build-up : H(t)= I Dose = 0.8 mg KA = 1 h-1 V = 80 L CL = 16 L.h-1 IC50 = 1.0 ng/mL n = 1.0 Imax = 1.0 Kin = 100 Runits.h-1 Kout = 1 h-1

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Indirect response models

R

Kin Kout R

Inhibition of build-up : H(t)= I Inhibition of loss :

R

Kin Kout R

H(t)= I Stimulation of build-up :

R

Kin Kout R

H(t)=S Stimulation of loss :

R

Kin Kout R

H(t)=S

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KPD model: analysis of effect-time profile in the absence of pharmacokinetic data

KE Dose

Virtual compartment

Pharmacokinetic-pharmacodynamic potency of a drug

KA

Dose = 800 mg KA = 1 h-1 KE = 0.2 h-1 EDK50 = EC50 . CL = 1 mg.L-1 . 16 L.h-1 = 16 mg.h-1

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Mechanistic model: example of a viral kinetic model based on the predator-prey principle (Lotka-Volterra)

Target cell (activated CD4+ cells): dT/dt = b – d1T – (1-INH)iVT Actively infected cells (short-lived): dA/dt = f1(1-INH)iVT – d2A + aL Latently infected resting cells (long lived): dL/dt = f2(1-INH)iVT – d3L – aL Infectious virus (copies HIV-1 RNA): dV/dt = p.A – C.V

RR0INH>1 growth RR0INH=1 survival RR0INH<1 extinction

Jacqmin et al., PAGE 2007

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Pre-clinical application: Modelling the anti-lipolytic effect of an adenosine A1-receptor agonist

The data were obtained from: E.A Van Schaick,. H.J.M.M. De Greef, M.W.E. Langemeijer, M.J. Sheehan, A.P. IJzerman, and M. Danhof,: Pharmacokinetic-pharmacodynamic modeling of the anti-lipolytic and anti-ketotic effects of the adenosine A1-receptor agonist N6-(p-sulphophenyl)adenosine in rats.

  • Br. J. Pharmacol., 122, 525-533 (1997)
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IC50 + SPA NEFA Kin Kout Effect = 1 - Triglycerides Imax . SPA

Would it be possible to analyse the dose-response-time data in absence of pharmacokinetics?

Pharmacokinetics

Dose SPA k12 k21 k10

Pharmacodynamics

EDK50 + DDR Imax . DDR Dose SPA k12 k21 k10 Dose DDR KDE NEFA KS KD Effect = 1 - Triglycerides

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The individual NEFA plasma concentration-time profiles are fitted well with an adapted K-PD model

400 g kg-1/15 min 120 g kg-1/60 min 60 g kg-1/15 min 60 g kg-1/5 min

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The parameters EDK50, /KDE, Emax, and baseline are similar Differences in KD/Kout usually occur when the effect is directly linked to the central compartment and the compound follows a multi- compartmental distribution

* Secondary parameters ** Imax was fixed for the 15 g in 5 min and 15 g in 15 min treatments

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Simulation

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Some principles (1)

  • Simulation models usually consist of
  • Structural model equations
  • Structural model parameters
  • Mean
  • Uncertainty
  • Correlation between parameter estimates
  • Random parameters
  • inter-individual variability
  • intra-individual variability
  • inter-occasion variability
  • Simulations are usually performed at different levels
  • Typical subject
  • Entire (sub-)population
  • Study
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Uncertainty and correlation of parameter estimates

Uncertainty Uncertainty & correlation D a t a d e n s i t y

Model 18

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Simulations excluding correlation between the parameters Model

  • Emax dose-response model
  • ED50 (mean [CV])= 10 mg [60%]
  • Emax (mean [CV])= 100 [30%]
  • Correlation not implemented

Results

  • 10, 50 and 90 percentiles of

response in function of dose

Simulations

  • 1500 replicates
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Simulations including correlation between the parameters Model

  • Emax dose-response model
  • ED50 (mean [CV])= 10 mg [60%]
  • Emax (mean [CV])= 100 [30%]
  • Correlation implemented = 0.8

Results

  • 10, 50 and 90 percentiles of

response in function of dose

Simulations

  • 1500 replicates

Desired effect

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Some principles (2)

  • Simulations can be performed to:
  • Describe observations
  • Explain observations
  • Understand the system
  • Interpolate and/or extrapolate
  • Estimate the risks associated to
  • Random effect
  • Uncertainty
  • Hypothesis
  • Evaluate different (if) scenarios or hypotheses
  • Optimize study designs
  • Others…
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Conclusion/recommendation

Magritte 1929

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Backup slides

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Analysis of the PK-PD data

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Parameterization: ensure that sampled parameters are meaningful and simulations realistic

  • Estimate transformed parameters
  • e.g. estimating log(ED50) will ensure values of

ED50 >0 when sampling from uncertainty

  • Assume log-normal distribution when acceptable
  • If response needs to be between 0 and 1, use logit

transformation

  • Evaluate the correlation in the parameter estimates and in the

inter-subject random effect

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Non-linear (mixed effect) modelling is recommended to estimate the fixed (mean) and random (inter-individual and residual variability) parameters of PK-PD models

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Empirical Bayesian Estimation is used to estimate the individual model parameters (e.g. POSTHOC function of NONMEM)

Where: m = number of parameters n = number of data points Cp’ = predicted serum level Cp = observed serum level

  • = standard deviation of drug assay

P’ = revised population parameter P = population parameter

  • = standard deviation of population parameter

http://www.rxkinetics.com/bayes.html

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Available software for modeling in PK-PD

  • NONMEM
  • MONOLIX
  • WinNonlin, WinNonMix
  • SAS
  • PROC NLIN
  • PROC MIXED
  • S-PLUS
  • lm, lmList
  • nls, nlminb
  • lme, nlme, etc
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Available software for simulation in PK-PD

  • NONMEM
  • MONOLIX
  • WinNonlin, WinNonMix
  • SAS
  • S-Plus
  • MATLAB
  • Pharsight Trial Simulator (TS2)
  • Berkeley Madonna
  • ACSL
  • Adapt
  • Stella
  • P-Pharm
  • Pspice
  • Mathematica
  • And many others …