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 development to support decisions that need to be made Candidate Drug Evaluation Global Development Selection Discovery Pre-clinical Phase I Phase IIa Phase IIb Phase III Explore Confirm Explore Confirm Explore Confirm Descriptive Drug & Disease (Semi-)mechanistic PK/PD models models 2 Exprimo confidential
Mechanistic versus descriptive (empirical) models: Mechanistic Descriptive Early stages of development Late stages of development • � • � Good understanding of Fair understanding of • � • � system system (grey box) Interpretable parameters Less meaningful parameters • � • � Interpolation and Interpolation • � • � extrapolation May require less data Usually requires a lot of • � • � data 3 Exprimo confidential
M&S throughout Discovery and Pre-clinical: Current phase Next phase Feasibility assessment mechanism • � Evaluation and selection appropriate • � of action biomarker(s) Define metrics candidate selection • � Optimize designs of early ph-I • � Assess safety margin • � studies with biomarkers Combined meta-analysis and objective • � review of all discovery and pre-clinical data Candidate Early Development Late Development Selection Discovery Pre-clinical Phase-I Phase-IIa Phase-IIb Phase-III Explanatory Confirmatory Explanatory Confirmatory Explanatory Confirmatory 4 Exprimo confidential
Why do we model in drug development? The systems are complex 1. � Nonlinearity and/or time dependency • � Complex data (multiple sources, noisy, errors...) • � To integrate information 2. � Across time, dose-levels, drugs and systems • � To predict and extrapolate 3. � We are not only interested in the specific observation • � We are often not primarily interested in the setting studied • � To optimize further studies 4. � The model can be used as a “knowledge repository” 5. � Describe what is currently known about mechanism of action • � and system The model might help to fill in the “gaps” in data 6. � The model can help us identify and quantify uncertainty 7. � 5 Exprimo confidential
Components of drug models e.g. Dose-Conc. relationship Conc.-Effect relationship Physiological mechanisms Maturation processes Relationships between parameters and compound/ system characteristics Inter-individual, inter-occasion and residual variabilities Uncertainty and correlation 6 Exprimo confidential
Pharmacokinetic-Pharmacodynamic modelling Pharmacology Pharmacokinetics Pharmacodynamics Pharmacotherapeutics Dose Concentration Effect Efficacy Clinics Safety 7 Exprimo confidential
Pharmacokinetic models Exprimo confidential
What happens when a drug is administered as an intravenous bolus? 9 Exprimo confidential
From ‘descriptive’ to ‘mechanistic’ model based on flow dynamic systems Kidneys Liver GFR Lungs CYP Vmax/Km 10 Exprimo confidential
Model with oral absorption (first order) and peripheral compartment G.I. Peripheral k 12 compartment k 21 11 Exprimo confidential
Physiologically-based pharmacokinetic model (PBPK) Q lung Q lung Lung Heart Heart Cl pulm Q Adipose Q Adipose Adipose Q Skin Q Skin Skin Q Bone Q Bone Bone Q Heart Q Heart Heart Venous blood Arterial blood Q Brain Q Brain Brain Q Muscle Q Muscle Muscle Q Stomac Stomach Q Pancreas Q Liver Q Liver Pancreas Liver Q Spleen Spleen Cl hepatic Q Gut Gut Q Kidney Q Kidney Kidney Cl renal 12 Exprimo confidential http://cdds.georgetown.edu/conferences/Theil.pdf
From in silico to in vivo In Silico-based Molecular descriptors Plasma Hepatocyte In vitro-based Solubility Permeability Lipophilicity, pKa protein binding clearance K a , F V ss , Kp’s CL Software-based Gastroplus Vss-Predictor 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 13 Exprimo confidential
Pharmacodynamic models Exprimo confidential
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 15 Exprimo confidential
Clark’s occupation theory RT or B MAX = 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) K 1 = association rate constant (min -1 ) K -1 = dissociation rate constant (min -1 ) K A = Association constant [ ] = concentration (nM) 16 Exprimo confidential
Some graphical representations B MAX = 8 nM K D = 2 nM B MAX = 8 nM K D = 2 nM B MAX = 8 nM K D = 2 nM 17 Exprimo confidential
From receptor occupancy to pharmacological effect A simple view: the E MAX 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 E MAX EC 50 18 Exprimo confidential
Some derived/simplified models log-linear effect concentration model linear effect concentration model 19 Exprimo confidential
From receptor occupancy to pharmacological effect A more complete view Stefenson Clark Ariëns Furchgott Generation Change Receptor Ligand of second Effect in cellular binding messenger activity Affinity Intrinsic Intrinsic activity efficacy e and � (S) K D � � and [R] t and f (S) System/tissue Drug specific specific 20 Exprimo confidential
E MAX model and sigmoid E MAX model � =2 � =1 � =1 � =2 � =0.5 � =0.5 21 Exprimo confidential
Operational model of agonism: effect of intrinsic activity (different drugs) 22 Exprimo confidential
Apparent dissociation between receptor occupancy and measured effect: Production of glucose by � -adrenoreceptor stimulation 23 Exprimo confidential
PK-PD models Exprimo confidential
Concentration–effect–time relationship: direct response � inhibition Dose = 0.8 mg KA = 1 h -1 V = 80 L CL = 16 L.h -1 IC 50 = 1.0 ng/mL n = 1.0 I max = 1.0 BSL = 100 25 Exprimo confidential
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. 26 Exprimo confidential
Effect compartment (or Link) model Dose = 0.8 mg KA = 1 h -1 V = 80 L CL = 16 L.h -1 IC 50 = 1.0 ng/mL n = 1.0 I max = 1.0 BSL = 100 Ke0 = 0.2 h -1 Plasma Plasma Biophase Biophase Biophase 27 Exprimo confidential
Concentration–effect–time relationship for an indirect response model with inhibition of build-up K in K out R Inhibition of build-up : R H(t)= I Dose = 0.8 mg KA = 1 h -1 V = 80 L CL = 16 L.h -1 IC 50 = 1.0 ng/mL n = 1.0 I max = 1.0 Kin = 100 Runits.h -1 Kout = 1 h -1 28 Exprimo confidential
Indirect response models K in K out R Inhibition of build-up : R H(t)= I K in K out R Inhibition of loss : R H(t)= I K in K out R Stimulation of build-up : R H(t)=S K in K out R Stimulation of loss : R H(t)=S 29 Exprimo confidential
KPD model: analysis of effect-time profile in the absence of pharmacokinetic data Dose Dose = 800 mg KA = 1 h -1 KA KE = 0.2 h -1 EDK 50 = EC 50 . CL = 1 mg.L -1 . 16 L.h -1 = 16 mg.h -1 Virtual compartment KE Pharmacokinetic-pharmacodynamic potency of a drug 30 Exprimo confidential
Mechanistic model: example of a viral kinetic model based on the predator-prey principle (Lotka-Volterra) Target cell (activated CD4+ cells): dT/dt = b – d 1 � T – (1- INH ) � i � V � T Actively infected cells (short-lived): dA/dt = f 1 � (1- INH ) � i � V � T – d 2 � A + a � L Latently infected resting cells (long lived): dL/dt = f 2 � (1- INH ) � i � V � T – d 3 � L – a � L Infectious virus (copies HIV-1 RNA): dV/dt = p.A – C.V RR0 INH >1 � growth RR0 INH =1 � survival RR0 INH <1 � extinction Jacqmin et al., PAGE 2007 31 Exprimo confidential
Pre-clinical application: Modelling the anti-lipolytic effect of an adenosine A 1 -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 A 1 -receptor agonist N 6 -(p-sulphophenyl)adenosine in rats. Br. J. Pharmacol. , 122 , 525-533 (1997) Exprimo confidential
Would it be possible to analyse the dose-response-time data in absence of pharmacokinetics? Pharmacokinetics Pharmacodynamics Dose Dose Dose I max . SPA � I max . DDR � Effect = 1 - k21 IC 50 � + SPA � Effect = 1 - k21 SPA EDK 50 � + DDR � SPA k12 DDR k12 k10 KDE k10 K out K in Triglycerides NEFA KD KS Triglycerides NEFA 33 Exprimo confidential
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