Introduction to Pharmacokinetic Modeling

Transcription

1 Introduction to Pharmacokinetic Modeling Introductory PBPK Modeling Tutorial PaSiPhIC July 13, 2011 Harvey J. Clewell, PhD, DABT Director, Center for Human Health Assessment The Hamner Institutes for Health Sciences Copyright 2009 by The Hamner Institutes for Health Sciences. May not be reproduced without permission

2 Pharmacokinetics Studies of the change in chemical distribution over time in the body Explores the quantitative relationship between Absorption, Distribution, Metabolism, and Excretion of a given chemical Classical models Data-based, empirical compartments Describes movement of chemicals with fitted rate constants Physiologically-based models: Compartments are based on real tissue volumes Mechanistically based description of chemical movement using tissue blood flow and simulated in vivo transport processes.

3 Alternative Approaches to Pharmacokinetic Modeling Non-compartmental Data summarization Compartmental Statistical analysis Physiologically Based Integration of Diverse Data Extrapolation

4 Teorell (1937) Provide a clear physiological description of determinants of drug disposition. Lacked the ability to solve the series of equations and simplified the systems. Over the years so-called compartmental PK analysis was developed to examine pharmacokinetic behavior. These simplified models give equations that have exact solutions and have provided many useful insights despite their very much simplified depiction of animal physiology. PK, more as study of systems of equations with exact solutions, rather than the study of PK processes.

5 Compartmental and physiological Teorell (1937) Dose N. Local k 1 modeling of drugs Blood circulation Tissue boundaries Subcutis etc. Drug depot Blood & equivalent blood volume k 4 k 2 k 3 k5 Kidney etc. elimination Tissues Symbol D B K T I Amount x y u z w Volume V 1 V 2 V 3 Concentration x/v 1 y/v 2 z/v 3 Perm. Coeff. k 1 k 4 k 2 Velocity Out K1=k1 /V1 K 4 = k 4 /V 2 k 3 =k 2 /V 3 k 5 Constant In neglected not existing k 2 =k 2 /V 2 Chemical Inactivation fixation etc. Inactivation Name of Resorption Elimination Tissue take up Inactivation process as output

6 Conventional compartmental PK modeling Tissue Concentration X X X X X X X X KO k 21 A2 A1 k 12 k out Tissue Concentration X X X X X X X X time time Collect Data Select Model C t = A e ka t + B e -kb t Fit Model to Data

7 Example of simple kinetic model: onecompartment model with bolus dose Dose Volume? Purpose: In a simple (1-compartment) system, determine volume of distribution Terminology: Compartment = a theoretical volume for compound Steady-state = no net change of concentration Bolus dose = instantaneous input into compartment Method: 1. Dose: Add known amount (A) of chemical 2. Experiment: Measure concentration of compound (C) 3. Calculate: A compartmental Volume (V)

8 Example of simple kinetic model: onecompartment model with bolus dose Basic assumption Well stirred, instant equal distribution within entire compartment Volume of distribution = A/C V is an operational volume V depends on site of measurement This simple calculation only works IF Compound is rapidly and uniformly distributed. The amount of chemical is known. The concentration of the solution is known. What happens if a compound is able to leave the container?

9 Describing the rates of drug processes one drug in the system Rate equations describe movement of drug between compartments The previous example had instantaneous dosing. Now, we need to describe the rate of loss from the compartment. Zero-order process Rate is constant, does not depend on drug concentration (Rate = k C 0 = k). First-order process Rate is proportional to concentration of ONE drug (Rate = k C 1 ).

10 Describing the rates of drug processes two drugs in the system Second-order process Rate is proportional to concentration of both drugs (Rate = k C1 C2). Saturable process Rate is dependent on interaction of two drugs. One reactant, the enzyme, is constant. Described using Michaelis-Menten equation Rate = (Vmax C)/(C + Km). M-M kinetics Michaelis-Menten kinetics can describe Metabolism Carrier-mediated transport across membranes Excretion Rate C

11 One-compartment model with bolus dose and first-order elimination Dose Conc? Concentration: Purpose: Examine how concentration changes with time Mass-balance equation (change in C over time): - da/dt = -k e x A, or - dc/dt = -k e x C where k e = elimination rate constant - Rearrange and integrate above rate equation C = C 0 x e -ke t, or ln C = ln C 0 - k e t Half-life (t 1/2 ): -Time to reduce concentration by 50% -replace C with C 0 /2 and solve for t t 1/2 = (ln 2)/k e = 0.693/k e

12 One-compartment model with bolus dose and first-order elimination Dose Con c Clearance: volume cleared per time unit - if k e = fraction of volume cleared per time unit, k e = CL/V (CL=ke*V) Calculating Clearance using Area Under the Curve (AUC): AUC = average concentration - integral of the concentration - C dt 10 CL = volume cleared over time (L/min) da/dt = - k e A = -k e V C da/dt = - CL C da = - CL C dt Dose = CL AUC CL = Dose / AUC Conc. 5 0 AUC Time

13 One-compartment model with continuous infusion and first-order elimination Calculating Clearance at Steady State: At steady state, there is no net change in concentration: dc/dt = k 0 /V k e C = 0 Steady State Rearrange above equation: k 0 /V = k e C ss Since CL = k e V, Conc. CL = k 0 /C ss Time

14 Two-compartment model with bolus dose and first-order elimination k k 21 k e Calculating rate of change in each compartment: Central Compartment (C1): dc1/dt = k 21 C 2 - k 12 C 1 - k e C 1 Peripheral (Deep) Compartment (C2): dc2/dt = k 12 C 1 - k 21 C 2 Conc. Time

15 Linear and non-linear kinetics Linear all elimination and distribution kinetics are 1 st order Doubling dose doubling concentration Conc. 10 AUC Conc Time Dose Time Non-linear at least one process is NOT 1 st order No direct proportionality between dose and compartment concentration Conc. Conc Time Time

16 Physiologically Based Pharmacokinetic Model iv dose Basis of Description Plasma Kidney Rapidly Perfused Skin Slowly Perfused Liver VMax, KM, KMI QC QKid QRap QSkn QSlw QLiv oral dose Model structure anatomy metabolism / transport processes Model parameters physiological data (organ weights, blood flows) biochemical data (partition coefficients, metabolism) Model equations system of mass-balance differential equations one equation for each tissue connected by equation for blood E.g., metabolizing tissue (liver): L L ( C C / P ) V C / P /( K C P ) da / dt = Q max + / A L L L L M L L

17 PBPK models Building a PBPK Model: 1. Define model compartments Represent tissues A simple model for an anaesthetic Chemical in air 2. Write differential equation for each compartment Lungs 3. Assign parameter values to compartments Compartments have defined volumes, blood flows 4. Solve equations for concentration Numerical integration software (e.g. Berkeley Madonna, ACSL) Venous side Other Fat tissues Liver Arterial side Elimination

18 Developing and Evaluating a PBPK Model Problem Identification Mechanisms of Toxicity Literature Evaluation Biochemical Constants Physiological Constants Model Formulation Simulation Refine Model Compare to Kinetic Data Evaluate Model (Clewell et al. 2007) Design/Conduct Critical Experiments Apply Model

19 Description for a Single Tissue Compartment Terms Q t = tissue blood flow Q t C art V t ; A t ; P t Tissue Q t C vt C vt = venous blood concentration P t = tissue blood partition coefficient V t = volume of tissue A t = amount of chemical in tissue mass-balance equation: da t = V t dc t = Q t C art - Q t C vt dt dt C vt = C t /P t (venous equilibration assumption)

20 Blood Flow Characteristics in Animals LUNG Right heart Left heart Liver Upper body Kidney Trunk Lower extremity Small intestine Spleen Large intestine Bischoff and Brown (1961)

21 Modeling Tissue Accumulation of Methotrexate Due to Its Interaction with a Critical Enzyme arterial blood Dihyrofolatereductase (DHFR) Methotrexate (tissue blood) Kd Methotrexate (intracellular) MTX-DHFR Complex R(t) MTX-Tissue venous blood R(t) - tissue partition Kd - MTX-DHFR dissociation constant

22 Compartments in Physiological Model for Methotrexate Plasma Q L - Q G Q G Liver G.I. Tract Gut absorption T T T C 1 C 2 C 3 C 4 Feces r 1 r 2 r 3 Gut Lumen Q K Kidney Q M Muscle Bischoff et al. (1971)

23 Methotrexate - Bischoff et al. (1971) Methotrexate Concentration mcg/g GL L K P M minutes mg/kg Methotrexate Concentration mcg/g minutes 0.12 mg/kg L K GL P M

24 Applications of PBPK Models in Drug Development Research and Evaluation Integrate information from different species and routes Provide a validated platform for predictive simulation of drug-drug interactions (DDI) Support more accurate estimation of equivalent human dosing to achieve same dose to target protein as in test animals Predict fetal exposure and lactation transfer Estimate variability of PK across special populations Obese, Elderly, Infants, Diseases Polymorphisms Improve understanding of PD by relating effect to dose at target tissue or binding to target protein (PBPK/PD)

25 Some Examples: Nicotine age-dependent pharmacokinetics Coumarin in vitro to in vivo extrapolation Coumaden consideration of polymorphisms All -Trans Retinoic Acid safety assessment Nicotine PBPK/PD modeling Antiparasitic prodrug dosage regimen optimization

26 Age-Dependent Dosimetry An age-dependent version of the PBPK model was developed to simulate the physiological and biochemical changes in humans associated with growth and aging. All physiological and biochemical parameters in the model change with time based on empirical data; only the chemical specific parameters remain constant. This model was used to simulate blood concentrations of nicotine and its metabolite cotinine for a constant daily oral dose of 1 mg/kg/day nicotine from birth to 75 years

27 Age-Dependent Internal Exposure to Ingested Nicotine (1 ug/kg/day) Blood Conc. of Nicotine (mg/l) 4.0E-4 2.5E-3 Nicotine Cotinine 2.0E-3 3.0E-4 1.5E-3 2.0E-4 1.0E-3 1.0E-4 5.0E-4 Blood Conc. of Cotinine (mg/l) 0.0E Age (years) 0.0E+0 (Clewell et al. 2004)

28 Coumarin In Vitro to In Vivo Extrapolation Chronic oral toxicity studies resulted in statistically significant increases in the incidence of parenchymal cell tumors of the liver in rats and alveolar/bronchiolar tumors of the lung in mice Species-specific differences in the carcinogenicity of coumarin are thought to be metabolism-mediated In vitro metabolism data in the mouse, rat, and human were used in a PBPK model to predict in vivo metabolism across species

29 Coumarin PBPK Model Metabolic parameters for the liver and lung based on in vitro study results Model was validated with time course data from in vivo exposure of humans and rodents (Clewell et al. 1999)

30 Venous Blood Concentrations of Coumarin and 7-Hydroxycoumarin in 2 Human Volunteers (Clewell et al. 1999)

31 Cancer Risk Estimates for Coumarin Intake of 0.1 mg/kg/day in the Human (Clewell et al. 1999) Risk Margin of Exposure Using External Dose: Mouse lung tumors Rat liver tumors Using Target Tissue Dose: Oral Exposure Mouse lung tumors Rat liver tumors Using Target Tissue Dose: Dermal Exposure Mouse lung tumors Rat liver tumors

32 Evaluating pharmacokinetic variability The pharmacokinetic variability across a population is a function of many chemicalspecific, genetic, and physiological factors. Speculation regarding the overall variability in pharmacokinetic sensitivity based on the observed variability of individual pharmacokinetic factors can be highly misleading. Analysis using a PBPK model and Monte Carlo techniques provides a more reliable approach for estimating population pharmacokinetic variability.

33 Example: impact of CYP2C9 Polymorphism on Coumaden (Warfarin) Internal Dose iv dose Plasma QC Kidney QKid Rapidly Perfused QRap Skin QSkn Slowly Perfused QSlw Liver QLiv oral dose (Gentry et al., 2002) VMax, KM, KMI PBPK Model for Coumaden

34 Metabolic Parameters for (S)-Warfarin for Three CYP2C9 Alleles Vmax (mg/hr/kg 3/4 ) Km (mg/l) Intrinsic Clearance Allele Reference Mean CV Mean CV (VmaxC/Km) CYP2C9*1 Haining et al., Takahashi et al., 1998b Sullivan-Klose et al., Rettie et al., Rettie et al., CYP2C9*2 Sullivan-Klose et al., Rettie et al., Rettie et al., Rettie et al., CYP2C9*3 Haining et al., Takahashi et al., 1998b Sullivan-Klose et al., baculovirus/insect cell system, purified enzyme 2 yeast expression, microsomes 3 Hep G2 cells, cell lysate 4 Hep G2 cells, particulate preparation (Haber et al., 2002) 5 expressed in insect cells, purified enzymes

35 Average Prevalence of CYP2C9 Alleles in the U.S. Population Prevalence S1 homozygous 78% S1/S2 heterozygous 12% S1/S3 heterozygous 9% S2 homozygous 1% S2/S3 heterozygous 1% S3 homozygous 0.5% (Haber et al., 2002)

36 Simulation of impact of genetic polymorphism on Warfarin internal dose Plasma Concentration (mg/l) 5 A. CYP2C9*1 Allele Hours Plasma Concentration (mg/l) 5 B. CYP2C9*2 Allele Hours Plasma Concentration (mg/l) 5 C. CYP2C9*3 Allele Hours (Gentry et al., 2002)

37 Frequency of (S)-Warfarin AUC Simulation of impact of genetic Simulation of Impact of Genetic Polymorphism on Warfarin Internal Exposure polymorphism on Warfarin internal dose Normal population Case 2 Total population Case 3 (S)-Warfarin AUC (Gentry et al., 2002)

38 All-trans Retinoic Acid -- Safety Assessment Evaluated as a topical skin treatment Potentially teratogenic at high doses Developed a PBPK model to assess dose metrics for teratogenicity Compared fetal doses expected from maternal dermal use with teratogenic doses in animal studies to estimate margin of safety

39

40 The PBPK model for ATRA includes conversion cisretinoic acid, ring and sidechain oxidation, and formation and enterohepatic circulation of the glucuronides. Each of double-lined box is a separate PK model for one of the metabolites. (Clewell et al. 1997)

41 13-cis-retinoic acid is produced via isomerization. It is also oxidized and glucuronidated. Estimates of fetal/embryo exposures account for all circulating active retinoids (not glucuronides). (Clewell et al. 1997)

42

43 Several dose metrics were calculated. The metrics in studies with overtly toxic responses were compared to those in human use situations for chemotherapy or for cosmeceutical usage. Therapy assumes use as noted in package insert; abuse is use over a much larger area of skin. In all cases, margins of safety are high. (Clewell et al. 1997)

44 Conclusions of PBPK Modeling for Retinoic Acid Modeling results: Topical exposure results in four to five orders of magnitude lower internal exposure than minimal teratogenic doses for any meaningful measure of fetal exposure FDA evaluation: Internal exposure calculations are relatively insensitive to changes in the PBPK model which preserve correspondence with the experimental data Result: Resolved FDA concern, moved forward to labeling discussions

45 Why PBPK/PD? PK/PD modeling typically assumes that the effect is driven by the drug concentration in the central compartment In some cases, the drug concentration in the effect compartment is not well represented by the central compartment Transport Lipophilicity Specific binding Use of PBPK modeling allows the effect to be driven by the drug concentration in the target tissue

46 Example of PBPK/PD Modeling Effect of nicotine on heart rate Nicotine stimulates sympathetic nervous system, with brain as the principle site of action Hysteresis plots of plasma nicotine concentration versus heart rate show a clockwise pattern, suggesting the development of acute tolerance A PBPK model was applied to relate heart rate to nicotine concentration in putative target tissue for effect (brain)

47 Apparent clockwise hysteresis Suggesting development of tolerance (Benowitz data)

48 PBPK Model (Plowchalk et al. 1992)

49 Plasma (left) and brain (right) profiles differ due to binding (Plowchalk et al. 1992)

50 PBPK/PD Description Resolves Hysteresis 95 Heart Rate (beats/minute) (debethizy, pers. comm.) Brain Nicotine Concentration

51 Use of PBPK Modeling to Optimize the Dosage Regimen of an Antiparasitic Prodrug Zhixia (Grace) Yan Division of Pharmacotherapy and Experimental Therapeutics UNC Eshelman School of Pharmacy

52 Prodrug X demonstrated reversible hepatotoxicity in humans Prodrug X is rapidly metabolized to the active metabolite, Y, in the liver The active metabolite, Y accumulated significantly in the liver Could the toxicity have been avoided using a more rational dosage regimen?

53 Dosage Optimization Strategy Characterize the hepatobiliary disposition of pafuramidine and furamidine. Develop and validate a whole-body physiologically-based pharmacokinetic (PBPK) model for pafuramidine and furamidine in rats. Develop a whole-body PBPK model for pafuramidine and furamidine in humans. Optimize dosage regimen based on the human PBPK model.

54 PBPK Predicted Prodrug X/Active metabolite Y Disposition in Human Plasma Concentration in Plasma (μm) X Y Time (h) Terminal t 1/2 (h) Observed Predicted X Y (2.5 d) 3x

55 An Optimized Dosage Regimen for Efficacy and Safety Furamidine Concentration (μm) Time (d) AUC 0-14d 5x 100 mg X twice daily 40 mg Y once daily Liver NOAEL Plasma C eff,min

56 References Clewell HJ, Andersen ME, Wills RJ, Latriano L A physiologically based pharmacokinetic model for retinoic acid and its metabolites. J Am Acad Dermatol 36:S Clewell, H.J., Gentry, P.R., Covington, T.R., Sarangapani, R., and Teeguarden, J.G Evaluation of the potential impact of age- and gender-specific pharmacokinetic differences on tissue dosimetry. Toxicol. Sci. 79: Clewell, H.J., Gentry, P.R., Gearhart, J.M., Allen, B.C.,and Andersen, M.E Comparison of cancer risk estimates for vinyl chloride using animal and human data with a PBPK model. Science of the Total Environment 274(1 3): Clewell, H., Gentry, R., Gearhart, J., Born, S., and Lehman-McKeeman, L Development of a Physiologically-Based Pharmacokinetic (PB-PK) Model and Human Health Risk Assessment for Coumarin. Presentation at Society for Risk Analysis Meeting. Clewell, H.J., Reddy, M.B., Lave, T., and Andersen, M.E Physiologically based pharmacokinetic modeling. In: Gad, SC, ed. Preclinical Development Handbook. John Wiley and Sons, Hoboken, NJ. Gentry, P.R., Hack, C.E., Haber, L., Maier, A., and Clewell, III, H.J An Approach for the Quantitative Consideration of Genetic Polymorphism Data in Chemical Risk Assessment: Examples with Warfarin and Parathion. Toxicol Sci 70: Plowchalk DR, Andersen ME, and debethizy JD A physiologically based pharmacokinetic model for nicotine disposition in the Sprague-Dawley rat. Toxicol Appl Pharmacol. 116(2):