Pharmacokinetic Modeling of Environmental Chemicals Part 1: Principles

1. Pharmacokinetic Modeling of Environmental ChemicalsPart 1: Principles Harvey J. Clewell, Ph.D. Director, Center for Human Health Assessment The Hamner Institutes for Health Sciences Research Triangle Park, North Carolina

3. 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.

4. intravenous inhalation Blood Conc - mg/L time - min Pharmacokinetics The study of the quantitative relationships between the absorption, distribution, metabolism, and eliminations (A-D-M-E) of chemicals from the body. (Chemical) k(abs) k(elim) urine, feces, air, etc. C1 V1 k12 k21 C2 V2

5. A2 k21 k12 Tissue Concentration Tissue Concentration X X A1 X X X X KO kout X X X X X X X X X X time time Select Model Fit Model to Data Collect Data Ct = A e –ka·t + B e-kb·t Conventional Compartmental PK Modeling

6. Volume? Example of Simple Kinetic Model:One-compartment model with bolus dose Purpose:In a simple (1-compartment) system, determine volume of distribution Dose Terminology: Compartment = a theoretical volume for chemical 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 chemical (C) in compartment 3. Calculate: A ‘compartmental’ Volume (V)

7. Example of Simple Kinetic Model:One-compartment model with bolus dose • Basic assumption: • Well stirred, instant equal distribution within entire compartment • Volume of distribution = A/C • In this classical model, 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 the chemical is able to leave the container?

8. Describing the Rates of Chemical Processes- 1 Chemical in the System • Rate equations: • Describe movement of chemical 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 chemical concentration rate = k x C0 = k • First-order process: • rate is proportional to concentration of ONE chemical rate = k x C1

9. M-M kinetics Describing the Rates of Chemical Processes- 2 Chemical Systems • Second-order process: • rate is proportional to concentration of both chemicals Rate = k x C1 x C2 • Saturable processes*: • Rate is dependent on interaction of two chemicals • One reactant, the enzyme, is constant • Described using Michaelis-Menten* equation Rate = (Vmaxx C)/ ( C + Km) *Michaelis-Menten kinetics can describe: • Metabolism • Carrier-mediated transport across membranes • Excretion

10. Dose Conc? 1-Comp model with bolus dose and 1st order elimination Purpose:Examine how concentration changes with time Mass-balance equation (change in C over time): - dA/dt = -ke x A, or - dC/dt = -ke x C where ke = elimination rate constant • Concentration; • - Rearrange and integrate above rate equation • C = C0 x e-ke · t, or • ln C = ln C0- ke· t • Half-life (t1/2): • -Time to reduce concentration by 50% • -replace C with C0/2 and solve for t • t1/2 = (ln 2)/ke = 0.693/ke

11. Conc AUC 1-Comp model with bolus dose and 1st order elimination Clearance: volume cleared per time unit - if ke = fraction of volume cleared per time unit, ke = CL/V (CL=ke*V) Dose Calculating Clearance using Area Under the Curve (AUC): AUC = average concentration - integral of the concentration -  C dt CL = volume cleared over time (L/min) dA/dt = - keA = -ke V C dA/dt = - CL · C  dA = - CL  C dt Dose = CL · AUC CL = Dose / AUC

12. 1-Comp model with continuous infusion and 1st order elimination Calculating Clearance at Steady State: • At steady state, there is no net change in concentration: dC/dt = k0/V – ke · C = 0 • Rearrange above equation: k0/V = ke · Css • Since CL = ke · V , CL = k0/Css Steady State

13. k12 1 2 k21 ke 2-Comp model with bolus dose and 1st order elimination Calculating Rate of Change in Chemical: • Central Compartment (C1): dC1/dt = k21· C2 - k12· C1 - ke· C1 • Peripheral (Deep) Compartment (C2): dC2/dt = k12· C1 - k21· C2

14. 100 10 1 Linear and Non-linear Kinetics • Linear: • All elimination and distribution kinetics are 1st order • Double dose double concentration • Non-linear: • At least one process is NOT 1st order • No direct proportionality between dose and compartment concentration

15. PBPK Modeling • Pharmacokinetic modeling is a valuable tool for evaluating tissue dose under various exposure conditions in different animal species. • To develop a full understanding of the biological responses caused by exposure to toxic chemicals, it is necessary to understand the processes that determine tissue dose and the interactions of chemical with tissues. • Physiological modeling approaches are used to uncover the biological determinants of chemical disposition

16. Physiologically Based Pharmacokinetics Qp Ci Cx Qc Qc Ca Lung QL Cvl Liver Qf Cvf Fat Qr Cvr Rapidly perfused (brain, kidney, etc.) Slowly perfused (muscle, bone, etc.) Qs Cvs

17. PBPK Models Building a PBPK Model: • Define model compartments • Represent tissues • Write differential equation for each compartment • Assign parameter values to compartments • Compartments have defined volumes, blood flows • Solve equations for concentration • Numerical integration software (e.g. Berkeley Madonna, ACSL) Simple model for inhalation

18. Parameterizing the Model: Experimental Determination • Partition Coefficients: • in vitro: vial equilibration (CTissue/Cair) dialysis (CTissue/Cbuffer) ultrafiltration (CTissue/Cbuffer) • in vivo: steady state (CTissue/CBlood) • Metabolism: • in vitro: tissue homogenate cell suspension tissue slice cell gas uptake • in vivo: direct measurement of metabolites

19. You can be wrong! Air Metabolic Constants Tissue Solubility Tissue Volumes Blood and Air Flows Experimental System Lung Body Tissue Concentration X Fat X X X X X X Liver X Model Equations Time Physiologically Based Pharmacokinetic (PBPK) Modeling Define Realistic Model Make Predictions Collect Needed Data Refine Model Structure

20. Design/Conduct Critical Experiments Problem Identification Extrapolation to Humans Physiological Constants Mechanisms of Toxicity Compare to Kinetic Data Biochemical Constants Model Formulation Literature Evaluation Validate Model Refine Model Simulation Approach for Developing a PBPK Model

21. Models in Perspective “…no model can be said to be ‘correct’. The role of any model is to provide a framework for viewing known facts and to suggest experiments.” -- Suresh Moolgavkar “All models are wrong and some are useful.” -- George Box

22. QT QT CVT CA Same as 1-compartment model with continuous infusion PBPK Model Compartment Types- Storage compartment • Rate in = QT · CA where QT = tissue blood flow, CA = arterial blood conc • Rate out = QT · CVT = QT · CT/PT where CVT = conc in tissue blood, CT = conc in tissue, PT = partition coefficient • Assume Well-stirred compartment, so that, CVT = CT/PT

23. QT QT CVT CA Same as 1-compartment model with continuous infusion PBPK Model Compartment Types- Storage compartment • Calculating Change in Amount: • Change in amount = rate in – rate out dA/dt = QT x (CA – CT/PT) dC/dt = QT x (CA – CT/PT) /V

24. Description for a Single Tissue Compartment Terms Qt = tissue blood flow Cvt = venous blood concentration QtCart QtCvt Pt = tissue blood partition coefficient Vt; At; Pt Vt = volume of tissue Tissue At = amount of chemical in tissue mass-balance equation: dAt =Vt dCt = QtCart - QtCvt dt dt Cvt = Ct/Pt (venous equilibration assumption)

25. Qalv Qalv Alveolar Space Calv (Cart/Pb) Cinh Qc Qc Lung Blood Cven Cart Qt Fat Tissue Group Cvt Cart Qm Muscle Tissue Group Cart Cvm Qr Richly Perfused Tissue Group Cart Cvr Liver Metabolizing Tissue Group Ql ( ) Cvl Cart Vmax Metabolites Km Then used in toxicology..... Is any of this really new? Ramsey and Andersen (1984)

26. Styrene & Saturable metabolism rate of loss in venous blood rate of uptake in arterial blood rate of change of amount in liver = - rate of loss by metabolism - dAl= Ql (Ca- Cvl) - Vm Cvl Km+ Cvl dt • Equations solved by numerical integration to simulate kinetic behavior. • With venous equilibration, flow limited assumptions.

27. 100 Conc = 1200 ppm Conc = 600 ppm 10 1 Venous Concentration – mg/lier blood 0.1 Conc = 80 ppm 0.01 0.001 0 5 10 15 20 25 TIME - hours Dose Extrapolation – Styrene How does it work?

28. Qalv Qalv Alveolar Space Calv (Cart/Pb) Cinh Qc Qc Lung Blood Cven Cart IV Oral Qt Fat Tissue Group Cvt Cart Qm Muscle Tissue Group Cart Cvm Qr Richly Perfused Tissue Group Cart Cvr Cvl Liver Metabolizing Tissue Group Ql ( ) Cart Vmax Metabolites Km What do we need to add/change in the models to incorporate another dose route – iv or oral?

29. Styrene - Dose Route Extrapolation What do we need to add/change in the models to incorporate these dose routes? 10 100 IV Oral 10 1.0 Styrene Concentration (mg/l) Styrene Concentration (mg/l) 1.0 0.1 0.1 0.01 0.01 3.0 2.4 3.6 1.2 2.8 0 0.6 1.8 2.0 1.6 2.4 0.8 0 0.4 1.2 Hours Hours

30. Qalv Qalv Alveolar Space Calv (Cart/Pb) Cinh Qc Qc Lung Blood Cven Cart Qt Fat Tissue Group Cvt Cart Qm Muscle Tissue Group Cart Cvm Qr Richly Perfused Tissue Group Cart Cvr Cvl Liver Metabolizing Tissue Group Ql ( ) Cart Vmax Metabolites Km What do we need to add/change in the models to describe another animal species? • Sizes • Flows • Metabolic Constants

31. 0.1 10 1.0 80 ppm 0.01 0.1 Blood Styrene Concentration (mg/l) Styrene Concentration (mg/l) 0.01 376 0.001 0.001 Exhaled Air 216 51 0.0001 0.00001 0.0001 40 16 32 48 0 24 8 3.0 7.5 9.0 1.5 4.5 6.0 0 Hours Hours Styrene - Interspecies Extrapolation What do we need to add/change in the models to change animal species?

32. ADVANTAGES OF SIMULATION MODELING IN PHYSIOLOGY AND ALSO IN PHARMACOKINETICS & RISK ASSESSMENT • Codification of facts and beliefs (organize available information) • Expose contradictions in existing data/beliefs • Explore implications of beliefs about the chemical • Expose serious data gaps limiting use of the model • Predict response under new/inaccessible conditions • Identify essentials of system structure • Provide representation of present state of knowledge • Suggest and prioritize new experiments

33. Other Stimulus RTK Adaptor MAPK TCDD Ligand Ah Receptor Transcription DRE A ‘Systems’ Approach for Dose Response Uptake Absorption Distribution Excretion Metabolism Interaction w/ cellular networks Effects

34. Exposure Tissue Dose Biological Interaction Perturbation Inputs Biological Function Impaired Function Adaptation Disease Morbidity & Mortality An Alternate View of PK and PD processes – Systems and Perturbations

35. Physiological Pharmacokinetic Modeling Principles References Andersen ME, Clewell HJ, Frederick CB. 1995. Applying simulation modeling to problems in toxicology and risk assessment -- a short perspective. Toxicol Appl Pharmacol 133:181-187. Brown, R.P., Delp, M.D., Lindstedt, S.L., Rhomberg, L.R., and Beliles, R.P. 1997. Physiological parameter values for physiologically based pharmacokinetic models. Toxicol Indust Health 13(4):407-484. Clewell, H.J., and Andersen, M.E. 1985. Risk Assessment Extrapolations and Physiological Modeling. Toxicol Ind Health, 1(4):111 131. Clewell, H.J., Andersen, M.E., Barton, H.A., 2002. A consistent approach for the application of pharmacokinetic modeling in cancer and noncancer risk assessment. Environ. Health Perspect. 110, 85–93. Dedrick, R.L. 1973. Animal scale up. J Pharmacokinet Biopharm 1:435 461. Dedrick, R.L., and Bischoff, K.B. 1980. Species similarities in pharmacokinetics. Fed Proc 39:54 59. Gerlowski, L.E. and Jain, R. J. (1983). Physiologically based pharmacokinetic modeling: principles and applications. J. Pharm. Sci., 72: 1103. Ramsey, J.C. and Andersen, M.E. (1984). A physiologically based description of the inhalation pharmacokinetics of styrene in rats and humans. Toxicol. Appl. Pharmacol. 73, 159. Reddy, M.B. (2005). PBPK modeling approaches for special applications: Dermal exposure models. In: Physiologically Based Pharmacokinetic Modeling: Science and Applications, eds. M.B. Reddy, R.S.H. Yang, H.J. Clewell, III, and M.E. Andersen. John Wiley & Sons, Hoboken, New Jersey, pp. 375-387. Yates, F.E. (1978). Good manners in good modeling: mathematical models and computer simulation of physiological systems. Amer. J. Physiol., 234, R159-R160. 1978.