Dosimetry & Physiologically Based Pharmacokinetics

1. Dosimetry & Physiologically Based Pharmacokinetics Melvin Andersen CIIT Centers for Health Research October 16, 2006 University of North Carolina

2. Exposure - Dose - Response Relationships Exposure absorption, distribution; metabolism Tissue Dose chemical actions; receptor binding Molecular Interactions receptor activation; tissue reactivity Early Cellular Interactions functional changes: i.e., enhanced contractility, hepatic failure Toxic Responses cancer; tissue disease; reproductive - neurologic effects

3. 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

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·time + B e-kb·time Conventional Compartmental PK Modeling

6. 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

7. Many Scientists Been Interested in PBPK Approaches • Haggard/Kety – Efficacy of anesthetic gases/vapors • Teorell – Drug pharmacokinetics • Mapleson – Inhaled gases & analog computation • Fiserova-Bergerova – Metabolized vapors in workplace • Rowland/Wilkinson – Clearance Concepts in PKs • Bischoff and Dedrick – Engineering approach for PBPK

8. Physiological Modeling Of Volatiles Haggard (1924) Physiological Modeling Of Drugs Teorell (1937) Kety (1951) Mapleson (1961) Riggs (1963) Fiserova-Bergerova (1974) Bischoff (1971) Dedrick (1973) Rowland and Wilkinson (1975) Volatile Organic Compounds Ramsey and Andersen (1984) CH2Cl2 Dioxin VCM & TCE ESTERS More widespread interest for use in Risk Assessment and Drug Industry

9. Diethyl Ether – Uptake into the Body Expired Air Inspired Air Dead Space Lung Ventilation PulmonaryBlood Body Tissue Capillary Blood From: Hagaard (1924)

10. Pulmonary Equilibration Terms: Qc = cardiac output Qp = alveolar ventilation Cinh = inhaled concentration Cexh = exhaled concentration Cart = arterial concentration Cven = venous concentration Pb =blood/air partition coefficient QpCexh QpCinh Cexh Cart QcCven QcCart Problem: Estimate amount taken up in first few breaths. Rate of uptake = QcCart

11. Haggard, 1924 The equation for net uptake: Qp (Cinh – Cexh) = Qc (Cart-Cven) In first few breaths Cven = 0. The equilibration assumption has Cexh = Cart/Pb, so Qp Cinh = Qc Cart + Qp Cart/Pb Cart = Qp Cinh Pb/(Pb Qc + Qp) Uptake = Qc Cart = Pb Qc Qp Cinh /(Pb Qc + Qp) Limiting conditions of solubility….

12. Pulmonary Uptake (1924) • Evaluate for limiting conditions: • Pb << 1; rate = PbQcCinh (poorly soluble) • Pb >> 1; rate = QpCinh (very soluble) • Former is blood flow limited; latter is ventilation limited. • Provided physiological insight in behavior, but no available techniques could solve equations for more complete biological description of mammalian system.

13. The System of Interest has a group of Parallel Physiological Compartments Lung Fat Body Muscle Kety (1951)

14. 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)

15. Kety (1951) • The kinetic behavior of the tissues is related to three tissue characteristics - volume, blood flow and partition coefficient. For infusion into a tissue at constant concentration, we have a simple exponential for filling: Ct = Pt * Cart (1 – e –(Qt/(Pt*Vt)*time)) Tissue filling or elimination occurs with a rate constant Qt/(Pt x Vt)

16. Input Concentration Invariant (Cart constant) Ct = Pt * Cart (1 – e –(Qt/(Pt*Vt)*time)) Steady State Unrealistic physiologically, but shows general dependence of rate parameters on physiological and chemical specific parameters

17. Mapleson’s Use of an Analog Computational Strategy Permits Solution of Sets of Equations for any Input Function Inspired tension Arterial tension Alveolar vent Dead space vent Circulation TISSUE 2 TISSUE 3 TISSUE 1 LUNGS Venous (=tissue Tension) Alveolar tension Alveolar vent Alveolar (=arterial) tension Blood flows x blood/gas coeffs. Inspired tension Tissue (=venous) tensions Lung tissue and arterial blood Lung air Tissue volumnes x tissue/gas coeffs. Mapleson (1963) expressed physiological model as an electrical analog. The time course of voltages can then be estimated to predict time course of chemical in the physiological system.

18. C1 R1 Qt + Qt Pt, Vt, Ct Ca Cvt R2 Vm Km Fiserova-Bergerova Introduces Metabolism into the Electrical Analog for Work on Occupational Chemicals Use electrical analog to study metabolized vapors and gases.

19. Compartmental and Physiological Modeling of Drugs Teorell (1937) Blood circulation Tissue boundaries k2 k3 k4 k1 k5 Chemical Inactivation “fixation” etc. Subcutis etc. Drug depot Dose N. Local Tissues Inactivation Blood & equivalent blood volume Kidney etc. elimination Symbol D B K T I Amount x y u z w Volume V1 V2 – V3 – Concentration x/V1 y/V2 - z/V3 - Perm. Coeff. k1’ – k4’ k2’ - Velocity Out K1=k1’/V1 - K4 = k4’/V2 k3=k2’/V3 k5 Constant In neglected - not existing k2=k2/V2 - Name of Resorption - Elimination Tissue take up Inactivation process as output

20. Teorell (1937) • Provided 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.

21. Blood Flow Characteristics in Animals & Digital Computation LUNG Right heart Left heart Upper body Liver Spleen Small intestine Large intestine Kidney Trunk Lower extremity Bischoff and Brown (1966)

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

23. Compartments in Physiological Model for Methotrexate Plasma QL -QG QG Liver G.I. Tract Gut absorption Feces C1 C2 C3 C4 T T T r3 r1 r2 Gut Lumen QK Kidney QM Muscle Bischoff et al. (1971)

24. 10 10 GL L K L GL 1.0 1.0 Methotrexate Concentration mcg/g Methotrexate Concentration mcg/g K P 0.1 0.1 P M M 0.01 0.01 120 240 0 180 60 120 240 0 180 60 minutes minutes 3 mg/kg 0.12 mg/kg Methotrexate - Bischoff et al. (1971)

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 Comparison 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 (ALSO IN TOXICOLOGY) • Organize available information • Expose contradictions • Explore implications of beliefs about the chemical • Expose data gaps • Predict response under new or inaccessible conditions • Identify what’s important • Suggest and prioritize new experiments Yates, F.E. (1978). Good manners in good modeling: mathematical models and computer simulation of physiological systems. Amer. J. Physiol., 234, R159-R160. 1978. Andersen et al., Applying simulation modeling to problems in toxicology and risk assessment: a short perspective. Toxicol. Appl. Pharmacol., 133, 181-187.

33. Learning from PBPK Models Cinh Cexh Lung Haggard, 1924 Kety, 1951 Mapelson, 1963 Fiserova-Bergerova, 1974 Ramsey & Andersen, 1984 Reitz et al., 1990 Fat Viscera Venous Blood Muscle/Skin Liver Elimination Metabolism (Vmax; Km) Vd

34. Initial Fits – Some Good, some not so good Plasma Concentration Fat Concentration Excretion Rate Exhaled D4

35. Liver Kcarrier Blood Lipid Compartment Kremoval Fat Revise the Model: • Account for lipid storage compartments within tissues • Account for lipid compartment to blood that transport compound from liver-peripheral tissue transport of chylomicrons, etc. Q Q Liver Cart Cvl Liver Lipid Compartment

36. Cexh Cinh Lung • Revised Model Structure: • Lipid storage in tissues • Liver • Lung • Chylomicron-like lipid blood transport • Second fat compartment Fat 2 Fat 1 Venous Blood Muscle/Skin Viscera Vd Liver Metabolism Blood Lipid Elimination

37. New Fits with Lipid Components in Blood Plasma Concentration Lung Concentration Exhaled D4 Plasma Then some experiments…..examine lipids in blood

38. 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 Define Realistic Model Make Predictions Collect Needed Data Refine Model Structure Physiologically Based Pharmacokinetic (PBPK) Modeling

39. Where are we heading – PK, PD, systems? Dose-Dependent Distribution of Dioxin

40. Induction is Non-Uniform in Liver • The PBPK model for dioxin protein induction needs to account for regional differences in response. • How was this be accomplished?

41. i n d u c i b l e s y n t h e s i s d e g r a d a t i o n b i n d i n g Liver Bulk Structure: Induction Equations: p r o t e i n K o ; K ( i n d ) k ( e l i m ) n k ( m a x ) [ A h - d i o x i n ] d [ P r ] / d t = k o + - k ( e l i m ) [ P r ] n n K b 1 + [ A h - d i o x i n ] Creating a Multi-Compartment Liver Acinus:

42. Visualization and Comparison with Immunohistochemistry • Simulation of geometric organization is necessary. The predicted induction in the various sub-compartments was used to ‘paint’ regions in a two-dimensional acinus. Representation of a field of acini in a liver section

43. Comparing the pathologist’s view with the modeler’s predictions…..

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

45. 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

46. Physiological Pharmacokinetic Modeling and its Applications in Safety & Risk Assessments References: Andersen, M.E., Clewell, H.J. III, Gargas, M.I., Smith, F.A., and Reitz, R.H. (1987). Physiologically-based pharmacokinetics and the risk assessment process for methylene chloride. Toxicol. Appl. Pharmacol. 87, 185 Andersen, M.E., Clewell, H.J., III, Gargas, M.L., MacNaughton, M.G., Reitz, R.H., Nolan, R., McKenna, M. (1991) Physiologically based pharmacokinetic modeling with dichloromethane, its metabolite, carbon monoxide, and blood carboxyhemoglobin in rats and humans. Toxicol. Appl. Pharmacol., 108, 14. Andersen, M.E., Mills, J.J., Gargas, M.L., Kedderis, L.B., Birnbaum, L.S., Neubert, D., and Greenlee, W.F. (1993). Modeling receptor-mediated processes with dioxin: Implications for pharmacokinetics and risk assessment. J. Risk Analysis, 13, 25. Bischoff, K.B. and Brown, R.H. (1966). Drug distribution in mammals. Chem. Eng. Prog. Sym. Series, 62: 33. Dedrick, R.L. (1973). Animal scale-up. J. Pharmacokinet. Biopharm., 1: 435. Bischoff, K.B., Dedrick, R.L., Zaharko, D.S., and Longstreth, J.A. (1971). Methotrexat pharmacokinetics. J. Pharm. Sci., 60: 1128 Gerlowski, L.E. and Jain, R. J. (1983). Physiologically based pharmacokinetic modeling: principles and applications. J. Pharm. Sci., 72: 1103.

47. Haggard, H.W. (1924). The absorption, distribution, and elimination of ethyl ether. II. Analysis of the mechanism of the absorption and elimination of such a gas or vapor as ethyl ether. J. Biol. Chem., 59: 753 Kety, S.S. (1951). The theory and applications of the exchange of inert gases at the lungs. Pharmacol. Rev., 3: 1. Levy, G. (1965). Pharmacokinetics of salicylate elimination in man. J. Pharm. Sci., 54: 959 Mapleson, W.W. (1963). An electrical analog for uptake and exchange of inert gases and other agents. J. Appl. Physiol., 18: 197 Riggs, D.S. (1963). The mathematical approach to physiological problems: A critical primer. MIT Press. Cambridge, MA, 445 pp 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. Rowland, M., Benet, L.Z., and Graham, G.G. (1973). Clearance concepts in pharmacokinetics. J. Pharmacokin. Biopharm., 1:123. Teorell, T. (1973a). Kinetics of distribution of substances administered to the body. I. The extravascular modes of administration. Arch. Int. Pharmacodyn., 57:205 Teorell, T. (1973b). Kinetics of distribution of substances administered to the body. I. The intravascular mode of administration. Arch. Int. Pharmacodyn., 57:226 Wilkinson, G.R. and Shand, D.G. (1975). A physiological approach to hepatic drug clearance. Clin. Pharmacol. Ther., 18: 377.