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

Exposure - Dose - Response Relationships 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 CIIT Centers for Health Research October, 2006

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 CIIT Centers for Health Research October, 2006

Pharmacokinetics Blood Conc - mg/L The study of the quantitative relationships between the absorption, distribution, metabolism, and eliminations (A-D-M-E) of chemicals from the body. (Chemical) intravenous inhalation time - min Blood Conc - mg/L k(abs) k(elim) urine, feces, air, etc. C1 V1 k21 k12 C2 V2 CIIT Centers for Health Research October, 2006

Conventional Compartmental PK Modeling X Tissue Concentration time k12 k21 kout KO A1 A2 X Tissue Concentration time Collect Data Select Model Fit Model to Data Ct = A e –ka·time + B e-kb·time CIIT Centers for Health Research October, 2006

Physiologically Based Pharmacokinetics Qp Ci Cx Qc Qc Lung Ca Cvl QL Liver Cvf Qf Fat Cvr Qr Rapidly perfused (brain, kidney, etc.) Slowly perfused (muscle, bone, etc.) Cvs Qs CIIT Centers for Health Research October, 2006

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 CIIT Centers for Health Research October, 2006

CH2Cl2 Dioxin VCM & TCE ESTERS Physiological Modeling Of Volatiles Haggard (1924) Physiological Modeling Of Drugs Teorell (1937) Mapleson (1961) Riggs (1963) Fiserova-Bergerova (1974) Kety (1951) 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 CIIT Centers for Health Research October, 2006

Diethyl Ether – Uptake into the Body Expired Air Inspired Air Dead Space Lung Ventilation Pulmonary Blood Body Tissue Capillary Blood From: Hagaard (1924) CIIT Centers for Health Research October, 2006

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 QcCart QcCven Problem: Estimate amount taken up in first few breaths. Rate of uptake = QcCart CIIT Centers for Health Research October, 2006

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…. CIIT Centers for Health Research October, 2006

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. CIIT Centers for Health Research October, 2006

The System of Interest has a group of Parallel Physiological Compartments Lung Fat Body Muscle Kety (1951) CIIT Centers for Health Research October, 2006

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) CIIT Centers for Health Research October, 2006

Ct = Pt * Cart (1 – e –(Qt/(Pt*Vt)*time)) 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) CIIT Centers for Health Research October, 2006

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 CIIT Centers for Health Research October, 2006

of Equations for any Input Function Mapleson’s Use of an Analog Computational Strategy Permits Solution of Sets of Equations for any Input Function Inspired tension Arterial tension Dead space vent Alveolar vent Circulation TISSUE 1 TISSUE 2 TISSUE 3 LUNGS Venous (=tissue Tension) Alveolar tension Alveolar vent Alveolar (=arterial) tension Inspired tension Blood flows x blood/gas coeffs. 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. CIIT Centers for Health Research October, 2006

Fiserova-Bergerova Introduces Metabolism into the Electrical Analog for Work on Occupational Chemicals Use electrical analog to study metabolized vapors and gases. + R1 C1 R2 Qt Ca Cvt Vm Km Pt, Vt, Ct CIIT Centers for Health Research October, 2006

Compartmental and Physiological Modeling of Drugs Teorell (1937) Blood circulation Tissue boundaries k1 k4 k2 k3 k5 Chemical Inactivation “fixation” etc. Dose N. Local Subcutis etc. Drug depot Tissues Blood & equivalent blood volume Inactivation 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 CIIT Centers for Health Research October, 2006

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. CIIT Centers for Health Research October, 2006

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) CIIT Centers for Health Research October, 2006

Modeling Tissue Accumulation of Methotrexate Due to Its Interaction with a Critical Enzyme arterial blood Dihyrofolatereductase (DHFR) Kd MTX-DHFR Complex Methotrexate (tissue blood) Methotrexate (intracellular) R(t) MTX-Tissue venous blood R(t) - tissue partition Kd - MTX-DHFR dissociation constant CIIT Centers for Health Research October, 2006

Compartments in Physiological Model for Methotrexate Plasma QL - QG QG Liver G.I. Tract Gut absorption T T T C1 C2 C3 C4 Feces r1 r2 r3 Gut Lumen QK Kidney QM Muscle Bischoff et al. (1971) CIIT Centers for Health Research October, 2006

Methotrexate - Bischoff et al. (1971) K P M 10 1.0 0.1 0.01 60 120 180 240 0.12 mg/kg minutes Methotrexate Concentration mcg/g GL GL L K P M 10 1.0 0.1 0.01 60 120 180 240 3 mg/kg minutes Methotrexate Concentration mcg/g CIIT Centers for Health Research October, 2006

Then used in toxicology..... Is any of this really new? Alveolar Space Lung Blood Fat Tissue Group Muscle Tissue Group Richly Perfused Tissue Group Liver Metabolizing ( ) Metabolites Vmax Km Cart Ql Qr Qm Qt Qc Calv (Cart/Pb) Qalv Cinh Cven Cvt Cvm Cvr Cvl Ramsey and Andersen (1984) CIIT Centers for Health Research October, 2006

Styrene & Saturable metabolism rate of change of amount in liver rate of uptake in arterial blood rate of loss in venous blood = - - 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. CIIT Centers for Health Research October, 2006

Dose Extrapolation – Styrene How does it work? 25 20 15 10 5 100 1 0.1 0.01 0.001 TIME - hours Venous Concentration – mg/lier blood Conc = 80 ppm Conc = 1200 ppm Conc = 600 ppm CIIT Centers for Health Research October, 2006

What do we need to add/change in the models to incorporate another dose route – iv or oral? Alveolar Space Lung Blood Fat Tissue Group Muscle Tissue Group Richly Perfused Tissue Group Liver Metabolizing ( ) Metabolites Vmax Km Cart Ql Qr Qm Qt Qc Calv (Cart/Pb) Qalv Cinh Cven Cvt Cvm Cvr Cvl IV Oral CIIT Centers for Health Research October, 2006

Styrene - Dose Route Comparison What do we need to add/change in the models to incorporate these dose routes? 100 10 IV Oral 10 1.0 Styrene Concentration (mg/l) Styrene Concentration (mg/l) 1.0 0.1 0.1 0.01 0.01 0.6 1.2 1.8 2.4 3.0 3.6 0.4 0.8 1.2 1.6 2.0 2.4 2.8 Hours Hours CIIT Centers for Health Research October, 2006

What do we need to add/change in the models to describe another animal species? Alveolar Space Lung Blood Fat Tissue Group Muscle Tissue Group Richly Perfused Tissue Group Liver Metabolizing ( ) Metabolites Vmax Km Cart Ql Qr Qm Qt Qc Calv (Cart/Pb) Qalv Cinh Cven Cvt Cvm Cvr Cvl Sizes Flows Metabolic Constants CIIT Centers for Health Research October, 2006

Styrene - Interspecies Extrapolation What do we need to add/change in the models to change animal species? 51 376 216 0.1 0.01 0.001 0.0001 1.5 3.0 4.5 6.0 7.5 9.0 Hours Styrene Concentration (mg/l) Blood 80 ppm Exhaled Air 8 16 24 32 40 48 0.00001 0.0001 0.001 0.01 0.1 1.0 10 Hours Styrene Concentration (mg/l) CIIT Centers for Health Research October, 2006

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. CIIT Centers for Health Research October, 2006

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 CIIT Centers for Health Research October, 2006

Initial Fits – Some Good, some not so good Fat Concentration Excretion Rate Exhaled D4 Plasma Concentration CIIT Centers for Health Research October, 2006

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. Kcarrier Blood Lipid Compartment Fat Kremoval Liver Q Q Liver Cart Cvl Liver Lipid Compartment CIIT Centers for Health Research October, 2006

Revised Model Structure: Lipid storage in tissues Liver Lung Chylomicron-like lipid blood transport Second fat compartment Cinh Cexh Lung Fat 2 Fat 1 Venous Blood Muscle/Skin Viscera Vd Liver Metabolism Blood Lipid Elimination CIIT Centers for Health Research October, 2006

New Fits with Lipid Components in Blood Lung Concentration Plasma Concentration Exhaled D4 Plasma Then some experiments…..examine lipids in blood CIIT Centers for Health Research October, 2006

Physiologically Based Pharmacokinetic (PBPK) Modeling Define Realistic Model Liver Fat Body Lung Air Collect Needed Data Metabolic Constants Tissue Solubility Tissue Volumes Blood and Air Flows Experimental System Model Equations Make Predictions X Tissue Concentration Time You can be wrong! Refine Model Structure CIIT Centers for Health Research October, 2006

Where are we heading – PK, PD, systems? Dose-Dependent Distribution of Dioxin CIIT Centers for Health Research October, 2006

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? CIIT Centers for Health Research October, 2006

Creating a Multi-Compartment Liver Acinus: d u c b l s y h g a K ; ( ) k m x [ A - ] 1 + P / = Induction Equations: Liver Bulk Structure: CIIT Centers for Health Research October, 2006

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 CIIT Centers for Health Research October, 2006

Comparing the pathologist’s view with the modeler’s predictions….. CIIT Centers for Health Research October, 2006

A ‘Systems’ Approach for Dose Response, Looking at Cells Uptake Absorption Distribution Excretion DRE TCDD Ligand Ah Receptor Transcription Other Stimulus MAPK Adaptor RTK Metabolism Interaction w/ cellular networks Effects CIIT Centers for Health Research October, 2006

Biological Interaction An Alternate View of PK and PD processes – Systems and Perturbations Inputs Biological Function Impaired Adaptation Disease Morbidity & Mortality Exposure Tissue Dose Biological Interaction Perturbation CIIT Centers for Health Research October, 2006

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. CIIT Centers for Health Research October, 2006

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. CIIT Centers for Health Research October, 2006