* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project
Dosimetry & Physiologically Based Pharmacokinetics Melvin Andersen CIIT Centers for Health Research October 16, 2006 University of North Carolina 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 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 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. intravenous (Chemical) k(abs) inhalation C1 k21 time - min C2 V1 k12 V2 k(elim) urine, feces, air, etc. A2 k21 X X X X X X KO X k12 A1 X kout Tissue Concentration Tissue Concentration Conventional Compartmental PK Modeling time Collect Data X X X X X X X X time Select Model Fit Model to Data Ct = A e –ka·time + B e-kb·time Physiologically Based Pharmacokinetics Ci Qp Cx Qc Qc Lung Ca Cvl Liver QL Cvf Fat Qf Cvr Cvs Rapidly perfused (brain, kidney, etc.) Slowly perfused (muscle, bone, etc.) Qr Qs 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 Physiological Modeling Of Volatiles Physiological Modeling Of Drugs Haggard (1924) 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 Diethyl Ether – Uptake into the Body Expired Air Dead Space Inspired Air Lung Ventilation Pulmonary Blood Body Tissue Capillary Blood From: Hagaard (1924) Pulmonary Equilibration Terms: QpCinh Cexh QpCexh Cart QcCart QcCven Qc Qp Cinh Cexh Cart Cven Pb = cardiac output = alveolar ventilation = inhaled concentration = exhaled concentration = arterial concentration = venous concentration = blood/air partition coefficient Problem: Estimate amount taken up in first few breaths. Rate of uptake = QcCart 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…. 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. The System of Interest has a group of Parallel Physiological Compartments Lung Fat Body Muscle Kety (1951) Description for a Single Tissue Compartment Terms Qt = tissue blood flow QtCart Vt; At; Pt QtCvt Tissue Cvt = venous blood concentration Pt = tissue blood partition coefficient Vt = volume of tissue At = amount of chemical in tissue mass-balance equation: dAt = Vt dCt = QtCart - QtCvt Cvt dt dt = Ct/Pt (venous equilibration assumption) 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) Input Concentration Invariant (Cart constant) –(Qt/(Pt*Vt)*time)) Steady State Conc. Ct = Pt * Cart (1 – e Time Unrealistic physiologically, but shows general dependence of rate parameters on physiological and chemical specific parameters Mapleson’s Use of an Analog Computational Strategy Permits Solution of Sets of Equations for any Input Function Inspired tension Dead space vent Arterial tension Alveolar vent Circulation TISSUE LUNGS 1 TISSUE 2 TISSUE 3 Venous (=tissue Tension) Alveolar tension Alveolar vent Alveolar (=arterial) tension Blood flows x blood/gas coeffs. Inspired tension Lung air Lung tissue and arterial blood Tissue (=venous) tensions 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. Fiserova-Bergerova Introduces Metabolism into the Electrical Analog for Work on Occupational Chemicals Use electrical analog to study metabolized vapors and gases. Qt Ca Pt, Vt, Ct Vm Km Qt Cvt + R1 C1 R2 Compartmental and Physiological Modeling of Drugs Teorell (1937) Blood circulation Tissue boundaries k4 k1 k2 k3 k5 Dose N. Local Subcutis etc. Drug depot Symbol D Amount x Volume V1 Concentration x/V1 Perm. Coeff. k 1’ Velocity Out K1=k1’/V1 Constant In neglected Name of Resorption process Blood & Kidney etc. equivalent elimination blood volume B y V2 y/V2 – - K u – k4’ K4 = k4’/V2 not existing Elimination Tissues Chemical Inactivation “fixation” etc. Inactivation T I z w V3 – z/V3 k2’ k3=k2’/V3 k5 k2=k2/V2 Tissue take up Inactivation as output 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. Blood Flow Characteristics in Animals & Digital Computation LUNG Right heart Left heart Upper body Liver Spleen Small intestine Kidney Large intestine Trunk Lower extremity Bischoff and Brown (1966) Modeling Tissue Accumulation of Methotrexate Due to Its Interaction with a Critical Enzyme arterial blood Dihyrofolatereductase (DHFR) Kd Methotrexate (tissue blood) Methotrexate (intracellular) R(t) venous blood MTX-DHFR Complex MTX-Tissue R(t) - tissue partition Kd - MTX-DHFR dissociation constant Compartments in Physiological Model for Methotrexate Plasma QL - QG QG Liver T T r1 G.I. Tract C1 T r2 r3 C2 C3 Gut absorption C4 Gut Lumen Feces QK Kidney QM Muscle Bischoff et al. (1971) 10 GL L 1.0 K P 0.1 M 0.01 0 60 120 180 minutes 3 mg/kg 240 Methotrexate Concentration mcg/g Methotrexate Concentration mcg/g Methotrexate - Bischoff et al. (1971) 10 L K GL 1.0 0.1 0.01 P M 0 60 120 180 minutes 0.12 mg/kg 240 Then used in toxicology..... Is any of this really new? Qalv Cinh Qc Cven Cvt Qalv Alveolar Space Calv (Cart/Pb) Qc Lung Blood Cart Fat Tissue Group Qt Cart Qm Cvm Muscle Tissue Group Qr Cvr Richly Perfused Tissue Group Cart Liver Ql Cvl ( Metabolizing Tissue Group Vmax Ramsey and Andersen (1984) Km ) Cart Cart Metabolites 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 dt Km + Cvl • Equations solved by numerical integration to simulate kinetic behavior. • With venous equilibration, flow limited assumptions. Dose Extrapolation – Styrene How does it work? Venous Concentration – mg/lier blood 100 10 Conc = 1200 ppm Conc = 600 ppm 1 0.1 0.01 Conc = 80 ppm 0.001 0 5 10 15 TIME - hours 20 25 What do we need to add/change in the models to incorporate another dose route – iv or oral? Qalv Qalv Alveolar Space Cinh Qc IV Cart Fat Tissue Group Cvt Oral Qc Lung Blood Cven Calv (Cart/Pb) Qt Cart Qm Cvm Muscle Tissue Group Qr Cvr Richly Perfused Tissue Group Cart Liver Ql Cvl ( Metabolizing Tissue Group Vmax Km ) Cart Cart Metabolites Styrene - Dose Route Comparison What do we need to add/change in the models to incorporate these dose routes? 10 Styrene Concentration (mg/l) Styrene Concentration (mg/l) 100 IV 10 1.0 0.1 0.01 0 0.6 1.2 1.8 Hours 2.4 3.0 3.6 Oral 1.0 0.1 0.01 0 0.4 0.8 1.2 1.6 Hours 2.0 2.4 2.8 What do we need to add/change in the models to describe another animal species? Qalv Qalv Alveolar Space Cinh Qc Sizes Flows Metabolic Constants Qc Lung Blood Cven Cart Fat Tissue Group Cvt Calv (Cart/Pb) Qt Cart Qm Cvm Muscle Tissue Group Qr Cvr Richly Perfused Tissue Group Cart Liver Ql Cvl ( Metabolizing Tissue Group Vmax Km ) Cart Cart Metabolites Styrene - Interspecies Extrapolation What do we need to add/change in the models to change animal species? 10 0.01 376 0.001 216 51 0.0001 Styrene Concentration (mg/l) Styrene Concentration (mg/l) 0.1 1.0 80 ppm 0.1 Blood 0.01 0.001 Exhaled Air 0.0001 0.00001 0 1.5 3.0 4.5 Hours 6.0 7.5 9.0 0 8 16 24 Hours 32 40 48 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. Cinh Cexh Lung Haggard, 1924 Kety, 1951 Mapelson, 1963 Fiserova-Bergerova, 1974 Ramsey & Andersen, 1984 Reitz et al., 1990 Viscera CH3 Muscle/Skin H3C O Si CH3 Si O O Si H3C Si H3C Fat Venous Blood Learning from PBPK Models O CH3 CH3 CH3 Liver Metabolism (Vmax; Km) Vd Elimination Initial Fits – Some Good, some not so good Male Rate - Multiple Exposures 1.E+02 D4 Exhalation Rate (mg/hr) Fat Concentration Exhaled D4 1.E+01 1.E+00 1.E-01 700 ppm 1.E-02 1.E-03 7 ppm 1.E-04 1.E-05 1.E-06 0 100 200 300 400 500 Time (hours) Male Rat - Single Dose Excretion Rate (mg/hr) 1.E+00 Excretion Rate 1.E-01 1.E-02 700 ppm 1.E-03 70 ppm 1.E-04 7 ppm 1.E-05 0 50 100 Time (hours) 150 200 Plasma Concentration 600 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. Liver Q Cart Liver Liver Lipid Compartment Q Cvl Kcarrier Blood Lipid Compartment Kremoval Fat • Revised Model Structure: Lung Fat 2 Fat 1 Muscle/Skin Viscera Vd Liver Metabolism Elimination Blood Lipid Venous Blood – Lipid storage in tissues • Liver • Lung – Chylomicron-like lipid blood transport – Second fat compartment Cexh Cinh New Fits with Lipid Components in Blood Plasma Concentration Lung Concentration M ale Rat - M ultiple Exposures M ale Rat - M ultiple Exposures 1.E+01 Exhaled D4 1.E+01 1.E+00 1.E-01 1.E-02 700 ppm 1.E-03 1.E-04 7 ppm 1.E-05 1.E-06 Plasma Concentration ( g/ml) D4 Exhalation Rate (mg/hr) 1.E+02 Plasma 1.E+00 1.E-01 700 ppm 1.E-02 0 100 200 300 Time (hours) 400 500 600 0 100 200 300 400 Time (hours) Then some experiments…..examine lipids in blood 500 600 Physiologically Based Pharmacokinetic (PBPK) Modeling Lung Body Fat Metabolic Constants Tissue Solubility Tissue Volumes Blood and Air Flows Experimental System Liver Model Equations Define Realistic Model Collect Needed Data Refine Model Structure You can be wrong! Tissue Concentration Air X X X X X X X X Time Make Predictions Where are we heading – PK, PD, systems? Dose-Dependent Distribution of Dioxin 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? Creating a Multi-Compartment Liver Acinus: Induction Equations: in d u c ib le s yn th e s is b in d in g p ro tein K o ; K (in d ) d [P r]/d t = ko + k(elim ) k(m a x) [Ah -dio xin ] K b1 Liver Bulk Structure: deg radatio n n + [Ah -d io xin ] n n - k(e lim ) [P r] Visualization and Comparison with Immunohistochemistry Simulation of geometric organization is necessary. The predicted induction in the various subcompartments was used to ‘paint’ regions in a twodimensional acinus. Representation of a field of acini in a liver section Comparing the pathologist’s view with the modeler’s predictions….. A ‘Systems’ Approach for Dose Response, Looking at Cells Uptake Absorption Distribution Metabolism Excretion Other TCDD Ligand Interaction w/ cellular networks RTK Stimulus Ah Receptor Adaptor MAPK Effects DRE Transcription An Alternate View of PK and PD processes – Systems and Perturbations Exposure Tissue Dose Biological Interaction Perturbation Inputs Biological Function Impaired Function Adaptation Disease Morbidity & Mortality 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. 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.