Physiologically Based Pharmacokinetic Modeling:

An Introduction

Hugh A. BartonUS Environmental Protection Agency

National Center for Computational ToxicologyResearch Triangle Park, NC

barton.hugh@epa.gov

Outline

• What is pharmacokinetics (PK)?• Why PK?• PK Modeling Methods• PBPK Model Components• PBPK Model Structures

This presentation does not represent official US EPA policy.

• AUC: area under the concentration-time curve (mg/L*hr)

• Cl or Cld: clearance (L/hr)• Cmax: maximum

concentration (mg/L or M)• ka: absorption rate constant

(1/hr)• Km: Michaelis-Menten

constant (M)• Vmax: maximal metabolism

rate

Abbreviations

• PD: pharmacodynamics• PK: pharmacokinetic• TD: toxicodynamics• TK: toxicokinetics• V or Vd: volume of

distribution (L) or tissue (L) (conversion of volume to mass assumes 1 g/mL, the density of water)

• Q: blood flow

What is Pharmacokinetics?

• What the body does to a chemical• Absorption, Distribution, Metabolism,

Excretion (ADME)• Kinetics: rates of change, • PK: chemical concentrations as a function

of time• Pharmacokinetics = Toxicokinetics• Pharmacodynamics: What the chemical

does to the body (PD=TD)

Why Use PK-based Analyses?• Improved candidate selection during chemical or drug

development– Cross-species comparisons of metabolism or absorption– Duration of action of different formulations

• Improved toxicity study design– Dose, species, dosing interval selection

• Improved toxicity study interpretation– Cross-species comparisons of metabolites or tissue

distribution– Links to pharmacodynamics and effects

• Improved risk and safety assessments– Understanding interspecies, dose, route-to-route

extrapolations– Evaluating population variability

• Modeling populations (e.g., polymorphisms) versus individuals• Modeling life stages (e.g., children, elderly, ill)

– Evaluating uncertainties

Dose-response AssessmentExposure:

external dose/concentration

Pharmacokinetics:internal tissue dose

Pharmacodynamics:action on target tissue

Response:measured toxicity

Low Information Default

Which Pharmacokinetic Analysis Method?

• Classical Compartmental Models • Noncompartmental Models• Population Pharmacokinetics • PBPK Models

Classical Compartmental

• Fits equations to data to estimate PK parameters• Requires in vivo data in relevant species• Can be “physiological”, e.g., methanol distributes

with total body water, but not a requirement• Limitations:

– Used for nonvolatiles, though adaptable for volatiles – PK changes with exposure difficult to address– Limited tissue distribution characterization

CleV1

V2

Cld

ka

0.001

0.010

0.100

1.000

10.000

0 500 1000 1500 2000 2500Time (hr)

Observed

PredictedPlas

ma

(µg/

mL)

Noncompartmental/Regression Analysis

• Mathematical analysis of plasma time course data: trapezoid rule, nonlinear regression– Uses assumption of

linear terminal phase to calculate AUC (zero to infinty) from data collected to final time point

• No model structure assumptions

• Requires in vivochemical concentration data in relevant species

• Calculates pharmacokinetic outputs such as – AUC: area under curve– CL: clearance– Vss: steady state

volume of distribution– Tmax: time of max.

concentration – Cmax: max. conc.

Population Pharmacokinetics

• Statistical analyses to characterize pharmacokinetic parameters for populations of people

• Often focuses on issues of limited data (sparse data) for each individual within the population versus extensive time course data for an individual

• PBPK models describe the organism as a set of tissue compartments interconnected by blood (plasma) flow

• Systems of differential equations based upon mass balance

Physiologically Based Pharmacokinetic (PBPK) Models

PBPK Analysis• Captures biological processes and hypotheses

explicitly – Varying degrees of detail or biological realism– Flexibility to reflect biology

• Can incorporate changes in PK due to chemical (e.g. GSH depletion, protein induction), growth/aging

• Facilitates analyses across species, doses and human population subgroups

• Limitations:– Greater requirements for in vitro or in vivo data– Statistical evaluation of uncertainty and variability more

challenging– Model development and implementation requires appropriate

expertise

PBPK Model Components

• Model Purpose/Goal• Deterministic Model

– Biological Hypotheses– Exposure conditions– Desired outputs

• Non-deterministic Model– Statistical model

• Data

Model Purpose: Basic QuestionsWhat do I need to know to carry out an analysis based upon

internal dosimetry (i.e., applying pharmacokinetics)?

• What toxic effects at what life stages? (i.e., potential critical studies)• What species (toxicity, PK, metabolism studies)?

– Toxicity testing animals – Humans

• What is known about the mode of action for each toxicity of interest?– Parent chemical and/or metabolite(s) (reactive or not?)– Interactions with macromolecules, cells, tissues, systems?– Critical for PK model structure and selection of dose metrics.

• How will model be used in safety or risk assessment?– Route-to-route extrapolation (What routes?)– Cross-species extrapolation– Cross-chemical extrapolation

PBPK Model Components

Physiological/Anatomical Biochemical/Physicochemical

ADME

• Tissue:blood partition coefficient

• Blood:air partition coefficient • Enzymatic rate constants• Equilibrium or rate constants

for protein binding• Transporter rate constants

• Tissue volumes• Blood flow rates• Cardiac output• Glomerular filtration rate• Alveolar ventilation rate• Hematocrit• Glutathione concentration• DNA concentration

What Tissues (Compartments)?• Absorption• Distribution

– Storage (e.g., fat, bone, serum protein binding)

– Distributional kinetics (e.g., total body water)

• Clearance – Metabolism– Excretion (e.g., urine, bile, hair)

• Target Tissues for Toxicity or surrogate (often blood)

Description for a Single Well-mixed Tissue Compartment

TERMSQt = tissue blood flow

Cvt = venous blood concentration

Pt = tissue blood partition coefficient

Vt = volume of tissue

At = amount of chemical in tissue

mass-balance equation: dAdt

VdCdt

Q C Q Ctt

tt art t vt= = −

venous equilibration assumption C CPvt t

t=

QtCartQtCvt

TISSUE

Vt; At; Pt

Cvt: free concentration in tissue available for clearance(s)

Diffusion Limited Distribution

TISSUE mass-balance equation:

( )tttbtt

tt PCCPA

dtdCV

dtdA /−==

TISSUE

QtCvtQtCart

Vt; At; Pt

Vtb; Atb

PAT

TISSUE BLOOD

TISSUE BLOOD mass-balance equation:

( ) ( )bttttvtartttb

tbtb CPCPACCQ

dtdCV

dtdA

−+−== /

permeability area cross-product for tissue (L/hr)

PAT:

Intracellular Fluid: 33 L

Capillary Wall

Blood:2 L RBC3 L plasma

Interstitial Fluid: 13 L

Liver Compartment

rate of change of amount in liver

rate of uptake inarterial blood

rate of loss in venous blood

rate of lossby metabolism= - -

( )vlm

vlmvlal

l

CKCVCCQ

dtdA

+−−=

When Cvl<<Km, if Vm/Km<<Ql (liver blood flow), then flow limited metabolism.

GTEH

CYPGST

QL

http://www.ncsu.edu/crsc/reports/ftp/pdf/crsc-tr02-17.pdf

Chemical-Specific Data• In vivo PK: chemical levels over time and doses

– Single or repeated exposures– Exposure (dosing) regimens: intravenous bolus or infusion, oral

bolus, inhalation, dermal– Serial determinations in multiple animals (e.g., tissue or blood

concentrations)– Repeated measures in same animal/human (e.g., serum, urine,

feces, exhaled breath, closed chamber atmosphere)• In vitro or ex vivo

– Partition coefficients: analysis of equilibrium chemical distribution to blood and tissues

– Protein binding rate or equilibrium constants– In vitro metabolism (e.g., estimates of Km and Vmax)– Changes in biochemistry following exposure (e.g., GSH depletion)

Examples of PBPK Models

• Pharmacological Agents • Volatile Organic Compounds• Mixtures• Vapors with Nasal Toxicity• Lifestages

Pharmacological Agents:

All-Trans Retinoic Acid

= submodel

Slowly Perfused

Fat

Placenta

Embryo

Liver

Intestine

Gut

Feces

CO2

13-CIS

4-OXO

Glucuronide

Qc

Qsk

Qr

Qs

Qf

Qpl

Ql

QgQg

kb

krko Do

kctktckf

Vmx , kmx

kCO2

Vmg , kmg

kh

ke

kv

Stratum Corneum

Dv

Plasma

Richly Perfused

Dsk

Dsc

Formulation

Viable Epidermis

Clewell HJ 3rd, Andersen ME, Wills RJ, Latriano L.

A physiologically based pharmacokinetic model for retinoic acid and its metabolites.

J Am Acad Dermatol. 1997 Mar;36(3 Pt 2):S77-85.

Key Factors in Risk Assessment for all-trans-Retinoic Acid

• Species differences in metabolism– rodents: oxidation to active form– primates: glucuronidation to inactive form

• Exposure route differences in bioavailability– rapid oral uptake can exceed capacity of

glucuronidation pathway– slow topical uptake subject to high affinity clearance

• Kinetic differences between isomers– all-trans: rapid glucuronidation/clearance–13-cis: slow oxidation/clearance

Water soluble model for dichloroacetate(Barton et al., 1999)

Metabolism

Rest of Body(Volume of

Distribution)

CVLQL

CVB

Liver

Urinary Clearance

CL

GI Lumen

ka

drinking water or gavage

Injection

Pharmacological Agents: Dichloroacetate

Pharmacological Agents: DiazepamMU

TE

AD

HT

SK

BR

LIST

SPL

LU

RE

KI

Ven

ous B

lood

Arte

rial

Blo

odmetab

Wide range of mathematical analyses:Gueorguieva I, Nestorov IA, Rowland M. Fuzzy simulation of pharmacokinetic models: case study of whole body physiologically based model of diazepam. J PharmacokinetPharmacodyn. 2004 Jun;31(3):185-213.

Gueorguieva I, Aarons L, Rowland M. Diazepam pharamacokinetics from preclinical to phase I using a Bayesian population physiologically based pharmacokinetic model with informative prior distributions in WinBUGS. J Pharmacokinet Pharmacodyn. 2006 Oct;33(5):571-94.

Gueorguieva I, Nestorov IA, Rowland M. Reducing whole body physiologically based pharmacokinetic models using global sensitivity analysis: diazepam case study. J Pharmacokinet Pharmacodyn. 2006 Feb;33(1):1-27.

Volatile Organic Compounds: Vinyl Chloride

QFFat

CACVF

QRRich

CACVR

QSSlow CA

CVS

QCLung

QPCI CX

QLLiver CA

CVL

KZERKA

KGSMCO2 KCO2

ReactiveMetabolites

(RISK)

GlutathioneConjugate(RISKG)

KFEEKGSM

Tissue / DNAAdducts(RISKM)

KBKOKS

GSH

VMAX1KM1

VMAX2KM2

Clewell HJ, Gentry PR, Gearhart JM, Allen BC, Andersen ME.

Comparison of cancer risk estimates for vinyl chloride using animal and human data with a PBPK model.

Sci Total Environ. 2001 Jul 2;274(1-3):37-66.

Human risk estimates (per million) for lifetime exposure to 1 ppb vinyl chloride in air based on the incident of liver

angiosarcoma in animal bioassays

Animal Bioassay Study 95% UCL Risk/million/ppbMales Females

Maltoni - mouse inhalation 1.52 3.27Maltoni - rat inhalation 5.17 2.24Feron - rat diet 3.05 1.1Maltoni - rat gavage 8.68 15.7

See Clewell et al 2001 and references therein.

Human risk estimates (per million) for lifetime inhalation of 1 ppb vinyl chloride in air based on the incident of liver angiosarcoma in human epidemiological studies

Epidemiological Study95% UCL

Risk/million/ppbFox & Collier 0.71 - 4.22Jones et al. 0.97 - 3.60Simonato et al. 0.40 - 0.79

See Clewell et al 2001 and references therein.

VOCs: Mixtures

Liver

Poorly Perf.

Richly Perf.

Lung

Metab Gut

Liver

Poorly Perf.

Richly Perf.

Lung

Metab Gut

( )vlim

vlmvlal

l

CKIKCVCCQ

dtdA

++−−=

]/1[

Barton HA, Creech JR, Godin CS, Randall GM, Seckel CS. Chloroethylene mixtures: pharmacokinetic modeling and in vitro metabolism of vinyl chloride, trichloroethylene, and trans-1,2-dichloroethylene in rat. ToxicolAppl Pharmacol. 1995 Feb;130(2):237-47

MS Bogdanffy, R Sarangapani, DR Plowchalk, A Jarabek, and ME Andersen A biologically based risk assessment for vinyl acetate-induced cancer and noncancer inhalation toxicity Toxicol. Sci. 1999 51: 19-35

Nasal Toxicity: Vinyl Acetate

Life Stage & Species Extrapolations

Body

Liver

Brain

Metab

Placenta

Lung

Richly Perf.

Poorly Perf.

Mammary

Liver

Gut

Maternal ModelNeonatal Model

Embryo/Fetal Model

Liver

PoorlyPerfused

RichlyPerfused

Lung

MetabolismGut

Conclusion

• Model purpose• Deterministic Biological Model

– PK Determinants (ADME)– Target Tissues– Exposure Routes

• Non-deterministic Model– Often statistical (likelihood based)– Describes relationship between data and

model

References ReviewsBarton HA. Computational pharmacokinetics during developmental windows

of susceptibility. J Toxicol Environ Health A. 2005 Jun 11-25;68(11-12):889-900

Barton HA, Pastoor TP, Baetcke K, Chambers JE, Diliberto J, Doerrer NG, Driver JH, Hastings CE, Iyengar S, Krieger R, Stahl B, Timchalk C. The acquisition and application of absorption, distribution, metabolism, and excretion (ADME) data in agricultural chemical safety assessments. CritRev Toxicol. 2006 Jan;36(1):9-35

Clewell HJ 3rd, Andersen ME, Barton HA. A consistent approach for the application of pharmacokinetic modeling in cancer and noncancer risk assessment. Environ Health Perspect. 2002 Jan;110(1):85-93.

Himmelstein KJ and Lutz RJ (1979) A Review of the Applications of Physiologically Based Pharmacokinetic Modeling. J PharmacokinetBiopharm 7(2):127-145.

Krishnan K and Andersen ME (2001) Physiologically Based Pharmacokinetic Modeling in Toxicology. In Principles and Methods in Toxicology, 4th

Edition, A. Wallace Hayes (Ed), Taylor & Francis, Philadelphia. pp 193-241.