Physiologically Based Pharmacokinetic Modeling:
An Introduction
Hugh A. BartonUS Environmental Protection Agency
National Center for Computational ToxicologyResearch Triangle Park, NC
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.