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Physiologically BasedPharmacokinetic Modeling:
An Introduction
Hugh A. Barton
US Environmental Protection Agency
National Center for Computational Toxicology
Research Triangle Park, [email protected]
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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.
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AUC: area under the
concentration-time curve(mg/L*hr)
Cl or Cld: clearance (L/hr)
Cmax: maximumconcentration (mg/L or M)
ka: absorption rate constant(1/hr)
Km: Michaelis-Mentenconstant (M)
Vmax: maximal metabolismrate
Abbreviations PD: pharmacodynamics
PK: pharmacokinetic TD: toxicodynamics
TK: toxicokinetics
V or Vd: volume ofdistribution (L) or tissue (L)(conversion of volume tomass assumes 1 g/mL, the
density of water) Q: blood flow
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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)
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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-routeextrapolations Evaluating population variability
Modeling populations (e.g., polymorphisms) versus individuals Modeling life stages (e.g., children, elderly, ill)
Evaluating uncertainties
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Dose-response AssessmentExposure:
externaldose/concentration
Pharmacokinetics:internal tissue dose
Pharmacodynamics:action on target tissue
Response:measured toxicity
Low Information Default
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Which Pharmacokinetic Analysis
Method?
Classical Compartmental Models Noncompartmental Models
Population Pharmacokinetics
PBPK Models
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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 2500
Time (hr)
Observed
PredictedPlasma(g/mL)
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Noncompartmental/Regression
Analysis
Mathematical analysis
of plasma time coursedata: trapezoid rule,nonlinear regression Uses assumption of
linear terminal phase to
calculate AUC (zero toinfinty) from datacollected to final timepoint
No model structure
assumptions Requires in vivo
chemical concentrationdata in relevant species
Calculates
pharmacokineticoutputs such as AUC: area under curve CL: clearance Vss: steady state
volume of distribution Tmax: time of max.
concentration Cmax: max. conc.
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Population Pharmacokinetics
Statistical analyses to characterizepharmacokinetic parameters forpopulations of people
Often focuses on issues of limited data(sparse data) for each individual withinthe population versus extensive time
course data for an individual
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PBPK models describe the organism as a set of tissuecompartments interconnected by blood (plasma) flow
Systems of differential equations based upon massbalance
Physiologically Based
Pharmacokinetic (PBPK) Models
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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 humanpopulation subgroups
Limitations: Greater requirements for in vitro or in vivo data
Statistical evaluation of uncertainty and variability morechallenging
Model development and implementation requires appropriateexpertise
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PBPK Model Components
Model Purpose/Goal
Deterministic Model Biological Hypotheses
Exposure conditions
Desired outputs
Non-deterministic Model
Statistical model Data
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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
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PBPK Model Components
Physiological/Anatomical Biochemical/Physicochemical
ADME
Tissue:blood partitioncoefficient
Blood:air partition coefficient
Enzymatic rate constants
Equilibriumor rate constantsfor protein binding
Transporter rate constants
Tissue volumes
Blood flow rates
Cardiac output
Glomerular filtration rate
Alveolar ventilation rate
Hematocrit
Glutathione concentration
DNA concentration
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What Tissues (Compartments)? Absorption
Distribution Storage (e.g., fat, bone, serumprotein binding)
Distributional kinetics (e.g., totalbody water)
Clearance Metabolism Excretion (e.g., urine, bile, hair)
Target Tissues for Toxicity or
surrogate (often blood)
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Description for a Single Well-mixed
Tissue CompartmentTERMS
Qt= tissue blood flow
Cvt= venous blood concentration
Pt= tissue blood partitioncoefficient
Vt = volume of tissue
At= amount of chemical in tissue
mass-balance equation:dA
dt V
dC
dt Q C Q C
t
t
t
t art t vt= =
venous equilibration assumption CC
Pvtt
t=
QtCartQtCvt
TISSUE
Vt; At; Pt
Cvt: free concentration in tissue available for clearance(s)
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Diffusion Limited Distribution
TISSUE mass-balance equation:
( )tttbt
tt
t PCCPAdt
dCV
dt
dA/==
TISSUE
QtCvtQtCart
Vt; At; Pt
Vtb; Atb
PAT
TISSUE BLOOD
TISSUE BLOOD mass-balance equation:
( ) ( )bttttvtartt
tbtb
tb CPCPACCQ
dt
dCV
dt
dA+== /
permeability areacross-product for
tissue (L/hr)
PAT:
IntracellularFluid: 33 L
Capillary Wall
Blood:
2 L RBC3 L plasma
InterstitialFluid: 13 L
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Liver Compartment
rate of change ofamount in liver rate of uptake inarterial blood rate of loss invenous blood rate of lossby metabolism= - -
( ) vlmvlm
vlal
l
CK
CV
CCQdt
dA
+
=
When Cvl
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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)
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Examples of PBPK Models
Pharmacological Agents
Volatile Organic Compounds
Mixtures
Vapors with Nasal Toxicity
Lifestages
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PharmacologicalAgents:
All-TransRetinoic 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 basedpharmacokinetic model forretinoic acid and its metabolites.
J Am Acad Dermatol. 1997Mar;36(3 Pt 2):S77-85.
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Key Factors in Risk Assessmentfor 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 ofglucuronidation pathway
slow topical uptake subject to high affinity clearance
Kinetic differences between isomers
all-trans: rapid glucuronidation/clearance
13-cis: slow oxidation/clearance
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Water soluble model
for dichloroacetate(Barton et al., 1999)
Metabolism
Rest of Body(Volume of
Distribution)
CVL
QL
CVB
Liver
Urinary
Clearance
CL
GILumen
ka
drinking water
or gavage
Injection
Pharmacological Agents:
Dichloroacetate
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Pharmacological Agents: Diazepam
MU
TE
AD
HT
SK
BR
LI
ST
SPL
LU
RE
KI
Venous
Blood
Arteria
lBlood
metab
Wide range of mathematicalanalyses:
Gueorguieva I, Nestorov IA, Rowland M. Fuzzy
simulation of pharmacokinetic models: casestudy of whole body physiologically basedmodel of diazepam. J PharmacokinetPharmacodyn. 2004 J un;31(3):185-213.
Gueorguieva I, Aarons L, Rowland M.
Diazepam pharamacokinetics from preclinical tophase I using a Bayesian populationphysiologically based pharmacokinetic modelwith informative prior distributions in WinBUGS.
J Pharmacokinet Pharmacodyn. 2006Oct;33(5):571-94.
Gueorguieva I, Nestorov IA, Rowland M.Reducing whole body physiologically basedpharmacokinetic models using global sensitivityanalysis: diazepam case study. JPharmacokinet Pharmacodyn. 2006
Feb;33(1):1-27.
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Volatile OrganicCompounds:Vinyl Chloride
QFFat
CA
CVF
QRRich
CA
CVR
QS
Slow CACVS
QCLung
QPCI CX
QL
Liver CACVL
KZER
KA
KGSMCO2
KCO2
Reactive
Metabolites(RISK)
Glutathione
Conjugate(RISKG)
KFEEKGSM
Tissue / DNAAdducts(RISKM)
KB
KOKS
GSH
VMAX1KM1
VMAX2KM2
Clewell HJ , Gentry PR, GearhartJ M, Allen BC, Andersen ME.
Comparison of cancer riskestimates for vinyl chloride usinganimal and human data with aPBPK model.
Sci Total Environ. 2001 J ul
2;274(1-3):37-66.
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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/ppb
Males Females
Maltoni - mouse inhalation 1.52 3.27
Maltoni - rat inhalation 5.17 2.24Feron - rat diet 3.05 1.1
Maltoni - rat gavage 8.68 15.7
See Clewell et al 2001 and references therein.
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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/ppb
Fox & Collier 0.71 - 4.22
Jones et al. 0.97 - 3.60
Simonato et al. 0.40 - 0.79
See Clewell et al 2001 and references therein.
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VOCs: Mixtures
Liver
PoorlyPerf.
Richly Perf.
Lung
Metab Gut
Liver
PoorlyPerf.
Richly Perf.
Lung
Metab Gut
( )vl
im
vlm
vlal
l
CKIK
CVCCQ
dt
dA
++
=
]/1[
Barton HA, Creech J R, Godin CS, Randall GM,Seckel CS. Chloroethylene mixtures:pharmacokinetic modeling and in vitrometabolism of vinyl chloride, trichloroethylene,and trans-1,2-dichloroethylene in rat. Toxicol
Appl Pharmacol. 1995 Feb;130(2):237-47
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MS Bogdanffy, R Sarangapani,DR Plowchalk, A J arabek, andME Andersen A biologicallybased risk assessment for vinyl
acetate-induced cancer andnoncancer inhalation toxicityToxicol. Sci. 1999 51: 19-35
Nasal Toxicity: Vinyl Acetate
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Life Stage & Species Extrapolations
Body
Liver
Brain
Metab
Placenta
Lung
Richly
Perf.
PoorlyPerf.
Mammary
Liver
Gut
Maternal ModelNeonatal Model
Embryo/Fetal Model
Liver
Poorly
Perfused
RichlyPerfused
Lung
MetabolismGut
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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
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References ReviewsBarton HA. Computational pharmacokinetics during developmental windows
of susceptibility. J Toxicol Environ Health A. 2005 J un 11-25;68(11-12):889-900
Barton HA, Pastoor TP, Baetcke K, Chambers J E, Diliberto J , Doerrer NG,Driver J H, Hastings CE, Iyengar S, Krieger R, Stahl B, TimchalkC. Theacquisition and application of absorption, distribution, metabolism, andexcretion (ADME) data in agricultural chemical safety assessments. CritRev Toxicol. 2006 J an;36(1):9-35
Clewell HJ 3rd, Andersen ME, Barton HA. A consistent approach for theapplication of pharmacokinetic modeling in cancer and noncancer riskassessment. Environ Health Perspect. 2002 J an;110(1):85-93.
Himmelstein KJ and Lutz RJ (1979) A Review of the Applications ofPhysiologically Based Pharmacokinetic Modeling. J PharmacokinetBiopharm7(2):127-145.
Krishnan K and Andersen ME (2001) Physiologically Based PharmacokineticModeling in Toxicology. In Principles and Methods in Toxicology, 4th
Edition, A. Wallace Hayes (Ed), Taylor & Francis, Philadelphia. pp 193-241.