1. 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

2. 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

3. 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

4. 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
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5. Conventional Compartmental PK ModelingX
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
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6. Physiologically Based PharmacokineticsQp 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
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7. 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
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8. 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

9. Diethyl Ether – Uptake into the Body
Expired
Air
Inspired
Air
Dead Space
Lung Ventilation
Pulmonary Blood
Body Tissue
Capillary Blood
From: Hagaard (1924)
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10. 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
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11. 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….
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12. 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.
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13. The System of Interest has a group of Parallel Physiological Compartments
Lung
Fat
Body
Muscle
Kety (1951)
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14. 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)
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15. 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)
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16. 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
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17. 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

18. 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
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19. 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 V V – V –
Concentration x/V y/V z/V
Perm. Coeff. k1’ – k4’ k2’
Velocity Out K1=k1’/V K4 = k4’/V k3=k2’/V k5
Constant In neglected not existing k2=k2/V
Name of Resorption Elimination Tissue take up Inactivation
process as output
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20. 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

21. 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

22. 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

23. 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

24. 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

25. 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)
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26. 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

27. 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

28. 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
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29. 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
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30. 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

31. 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
0.0001
0.001
0.01
0.1
1.0 10
Hours
Styrene Concentration (mg/l)
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32. 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-R
Andersen et al., Applying simulation modeling to problems in toxicology and risk assessment: a short perspective. Toxicol. Appl. Pharmacol., 133,
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33. 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
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34. Initial Fits – Some Good, some not so good
Fat Concentration
Excretion Rate
Exhaled D4
Plasma Concentration
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35. 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
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36. 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

37. New Fits with Lipid Components in Blood
Lung Concentration
Plasma Concentration
Exhaled D4
Plasma
Then some experiments…..examine lipids in blood
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38. 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
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39. Where are we heading – PK, PD, systems?
Dose-Dependent Distribution of Dioxin
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40. 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?
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41. 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:
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42. 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
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43. Comparing the pathologist’s view with the modeler’s predictions…..
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44. 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

45. 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

46. 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.
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47. 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.
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