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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.