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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.

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slide1
Dosimetry & Physiologically Based Pharmacokinetics

Melvin Andersen

CIIT Centers for Health Research

October 16, 2006

University of North Carolina

slide2
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

slide3
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
slide4
intravenous

inhalation

Blood Conc - mg/L

time - min

Pharmacokinetics

The study of the quantitative relationships between the absorption,

distribution, metabolism, and eliminations (A-D-M-E) of chemicals

from the body.

(Chemical)

k(abs)

k(elim)

urine,

feces,

air, etc.

C1 V1

k12

k21

C2 V2

slide5
A2

k21

k12

Tissue Concentration

Tissue Concentration

X

X

A1

X

X

X

X

KO

kout

X

X

X

X

X

X

X

X

X

X

time

time

Select

Model

Fit Model to Data

Collect

Data

Ct = A e –ka·time + B e-kb·time

Conventional Compartmental PK Modeling

slide6
Physiologically Based Pharmacokinetics

Qp

Ci

Cx

Qc

Qc

Ca

Lung

QL

Cvl

Liver

Qf

Cvf

Fat

Qr

Cvr

Rapidly perfused (brain, kidney, etc.)

Slowly perfused (muscle, bone, etc.)

Qs

Cvs

slide7
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
slide8
Physiological Modeling

Of Volatiles

Haggard (1924)

Physiological Modeling

Of Drugs

Teorell (1937)

Kety

(1951)

Mapleson (1961)

Riggs (1963)

Fiserova-Bergerova (1974)

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

slide9
Diethyl Ether – Uptake into the Body

Expired

Air

Inspired

Air

Dead Space

Lung Ventilation

PulmonaryBlood

Body Tissue

Capillary Blood

From: Hagaard (1924)

slide10
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

QcCven

QcCart

Problem: Estimate amount taken up in first few breaths.

Rate of uptake = QcCart

slide11
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….

slide12
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.
slide13
The System of Interest has a group of Parallel Physiological Compartments

Lung

Fat

Body

Muscle

Kety (1951)

slide14
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)

slide15
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)

slide16
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

slide17
Mapleson’s Use of an Analog Computational Strategy Permits Solution of Sets

of Equations for any Input Function

Inspired tension

Arterial tension

Alveolar

vent

Dead

space

vent

Circulation

TISSUE

2

TISSUE

3

TISSUE

1

LUNGS

Venous

(=tissue

Tension)

Alveolar tension

Alveolar

vent

Alveolar (=arterial) tension

Blood flows x

blood/gas coeffs.

Inspired

tension

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.

slide18
C1

R1

Qt

+

Qt

Pt, Vt, Ct

Ca

Cvt

R2

Vm

Km

Fiserova-Bergerova Introduces Metabolism into the Electrical Analog for Work on Occupational Chemicals

Use electrical analog to study metabolized vapors and gases.

slide19
Compartmental and Physiological Modeling of Drugs

Teorell

(1937)

Blood circulation

Tissue boundaries

k2

k3

k4

k1

k5

Chemical

Inactivation

“fixation” etc.

Subcutis etc.

Drug depot

Dose N.

Local

Tissues

Inactivation

Blood &

equivalent

blood volume

Kidney etc.

elimination

Symbol D B K T I

Amount x y u z w

Volume V1 V2 – V3 –

Concentration x/V1 y/V2 - z/V3 -

Perm. Coeff. k1’ – k4’ k2’ -

Velocity Out K1=k1’/V1 - K4 = k4’/V2 k3=k2’/V3 k5

Constant In neglected - not existing k2=k2/V2 -

Name of Resorption - Elimination Tissue take up Inactivation

process as output

slide20
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.
slide21
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)

slide22
Modeling Tissue Accumulation of Methotrexate Due to Its Interaction with a Critical Enzyme

arterial blood

Dihyrofolatereductase (DHFR)

MTX-DHFR

Complex

Kd

Methotrexate

(intracellular)

Methotrexate

(tissue blood)

R(t)

MTX-Tissue

venous blood

R(t) - tissue partition

Kd - MTX-DHFR dissociation constant

slide23
Compartments in Physiological Model

for Methotrexate

Plasma

QL -QG

QG

Liver

G.I. Tract

Gut

absorption

Feces

C1

C2

C3

C4

T

T

T

r3

r1

r2

Gut Lumen

QK

Kidney

QM

Muscle

Bischoff et al. (1971)

slide24
10

10

GL

L

K

L

GL

1.0

1.0

Methotrexate Concentration mcg/g

Methotrexate Concentration mcg/g

K

P

0.1

0.1

P

M

M

0.01

0.01

120

240

0

180

60

120

240

0

180

60

minutes

minutes

3 mg/kg

0.12 mg/kg

Methotrexate - Bischoff et al. (1971)

slide25
Qalv

Qalv

Alveolar Space

Calv (Cart/Pb)

Cinh

Qc

Qc

Lung Blood

Cven

Cart

Qt

Fat Tissue Group

Cvt

Cart

Qm

Muscle Tissue

Group

Cart

Cvm

Qr

Richly Perfused

Tissue Group

Cart

Cvr

Liver

Metabolizing

Tissue Group

Ql

(

)

Cvl

Cart

Vmax

Metabolites

Km

Then used in toxicology.....

Is any of this really new?

Ramsey and Andersen (1984)

slide26
Styrene & Saturable metabolism

rate of loss

in venous

blood

rate of uptake

in arterial

blood

rate of change

of amount

in liver

=

-

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.
slide27
100

Conc = 1200 ppm

Conc = 600 ppm

10

1

Venous Concentration – mg/lier blood

0.1

Conc = 80 ppm

0.01

0.001

0

5

10

15

20

25

TIME - hours

Dose Extrapolation – Styrene

How does it work?

slide28
Qalv

Qalv

Alveolar Space

Calv (Cart/Pb)

Cinh

Qc

Qc

Lung Blood

Cven

Cart

IV

Oral

Qt

Fat Tissue Group

Cvt

Cart

Qm

Muscle Tissue

Group

Cart

Cvm

Qr

Richly Perfused

Tissue Group

Cart

Cvr

Cvl

Liver

Metabolizing

Tissue Group

Ql

(

)

Cart

Vmax

Metabolites

Km

What do we need to add/change in the models to incorporate another dose route – iv or oral?

slide29
Styrene - Dose Route Comparison

What do we need to add/change in the models to incorporate these dose routes?

10

100

IV

Oral

10

1.0

Styrene Concentration (mg/l)

Styrene Concentration (mg/l)

1.0

0.1

0.1

0.01

0.01

3.0

2.4

3.6

1.2

2.8

0

0.6

1.8

2.0

1.6

2.4

0.8

0

0.4

1.2

Hours

Hours

slide30
Qalv

Qalv

Alveolar Space

Calv (Cart/Pb)

Cinh

Qc

Qc

Lung Blood

Cven

Cart

Qt

Fat Tissue Group

Cvt

Cart

Qm

Muscle Tissue

Group

Cart

Cvm

Qr

Richly Perfused

Tissue Group

Cart

Cvr

Cvl

Liver

Metabolizing

Tissue Group

Ql

(

)

Cart

Vmax

Metabolites

Km

What do we need to add/change in the models to describe another animal species?

  • Sizes
  • Flows
  • Metabolic Constants
slide31
0.1

10

1.0

80 ppm

0.01

0.1

Blood

Styrene Concentration (mg/l)

Styrene Concentration (mg/l)

0.01

376

0.001

0.001

Exhaled Air

216

51

0.0001

0.00001

0.0001

40

16

32

48

0

24

8

3.0

7.5

9.0

1.5

4.5

6.0

0

Hours

Hours

Styrene - Interspecies Extrapolation

What do we need to add/change in the models to change animal species?

slide32
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.

learning from pbpk models
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

slide34
Initial Fits – Some Good, some not so good

Plasma Concentration

Fat Concentration

Excretion Rate

Exhaled D4

revise the model
Liver

Kcarrier

Blood Lipid Compartment

Kremoval

Fat

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.

Q

Q

Liver

Cart

Cvl

Liver Lipid Compartment

slide36
Cexh

Cinh

Lung

  • Revised Model Structure:
    • Lipid storage in tissues
      • Liver
      • Lung
    • Chylomicron-like lipid blood transport
    • Second fat compartment

Fat 2

Fat 1

Venous Blood

Muscle/Skin

Viscera

Vd

Liver

Metabolism

Blood Lipid

Elimination

slide37
New Fits with Lipid Components in Blood

Plasma Concentration

Lung Concentration

Exhaled

D4

Plasma

Then some experiments…..examine lipids in blood

slide38
You can be wrong!

Air

Metabolic Constants

Tissue Solubility

Tissue Volumes

Blood and Air Flows

Experimental System

Lung

Body

Tissue Concentration

X

Fat

X

X

X

X

X

X

Liver

X

Model Equations

Time

Define Realistic Model

Make

Predictions

Collect Needed

Data

Refine Model Structure

Physiologically Based Pharmacokinetic (PBPK) Modeling

slide39
Where are we heading – PK, PD, systems?

Dose-Dependent Distribution of Dioxin

slide40
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?
slide41
i

n

d

u

c

i

b

l

e

s

y

n

t

h

e

s

i

s

d

e

g

r

a

d

a

t

i

o

n

b

i

n

d

i

n

g

Liver Bulk

Structure:

Induction

Equations:

p

r

o

t

e

i

n

K

o

;

K

(

i

n

d

)

k

(

e

l

i

m

)

n

k

(

m

a

x

)

[

A

h

-

d

i

o

x

i

n

]

d

[

P

r

]

/

d

t

=

k

o

+

-

k

(

e

l

i

m

)

[

P

r

]

n

n

K

b

1

+

[

A

h

-

d

i

o

x

i

n

]

Creating a Multi-Compartment

Liver Acinus:

slide42
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

a systems approach for dose response looking at cells
Other

Stimulus

RTK

Adaptor

MAPK

TCDD

Ligand

Ah Receptor

Transcription

DRE

A ‘Systems’ Approach for Dose Response, Looking at Cells

Uptake

Absorption

Distribution

Excretion

Metabolism

Interaction w/ cellular networks

Effects

slide45
Exposure

Tissue Dose

Biological Interaction

Perturbation

Inputs

Biological

Function

Impaired

Function

Adaptation

Disease

Morbidity &

Mortality

An Alternate View of PK and PD processes – Systems and Perturbations

slide46
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.

slide47
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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