Pharmacokinetics

Part 1: Principles

Abdulfattah Alhazmi, MSc. Pharm.Faculty of Pharmacy

Dept. of Clinical Pharmacy

External exposure

Absorbed dose

Target dose

Tissue interaction

Early eff ect

Adverse eff ect

Disease/ injury

Pharmacokinetics

Pharmacodynamics

External exposure

Absorbed dose

Target dose

Tissue interaction

Early eff ect

Adverse eff ect

Disease/ injury

Pharmacokinetics

Pharmacodynamics

Pharmacokinetics• Studies of the change in chemical distribution over

time in the body

• Explores the quantitative relationship between Absorption, Distribution, Metabolism, and Excretion of a given chemical

• Classical models– ‘Data-based’, empirical compartments– Describes movement of chemicals with fitted rate constants

• Physiologically-based models:– Compartments are based on real tissue volumes– Mechanistically based description of chemical movement

using tissue blood flow and simulated in vivo transport processes.

Pharmacokinetics

The study of the quantitative relationships between the absorption,distribution, metabolism, and eliminations (A-D-M-E) of chemicalsfrom the body.

(Chemical)

k(abs)

C1 V1

C2 V2

k21 k12

k(elim) urine,feces,air, etc.

intravenous

inhalation

time - min

Blo

od

Con

c -

mg

/L

Conventional Compartmental PK Modeling

CollectData

Select Model

Fit Model to Data

Ct = A e –ka·t + B e-kb·t

X

X

X

X

X

XX X

Tis

su

e C

on

cen

trati

on

time

k12k21

koutKOA1

A2

X

X

Tis

su

e C

on

cen

trati

on

time

XX X

X

XX

Example of Simple Kinetic Model:One-compartment model with bolus

dose

Terminology:Compartment = a theoretical volume for chemicalSteady-state = no net change of concentrationBolus dose = instantaneous input into compartment

Method:1. Dose: Add known amount (A) of chemical2. Experiment: Measure concentration of chemical (C) in compartment3. Calculate: A ‘compartmental’ Volume (V)

Volume?

DosePurpose: In a simple (1-compartment) system, determine volume of distribution

• Basic assumption:– Well stirred, instant equal distribution within entire

compartment

• Volume of distribution = A/C– In this classical model, V is an operational volume

• V depends on site of measurement

• This simple calculation only works IF:– Compound is rapidly and uniformly distributed– The amount of chemical is known– The concentration of the solution is known.

Example of Simple Kinetic Model:One-compartment model with

bolus dose

What happens if the chemical is able to leave the container?

• Rate equations: – Describe movement of chemical between compartments

• The previous example had instantaneous dosing• Now, we need to describe the rate of loss from the

compartment

• Zero-order process: – rate is constant, does not depend on chemical concentration

rate = k x C0 = k

• First-order process: – rate is proportional to concentration of ONE chemical

rate = k x C1

Describing the Rates of Chemical Processes

- 1 Chemical in the System

Describing the Rates of Chemical Processes

- 2 Chemical Systems• Second-order process:

– rate is proportional to concentration of both chemicalsRate = k x C1 x C2

• Saturable processes*: – Rate is dependent on interaction of two chemicals– One reactant, the enzyme, is constant– Described using Michaelis-Menten* equation

Rate = (Vmaxx C) / ( C + Km)

*Michaelis-Menten kinetics can describe:– Metabolism– Carrier-mediated transport across membranes– Excretion

M-M kinetics

0

5

10

0 5 10 15 20 25C

Rat

e

1-Comp model with bolus dose and 1st order elimination

Purpose: Examine how concentration changes with time

Conc?

DoseMass-balance equation (change in C over time): - dA/dt = -ke x A, or - dC/dt = -ke x C

where ke = elimination rate constantConcentration;

- Rearrange and integrate above rate equation C = C0 x e-ke · t, or

ln C = ln C0 - ke · t

Half-life (t1/2):

-Time to reduce concentration by 50% -replace C with C0/2 and solve for t

t1/2 = (ln 2)/ke = 0.693/ke

1-Comp model with bolus dose and 1st order elimination

Clearance: volume cleared per time unit - if ke = fraction of volume cleared per time unit,

ke = CL/V (CL=ke*V)

Conc

Dose

Calculating Clearance using Area Under the Curve (AUC):

AUC = average concentration - integral of the concentration - C dt

CL = volume cleared over time (L/min)dA/dt = - keA = -ke V CdA/dt = - CL · C dA = - CL C dt Dose = CL · AUCCL = Dose / AUC

0

5

10

0 5 10 15 20 25Time

Con

c.

AUC

1-Comp model with continuous infusion and 1st order elimination

Calculating Clearance at Steady State:• At steady state, there is no net change in concentration:

dC/dt = k0/V – ke · C = 0

• Rearrange above equation:k0/V = ke · Css

• Since CL = ke · V ,

CL = k0/Css

Time

Con

c.

Steady State

2-Comp model with bolus dose and 1st order elimination

Calculating Rate of Change in Chemical:– Central Compartment (C1):

dC1/dt = k21· C2 - k12· C1 - ke· C1

– Peripheral (Deep) Compartment (C2): dC2/dt = k12· C1 - k21· C2

1 2

ke

k12

k21

Time

Con

c.

• Linear:– All elimination and distribution kinetics are 1st order

• Double dose double concentration

• Non-linear:– At least one process is NOT 1st order

• No direct proportionality between dose and compartment concentration

Linear and Non-linear Kinetics

0

10

20

30

0 5 10 15 20 25Time

Con

c.

1

10

100

0 5 10 15 20 25Time

Con

c.

1

10

100

0 5 10 15 20 25Time

Conc.

Dose

AU

C

Time

Conc.

1

100

10

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

Physiologically Based Pharmacokinetics

Qc

Cvl

Cvf

Cvr

Cvs

Qc

Ca

QL

Qf

Qr

Qs

Ci Cx

Qp

Lung

Liver

Fat

Rapidly perfused (brain, kidney, etc.)

Slowly perfused (muscle, bone, etc.)

PBPK ModelsBuilding a PBPK Model:1. Define model compartments

– Represent tissues

2. Write differential equation for each compartment

3. Assign parameter values to compartments– Compartments have defined

volumes, blood flows

4. Solve equations for concentration– Numerical integration

software (e.g. Berkeley Madonna, ACSL)

Veno

us s

ide

Arte

rial sid

e

Lungs

Other

Fat tissues

Liver

Chemicalin air

EliminationVeno

us s

ide

Arte

rial sid

e

Lungs

Other

Fat tissues

Liver

Chemicalin air

Elimination

Lungs

Other

Fat tissues

Liver

Chemicalin air

Elimination

Lungs

Other

Fat tissues

Liver

Chemicalin air

Elimination

Simple model for inhalation

Parameterizing the Model:

Experimental Determination– Partition Coefficients:

• in vitro: vial equilibration (CTissue/Cair) dialysis (CTissue/Cbuffer) ultrafiltration (CTissue/Cbuffer)

• in vivo: steady state (CTissue/CBlood)

– Metabolism:• in vitro: tissue homogenate

cell suspension tissue slice cell gas uptake

• in vivo: direct measurement of metabolites

Physiologically Based Pharmacokinetic (PBPK) Modeling

Define Realistic Model

Collect NeededData

Refine Model Structure

Make Predictions

Metabolic Constants

Tissue Solubility

Tissue Volumes

Blood and Air Flows

Experimental System

Model Equations

X

X

X

X

X

XX X

Tiss

ue C

once

ntr

ati

on

Time

You can be wrong!

Liver

Fat

Body

Lung

Air

Approach for Developing a PBPK Model

ProblemIdentification

LiteratureEvaluation

BiochemicalConstants

ModelFormulation

Simulation

Compare toKinetic Data

Design/ConductCritical Experiments

PhysiologicalConstants

Mechanismsof Toxicity

ValidateModel

Extrapolationto Humans

RefineModel

Models in Perspective

“…no model can be said to be ‘correct’. The role of any model is to provide a framework for viewing known facts and to suggest experiments.”

-- Suresh Moolgavkar

“All models are wrong and some are useful.”

-- George Box

PBPK Model Compartment Types- Storage compartment

• Rate in = QT · CA where QT = tissue blood flow, CA = arterial blood conc

• Rate out = QT · CVT = QT · CT/PT where CVT = conc in tissue blood, CT = conc in tissue, PT = partition

coefficient

• Assume Well-stirred compartment, so that, CVT = CT/PT

Lungs

Other

Fat tissues

Liver

Chemicalin air

Elimination

Lungs

Other

Fat tissues

Liver

Chemicalin air

Elimination

Lungs

Other

Fat tissues

Liver

Chemicalin air

Elimination

Same as 1-compartment model with continuous infusion

QTQT

CACVT

PBPK Model Compartment Types- Storage compartment

• Calculating Change in Amount:– Change in amount = rate in – rate out

dA/dt = QT x (CA – CT/PT)

dC/dt = QT x (CA – CT/PT) /V

Lungs

Other

Fat tissues

Liver

Chemicalin air

Elimination

Lungs

Other

Fat tissues

Liver

Chemicalin air

Elimination

Lungs

Other

Fat tissues

Liver

Chemicalin air

Elimination

Same as 1-compartment model with continuous infusion

QTQT

CACVT

Time

Conc

. CA

CVT

Time

Conc

. CA

CVT

Description for a Single Tissue Compartment

(venous equilibration assumption)

Qt = tissue blood flow

Cvt = venous blood concentrationPt = tissue blood partition coefficientVt = volume of tissue

At = amount of chemical in tissue

QtCart QtCvt

Vt; At; Pt

Tissue

Cvt = Ct/Pt

mass-balance equation: dAt = Vt dCt = QtCart - QtCvt

dt dt

Terms

Then used in toxicology.....Is any of this really new?

Ramsey and Andersen (1984)

Alveolar Space

Lung Blood

Fat Tissue Group

Muscle TissueGroup

Richly PerfusedTissue Group

LiverMetabolizingTissue Group( )

MetabolitesVmax

Km

Cart

Ql

Cart

Qr

Cart

Qm

Cart

Qt

Cart

Qc

Calv (Cart/Pb)

QalvQalv

Cinh

Qc

Cven

Cvt

Cvm

Cvr

Cvl

• Equations solved by numerical integration to simulate kinetic behavior.

• With venous equilibration, flow limited assumptions.

Styrene & Saturable metabolism

rate of change of amount

in liver

rate of uptake in arterial

blood

rate of loss in venous

blood

rate of lossby metabolism= - -

dAl = Ql (Ca - Cvl) - Vm Cvl

dt Km + Cvl

2520151050

100

10

1

0.1

0.01

0.001

TIME - hours

Ven

ou

s C

on

cen

trati

on

– m

g/l

ier

blo

od

Conc = 80 ppm

Conc = 1200 ppmConc = 600 ppm

Dose Extrapolation – Styrene

How does it work?

Alveolar Space

Lung Blood

Fat Tissue Group

Muscle TissueGroup

Richly PerfusedTissue Group

LiverMetabolizingTissue Group( )

MetabolitesVmax

Km

Cart

Ql

Cart

Qr

Cart

Qm

Cart

Qt

Cart

Qc

Calv (Cart/Pb)

QalvQalv

Cinh

Qc

Cven

Cvt

Cvm

Cvr

Cvl

What do we need to add/change in the models to incorporate another dose

route – iv or oral?

IV

Oral

Styrene - Dose Route Extrapolation

100

10

1.0

0.1

0.010 0.6 1.2 1.8 2.4 3.0 3.6

Hours

IV

Sty

ren

e C

on

cen

trati

on

(m

g/l

) 10

1.0

0.1

0.010 0.4 0.8 1.2 1.6 2.0 2.4

Hours

Oral

Sty

ren

e C

on

cen

trati

on

(m

g/l

)

2.8

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

Alveolar Space

Lung Blood

Fat Tissue Group

Muscle TissueGroup

Richly PerfusedTissue Group

LiverMetabolizingTissue Group( )

MetabolitesVmax

Km

Cart

Ql

Cart

Qr

Cart

Qm

Cart

Qt

Cart

Qc

Calv (Cart/Pb)

QalvQalv

Cinh

Qc

Cven

Cvt

Cvm

Cvr

Cvl

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

species?

SizesFlowsMetabolic Constants

Styrene - Interspecies Extrapolation

51

376

216

0.1

0.01

0.001

0.00010 1.5 3.0 4.5 6.0 7.5 9.0

Hours

Sty

ren

e C

on

cen

trati

on

(m

g/l

)

Blood

80 ppm

Exhaled Air

0 8 16 24 32 40 48

0.00001

0.0001

0.001

0.01

0.1

1.0

10

Hours

Sty

ren

e C

on

cen

trati

on

(m

g/l

)

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

ADVANTAGES OF SIMULATION MODELING IN PHYSIOLOGY AND ALSO IN

PHARMACOKINETICS & RISK ASSESSMENT

Codification of facts and beliefs (organize available information)Expose contradictions in existing data/beliefsExplore implications of beliefs about the chemicalExpose serious data gaps limiting use of the modelPredict response under new/inaccessible conditionsIdentify essentials of system structureProvide representation of present state of knowledgeSuggest and prioritize new experiments

A ‘Systems’ Approach for Dose Response

DRE

TCDD

Ligand

Ah Receptor

Transcription

Other

Stimulus

MAPK

Adaptor

RTK

Uptake

Absorption

Distribution

Metabolism

Excretion

Interaction w/ cellular networks

Effects

Inputs BiologicalFunction

ImpairedFunction

Adaptation DiseaseMorbidity &

Mortality

Exposure

Tissue Dose

Biological Interaction

Perturbation

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

Physiological Pharmacokinetic Modeling Principles

References

Andersen ME, Clewell HJ, Frederick CB. 1995. Applying simulation modeling to problems in toxicology and risk assessment -- a short perspective. Toxicol Appl Pharmacol 133:181-187.

Brown, R.P., Delp, M.D., Lindstedt, S.L., Rhomberg, L.R., and Beliles, R.P. 1997. Physiological parameter values for physiologically based pharmacokinetic models. Toxicol Indust Health 13(4):407-484.

Clewell, H.J., and Andersen, M.E. 1985. Risk Assessment Extrapolations and Physiological Modeling. Toxicol Ind Health, 1(4):111 131.

Clewell, H.J., Andersen, M.E., Barton, H.A., 2002. A consistent approach for the application of pharmacokinetic modeling in cancer and noncancer risk assessment. Environ. Health Perspect. 110, 85–93.

Dedrick, R.L. 1973. Animal scale up. J Pharmacokinet Biopharm 1:435 461.

Dedrick, R.L., and Bischoff, K.B. 1980. Species similarities in pharmacokinetics. Fed Proc 39:54 59.

Gerlowski, L.E. and Jain, R. J. (1983). Physiologically based pharmacokinetic modeling: principles and applications. J. Pharm. Sci., 72: 1103.

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.

Reddy, M.B. (2005). PBPK modeling approaches for special applications: Dermal exposure models. In: Physiologically Based Pharmacokinetic Modeling: Science and Applications, eds. M.B. Reddy, R.S.H. Yang, H.J. Clewell, III, and M.E. Andersen. John Wiley & Sons, Hoboken, New Jersey, pp. 375-387.

Yates, F.E. (1978). Good manners in good modeling: mathematical models and computer simulation of physiological systems. Amer. J. Physiol., 234, R159-R160. 1978.