Mar 30, 2011 (E. Landaw) M263 Clinical Pharmacology Pharmacokinetics & Pharmacodynamics Basic Concepts Basic Concepts Issues in Pharmacokinetics (PK) Issues

M263 Clinical PharmacologyMar 30, 2011 (E. Landaw)

Pharmacokinetics & Pharmacodynamics

Basic Concepts Issues in Pharmacokinetics (PK)

Clearance Half-lives and Residence Times Distribution Volumes Absorption & Bioavailability

Measures Compartmental Modeling

Pharmacodynamics (PD) Steady State Models Linking of PK & PD

Some Resources Texts

M Rowland & RN Tozer Clinical Pharmacokinetics 4th ed., Lippincott Williams & Wilkins 2011

AJ Atkinson et al. (eds). Principles of Clinical Pharmacology, Academic Press, 2nd Edition 2007

Web sites www.cc.nih.gov/training/training/principle

s.html

www.boomer.org/pkin/ (links to PK/PD resources)

Journals: Clinical Pharmacology & Therapeutics

(www.ascpt.org) J. Pharmacokinetics & Pharmacodynamics

http://www.cc.nih.gov/training/training/principles.html



http://www.boomer.org/pkin/

Basic - Definitions Pharmacokinetics (PK) –

quantitative analysis of the kinetics (time course) and steady state (SS) relationships of drug “What the body does to the

drug”

Absorption Distribution Metabolism Excretion

Elimination

Basic - Definitions Pharmacodynamics (PD) –

quantitative analysis of relation of drug concentration at an effect site (Ce) to drug effect (E).

“What the drug does to the body”

Understand Dose-Effect relationships

SS: Ce measured plasma concentration

Non-SS: may need to use PK to infer Ce

Dosing Regimen

dose, frequency, route

Concentrations

Plasma, urine, tissue,…Parent and metabolites

EFFECTS

Rx, Toxic

Effect Site Concentrations

source: A. Atkinson

Steady State vs. Kinetic Studies

Steady state (SS) with constant IV infusion when conc. not changing with

time plasma conc. CSS reflects Ctissue

(usually) PK (+load) determine time until

~SS

SS from Repetitive dosing (oral, IM, etc.) eventually reach constant

“Profile SS” Cmax= peak ; Cmin= trough ;

average CSS

source: Rowland & Tozer

Repetitive Dosing and “Profile SS”

Cmax

Cmin

Steady State vs. Kinetic Studies

Many PK/PD concepts are for SSClearance; Volume of distribution

SS PD effect for given SS conc.

(time to PD SS may be longer than time to plasma SS)

But some studies are kinetice.g., single oral dose or I.V. bolus

Tracer kinetic studies; PETAim may be infer SS under rep. dosing

Linear vs Nonlinear System

“Linear Pharmacokinetics” double the dose concentration

doubles AUC proportional to dose Superposition principle (example): If {I.V. bolus} Civ(t) and {oral dose}

Coral(t) , then {both dosing together} C(t) Civ(t) + Coral(t)

holds for small enough doses (microdoses)

linearity for large doses if transport, binding, and elimination remain first order

“Nonlinear Kinetics” Example

Linear vs Nonlinear System single kinetic study + linearity can

predict response to any input, including getting to SS

but for NONlinear systems: CL, V, etc. not constant; depend on

CSS, Dose requires testing at different doses;

models time to SS not predicted by single

dose study Common nonlinearities

Saturation kinetics (Michaelis-Menten)

Saturable plasma protein, tissue binding

Threshold effects (e.g., glucose spilling)

Induction; Neuro./hormonal regulation

Importance of Experiment Design

Quality & interpretation of PK/PD data depend critically on design: Dose(s), route, and form (bolus vs

infusion) What to sample

Plasma, urine, tissue, PET, … Total vs. unbound concentrations Parent compound, metabolites PD Effect measures

What times to sample in a kinetic study

Train team: record what was done, not just asked






Organ Clearance Physiology: organ clearance as SS

concept

“E” = Single pass extraction fraction: E = Elim. flux/ input flux = (Carterial –

Cvenous)/Carterial

Clearance Elim. flux/Cref (vol/time)

If use Carterial as Cref , Clearance = EQ

Carterial

Organ of eliminationQ blood flow

Cvenous

Elim. Flux = Q(Carterial – Cvenous) (mass/time)

Organ Clearance Clearance Elim. flux/Cref

Elimination (metabolism, transport) often function of unbound Cu (i.e., free fraction)

Cu = fuC (but fu not routine measurement)

Clearance = EQ high E (E>0.7), CL sensitive to Q,

not fu

low E (E<0.3) Q transit time E

CL sensitive to fu, CYP induction or inhibition

but SS “exposure” = fuAUC not sensitive to fu

Renal Clearance (CLR) Net Elim. flux = filtration + secretion

– reabsorb.

Net CLR = (urine exc. rate)/(mid-collection C)

(or use 24 hour urine collection and C(t) )

Renal Filtration flux = GFR fuC

GFR CLcreat= 120 ml plasma water/minute

CLR << GFR fu significant reabsorption

CLR >> GFR fu significant secretion

Total Clearance (CLT or just

CL) SS Clearances add:

CL = CLR + CLH + nonrenal/nonhepatic clearance

Estimating CL from single dose kinetic study i.v. Dose: CL = Dose/ ∫

C(t)dt =

Dose/AUC

Oral Dose: CL = FOral Dose/AUCwhere F = fraction of dose reaching

“central pool” (plasma + tissue in rapid equilibrium with

plasma)

CLoral CL/F = Oral Dose/AUC

0

Estimating AUC Trapezoidal rule:

Fit model of data to entire C(t). e.g.,

C(t) = A1exp(-1t) +… + Anexp(-nt)

AUC = A1/1 +… + An/n

.. . . . .

C(t)

t

May need to fit single exponential at end to estimate tail area to


Using Profile SS to estimate AUC

single dose AUC (from 0 to )

Profile SS after multiple repeated doses:

use area under one cycle to estimate single dose AUC

Predicting SS Concentration

Constant flux infusion I (mass/time)

SS plasma conc. CSS = C() total CL = (total Elim. Flux)/Cref

Here Cref is CSS

Since patient at steady state, Elim. Flux = I

Therefore, CSS = I / CL

Predicting SS Concentration

For i.v infusion flux I: CSS = I / CL

For repetitive oral dose D every T units of time, at Profile Steady State:

average CSS = (FD/T) / CL .

i.e. average CSS = (D/T) / CLoral

where CLoral estimated from kinetic study by

CLoral = Oral Dose/AUC =

CL/F

Half-lives and Residence Times 1-compartment approximation for body:

Drug distributes in single, well-mixed central pool

1st order elimination rate k (time-1); volume V

k = CL/V V = Dose/C(0) t1/2 = 0.693/k (half-life of drug in

whole body) MRT = 1/k (Mean Residence

Time in body) V = total drug distribution volume =

CL MRT

V C(t) = (Dose/V)exp(-kt)

t

logC(t)

k

0

. . . .

“Is this single exponential decay?”

0

10

20

30

40

0 4 8 12 16 20 24

time after IP injection (hours)

se

rum

co

nc

en

tra

tio

n (

nM

)

“What’s the half-life of this drug?”

conc. on LOG scale suggests “No!”

0.1

1

10

100

0 4 8 12 16 20 24

time after IP injection (hours)

se

rum

co

nc

en

tra

tio

n (

nM

)

initial t1/2 0.6 hours

terminal t1/2 14 hours

Half-lives and Residence Times

multi-compartment approximation for body: Drug distributes in central + peripheral

pool(s) C(t) exhibits elimination and

distribution kinetics

2 or more “half-lives,” but terminal half-life not always the main factor for dosing, accumulation, etc.

Relative importance each half-life depends on Ai/i

V1

t

logC(t)

0

. . . .C(t) = A1exp(-1t) + A2exp(-2t)

. . .

Schentag et al. JAMA 238:327-9, 1977


Caution: Interpreting Terminal t1/2

Terminal t1/2 often related to elimination

BUT NOT ALWAYS! counterexample:

gentamicin CLcr 6 – 107 ml/min terminal t1/2 in all

90 hrs renal impairment

affects mainly first half-life

avg CSS still (D/T)/CLoral

but dosing interval T to achieve desired Cmax/Cmin trickier to compute

Mean Residence Time (MRT)

MRT = mean time molecule of drug resides in body before being irreversibly eliminated

Assumes linear system May be useful summary

measure when there are multiple half-lives

Effective (overall) half-life = 0.693MRT

Mean Residence Time Estimating MRT from kinetic

studies: Measure plasma concentration C(t)

MRT AUMC/AUC ∫

tC(t)dt /AUC

Equality if elimination is exclusively from central pool and no traps. Need to use a model if there is peripheral elimination.

Measure total amount in body A(t) (e.g., total body scan)

MRT = ∫

A(t)dt/ A(0)

0

0

Mean Residence Time 1-compartment model

MRT = 1/k = V1/CL half-life = 0.693×MRT time to reach 90% SS following

constant flux infusion is 2.3 MRT’s = 3.3 half-lives

Multi-exponential model AUMC/AUC = w1(1/1) + … + wn(1/n)

where wi (Ai/i ) and w1 + … + wn = 1

2.3 MRT’s (i.e., 3.3 effective half-lives) is time to reach at least 84% SS

Distribution Volumes

Volume of Central Pool (V1) V1 = Dose/C(0) generally need several

recirculation times before well-mixed assumption holds

V1 often a little larger than plasma, even with multiexponential decay (includes tissues in rapid equilibrium with plasma by time of first sampling)

multi-compartment approximation for body: Drug distributes in central +

peripheral pool(s) C(t) exhibits elimination and

distribution kinetics

Back-extrapolated C(0) = A1 + A2

V1 = Dose/C(0)

V1

t

logC(t)

0

. . . .C(t) = A1exp(-1t) + A2exp(-2t)

. . .

SS Distribution Volume (VSS, VD or just V)

Assume body at SS (e.g., iv infusion)

A() is total amount (mass) of drug in body

Define V = A() / CSS

Hypothetical volume SS mass would have to occupy to yield same concentration as CSS

V = CL MRT Provides insights into

distribution, permeation, tissue binding, etc.

back-extrapolated C(0) from terminal decay (i.e., Vextrap) may overestimate V


t1/2 depends on CL and V

Absorption & Bioavailability

source: A. Atkinson

Bioavailability Measures of extent and rate of

absorption from admin. site to measurement site (latter usually central pool, i.e. plasma)

i .v. administration is “gold standard” for complete and instantaneous absorption

single oral dose: “informal” measures are:

tpeak

Cpeak

Bioavailability – formal measures

“F” estimates extent of absorption Separate i.v. and oral studies F = (Doseiv/Doseoral) AUCoral/AUCiv

fraction of administered dose reaching plasma

MAT (mean absorption time) AUMCoral/AUCoral - AUMCiv/AUCiv

Absorption rate constant (compart. model)

Absorption flux time course (deconvolution)

Example: Rifampicin pretreatment reduces oral

digoxin bioavailability

Example: Physiological PKPrediction, Scale-up , (Allometry)

Cho et al. Drug Metab. Dispos. 21:125-132.1993

Example: Compartmental Modeling

Metabolism Distribution phencyclidine analogs






Dose-Effect Relationships

Covariates age sex body size organ

function disease other drugs genes/

markers

Drug

Dose

Effect(s)

PK

C(t)PD

source: Frank M. Balis

Dose-Effect Endpoints

Graded

Quantal

• Continuous scale (dose ® effect)

• Measured in a single biologic unit

• Relates dose to intensity of effect

• All-or-none pharmacologic effect

• Population studies

• Relates dose to frequency of effect


Simplest PD Model for Graded Effect

(Effect 10 Drug-Receptor complex)

k1

k2

Drug

Receptor

Effect

Drug-Receptor Complex

Effect =Maximal effect • [Drug]

KD + [Drug]

(KD = k2/k1)

Ligand-binding domain

Effector domain


0

20

40

60

80

100

0 200 400 600 800

Graded Dose-Effect Curve

% of Maximal

Effect

[Drug]EC50

Maximal effect


Dose-Effect Parameters

POTENCY:

EFFICACY:

The sensitivity of an organ or tissue to the drug

The maximum effect


Comparing Dose-Effect Curves

0

20

40

60

80

100

1 10 100 1000

% of Maximal

Effect

[Drug]

Drug A

Drug C

Drug B

Effect =Maximal effect • [Drug]

KD + [Drug]


Pharmacodynamic Models

Fixed effect model

Linear model

Log-linear model

Emax model

Sigmoid Emax model

Effect = E0 + S•[Drug]

Effect = I + S•Log([Drug])

Effect = EC50 + [Drug]H

Emax•[Drug]H

H


Sigmoid Emax PD Model

0

20

40

60

80

100

0 20 40 60 80 100

0

20

40

60

80

100

1 10 100

[Drug]

Effect (%) Effect (%)

EC50EC50

H = 0.1

H = 5

H = 2H = 1

H = 0.5


Concentration and Effect vs. Time

0

2

4

6

8

10

0

20

40

60

80

100

0 5 10 15 20 25

Conc./ Amount

Effect[% of EMAX]

Time

Central Compartment

Peripheral Compartment

Effect Compartment

Effect

Non-Steady State


Hysteresis and Proteresis Loops

0

1

2

3

4

0 1 2 3 40

1

2

3

4

0 1 2 3 4

Plasma Drug Concentration

Intensity of Drug Effect

Intensity of Drug EffectHysteresis Loop

(Counterclockwise)Proteresis Loop

(Clockwise)

• Equilibration delay in plasma and effect site conc.

• Formation of active metabolite

• Receptor up-regulation

• Tolerance

• Receptor tachyphylaxis

PK/PD Applications Drug discovery/development

Scaling (cell culture animal human) Feasible dosing, drug delivery Predict and quantify inter- & intra-

patient variability Regulatory issues (FDA)

Basic and Clinical Sciences Understand in vivo mechanisms Quantify PK and PD study endpoints Design of clinical studies

Dosing regimens Timing of samples Identify important covariates

PK/PD Applications Therapy

Optimal treatment strategies Individualization of therapy Clinical monitoring (PD) or predicting

(PK/PD) efficacy and toxicity endpoints

Pharmacogenetics/pharmacogenomics Hereditary variations in response (PK or

PD) Identification of genes or loci Genome-based drug discovery Predict efficacy and potential adverse

effects

Documents

Mar 30, 2011 (E. Landaw) M263 Clinical Pharmacology Pharmacokinetics & Pharmacodynamics Basic Concepts Basic Concepts Issues in Pharmacokinetics (PK) Issues