the general concepts of pharmacokinetics and pharmacodynamics

The General Concepts of Pharmacokinetics and Pharmacodynamics

Hartmut Derendorf, PhDUniversity of Florida

PHARMACOKINETICS

what the body does to the drug

PHARMACODYNAMICS

what the drug does to the body

Pharmacokineticsconc. vs time

Co

nc

.

Time0 25

0.0

0.4

PK/PDeffect vs time

Time

Eff

ec

t

0

1

0 25

Pharmacodynamicsconc. vs effect

0

1

10-4 10-3Conc (log)

Eff

ec

t

Pharmacokinetics

the time course of drug and metabolite concentrations in the body

Pharmacokinetics helps

to optimize drug therapy:

dose

dosage regimen

dosage form

What happens to a drug after its administration ?

("Fate of drug")

Liberation

Absorption

Distribution

Metabolism

Excretion

Clearance

Volume of distribution

Half-life

Bioavailability

Protein Binding

Pharmacokinetic Parameters

Clearance

quantifies ELIMINATION

is the volume of body fluid cleared per time unit (L/h, mL/min)

is usually constant

Clearance

Eliminating Organ

CL = Q·E

Q Blood Flow

E Extraction Ratio

Clearance

Parameters: Blood Flow, intrinsic clearance, protein bindingGood prediction of changes in clearance

Steady state

Q

Ci CoEliminating

Organ

int

int

CLfQ

CLfQCL

EQCL

C

CCE

u

u

i

oi

High-extraction drugs

Low-extraction drugs

QCL

intCLfCL u

int

int

int

CLfQ

CLfQ

CLfQCL

u

u

u

int

int

int

CLfQ

CLfQ

CLfQCL

u

u

u

Clearance

Clearance can be calculated from

Excretion rate / Concentratione.g. (mg/h) / (mg/L) = L/h

Dose / Area under the curve (AUC)e.g. mg / (mg·h/L) = L/h

Clearance

Total body clearance is the sum of the individual organ clearances

CL = CLren + CLhep + CLother

Volume of Distribution

- quantifies DISTRIBUTION

- relates drug concentration (Cp) to amount of drug in the body (X)

- gives information on the amount of drug distributed into the tissues

Vd = X / Cp

Apparent Volume of DistributionX

V

C2 = X / Vd

Vd = X / C2

X

V

C1 = X / V

V = X / C1

C1 C2

C1 > C2

V < Vd

Volume of Distribution

Dicloxacillin 0.1 L/kgGentamicin (ECF) 0.25 L/kgAntipyrine (TBW) 0.60 L/kgCiprofloxacin 1.8 L/kgAzithromycin 31 L/kg

Half-Life

Half-life is the time it takes for the concentration to fall to half of its previous value

Half-life is a secondary pharmacokinetic parameter and depends on clearance and volume of distribution

CL

Vdt

693.02/1

Half-Life

k elimination rate constantCL clearanceVd volume of distribution

kkt

693.02ln2/1

Bioavailability

f is the fraction of the administered dose that reaches the systemic circulation

- quantifies ABSORPTION

iv

po

AUC

AUCF

BioavailabilityRate and Extent of

Absorption

Cmax

0

10

20

30

40

50

60

70C

on

ce

ntr

atio

n (

ng

/ml)

Cmax

0 2 4 6 8 10 12

Time (hours) tmaxtmax

Protein Binding

• reversibe vs. irreversible

• linear vs. nonlinear

• rapid equilibrium

The free (unbound) concentration

of the drug at the receptor site

should be used in PK/PD

correlations to make prediction for

pharmacological activity

vascular space extravascular space

plasma protein binding

blood cell binding,

diffusion into blood cells,

binding to intracellular biological material

tissue cell binding,

diffusion into tissue cells,

binding to intracellular biological material

binding to extracellular biological material

Interstitium

CapillaryCell

PerfusateDialysate

Microdialysis

Microdialysis

Pharmacokinetic profile of cefpodoxime (400 mg oral dose, n = 6)

0

1

2

3

4

5

6

0 2 4 6 8 10

Time (h)

Co

nc

en

tra

tio

n (

mg

/L)

plasma muscle free plasma

Pharmacokinetic profile of cefixime (400 mg oral dose, n = 6)

0

1

2

3

4

5

6

0 2 4 6 8 10

Time (h)

Co

nc

en

trato

in (

mg

/L) plasma muscle free plasma

Mean ± SD

Pharmacokinetics

Cefpodoxime Cefixime

AUCP [mg*h/L] 22.4 (8.7) 25.7 (8.4)

AUCT [mg*h/L] 15.4 (5.2) 7.4 (2.1)

Cmax, P [mg/L] 3.9 (1.2) 3.4 (1.1)

Cmax,T [mg/L] 2.1 (1.0) 0.9 (0.3)

Two-compartment model

Xp

E

D

k12

Dose

Xc Drug in the central compartment

Xp Drug in the peripheral compartment

Drug eliminated

Xc

k10

k21

Two-compartment model

0 1 2 3 4 5 6 7 8

Time (hours)

10-1

100

101

102

103

C (n

g/m

l)

Short-term infusion

T

Cmax

C

18 19 20 21 22 23 24

t (h)

100

101

102

103

Cp (µ

g/m

l)

C* Cmin

*max

min

k

Three-compartment model

Xp

E

D

k12

D Dose

E Drug eliminated

Xck

10

k21

k31

k13

Xps

d

Xc Drug in the central compartment

Xps Drug in the shallow peripheral compartment

Xpd Drug in the deep peripheral compartment

XC

XPs

XPd

t [h]

0 48 96 144 192 240 288 336

X [m

g]

0

100

200

300

400

500

600

Drug Delivery

Pharmacokinetics

Pharmacodynamics

Biopharmaceutics

PK-PD-Modeling

?

?

Questions• What are the effects of protein binding on antibiotic

activity and interpretation of plasma levels?• What are the effects of a change in protein binding on

unbound concentrations?• Why do we monitor post-distribution peaks as indicators

of aminoglycoside activity?• Why do we monitor troughs as indicators of

aminoglycoside toxicity?• How do you interpret a high tissue level of a macrolide?

Compartment Models

Parameters: Rate constants, interceptsLinear and nonlinear regression

Complete concentration-time-profilesSteady-state and non-steady-state

Intravenous bolus

X E

D

k

D Dose

X Drug in the body

E Drug eliminated

One compartment model

Intravenous bolusPlasma concentration (single dose)

tkeCC 0

Vd

DC 0

D DoseC0 Initial ConcentrationVd Volume of Distribution

Normal Plot Semilogarithmic Plot

Intravenous bolus

Intravenous bolusPlasma concentration (multiple dose, steady state)

CC e

e

k t

k

0

1

CC

e kmax

0

1 CC e

e

k

kmin

0

1

Peak Trough

Intravenous bolusMultiple Dose

First-order absorption

A E

D

k

Dose

Drug at absorption site

Drug in the body

Drug eliminated

Xka

f

One compartment model

Oral administrationPlasma concentration (single dose)

CF D k

k k Vde ea

a

k t k ta

Oral administration

t [h]

0 2 4 6 8 10 12

Cp

[ng/

mL]

0

100

200

300

400

Oral administration

Average concentration (multiple dose, steady state)

CF D

CL

Oral administrationMultiple Dose

One compartment model

A E

D

k

Dose

Drug at absorption site

Drug in the body

Drug eliminated

XR0

f

Zero-order absorption

Constant rate infusionPlasma concentration (during infusion)

CR

CLe k t 0 1

Constant rate infusion

Constant rate infusionPlasma concentration (steady state)

CR

CL 0

Two-compartment modelPlasma concentration (single i.v. bolus dose)

C a e b et t

-phase: distribution phase

-phase: elimination phase

t [h]

0 1 2 3 4 5 6 7 8

Cp

[g/

mL]

0.1

1

10

100

Two-compartment model

Two-compartment model

Xp

Xc

Xp

Xc

Xp

Xc

initially steady state elimination phase

VD

Cc 0

Vdk

kVss c

1 12

21

VdCL

area

Volume of distribution

Significance of Pharmacokinetic Parameters for Dosing

CLCDF

CLCR

desired

desired

0

VdCLD desired

)min(

)max(

desired

desired

C

CPTR

693.0

)ln( 2/1tPTR

Maintenance Dose

Loading Dose

Fluctuation

Dosing Interval