Useful Pharmacokinetic Equations - University of Florida

Useful Pharmacokinetic Equations

Symbols

D = dose

= dosing interval CL = clearance Vd = volume of distribution ke = elimination rate constant ka = absorption rate constant F = fraction absorbed (bioavailability) K0 = infusion rate T = duration of infusion C = plasma concentration

General

Elimination rate constant

ln

C1

ke

CL Vd

C2

t2 t1

ln C1 ln C2

t2 t1

Half-life

t1/ 2

0.693 Vd CL

ln(2) ke

0.693 ke

Intravenous bolus

Trough (multiple dose)

Cmin

C0 ek e 1 ek e

Average concentration (steady state)

Cpss

D CL

Oral administration

Plasma concentration (single dose)

C F D k a eket e ka t

Vd k a k e

Time of maximum concentration (single

dose)

ln

k

a

tmax

ke ka ke

Plasma concentration (multiple dose)

C F D ka Vd k a k e

e ket 1 e ke

e ka t 1 e ka

Initial concentration

C0

D Vd

Plasma concentration (single dose) C C0 eke t

Plasma concentration (multiple dose)

C

C0 ek e t 1 ek e

Peak (multiple dose)

Cmax

C0 1 ek e

Time of maximum concentration (multiple

dose)

tmax

ln

k k

a e

1 ek e 1 eka

ka ke

Average concentration (steady state) C FD CL

Clearance Cl Dose F

AUC

Cl ke Vd

Equations/Useful_pharmacokinetic_equ_5127

1

Constant rate infusion

Plasma concentration (during infusion)

C k0 1 eke t CL

Plasma concentration (steady state) C k0

CL

Calculated clearance (Chiou equation)

CL

2 k0

C1 C2

2 Vd C1 C1 C2 t2

C2 t1

Short-term infusion

Peak (single dose)

Cmax(1)

D CL T

1 ekeT

Trough (single dose) Cmin(1) Cmax(1) eke T

Peak (multiple dose)

Cmax

D CL T

1 ekeT 1 eke

Trough (multiple dose)

Cmin Cmax eke T

Calculated elimination rate constant

ke

ln

C max

C min

t

with Cmax* = measured peak and Cmin* =

measured trough,

measured over the time interval t

Equations/Useful_pharmacokinetic_equ_5127

Calculated peak

C max

C e max

ket

with Cmax* = measured peak, measured at time

t* after the end of the infusion

Calculated trough

C min

C min

eket

with Cmin* = measured trough, measured at time t* before the start of the next infusion

Calculated volume of distribution

Vd

D ke T

[Cmax

1 eke T (Cmin eke

T

)]

Calculated recommended dosing interval

ln

C

max(desired

)

Cmin(desired) T

ke

Calculated recommended dose

1 eke D Cmax(desired) k e V T 1 ekeT

Two-Compartment-Body Model

C a et b et

AUC a / b /

Vd area Vd ss Vc

Creatinine Clearance

CL creat

(male)

(140

age) weight 72 Cpcreat

CL creat

(female)

(140

age) weight 85 Cpcreat

With weight in kg, age in years, creatinine plasma conc.

in mg/dl and CLcreat in ml/min

2

Ke for aminoglycosides

Ke = 0.00293(CrCL) + 0.014

Metabolic and Renal Clearance

EH = ClH =

Clint fub QH Clint fub

EH QH =

QH Clint fub QH Clint fub

FH =

QH QH Clint fub

Clren =

RBFE = GFR Cin C out C in

Clren

=

rate of excretion plasma concentration

Clren

=

fu

GFR

Rate

of

secretion - Rate of reabsorption Plasma concentration

Clren =

Urine flow urine concentration Plasma concentration

Ideal Body Weight

Male IBW = 50 kg + 2.3 kg for each inch over 5ft in height

Female IBW = 45.5 kg + 2.3 kg for each inch over 5ft in height

Obese ABW = IBW + 0.4*(TBW-IBW)

Volume of Distribution

VVP VT K P

V

VP

VT

fu fuT

Clearance

Cl Dose AUC

Cl ke Vd

Equations/Useful_pharmacokinetic_equ_5127

3

For One Compartment Body Model

For a single I.V. bolus administration:

C0

D V

If the dosing involves the use of I.V. bolus administration:

C C0 eket

For a single short-term I.V. infusion:

Since = t for Cmax

If the dosing involves the use of I.V. infusion:

Cmax

D VkeT

1 ekeT

Cmin Cmax eke ( T )

For multiple I.V. bolus administration:

Cn(t)

D V

1 enke 1 eke

eket

at peak: t = 0; at steady state n

at trough: t =

Cmax ss

D V

(

1

1 e ke

)

Cmin ss Cmax ss eke

For multiple short-term I.V. infusion at steady state:

Cmax

D VkeT

1 ekeT 1 eke

Cmin Cmax eke ( T )

Last modified 2010 C:\Current Data\pha5127_Dose_Opt_I\equations\5127-28-equations.doc

If the dosing involves a I.V. infusion (more equations):

If the dosing involves oral administration:

Ct

D ekeT VkeT

1 eket

(most general eq.)

during infusion t = T so,

Ct

D VkeT

1 eket

(during infusion)

at steady state t , e-ket, t 0 so,

Cpss

D

k k 0 0 (steady state)

VkeT Vke CL

remembering

k0

D T

and

CL V ke

For a single oral dose:

For multiple oral doses:

C

F D

V ka

ka ke

eket

ekat

C

F D

V ka

ka ke

1

eket eke

ekat 1 eka

tmax

ln kkae

ka

1

ke

tmax

ln

ka ke

1 1

eke eka

ka

1

ke

Last modified 2010 C:\Current Data\pha5127_Dose_Opt_I\equations\5127-28-equations.doc

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