PDF Useful Pharmacokinetic Equations - College of Pharmacy
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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