Distribution and Pharmacokinetics Models - Pesticide Biotransformation and Disposition - page 129

Therefore, C t is equal to one-half of C 0 after one half-life has passed since the dose was
administered, and:

C

0

= C exp ( k t ). (22)

0 e 1 2 /

2

Equation (22) can be solved for t 1/2 ,

0 693 .

, (23)

t

=

1 2 /

k

e
which may also be estimated by inspection of the graph of log C t vs. t ( Figure 6.4 ). The
reader should however be aware that the terminal half-life is not necessarily the time
taken for the administered dose to decline by half, but rather the time required for
plasma concentration to decline by half during the terminal phase of the concentration-
time profile ( Toutain and Bousquet-Melou, 2004b ). The reader should compare Figure
6.4 (one-compartment model) and Figure 6.9 (two-compartment model) to see why
this is important for the latter and why Eq. (23) is replaced with Eq. (52).
Plasma clearance (Cl, L/h) is a measure of the inherent ability to remove a chemical
from the body and it is often normalized by body weight (L/h/kg). Cl represents the
volume of plasma that is cleared of the chemical per unit time and is the ratio of the
rate of elimination (mass/time) and concentration (mass/volume):

dA dt
C

/ k A

C

k CV
C

e t e t d

t

Cl = = = = k V . (24)

e d

t t

Integration of Eq. (24) yields:

Dose
AUC

Cl = . (25)

Equation (24) can also be rearranged to solve for:

Cl

k = . (26)

e

V

d

Substitution of Eq. (25) into Eq. (26) and rearrangement leads to the equation for V d :

Dose

V .

= (27)

d

AUC k ×

e

Alternatively, the half-life can be calculated using V area and Cl area using iv data only
as follows:

0 693 . × V

area

t = . (28)

1 2 /

Cl

area