126
the metabolic clearance (Cl^ ). The metabolic clearance of the parent
drug (Cl t) and the apparent volume of distribution (Vm) of the
metabolite that is excreted in the urine and the bile can be estimated
by integrating the above equation between 0 and t with respect to time
and considering the stoichiometry of the total metabolite
M, = k V J Cpdt=Cl ^ AUC.
t m c 0 r met t
= U + V m + B Eq. 32
m m m
where AUCfc is the area under the parent drug (1) concentration-time
curve, U and B are the amounts of metabolite excreted into the urine
m m
and bile respectively up to that time and m is the metabolite
concentration in plasma. If it can be assumed that a constant fraction
of the hepatically formed metabolite is partitioned into the bile, i.e.,
there is a constant biliary clearance, then constant biliary clearance,
then
B = CL. AUC.
m B t
Substituting the value of B^ into equation 32,
(Cl CL, ) AUC. = U + V m
' met B t mm
The equation can be rearranged^ into
Eq. 33
Eq. 34
U /m = -V + (Cl Cln ) AUC. /m Eq. 35
m m met B t ^
or U /AUC. = -V m/AUC, + (Cl CL ) Eq. 36
m t m t met B ^
where ( Cl Cl_. ) and V can be obtained from the slopes and
met B m
intercepts of the appropriate plots of the designated quotients of AUC^