= - (ke + km) * V * Cp
Equation V-4. Rate of Change of V x dCp
with terms for excretion and metabolism
and since we call ke + km = kel
Equation V-5. Rate of Change of V x Cp
This is the same as before with one elimination pathway. The integrated equation will also be exactly the same as before:-
V * Cp = DOSE * e- kel * t
For U, the amount excreted into urine
Equation V-6. Rate of Change of U versus Time
notice we have ke here in place of kel
Then substituting for Cp we get
Equation V-7. Rate of Change of U versus Time
after integrating we get
Equation V-8. Integration Equation for U versus Time
Again, note: ke is in the numerator of Equation V-8 and not kel
For M, the amount of drug which has been metabolized the equations are:-
Equation V-9. Rate of Change of M versus Time
and
Equation V-10. Integration Equation for M versus Time
At t = 
; e-kel * t
---> 0
Equation V-11. Equation for U
versus Time
and
Equation V-12 Equation for M versus Time
NOTE:-
U + M = DOSE
This provides two new parameters, the fraction excreted unchanged in urine, fe, and the fraction metabolized, fm
Equation V-13. Fraction Excreted as Unchanged Drug
Equation V-14. Fraction Excreted as Metabolite
The plots we did before for U, dU/dt, and A.R.E. have the same significance as before
Copyright 2001 David W.A. Bourne
