Example: A drug is metabolized completely to one metabolite. Calculate the plasma drug and metabolite concentrations 1 and 10 hours after iv administration of 1000 mg of the parent drug.
(k=0.4hr -1, Vd = 30L, k(m) = 0.2 hr-1 and Vd(m) = 22 L)

Drug

Metabolite

Drug Conc:

Cp = Cpo e-kt

Metabolite Conc:

Cp(m) =

k D

Vd(m)( k(m) - k) (e-k t - e-k(m) t)

After 1 hour:

a-Parent drug:

Cp =

1000 mg

30L (e-0.4hr -1 1hr) = 22.3mg/L

b-Metabolite:

Cp(m) =

0.4 hr-1 1000 mg

22L (0.2 hr -1 - 0.4 hr -1) (e-0.4hr -1 1hr -e -0.2hr -1 1hr) = 13.5mg/L

After 10 hour:

a-Parent drug:

Cp =

1000 mg

30L (e-0.4hr -1 10hr) = 0.61mg/L

b-Metabolite:

Cp(m) =

0.4 hr-1 1000 mg

22L (0.2 hr -1 - 0.4 hr -1) (e-0.4hr -1 10hr -e -0.2hr -1 10hr) = 10.6mg/L
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