Metabolite Elimination

b- When k < k(m)

i.e. the metabolite half life is shorter than the parent drug half life.

The metabolite conc declines at a rate dependent on its rate of formation, which is equal to the parent drug elimination rate.

The decline in the metabolite conc is limited
by its formation rate and the metabolite
conc declines parallel to the drug conc.
( formation rate limited metabolite)

Mathematically:

Cp(m) =

k D

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

The term e-k(m) t approaches zero faster than the term e-k t (because k < k(m))

As time gets bigger, the equation is reduced to:

Cp(m) =

k D

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