Mathematical Expressions

The mathematical expressions that describe the change in the amount of the drug in the body with time.


a- If you know the amount of drug in the body at two different time points (the time difference between these two points is t, you can calculate the elimination rate constant.

InA2 = InA1-kt
log A2 = log A1 -

kt

2.303
A2 = A1e-kt
You can substitute for the
value of A1, A2 and t in any of
these equation to calculate the
elimination rate constant
A1
A2
t

Example:


After administration of an iv dose of theophylline the amount of theophylline remaining in the body after 3 hours was 250 mg and after 8 hours was 100 mg. Calculate the elimination rate constant of theophylline in this patient.


A8hr = A3hr e-k(8-3)hr
100 mg = 250 mg e-k(5hr)
lOO mg/250 mg= e-k(5hr)
In lOO/250 = - k (5 hr)
-0.916 = - k (5 hr)
k = 0.183hr-1
You can substitute for the
value of A1, A2 and t in any of
these equation to calculate the
elimination rate constant
A1 = 250 mg
A2 = 100 mg
5hr
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