Example: Theophylline pharmacokinetic parameters determined after oral administration of a single dose to a patient were: k= 0.115 hr-1, ka = 0.3 hr-1, Vd = 30 L, and F = 0.85. What is the theophylline doses from the same product that will achieve a maximum concentration of 10 and 20 mg/L in the same patient ?

a- Calculate tmax

b- Find out the dose that will achieve Cpmax of 10 mg/L

tmax =

ln ka - ln k

ka - k
Cpmax =

F D ka

Vd (ka - k) (e -k tmax - e-ka tmax)
tmax =

In 0.3-In0.115

(0.3-0.115) hr-1 = 5.18 hr
10 mg/L =

(0.85) D 0.3hr-1

30 L (0.3-0.115)hr-1 ( e-0.115hr-15.18hr -e-0.3hr-15.18hr)

Dose = 640mg

Administration of (640x2)=1280 mg should achieve Cpmax of 20 mg/L.

Administartion of 640 mg should achieve maximum concentration of 10 mg/L
Administartion of 1280 mg should achieve maximum concentration of 20 mg/L
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