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Time to reach steady state

Another important factor is the time to reach the steady state concentration. For instance, the time to reach half the steady state can be derived:

Since

(see Equation VI-3)

and

then

or

ekel * tHALF = 2

taking the antilog of both sides

kel * tHALF = ln 2 = 0.693

Thus

tHALF = 0.693/kel = t1/2 for elimination

Thus the approach to Cpss is exponential in nature and is controlled by the elimination process NOT the infusion process. NOTE however that the value of Cpss IS controlled by k0.

Halfwayto steady stateinonehalf-life
75%""2"
87.5%""3"
94%""4"

For theophylline with a t1/2 equal to 4 hours the time to reach 94% of steady state will be 16 hours. We could calculate how long it might take to reach a therapeutic concentration. For theophylline this might be 10 mg/L

Thus

(see Equation VI-2)

Using the values from before

k0 = 60 mg/hr; kel = 0.17 hr- 1; V = 25 L; and Crequired = 10 mg/L

0.708 = 1 - e- 0.17 * t thus 0.292 = e- 0.17 * t

therefore

- 0.17 * t = - 1.231 or t = 7.24 hr


Figure VI-2. Plot of Cp versus Time showing Approach to Steady State

Thus if we started an infusion to achieve a steady state plasma concentration of approximately 15 mg/L (actually 14.1 mg/L) it would take 7.25 hours to reach a therapeutic level.


This page was last modified: 12 February 2001

Copyright 2001 David W.A. Bourne


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