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.
Halfway | to steady state | in | one | half-life |
75% | " | " | 2 | " |
87.5% | " | " | 3 | " |
94% | " | " | 4 | " |
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
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.
Copyright 2001 David W.A. Bourne