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Continuous IV Infusion - 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

and

then

taking the ln of both sides

Thus

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

Halfway - 50%	to steady state	in	one	half-life
75%	to steady state	in	2	half-life
87.5%	to steady state	in	3	half-life
94%	to steady state	in	4	half-life

For theophylline with a t_1/2 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

Using the values from before

k0 = 60 mg/hr; kel = 0.17 hr^{- 1}; V = 25 L; and C_required = 10 mg/L

thus

and taking the ln of both sides gives -0.17 * t = -1.231 thus t = 7.24 hr

Figure 15.3.1 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 of 10 mg/L.