# Intravenous Infusion

## Continuous IV Infusion - Time to Reach Steady State

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

Since

and

then

or

taking the ln of both sides

Thus

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 - 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 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

Using the values from before

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

thus

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

Figure 6.3.1 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. This is probably too long so another strategy should be explored.