Example: A patient received a constant rate iv infusion of 45 mg/hr theophylline until a steady state was achieved. The infusion was terminated and the plasma conc measured 2 and 10 hours after stopping the infusion were 12.28 mg/L and 5.52 mg/L, respectively. Calculate k and Vd of theophylline.

These concentrations can be used to calculate the s.s. conc and the elimination rate constant (k)

Draw the best line that goes through the two samples. Calculate k from the slope of the line

Back extrapolate the line to the time of stopping the infsuion to calcualte the s.s. conc

The CLT can be calculated from the infusion rate and the s.s. conc

The Vd can be calculated from the CLT and k

CLT =

Ko

Cps.s.

CLT

Vd =k
Slope = -k/2.303

Graphically: k = 0.1 hr-1

Steady state conc (y-intercept) = 15 mg/L

y-intercept is time zero when the infusion was stopped

CLT =

45 mg/hr

15 mg/L = 3 L/hr
Vd =

3 L/hr

0.1 hr -1 = 30L
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