The equation for Cp versus time is shown above. At the end of the infusion period when t = T the plasma concentration can be calculated as:-


Equation VI-5. Concentration at the End of an IV Infusion

Once the infusion is stopped all we have is a first order elimination.




Equation VI-6. Concentration after an IV Infusion has Stopped

where t is time counted from the start of the infusion. Then t - T is the time since the end of the infusion. Then


Equation VI-7. Concentration during and after an IV Infusion

for t > T


If t is less than or equal to T then set T = t. Then the term e-kel * (t-T) becomes = 1 and is not needed.


Figure VI-5. Linear Plot of Cp versus Time for Interrupted Infusion. Showing Monoexponential Rise and Fall

Using a JAVA aware browser you can create your own version of Figure VI-5.
If we use the previous example data, thus V = 25 L; kel = 0.17 hr-1; T = 0.5 hour; and k0 = 735 mg/hr, what would be the plasma concentration be at 4.5 hours (t = 4.5 hours).


That is if we stop the loading infusion and don't start the maintenance infusion.


Figure VI-6. Semi-log Plot of Cp versus Time. NOTE: Intercept is not Cp0

Using a JAVA aware browser you can create your own version of Figure VI-6.

= 14.1 x 0.5 = 7.05 mg/L


Thus 4 hours after the infusion was stopped the Cp has fallen to half the value at the end of the infusion, remember we started with the drug half-life equal to 4 hours.

Example Calculation: Following a two-hour infusion of 100 mg/hr plasma was collected and analysed for drug concentration. Calculate kel and V.
Time (hr) 3 5 9 12 18 24
Cp (mg/L) 12 9 8 5 3.9 1.7

Figure VI-7. Plot of Cp Versus Time after a Two-Hour Infusion

The red line drawn through the data points and back to the Y-axis represents the best-fit line.

Javascript Calculators using Equation VI-7

Calculate kel and V given post infusion Cp versus time data

Enter a value for the infusion rate and duration (< 3 hr)
Infusion rate k0 (zero order mass/time)
Infusion duration < 3 (time)
Cp at 4 hours (mg/L)
Cp at 5 hours (mg/L)
Cp at 6 hours (mg/L)
Cp at 9 hours (mg/L)
Cp at 12 hours (mg/L)
Cp at 24 hours (mg/L)
kel (first order reciprocal time)
V (volume)

HyperCard Stack

One Compartment Model - IV Infusion
First Semester Exam 1995 Students
Third Homework Set 1995 Students
For practice try estimating various parameter values from post infusion data. Compare your answers with the computer! These problems include graphing post infusion drug concentration data on semi-log graph paper and estimating parameters from the slope and intercept of the best-fit line.
This page was last modified: 25 May 2002

Copyright 2002 David W.A. Bourne