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Post Infusion

Before moving on to discussing various routes of drug administration, we can look at the equation for plasma concentration after an infusion is stopped.

Remember that the equation for plasma concentration versus time during an IV infusion is

Equation 15.6.1 Drug Concentration during an IV Infusion

If the infusion is continued indefinitely then the plasma concentration approaches a steady state plasma concentration.

If however the infusion is stopped the plasma concentration can be expected to fall.

Scheme or diagram

Figure 15.6.1 During and After an IV Infusion - One Compartment Model

The scheme shown to represent 'after the infusion is stopped' is the same as that for the bolus injection.

Equations

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 15.6.2 Concentration at the End of an IV Infusion

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

Then


Equation 15.6.3 Concentration after an IV Infusion has Stopped

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

Equation 15.6.4 Concentration during and after an IV Infusion

Equation 15.6.4 can be used as shown when t is greater than T (that is for drug concentrations after the infusion has stopped). However, if t is less than or equal to T you should set T = t before using the equation. In this way the term e-kel * (t-T) becomes equal to 1 and can be dropped from the equation and the equation reverts to Equation 15.6.1.

Figure 15.6.2 Linear Plot of Cp versus Time for Interrupted Infusion. Showing Mono exponential Rise and Fall

Click on the figure to view the Java Applet window

If we use the previous example data, 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 15.6.3 Semi-log Plot of Cp versus Time. NOTE: Intercept is not Cp0

Click on the figure to view the Java Applet window

Thus 4 hours after the infusion was stopped the drug concentration has fallen to half the value at the end of the infusion. Remember the drug half-life was 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 15.6.4 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.

Rearranges to

Javascript Calculators using Equation 16.6.4

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 calculating required infusion rates and parameter values. Compare your answers with the computer! These problems include bolus/infusion and fast/slow infusion regimen cacluations as well as parameters determinations from two post infusion drug concentrations.

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.

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Copyright 2001-3 David W. A. Bourne (david@boomer.org)

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