# Chapter 19

# Multi-Compartment Pharmacokinetic Models

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### Student Objectives for this Chapter

- To draw the scheme and write the differential equations appropriate to a multi-compartment pharmacokinetic model
- To recognize and use the integrated equations for these models to calculate parameter values and for dosage regimen calculations
- To calculate the parameters of these models using the method of residuals

So far we have talked about the pharmacokinetics of drugs in terms of a one compartment model. We have assumed that the drug, once administered is mixed instantaneously in the blood and that the drug distributes throughout the body rapidly reaching equilibrium throughout the tissue into which the drug enters. We have in essence considered that the body acts as a well mixed container.

**Figure 19.1.1 Linear Plot of Cp Versus Time for a One-Compartment - IV Bolus**

With first order drug elimination we found that the plasma concentration will fall monoexponentially with time following IV bolus administration.

**Figure 19.1.2 Semi-Log Plot of Cp Versus Time**

And the log of the plasma concentration will fall as a straight line.

**Figure 19.1.3 Semi-Log Plot of Cp Versus Time. Two-Compartment - IV Bolus. Note Fast and Slow Processes**
Commonly we find with real data, especially if we have a number of early data points, that the log Cp versus time plot is not a straight line. We see an initial early deviation from the straight line, followed by a log-linear
phase. The initial phase is a more rapid drop in plasma concentration before settling into the log-linear fall in plasma concentration.

This suggests that the body is not behaving as a single well mixed compartment. There appears, mathematically, to be distribution between two (or more) compartments. That is we don't have instantaneous equilibrium between the drug in all the various tissues of the body. In the next approximation we can consider that the body is behaving as two distinct compartments. These compartments can be called the central compartment and the peripheral compartment. Exact anatomical assignment to these compartments is not always
possible. However, generally the rapidly perfused tissues often belong in the
central compartment.

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