# Chapter 19

# Multi-Compartment Pharmacokinetic Models

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## Effect of k12 and k21 on Drug Concentration versus Time

### Changing the Ratio of k12 to k21

**Figure 19.4.1 Plot of Cp versus Time Showing the Effect of Different k12/21 Ratio Values**

Click on the figure to view as an interactive graph

From the k12 and k21 values we can assess the extent of distribution of drug into the peripheral compartment. The higher the ratio k12/k21 the greater the distribution of drug into the peripheral compartment. The larger the individual values of k12 and k21 the faster is the transfer between the central and peripheral compartments and the more the body behaves as a single compartment.

As the ratio increases the distribution phase is more pronounced. Conversely with the ratio 1/4 there is very little distribution phase. Also note that the β value or the slope of the terminal phase is changing even though the kel is fixed at 0.2 hr^{-1}.

### Changing the Magnitude of k12 and k21 with the Same Ratio

With faster and faster distribution the initial drop in plasma concentration becomes quite rapid. If you were sampling every 30 minutes, the initial phase would be missed. The data would look just like a one compartment model. Redrawing the slow plot with k12/k21 (0.5/0.25) over 24 hours and gives a plot that is definitely still biexponential.

**Figure 19.4.2 Plot of Cp versus Time Showing the Effect of Different k12/21 Magnitudes**

Click on the figure to view as an interactive graph

Simulate other concentration versus time curves after IV bolus administration with the two compartment pharmacokinetic model using
macro constants (A, B, α and β) Interactive plot

or micro constants (kel, k12, k21, and V1) Interactive plot

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