Structural Biochemistry/One Compartment Model with Absorption

Introduction
The one compartment model with absorption, also known as the single compartment model, is a model that represents a drug that rapidly equilibrates with the extravascular tissue compartment. In another words, the one compartment model is the simplest way of describing a drug that is almost instantaneously distributed throughout the body. For a drug that does not equilibrate immediately, a two compartment model must be used. The two-compartment model generally represents a drug that slowly equilibrates with the tissue compartment. This model involves two compartments which are the central and peripheral compartments. 1

One-Compartment Model with Absorption
In a one-compartment model, the body is considered to be one unit; thus there is only one volume of distribution, often denoted Vd. We assume that with the one-compartment model, the drug is distributed throughout the body immediately at the instant when the drug enters the body. The elimination of the drug is assumed to follow first order kinetics in this model. Therefore, when taking the log of the concentration of drug in the body and plotting it against time (“log of concentration vs. time”), the resulting model will be linear. An important thing to remember is that the first order kinetics is an assumption that applies to the linear model, not the one compartment model. That being said, a change in dosage of the drug will not be reflected in the pharmacokinetic parameters (kel, Vd, Cp), but rather in the proportional change in drug concentration within the body. Because elimination follows first order kinetics, the rate of elimination is only dependent on one factor and that is the amount of drug in the body. The amount of drug in the body is proportional to the rate of elimination. 2

First Order Kinetics
First order kinetics in a one-compartment model can be easily displayed by generating various graphs. Firstly, the concentration of drug in the body should be collected at various times. Then a plot of this data should generate a graph similar to this:


 * If the rate of change of each point on the “concentration vs. time” plot is taken, a new plot can be generated. (See figure 4.3.1) 3


 * Taking this rate of change and plotting it against the concentration of drug in blood (resulting in “rate of change vs. concentration” graph), a linear curve can be generated. (See figure 4.3.2) 3


 * Simple derivations will lead to this mathematical representation of the behavior of the one-compartment model.(See figure 4.3.3) 3


 * As shown in equation 4.3.1, the kel remains constant regardless of the change in dosage. This proves that in a one-compartment model, the pharmacokinetic parameters do not change with any given dosage. From equation 4.3.1, we can also conclude that the rate of elimination, denoted as -∆Cp/∆t, is only dependent on the concentration of drug in the body, Cp. (See equation 4.3.1) 3

Uses of One-Compartment Model
The one compartment model is a simplification for when a drug rapidly equilibrates in the body. Although the drug is said to be in equilibrium, the drug concentration in fluid or the tissue will not always be equal. Thus, when the drug is said to be in equilibrium, it is assumed that the drug concentration in tissue/fluids is always proportional to the drug concentration in the body at all times. 3

This model is not completely accurate because only a very few drugs have proven to instantly equilibrate and disperse throughout the body. However, for the sake of simplicity, when a drug is said to have minimal distribution we can assume that the one-compartment model will serve as an adequate approximation. 2