Pharmacokinetic modeling

Relationship between concentration and effect

The magnitude and total duration of any pharmacological effect directly depend on the concentration of the drug achieved in target organs. The primary therapeutic goal of a physician is always to maintain a strictly defined drug level in the tissues.

However, a significant practical problem arises: directly measuring the amount of the substance in the target organ of a living patient is practically impossible. The solution is regular blood sampling from the vascular bed. Measuring the level of the active substance in blood plasma provides an objective picture, since there is a clear correlation between how much drug is circulating in the bloodstream and how much has accumulated in the target organs.

Pharmacokinetic curve

The drug level in plasma is never static. It is continuously influenced by four fundamental processes:

• Absorption — entry from the site of administration.
• Distribution — transport through organs and tissues.
• Deposition — temporary accumulation in body structures.
• Elimination — removal of the substance from the body, which combines biotransformation (metabolism) and excretion.

To quantify these stages, a pharmacokinetic curve is constructed — a graphical display of how plasma concentration changes over time. The shape of the graph strongly depends on the route of administration. If administered intravenously (as a bolus), the substance enters instantly, the curve starts at the maximum point ($C_0$), and immediately enters the decline phase. For extravascular routes (e.g., per os administration), the curve starts at zero, has a pronounced growth phase due to absorption, reaches a peak, and only then drops.

One-compartment model

For mathematical calculations, the human body is conventionally represented as a system of reservoirs (compartments). The simplest option is the one-compartment pharmacokinetic model. In this model, the entire body is viewed as a single compartment completely filled with fluid.

The main postulate of this concept states that after administration, the drug distributes throughout the entire volume instantaneously and absolutely uniformly. The key parameters here are the administered dose (denoted as D) and the initial concentration of the substance immediately after complete distribution (denoted as $C_0$). The loss of the drug from this single compartment occurs solely due to elimination processes.

Two-compartment model and kinetics phases

To more accurately describe drug behavior (especially after intravenous administration), a two-compartment pharmacokinetic model is used. In this case, the body is divided into two communicating sectors:

1. Central compartment — includes the blood itself and well-perfused organs. This is where the drug initially enters and from which it is eliminated.
2. Peripheral compartment — poorly perfused tissues, where the substance gradually distributes from the central sector.

Constant redistribution occurs between the compartments. The concentration graph in such a model has a biphasic character, forming a biexponential curve. It clearly shows a steep initial drop (the so-called $\alpha$-phase, reflecting distribution) and a long, shallow "tail" ($\beta$-phase, indicating elimination). In a simplified version (monoexponential curve), the logarithm of concentration drops linearly, which graphically determines the time required for the concentration to drop by half — the half-life.

Briefly: answers to topical questions

Class and exam questions

What else to study on this topic

• Mathematical calculation of inter-compartmental transition rate constants
• Biotransformation and excretion processes that constitute elimination
• Graphical determination of the half-life from a monoexponential curve
• Features and applications of multicompartment pharmacokinetic models

Other topics in "General Pharmacology"

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