Compartmental models in pharmacokinetics

Compartmental models in pharmacokinetics are used to describe how drugs are distributed and eliminated in the body. These models simplify the complex processes of drug absorption, distribution, metabolism, and excretion by dividing the body into compartments, each representing a different tissue or group of tissues with similar properties. 

1. One-Compartment Model

Description:

• This is the simplest model, where the body is represented as a single, homogeneous compartment.
• The drug is assumed to distribute instantaneously and evenly throughout this compartment.

Assumptions:

• The drug is uniformly distributed.
• The rate of drug elimination is proportional to the concentration in the compartment.

Use:

• Suitable for drugs that distribute quickly and uniformly throughout the body, like certain intravenous drugs.

Mathematical Representation:

• The concentration-time profile follows exponential decay: $C(t)=C_0\cdot e^{-kt}$ where $C(t)$ is the drug concentration at time $t$, $C_0$ is the initial concentration, and $k$ is the elimination rate constant.

2. Two-Compartment Model

Description:

• This model divides the body into two compartments: a central compartment (e.g., blood and well-perfused tissues) and a peripheral compartment (e.g., less perfused tissues like fat or muscle).

Assumptions:

• The drug is distributed between the central and peripheral compartments at different rates.
• Elimination occurs primarily from the central compartment.

Use:

• Useful for drugs with more complex distribution patterns, where there is a noticeable delay in reaching equilibrium between the central and peripheral compartments.

Mathematical Representation:

• The concentration-time profile is typically biphasic with a rapid initial decline (distribution phase) followed by a slower terminal phase (elimination phase).

3. Three-Compartment Model

Description:

• The body is divided into three compartments: a central compartment, a peripheral compartment, and an additional compartment (e.g., a deep tissue compartment).

Assumptions:

• Drugs are distributed among these three compartments at different rates.
• Elimination occurs from the central compartment, while distribution and equilibration occur between all three compartments.

Use:

• Appropriate for drugs with complex distribution and elimination characteristics, often seen in cases where a drug has multiple phases of distribution and elimination.

Mathematical Representation:

• The concentration-time profile is more complex, often showing multi-phasic declines.

4. Multiple Compartment Models

Description:

• These models extend beyond three compartments and are used for highly complex pharmacokinetics involving more compartments.

Assumptions:

• Drugs distribute among multiple compartments at different rates.
• Elimination usually occurs from one or more specific compartments.

Use:

• Typically used for highly complex scenarios and detailed pharmacokinetic studies, often in research settings.

Mathematical Representation:

• The concentration-time profiles can be very complex and require advanced mathematical techniques to describe.

5. Physiologically-Based Pharmacokinetic (PBPK) Models

Description:

• These models are more detailed and based on physiological parameters of the body, such as organ blood flow rates and tissue compositions.

Assumptions:

• The body is divided into compartments that represent actual organs or tissues.
• Drug distribution and elimination are modeled based on physiological and biochemical properties.

Use:

• Provides a more realistic representation of drug behavior in the body and is useful for predicting pharmacokinetics in different populations or conditions.

Mathematical Representation:

• Often involves a system of differential equations based on physiological parameters.

In pharmacokinetics, compartmental models range from simple (one-compartment) to highly complex (multiple compartments and PBPK models). The choice of model depends on the drug's distribution characteristics and the desired level of detail for predicting drug behavior in the body.