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Multicompartment Models: Overview

Multicompartment Models: Overview

Multicompartment models are mathematical constructs that depict how drugs are distributed and eliminated within the body. They segment the body into several compartments, symbolizing various physiological or anatomical areas connected through drug transfer processes such as absorption, metabolism, distribution, and elimination.
These models offer a more comprehensive representation of drug behavior in the body than one-compartment models. They accommodate the complexity of drug distribution,...

Three-Compartment Open Model

Three-Compartment Open Model

The three-compartment open model is a pharmacokinetic model used to describe the distribution and elimination of drugs following extravascular administration. It comprises a central compartment representing the plasma and two peripheral compartments. The highly perfused peripheral compartment represents organs and tissues with a rich blood supply, such as the liver, kidneys, and lungs. The scarcely perfused peripheral compartment represents tissues with lower blood supply, such as adipose...

Compartment Models: Single-Compartment Model

Compartment Models: Single-Compartment Model

The single-compartment model serves as a simplified representation of the human body. This model assumes that the body functions as a single, well-mixed open compartment. When a drug is administered intravenously, it enters the body and quickly distributes uniformly. The drug then undergoes biotransformation and elimination, ultimately leaving the body. The volume of this compartment is referred to as the apparent volume of distribution into which the drug can uniformly distribute. In this...

Compartment Models: Two-Compartment Model

Compartment Models: Two-Compartment Model

The two-compartment model divides the body into central and peripheral compartments to account for varying blood perfusion rates among organs and tissues, affecting drug distribution. The central compartment includes blood and highly perfused tissues with rapid drug distribution, while the peripheral compartment contains tissues with slower drug distribution. After a single IV bolus dose, the drug concentration is high in plasma and low in tissues. The drug distribution between compartments...

Mechanistic Models: Overview of Compartment Models

Mechanistic Models: Overview of Compartment Models

Mechanistic models, a category encompassing both physiological and compartmental modeling, differ from empirical models' approaches to incorporating known factors about the systems being modeled. Empirical models describe data with minimal assumptions, while mechanistic models aim to provide a robust description of available data by specifying assumptions and integrating known factors about the system. Compartmental analysis is a key example of a mechanistic model in pharmacokinetics and...

Model Approaches for Pharmacokinetic Data: Compartment Models

Model Approaches for Pharmacokinetic Data: Compartment Models

Compartmental analysis is a widely adopted approach to characterizing drug pharmacokinetics. It uses compartment models that conceptualize the body as a collection of reversibly communicating compartments, each representing a group of tissues exhibiting similar drug distribution characteristics. The movement rate of the drug between these compartments is typically described by first-order kinetics.
Two primary types of compartment models are recognized: mammillary and catenary. The more...

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Related Experiment Video

Updated: May 19, 2026

The Use of Chemostats in Microbial Systems Biology

The Use of Chemostats in Microbial Systems Biology

Published on: October 14, 2013

Stability analysis of multi-compartment models for cell production systems.

Yukihiko Nakata¹, Philipp Getto, Anna Marciniak-Czochra

¹BCAM-Basque Center for Applied Mathematics, Bizkaia Technology Park, Derio, Spain. nakata@bcamath.org

Journal of Biological Dynamics

|August 10, 2012

Summary

This study models hierarchical cell production, finding that stem cell populations can become unstable during differentiation. Increased mature cell death stabilizes these systems.

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Last Updated: May 19, 2026

The Use of Chemostats in Microbial Systems Biology

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Area of Science:

Mathematical Biology
Cellular Dynamics
Population Modeling

Background:

Hierarchical cell production systems are crucial for tissue maintenance and regeneration.
Regulation of stem cell division by mature cell levels is a key biological process.
Understanding population stability is vital for predicting tissue behavior.

Purpose of the Study:

To analyze the stability of equilibria in two- and three-compartment cell production models.
To investigate how cell division regulation affects population dynamics.
To adapt ecological reproduction numbers for stem cell dynamics.

Main Methods:

Development and analysis of two- and three-compartment mathematical models.
Investigation of equilibrium structures and local stability properties.
Application of adapted reproduction numbers to interpret model behavior.

Main Results:

In the two-compartment model, the positive equilibrium is always stable when it exists.
The three-compartment model exhibits an instability region linked to the intermediate differentiation stage.
This instability region diminishes with increasing mature cell mortality rates.

Conclusions:

The intermediate differentiation stage can introduce population instabilities in complex cell production systems.
Mature cell mortality plays a stabilizing role in these hierarchical models.
Mathematical modeling provides insights into stem cell population regulation and stability.