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Three-Compartment Open Model01:06

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...
Two-Compartment Open Model: Extravascular Administration01:12

Two-Compartment Open Model: Extravascular Administration

The two-compartment model for extravascular administration represents a drug's absorption and distribution process. It features a central compartment, where the drug is first absorbed, and a peripheral compartment, which illustrates the drug's distribution throughout the body. The rate of change in drug concentration in the central compartment is calculated by three exponents: absorption, distribution, and elimination.
The absorption exponent (ka) indicates the speed at which the drug is...
Compartment Models: Two-Compartment Model01:20

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...
Multicompartment Models: Overview01:14

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,...
Two-Compartment Open Model: Overview01:05

Two-Compartment Open Model: Overview

Multicompartmental models are crucial tools in pharmacokinetics, providing a framework to understand how drugs move within the body. The two-compartment model is a crucial subtype, segmenting the body into central and peripheral compartments. The central compartment represents areas with high blood flow, such as plasma and highly perfused organs like the kidneys and liver, while the peripheral compartment signifies tissues with lower blood flow, like adipose tissue and muscle tissue.
The...
One-Compartment Open Model for Extravascular Administration: First-Order Absorption Model01:15

One-Compartment Open Model for Extravascular Administration: First-Order Absorption Model

The first-order absorption model for extravascular administration describes the rate at which a drug is absorbed and eliminated, following the principles of first-order kinetics. This model is vital as it provides a mathematical representation of drug behavior within the body. It also allows for the prediction and interpretation of drug absorption and elimination based on the rate of change in drug concentration over time. This model can be visualized as a plasma concentration-time profile...

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Related Experiment Video

Updated: May 13, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

Local accumulation times for source, diffusion, and degradation models in two and three dimensions.

Peter V Gordon1, Cyrill B Muratov, Stanislav Y Shvartsman

  • 1Department of Mathematics, The University of Akron, Akron, Ohio 44325, USA.

The Journal of Chemical Physics
|March 22, 2013
PubMed
Summary

We analyzed transient dynamics in reaction-diffusion models relevant to biology. The local accumulation time characterizes transient timescales but requires multi-scale analysis near localized sources.

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Related Experiment Videos

Last Updated: May 13, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

Planar Gradient Diffusion System to Investigate Chemotaxis in a 3D Collagen Matrix
09:26

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Published on: June 12, 2015

A Method for Determination and Simulation of Permeability and Diffusion in a 3D Tissue Model in a Membrane Insert System for Multi-well Plates
10:33

A Method for Determination and Simulation of Permeability and Diffusion in a 3D Tissue Model in a Membrane Insert System for Multi-well Plates

Published on: February 23, 2018

Area of Science:

  • Mathematical Biology
  • Chemical Kinetics
  • Cellular Dynamics

Background:

  • Reaction-diffusion models are crucial for understanding biological pattern formation and chemical signaling.
  • Transient dynamics precede steady states in many biological processes, influencing cellular and developmental outcomes.
  • The interplay of diffusion, production, and degradation shapes spatio-temporal concentration profiles.

Purpose of the Study:

  • To analyze the transient dynamics in reaction-diffusion systems modeling biological processes.
  • To derive and characterize the local accumulation time as a measure of transient timescales.
  • To assess the sufficiency of local accumulation time for describing dynamics across different spatial scales.

Main Methods:

  • Derivation of analytical expressions for local accumulation time in 2D and 3D systems.
  • Analysis of the dependence of local accumulation time on model parameters, including degradation kinetics.
  • Investigation of the spatial relevance of local accumulation time for concentration dynamics.

Main Results:

  • Expressions for local accumulation time were derived for systems with first-order degradation kinetics.
  • The local accumulation time effectively characterizes transient timescales, particularly far from localized sources.
  • A multi-scale description is necessary for accurately capturing transient dynamics near tightly localized sources in 2D and 3D.

Conclusions:

  • Local accumulation time provides a valuable metric for transient dynamics in reaction-diffusion systems.
  • The utility of local accumulation time as a sole descriptor is limited in regions close to concentrated sources.
  • Accurate modeling of biological transients, especially near sources, necessitates consideration of multi-scale phenomena.