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

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

Extravascular administration, such as oral or intramuscular routes, is a non-invasive drug delivery method, often preferred for ease and patient compliance. A key factor here is absorption, which dictates how quickly and effectively the drug enters the bloodstream from the administration site. Absorption follows either zero-order or first-order kinetics.
Zero-order absorption maintains a steady rate irrespective of the amount of drug left to be absorbed, making it a constant process. In the...

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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 Model

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...

Operon Model

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The operon model represents a fundamental mechanism of gene regulation in prokaryotes, enabling coordinated expression of genes involved in related metabolic or functional pathways. Operons consist of structural genes, a promoter, and an operator, with transcription regulated by repressors, activators, and small effector molecules.Structure and Function of OperonsAn operon is a cluster of structural genes transcribed together under the control of a single promoter. The promoter region...

Two-Compartment Open Model: Extravascular Administration

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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.
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Related Experiment Video

Updated: May 14, 2026

A Model of Chronic Nutrient Infusion in the Rat

A Model of Chronic Nutrient Infusion in the Rat

Published on: August 14, 2013

A closed NPZ model with delayed nutrient recycling.

Matt Kloosterman¹, Sue Ann Campbell, Francis J Poulin

¹Department of Applied Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1, Canada, mklooste@uwaterloo.ca.

Journal of Mathematical Biology

|February 16, 2013

Summary

This summary is machine-generated.

This study shows that the amount of biomass and the delay in nutrient recycling significantly impact planktonic ecosystems. Too little biomass or too long a delay can cause species extinction and alter ecosystem stability.

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Last Updated: May 14, 2026

A Model of Chronic Nutrient Infusion in the Rat

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Published on: August 14, 2013

Mesocosm-Scale Constructed Wetland Design for Wastewater Treatment

Mesocosm-Scale Constructed Wetland Design for Wastewater Treatment

Published on: May 2, 2025

An Anoxia-starvation Model for Ischemia/Reperfusion in C. elegans

An Anoxia-starvation Model for Ischemia/Reperfusion in C. elegans

Published on: March 11, 2014

Area of Science:

Marine Ecology
Mathematical Biology
Oceanography

Background:

Planktonic ecosystems are crucial for marine food webs and global biogeochemical cycles.
Nutrient recycling dynamics are fundamental to understanding plankton population stability.
Time delays in ecological processes can lead to complex system behaviors.

Purpose of the Study:

To investigate the impact of biomass quantity and nutrient recycling delay on a closed Nutrient-Phytoplankton-Zooplankton (NPZ) model.
To quantify the role of delay distribution properties in ecosystem dynamics.
To determine how these factors influence equilibrium solutions and stability.

Main Methods:

Development of a delay-dependent conservation law to quantify total biomass.
Analytical and numerical techniques to explore model behavior.
Simulations to verify theoretical findings.

Main Results:

Biomass quantity and delay length are critical for the existence of equilibrium solutions.
Sufficiently small biomass or sufficiently long delays can lead to species extinction.
Variations in biomass and delay significantly affect the stability of equilibrium solutions.

Conclusions:

The interplay between biomass and nutrient recycling delays is a key determinant of planktonic ecosystem stability and persistence.
The findings highlight the sensitivity of NPZ models to temporal dynamics and resource availability.
This research provides insights into the resilience and potential collapse of marine ecosystems under varying conditions.