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Two-Compartment Open Model: IV Infusion

Two-Compartment Open Model: IV Infusion

A two-compartment model is a vital tool in pharmacokinetics, providing an essential understanding of drug behavior, especially for those administered via zero-order intravenous infusion. This model outlines two compartments: the central compartment, where elimination occurs, and the peripheral compartment.
The model illustrates the decrease in plasma drug concentration from the central compartment with a specific equation. It shows that under steady-state conditions, the drug's input rate...

Determination of Multiple Dosing Parameters: Steady-State, Minimum and Maximum Concentrations

Determination of Multiple Dosing Parameters: Steady-State, Minimum and Maximum Concentrations

Gentamicin, an aminoglycoside antibiotic, is commonly administered via intermittent intravenous infusion to treat severe infections. An intermittent one-hour infusion of gentamicin, administered at eight-hour intervals, allows for precise control of plasma drug concentrations, minimizing toxicity while ensuring therapeutic efficacy. Pharmacokinetic principles govern the dynamics of plasma concentrations and can be mathematically described using specific equations.The plasma drug concentration...

One-Compartment Open Model for IV Bolus Administration: Estimation of Clearance

One-Compartment Open Model for IV Bolus Administration: Estimation of Clearance

Clearance is a key pharmacokinetic parameter that quantifies the volume of body fluid from which a drug is entirely removed within a specific time frame. It is crucial in assessing how a drug is eliminated from the body and has critical clinical applications.
In the one-compartment open model for intravenous (IV) bolus administration, clearance is estimated by dividing the elimination rate by the plasma drug concentration. This equation leverages the elimination rate constant and the apparent...

Fundamental Mathematical Principles in Pharmacokinetics: Calculus and Graphs

Fundamental Mathematical Principles in Pharmacokinetics: Calculus and Graphs

The fundamental mathematical principles, such as calculus and graphs, play crucial roles in analyzing drug movement and determining pharmacokinetic parameters. Differential calculus examines rates of change and helps to determine the dissolution rate of drugs in biofluids, as well as how drug concentrations change over time. For instance, it can help calculate the rate of elimination of a drug from the body based on its concentration-time profile.
On the other hand, integral calculus focuses on...

One-Compartment Open Model for IV Bolus Administration: General Considerations

One-Compartment Open Model for IV Bolus Administration: General Considerations

The one-compartment model is a pharmacokinetic tool that models the body as a single, uniform compartment, facilitating the understanding of drug distribution and elimination. This model is particularly beneficial for intravenous (IV) bolus administration, where the drug rapidly circulates throughout the body.
The drug's presence in the body is defined by an equation representing the difference between the rates of drug entry and exit. Key parameters—elimination rate constant, half-life,...

One-Compartment Model: IV Infusion

One-Compartment Model: IV Infusion

Intravenous (IV) infusion is often utilized when continuous and controlled drug delivery is necessary, such as during surgery or in the treatment of chronic diseases. This method offers numerous advantages, including immediate drug action, precise control over dosage, and bypassing the first-pass metabolism.
The one-compartment model for IV infusion uses mathematical equations to describe the rate of change in drug quantity in the body. At steady-state or infusion equilibrium, the drug input...

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Related Experiment Video

Updated: Jun 28, 2026

Use of Cerebral Open-Flow Microperfusion for the Longitudinal Collection of Interstitial Fluid in an Animal Model of Glioblastoma

Use of Cerebral Open-Flow Microperfusion for the Longitudinal Collection of Interstitial Fluid in an Animal Model of Glioblastoma

Published on: December 23, 2025

Mathematical model for G-CSF administration after chemotherapy.

Catherine Foley¹, Michael C Mackey

¹Department of Mathematics and Centre for Nonlinear Dynamics, Mcgill University, 3655 Promenade Sir William Osler, Montreal, Quebec, Canada H3G 1Y6. foley@math.mcgill.ca

Journal of Theoretical Biology

|November 15, 2008

Summary

Granulocyte-colony stimulating factor (G-CSF) treatment timing impacts neutrophil recovery after chemotherapy. Mathematical modeling reveals that altering G-CSF initiation or duration can cause distinct neutrophil count responses due to model dynamics.

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Published on: February 24, 2023

Area of Science:

Mathematical Biology
Hematology
Pharmacodynamics

Background:

Chemotherapy often causes neutropenia, a dangerous reduction in neutrophil levels.
Granulocyte-colony stimulating factor (G-CSF) is a key therapeutic agent for managing neutropenia.
Understanding G-CSF's regulatory effects on neutrophil production is crucial for optimizing treatment.

Purpose of the Study:

To develop a delay differential equation model for neutrophil production regulation by G-CSF.
To investigate the impact of delayed G-CSF administration on neutrophil recovery post-chemotherapy.
To analyze the effects of varying G-CSF treatment duration on neutrophil counts.

Main Methods:

Development of a mathematical model incorporating G-CSF effects on neutrophil dynamics.
Analytical and numerical simulations to explore model behavior.
Examination of two recombinant G-CSF forms: filgrastim and pegfilgrastim.

Main Results:

Model analysis revealed that the timing of G-CSF initiation significantly influences neutrophil count trajectories.
Varying the duration of filgrastim treatment also led to qualitative differences in neutrophil responses.
The observed phenomena are explained by the mathematical model's prediction of coexisting stable solutions.

Conclusions:

The mathematical model provides insights into the complex dynamics of G-CSF therapy.
Treatment initiation timing and duration are critical factors affecting neutrophil recovery.
The model's prediction of multiple stable states helps explain diverse clinical responses to G-CSF.