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Digital Planimetry for Assessing Wound Closure Kinetics in a Mouse Model

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Published on: January 10, 2025

Computational approaches to solving equations arising from wound healing.

Jennifer A Thackham¹, D L Sean McElwain, Ian W Turner

¹School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, 4001, Australia. j.thackham@qut.edu.au

Bulletin of Mathematical Biology

|December 17, 2008

Summary

This summary is machine-generated.

Numerical methods for advection-dominated wound healing models are crucial. Flux limiting is identified as the most accurate and appropriate approach for solving these complex mathematical models in both one and two dimensions.

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Area of Science:

Mathematical Biology
Computational Science
Biomedical Engineering

Background:

Wound healing models often involve cell movement (chemotaxis) dominating random motion.
This leads to advection-dominated mathematical models requiring careful numerical solutions.
Existing numerical approaches may be inappropriate for these models.

Purpose of the Study:

To evaluate and compare numerical algorithms for solving advection-dominated wound healing models.
To identify the most accurate and reliable numerical method for these problems.
To validate findings in both one and two-dimensional scenarios.

Main Methods:

Four algorithms were tested: MATLAB's pdepe.m, NAG's d03pcf.f, and two finite volume methods (upwinding and flux limiting).
One-dimensional test problems with analytic solutions were used for validation, analyzing average absolute difference and mass balance error.
Two-dimensional test problems, including one with an analytic solution and a angiogenesis model, were also analyzed.

Main Results:

Flux limiting demonstrated superior accuracy and mass balance compared to other methods for one-dimensional advection-dominated wound healing problems.
Analysis of a coupled nonlinear three-species model confirmed flux limiting's appropriateness for advection-dominated equations.
Results from two-dimensional problems further supported flux limiting as the ideal treatment for advective terms in these models.

Conclusions:

Flux limiting is the optimal numerical approach for advection-dominated wound healing models.
This method ensures better accuracy and mass balance in simulations.
The findings are applicable to both simplified and complex multi-dimensional wound healing simulations.