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Stability of a two-dimensional biomorphoelastic model for post-burn contraction
Ginger Egberts1,2, Fred Vermolen3,4, Paul van Zuijlen5,6,7
1Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands. G.Egberts@tudelft.nl.
Journal of Mathematical Biology
|March 25, 2023
Summary
This study analyzes the stability of a 2D post-burn contraction model, integrating morphoelasticity with a chemical-biological framework. We establish stability conditions based on signaling molecule decay rates for continuous and discrete models, examining eigenvalue convergence.
Area of Science:
- Computational modeling
- Biophysics
- Mathematical biology
Background:
- Post-burn contraction is a significant clinical challenge.
- Morphoelasticity and chemical-biological models offer insights into tissue remodeling.
- Understanding the stability of these models is crucial for predicting long-term outcomes.
Purpose of the Study:
- To perform a stability analysis of a 2D post-burn contraction model.
- To investigate the influence of signaling molecule decay rates on model stability.
- To compare the stability of continuous and semi-discrete model representations.
Main Methods:
- Developed a 2D computational model combining morphoelasticity with a chemical-biological system.
- Incorporated cellular densities, collagen density, and chemoattractant concentrations.
- Formulated stability conditions for both continuous partial differential equations and semi-discrete representations.
- Analyzed spatial eigenvalues to assess model stability and convergence.
Main Results:
- Derived stability conditions dependent on the decay rate of signaling molecules.
- Identified differences in spatial eigenvalues between continuous and semi-discrete models.
- Demonstrated the convergence of the semi-discrete model to the continuous model.
Conclusions:
- The stability of post-burn contraction models is significantly influenced by signaling molecule dynamics.
- The semi-discrete model provides a reliable approximation of the continuous model's stability.
- This work contributes to a better understanding of the biomechanical and biochemical factors governing scar contracture.
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