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Stability of a one-dimensional morphoelastic model for post-burn contraction.
Ginger Egberts1,2, Fred Vermolen3, Paul van Zuijlen4,5,6
1Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands. G.Egberts@tudelft.nl.
Journal of Mathematical Biology
|August 6, 2021
Summary
This study introduces a morphoelastic model for scar formation, analyzing stability constraints for wound healing simulations. The findings ensure realistic modeling of skin trauma by validating mechanical and biological components.
Area of Science:
- Computational Biology
- Biomechanics
- Mathematical Modeling
Background:
- Scar formation after skin trauma involves complex mechanical and biological processes.
- Permanent deformations and residual stresses are key challenges in modeling wound healing.
- Existing models may not fully capture the interplay between mechanical forces and cellular/molecular components.
Purpose of the Study:
- To develop and analyze a one-dimensional morphoelastic model for scar formation.
- To establish stability constraints for both continuous and semi-discrete versions of the model.
- To provide a biological interpretation of model stability and its implications for wound healing.
Main Methods:
- Formulation of a morphoelastic model incorporating mechanical (strain, displacement) and biological (signaling molecules, cell densities, collagen) factors.
- Derivation of stability constraints for the one-dimensional model.
- Analysis of truncation error between continuous and semi-discrete eigenvalues.
- Numerical validation of stability constraints and biological interpretation.
Main Results:
- Stability constraints were derived for the morphoelastic scar formation model.
- The truncation error between continuous and semi-discrete eigenvalues was quantified.
- Mechanical components reach equilibria monotonically or non-monotonically based on viscosity.
- Chemical model parameters must satisfy stability constraints related to signaling molecule decay rates.
Conclusions:
- The derived stability constraints are crucial for ensuring realistic simulations of scar formation.
- Model parameters, particularly those governing chemical signaling, must adhere to stability criteria to prevent unphysical outcomes.
- The study provides a framework for understanding and controlling the stability of morphoelastic models in wound healing research.
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