The force of cell-cell adhesion in determining the outcome in a nonlocal advection diffusion model of wound healing

Glenn Webb; Glenn Webb

doi:10.3934/mbe.2022403

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 9: 8689-8704. doi: 10.3934/mbe.2022403

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The force of cell-cell adhesion in determining the outcome in a nonlocal advection diffusion model of wound healing

Glenn Webb ^,

Mathematics Department, Vanderbilt University, Nashville, TN, USA

Academic Editor: Feng-Bin Wang

Received: 31 December 2021 Revised: 19 May 2022 Accepted: 09 June 2022 Published: 16 June 2022

A model of wound healing is presented to investigate the connection of the force of cell-cell adhesion to the sensing radius of cells in their spatial environment. The model consists of a partial differential equation with nonlocal advection and diffusion terms, describing the movement of cells in a spatial environment. The model is applied to biological wound healing experiments to understand incomplete wound closure. The analysis demonstrates that for each value of the force of adhesion parameter, there is a critical value of the sensing radius above which complete wound healing does not occur.
- nonlocal,
- advection,
- diffusion,
- adhesion,
- wound healing experiment
Citation: Glenn Webb. The force of cell-cell adhesion in determining the outcome in a nonlocal advection diffusion model of wound healing[J]. Mathematical Biosciences and Engineering, 2022, 19(9): 8689-8704. doi: 10.3934/mbe.2022403

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Abstract

A model of wound healing is presented to investigate the connection of the force of cell-cell adhesion to the sensing radius of cells in their spatial environment. The model consists of a partial differential equation with nonlocal advection and diffusion terms, describing the movement of cells in a spatial environment. The model is applied to biological wound healing experiments to understand incomplete wound closure. The analysis demonstrates that for each value of the force of adhesion parameter, there is a critical value of the sensing radius above which complete wound healing does not occur.

References

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