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A new nonlinear model of reaction-diffusion-advection applied to some scar anomalies and cutaneous mosaicism

Author

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  • Ochoa-Gutiérrez, H. Osmart
  • Montes-Pérez, Areli
  • Morales, Marco A.

Abstract

In this work is present a mathematical model for explain the cutaneous regeneration using new mechanochemical model-advection formed by three nonlinear partial differential equations that consider the dermis, epidermis and basal lamina, as well as cellular densities and chemical concentrations for the human skin, respectively. The model incorporates the simulation of the following biological processes: cellular diffusion in the epidermis, long-range spatial interaction (non-linear diffusion effects) in the dermis, chemical diffusion for the epidermis, cellular proliferation in the dermis and epidermis, chemotaxis for the epidermis, haptotaxis for the dermis and nonlinear chemical kinetics of biochemical substances of the skin. The nonlinear partial differential equations of new model are solved numerically. Their numerical solutions are presented as bidimensional patterns, which reproduces the morphogenesis of extracellular matrix, including the scaring of healthy skin in the form of keloid and contractile scars, as well as the reproduction of some of their pathologies, such as vitiligo and Blaschko lines.

Suggested Citation

  • Ochoa-Gutiérrez, H. Osmart & Montes-Pérez, Areli & Morales, Marco A., 2026. "A new nonlinear model of reaction-diffusion-advection applied to some scar anomalies and cutaneous mosaicism," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 240(C), pages 612-632.
    • Handle: RePEc:eee:matcom:v:240:y:2026:i:c:p:612-632
    DOI: 10.1016/j.matcom.2025.07.029
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    References listed on IDEAS

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    1. Marco A. Morales & Irving Fernández-Cervantes & Ricardo Agustín-Serrano & Andrés Anzo & Mercedes P. Sampedro, 2016. "Patterns formation in ferrofluids and solid dissolutions using stochastic models with dissipative dynamics," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(8), pages 1-17, August.
    2. Raphael Wittkowski & Adriano Tiribocchi & Joakim Stenhammar & Rosalind J. Allen & Davide Marenduzzo & Michael E. Cates, 2014. "Scalar φ4 field theory for active-particle phase separation," Nature Communications, Nature, vol. 5(1), pages 1-9, September.
    3. Mimura, Masayasu & Tsujikawa, Tohru, 1996. "Aggregating pattern dynamics in a chemotaxis model including growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 230(3), pages 499-543.
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