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Modelling Keloids Dynamics: A Brief Review and New Mathematical Perspectives

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Abstract

Keloids are fibroproliferative disorders described by excessive growth of fibrotic tissue, which also invades adjacent areas (beyond the original wound borders). Since these disorders are specific to humans (no other animal species naturally develop keloid-like tissue), experimental in vivo/in vitro research has not led to significant advances in this field. One possible approach could be to combine in vitro human models with calibrated in silico mathematical approaches (i.e., models and simulations) to generate new testable biological hypotheses related to biological mechanisms and improved treatments. Because these combined approaches do not really exist for keloid disorders, in this brief review we start by summarising the biology of these disorders, then present various types of mathematical and computational approaches used for related disorders (i.e., wound healing and solid tumours), followed by a discussion of the very few mathematical and computational models published so far to study various inflammatory and mechanical aspects of keloids. We conclude this review by discussing some open problems and mathematical opportunities offered in the context of keloid disorders by such combined in vitro/in silico approaches, and the need for multi-disciplinary research to enable clinical progress.

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Acknowledgements

RE and OA acknowledge funding from a French Agence Nationale de Recherche (ANR) Grant Number ANR-21-CE45-0025-01; SPAB and SU acknowledge funding from a Luxembourg National Research Fund (FNR) Grant Number INTER/ANR/21/16399490; G.R. acknowledges funding from an ANR Grant Number ANR-21-CE45-0025-03; FC’s work is partially supported by the I-Site BFC project NAANoD, the EIPHI Graduate School (contract ANR-17-EURE-0002) and the ANR project S-KELOID (ANR-21-CE45-0025-04). FC is also grateful to the Center for Mathematical Modelling Grant FB20005.

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  1. Laboratoire de Mathématiques de Besançon, Université de Franche-Comté, 25000, Besançon, France

    R. Eftimie & O. E. Adebayo

  2. INSERM CIC-1431, CHU Besançon, F-25000, Besançon, France

    G. Rolin

  3. EFS, INSERM, UMR 1098 RIGHT, Université de Franche-Comté, F-25000, Besançon, France

    G. Rolin

  4. Institut de Mathématiques de Bourgogne, Université de Franche-Comté, 21078, Dijon, France

    F. Chouly

  5. Institute for Computational Engineering, Faculty of Science, Technology and Communication, University of Luxembourg, Esch-sur-Alzette, Luxembourg

    S. Urcun & S. P. A. Bordas

  6. Center for Mathematical Modelling and Department of Mathematical Engineering, University of Chile and IRL 2807 – CNRS, Santiago, Chile

    F. Chouly

  7. Departamento de Ingeniería Matemática, CI2MA, Universidad de Concepción, Casilla 160-C, Concepción, Chile

    F. Chouly

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Eftimie, R., Rolin, G., Adebayo, O.E. et al. Modelling Keloids Dynamics: A Brief Review and New Mathematical Perspectives. Bull Math Biol 85, 117 (2023). https://doi.org/10.1007/s11538-023-01222-8

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