Modelling Keloids Dynamics: A Brief Review and New Mathematical Perspectives.

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.

An open source pipeline for design of experiments for hyperelastic models of the skin with applications to keloids.

The aim of this work is to characterize the mechanical parameters governing the in-plane behavior of human skin and, in particular, of a keloid-scar. We consider 2D hyperelastic bi-material model of a keloid and the surrounding healthy skin. The problem of finding the optimal model parameters that minimize the misfit between the model observations and the in vivo experimental measurements is solved using our in-house developed inverse solver that is based on the FEniCS finite element computational platform. The paper focuses on the model parameter sensitivity quantification with respect to the experimental measurements, such as the displacement field and reaction force measurements. The developed tools quantify the significance of different measurements on different model parameters and, in turn, give insight into a given model's ability to capture experimental measurements. Finally, an a priori estimate for the model parameter sensitivity is proposed that is independent of the actual measurements and that is defined in the whole computational domain. This estimate is primarily useful for the design of experiments, specifically, in localizing the optimal displacement field measurement sites for the maximum impact on model parameter inference.