Mathematical investigation of normal and abnormal wound healing dynamics: local and non-local models.

The movement of cells during (normal and abnormal) wound healing is the result of biomechanical interactions that combine cell responses with growth factors as well as cell-cell and cell-matrix interactions (adhesion and remodelling). It is known that cells can communicate and interact locally and non-locally with other cells inside the tissues through mechanical forces that act locally and at a distance, as well as through long non-conventional cell protrusions. In this study, we consider a non-local partial differential equation model for the interactions between fibroblasts, macrophages and the extracellular matrix (ECM) via a growth factor (TGF-$ \beta $) in the context of wound healing.

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.

Société de Biomécanique Young Investigator Award 2021: Numerical investigation of the time-dependent stress-strain mechanical behaviour of skeletal muscle tissue in the context of pressure ulcer prevention.

Background: Pressure-induced tissue strain is one major pathway for Pressure Ulcer development and, especially, Deep Tissue Injury. Biomechanical investigation of the time-dependent stress-strain mechanical behaviour of skeletal muscle tissue is therefore essential. In the literature, a viscoelastic formulation is generally assumed for the experimental characterization of skeletal muscles, with the limitation that the underlying physical mechanisms that give rise to the time dependent stress-strain behaviour are not known.

Cortex tissue relaxation and slow to medium load rates dependency can be captured by a two-phase flow poroelastic model.

This paper investigates the complex time-dependent behavior of cortex tissue, under adiabatic condition, using a two-phase flow poroelastic model. Motivated by experiments and Biot's consolidation theory, we tackle time-dependent uniaxial loading, confined and unconfined, with various geometries and loading rates from 1μm/s to 100μm/s. The cortex tissue is modeled as the porous solid saturated by two immiscible fluids, with dynamic viscosities separated by four orders, resulting in two different characteristic times.

Digital twinning of Cellular Capsule Technology: Emerging outcomes from the perspective of porous media mechanics.

Spheroids encapsulated within alginate capsules are emerging as suitable in vitro tools to investigate the impact of mechanical forces on tumor growth since the internal tumor pressure can be retrieved from the deformation of the capsule. Here we focus on the particular case of Cellular Capsule Technology (CCT). We show in this contribution that a modeling approach accounting for the triphasic nature of the spheroid (extracellular matrix, tumor cells and interstitial fluid) offers a new perspective of analysis revealing that the pressure retrieved experimentally cannot be interpreted as a direct picture of the pressure sustained by the tumor cells and, as such, cannot therefore be used to quantify the critical pressure which induces stress-induced phenotype switch in tumor cells.

Predictiveness of different preoperative risk assessments for postoperative bleeding after coronary artery bypass grafting surgery.

Aim: Postoperative bleeding is a significant cause of morbidity and mortality in patients undergoing cardiac surgery. Studies have been conducted, and guidelines have been published regarding patient blood management and aiming to prevent blood loss in the perioperative period. Various bleeding risk assessments were developed for preoperative period.