A Cell-Regulatory Mechanism Involving Feedback between Contraction and Tissue Formation Guides Wound Healing Progression

Abstract

Wound healing is a process driven by cells. The ability of cells to sense mechanical stimuli from the extracellular matrix that surrounds them is used to regulate the forces that cells exert on the tissue. Stresses exerted by cells play a central role in wound contraction and have been broadly modelled. Traditionally, these stresses are assumed to be dependent on variables such as the extracellular matrix and cell or collagen densities. However, we postulate that cells are able to regulate the healing process through a mechanosensing mechanism regulated by the contraction that they exert. We propose that cells adjust the contraction level to determine the tissue functions regulating all main activities, such as proliferation, differentiation and matrix production. Hence, a closed-regulatory feedback loop is proposed between contraction and tissue formation. The model consists of a system of partial differential equations that simulates the evolution of fibroblasts, myofibroblasts, collagen and a generic growth factor, as well as the deformation of the extracellular matrix. This model is able to predict the wound healing outcome without requiring the addition of phenomenological laws to describe the time-dependent contraction evolution. We have reproduced two in vivo experiments to evaluate the predictive capacity of the model, and we conclude that there is feedback between the level of cell contraction and the tissue regenerated in the wound.

Mathematical modelling of angiogenesis using continuous cell-based models

“…(2014), Valero et al. (2014) and Gaffney et al. (2002), Maggelakis (2003), Maggelakis (2004) in the context of angiogenesis.…”

Semi-stochastic cell-level computational modelling of cellular forces: application to contractures in burns and cyclic loading

“…In the very early stages, the wound expands a little as a result of the many fibroblasts outside the wound that are pulling. This is believed to trigger differentiation to myofibroblasts, see for instance Valero et al (2014). We did not take this triggering mechanism into account in the present model.…”

“…Subsequently, cell differentiation from a fibroblast to a myofibroblast has been incorporated as a stochastic process. It is well-known that differentiation of fibroblasts to myofibroblasts takes place as a result of expansion forces (Valero et al 2014) of the wound and as a result of a high levels of VEGF. Therewith, this differentiation predominantly takes place near the edge of the wound.…”

“…In this study, we present a simplified framework for the modelling of contractures, which can be used in more realistic mathematical models to actually predict the likelihood for the occurrence of contractures, as well as the likelihood for the occurrence of excessive scar formation. Mathematical models for wound contraction can be found in the papers by Olsen et al (1995), Murray (2004) and Vermolen and Javierre (2012) and most recently in Valero et al (2014), where the last mentioned paper provides a breakthrough in modelling regarding the relation between myofibroblasts and local dilatations. A second application involves modelling cyclic loading where the present model allows to quantify the impact of phase perturbations in the cycles of individual cells on heart performance.…”

Particle methods to solve modelling problems in wound healing and tumor growth

“…As the fibroblasts move into the wound area, they pull the tissue and under unfavourable chemical and mechanical circumstances they are able to differentiate to myofibroblasts, which are cells that pull at a larger force on the surrounding tissue, produce more, excessive collagen, and furthermore shorten the chemical bonds of the long polymeric chains that constitute the collagen. These chemically and mechanically unfavourable conditions typically refer to the concentration of certain cytokines (growth factors) and/or to pulling forces that the fibroblasts experience, which make them differentiate to myofibroblasts, see [45] for instance for a modelling study. It can be seen that the wound area decreases over time and that the wound region changes shape from the initial rectangular shape to a more star-shape due to the internal forces exerted by the (myo)fibroblasts.…”