We propose a mathematical formalism and method for simulating the effects of the mechanochemical environment on the differentiation path and fate of stem cells. We provide a numerical methodology used for the numerical approximation of solutions of partial differential equations, based on a finite element approach, to describe the time evolution and spatial distribution of chemical and mechanical signals. Further, all cells are considered as independent entities, which may migrate through the domain of computation and which are subject to differentiation, division, and evolution of geometry. The model is applied to the development of adipose and muscle tissue. The developed framework is generic and can be applied to other similar biological processes and medical applications.@en

Traumatic and chronic wounds are a considerable medical challenge that affects many populations and their treatment is a monetary and time-consuming burden in an ageing society to the medical systems. Because wounds are very common and their treatment is so costly, approaches to reveal the responses of a specific wound type to different medical procedures and treatments could accelerate healing and reduce patient suffering. The effects of treatments can be forecast using mathematical modelling that has the predictive power to quantify the effects of induced changes to the wound-healing process. Wound healing involves a diverse and complex combination of biophysical and biomechanical processes. We review a wide variety of contemporary approaches of mathematical modelling of gap closure and wound-healing-related processes, such as angiogenesis. We provide examples of the understanding and insights that may be garnered using those models, and how those relate to experimental evidence. Mathematical modelling-based simulations can provide an important visualization tool that can be used for illustrational purposes for physicians, patients and researchers.@en

In this paper, a cell-colony based formalism for the healing of superficial wounds is presented. The paper incorporates the migration, proliferation, and death of constituent cells, in the context of wound healing. The present study considers wound healing under ischemic conditions where a bacterial infection develops, which impairs the motility of the constituent cells. In this work, the performance of the immune response system is incorporated in the sense that migrating leukocyte are modelled which engulf the infectious pathogens. The model is based on both deterministic and stochastic principles. Simulation results are discussed in a biological context.@en