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.
Keywords: angiogenesis; cell deformation; cell migration; cellular automata models; partial differential equations; particle methods.
On the Mathematical Modeling of Wound Healing Angiogenesis in Skin as a Reaction-Transport ProcessJA Flegg et al. Front Physiol 6, 262. PMID 26483695. - ReviewOver the last 30 years, numerous research groups have attempted to provide mathematical descriptions of the skin wound healing process. The development of theoretical mod …
Macromolecular Crowding: Chemistry and Physics Meet Biology (Ascona, Switzerland, 10-14 June 2012)G Foffi et al. Phys Biol 10 (4), 040301. PMID 23912807.More than 60 years of biochemical and biophysical studies have accustomed us to think of proteins as highly purified entities that act in isolation, more or less freely d …
A Mathematical Model for the Capillary Endothelial Cell-Extracellular Matrix Interactions in Wound-Healing AngiogenesisL Olsen et al. IMA J Math Appl Med Biol 14 (4), 261-81. PMID 9415995.Angiogenesis, the process by which new blood capillaries grow into a tissue from surrounding parent vessels, is a key event in dermal wound healing, malignant-tumour grow …
Wound Healing Angiogenesis: The Clinical Implications of a Simple Mathematical ModelJA Flegg et al. J Theor Biol 300, 309-16. PMID 22326476.Nonhealing wounds are a major burden for health care systems worldwide. In addition, a patient who suffers from this type of wound usually has a reduced quality of life. …
A Current Perspective on Wound Healing and Tumour-Induced AngiogenesisJA Flegg et al. Bull Math Biol 82 (2), 23. PMID 31970503. - ReviewAngiogenesis, or capillary growth from pre-existing vasculature, is an essential component of several physiological processes, both vital and pathological. These include …