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Review
, 6 (5), 20160038

Review on Experiment-Based Two- And Three-Dimensional Models for Wound Healing

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Review

Review on Experiment-Based Two- And Three-Dimensional Models for Wound Healing

Daphne Weihs et al. Interface Focus.

Abstract

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.

Figures

Figure 1.
Figure 1.
An in silico simulation of a cell-based model shows the closing of a gap in a cell monolayer. (a) A snapshot in time, where the red lines represent the venules underneath the gap location, being at a lower plane they are not affected by formation of the superficial wound. The red circles, white circles and the black dots are, respectively, the vital tissue-constituent cells, the immune cells and the pathogens, i.e. bacteria. (b) Simulated time-dependent gap size under different bacterial pathogen proliferation rates. The simulations have been described in more detail in [56].
Figure 2.
Figure 2.
A snapshot at a specific time instant of 45 h post-gap formation of an in silico simulation of a hybrid model to identify simultaneous changes in cytokine concentration, immune cell localization and differentiation of fibroblasts into myofibroblasts that cause increased contraction. (a) Concentration of tissue plasminogen activator (tPA) increases in the wound site, which is located on the top-left of the computational domain; the result was obtained using the finite-element method. (b) The orientation of the collagen network (x) was typically in line with the paths of migration of the myofibroblasts (blue circles). The myfibroblasts apply contractions (arrows) that deform the wound edges, marked by the rectangle. The immune cells (red circles) accumulate and are confined to the edge of the wound area. More details are provided in [58].
Figure 3.
Figure 3.
A snapshot of an in silico simulation of a cell-based model showing sprouting during angiogenesis. Top: the interface between the ECM and extracellular fluid (sprout formation), where the colour represents the scaled vertical coordinate (red is high, blue is low); bottom: projections of the endothelial cells, where green and red, respectively, represent the stalk and tip cells. More information in [62].
Figure 4.
Figure 4.
Snapshot of a computer simulation of immune cell (red mesh, with central nucleus in black) that deforms when extending itself to simultaneously engulf three pathogens. The pathogens (red circles) secrete a chemical that attracts the immune cell. More details in [43].
Figure 5.
Figure 5.
Immune cells (white with black nuclei) transmigrate through the venule walls to engulf pathogens (small empty symbols, total 18 bacteria). The venule walls are represented by the purple ellipses, and are approximated in the model by a thin, straight layer of width equal to the vertical ‘radius’ of the ellipses representing the endothelial cell layer. More details regarding these simulations can be found in [68].

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