A multiscale hybrid mathematical model of epidermal‐dermal interactions during skin wound healing

Abstract

Following injury, skin activates a complex wound healing programme. While cellular and signalling mechanisms of wound repair have been extensively studied, the principles of epidermal‐dermal interactions and their effects on wound healing outcomes are only partially understood. To gain new insight into the effects of epidermal‐dermal interactions, we developed a multiscale, hybrid mathematical model of skin wound healing. The model takes into consideration interactions between epidermis and dermis across the basement membrane via diffusible signals, defined as activator and inhibitor. Simulations revealed that epidermal‐dermal interactions are critical for proper extracellular matrix deposition in the dermis, suggesting these signals may influence how wound scars form. Our model makes several theoretical predictions. First, basal levels of epidermal activator and inhibitor help to maintain dermis in a steady state, whereas their absence results in a raised, scar‐like dermal phenotype. Second, wound‐triggered increase in activator and inhibitor production by basal epidermal cells, coupled with fast re‐epithelialization kinetics, reduces dermal scar size. Third, high‐density fibrin clot leads to a raised, hypertrophic scar phenotype, whereas low‐density fibrin clot leads to a hypotrophic phenotype. Fourth, shallow wounds, compared to deep wounds, result in overall reduced scarring. Taken together, our model predicts the important role of signalling across dermal‐epidermal interface and the effect of fibrin clot density and wound geometry on scar formation. This hybrid modelling approach may be also applicable to other complex tissue systems, enabling the simulation of dynamic processes, otherwise computationally prohibitive with fully discrete models due to a large number of variables.

More than just bricks and mortar: Fibroblasts and ECM in skin health and disease

“…Hypertrophic scars and keloids are the two major types of fibrotic skin pathologies induced in response to wounding. Their mechanisms, similarities and differences have been the subject of intense research, as exemplified by recent papers in Experimental Dermatology 59–64 . This topic is also highlighted in several reviews in this issue.…”

Mathematical model and computational scheme for multi-phase modeling of cellular population and microenvironmental dynamics in soft tissue

“…In [ 31 ], skin wound healing is modeled by a cell-ECM system coupled with two chemicals, defined as activator and inhibitor. The equations describing the components are similar to Eq (1) , except that the mass transfer terms have explicit forms limited to specific processes, such as diffusion and chemotaxis.…”

Integrative Models for TGF-β Signaling and Extracellular Matrix

“…These simplifications are extreme and could lead to inaccurate conclusions for processes depending critically on the dynamical structuring of the ECM, such as wound repair for instance. Hybrid approaches combining discrete cell positions with continuous description of collagen matrix and other ECM components have been used to study the role of the TGF-β/ECM interactions in wound repair [Dallon et al, 2001, Wang et al, 2019, Cumming et al, 2009. In these models, fibroblasts and immune cell motility and proliferation are affected by TGF-β, and cells interact one with another or with the collagen chemically or by direct, physical contact.…”