A Finite Element Model for Wound Healing

Wound healing proceeds by a number of (partially) overlapping steps: bleeding, blood clotting, removal of contaminants and bacteria, wound closure by cell mitosis and migration towards the wound center, repair of the vascular network, and wound contraction along lines of equal tension. We consider a model due to Adam [1] for the closure of a wound. The model is based on an epidermal growth factor that stimulates cell division and growth. Cell division, and hence also wound closure, takes place if the epidermal growth factor exceeds a threshold value. In the model, a wound heals as a result of a generic growth factor. Consider a computational domain, Ω, then the wound is located within Ω. The wound is surrounded by an active layer, denoted by Ωa, in which the growth factor is produced. The growth factor is also subject to decay and diffusion, which is formulated mathematically by ∂c ∂t = D∆c+ Pf(x, y)− λc,