A mathematical system for human implantable wound model studies
Keywords:PDE model, Inflammatory phase, Repair phase, Dermal, Cutaneous
In this work, we present a mathematical model, which accounts for two fundamental processes involved in the repair of an acute dermal wound. These processes include the inflammatory response and fibroplasia. Our system describes each of these events through the time evolution of four primary species or variables. These include the density of initial damage, inflammatory cells, fibroblasts and deposition of new collagen matrix. Since it is difficult to populate the equations of our model with coefficients that have been empirically derived, we fit these constants by carrying out a large number of simulations until there is reasonable agreement between the time response of the variables of our system and those reported by the literature for normal healing. Once a suitable choice of parameters has been made, we then compare simulation results with data obtained from clinical investigations. While more data is desired, we have a promising first step towards describing the primary events of wound repair within the confines of an implantable system.