*WINNER* Electrotherapeutic Assisted Wound Healing: Modelling of the Electrostatic Field in a Porous Gel or Healing Media
Among the many advances in the biomedical sciences in the last decade, the bio-mathematical foundation to homeostatic wound healing deserves further attention in the scientific community. Recent new contributions (Jorgensen, 2017) have made progress experimentally in understanding transport of biomedicines in hydrogels of potential use as an effective scaffolding material to facilitate wound healing. In addition, work has been done (Oyanader et al, 2020) to increase the understanding of the electro-convective-diffusive transport of biomolecules in wound healing in electrotherapeutic assisted wound healing applications, theoretically. This contribution will focus on the modeling of the electrostatic electrical field effects in the wound microenvironment of the scaffolding material by using idealized pore domains to describe pore morphology. The driving interest of our study is to understand the effects of the electrokinetic forces on the diffusion and migration of thrombin to induce the conversion of fibrinogen to fibrin, as this would be one of the initial steps in the early-phases of the wound healing process. Specifically, the electrostatic Laplace equation, in a pore domain of cylindrical geometry, will be solved via the use of area-averaging methods and its solution will be parametrically illustrated for a set of values of the applied voltages. The role of material, scale, and electro-migration on the transport of bio nutrients and medicines via the use of the molar species continuity equation will be discussed. Future steps in the research project will be highlighted.