Electrotherapeutic Assisted Wound Healing: Comparison of the Electrostatic Potential in Porous Gel or Healing Media in Cartesian and Cylindrical Geometries

Abstract

Understanding the formulation and the modeling of distinct approaches used in the bio-mathematical foundation to homeostatic wound healing modeling is a critical task to advance the field. In recent contributions (Jorgensen, 2017), researchers have made progress experimentally in understanding transport of biomedicines in hydrogels of potential use as an effective scaffolding material to facilitate wound healing. This effort has been complemented by modelling approaches (Dawson et. al., 2021) to increase the understanding of the electro-convective diffuse transport of biomolecules in wound healing in electrotherapeutic assisted wound healing applications. This contribution will focus on the methodology for modeling of the electrostatic potential effects in the wound microenvironment of the scaffolding material and the role that the chosen geometry plays on the electrostatic potential behavior. Specifically, the impact of the diffusion and the migration of thrombin to induce the conversion of fibrinogen to fibrin will be discussed in the rectangular and cylindrical geometry. Anchored by the RF Model to guide our efforts, elements of the EKHD will be used to formulate the microscopic scale models that, then, by following an area-averaging algorithm approach will be upscaled to the entire capillary domain. The solutions will be compared analytically and graphically through a set of parametric values. Future and ongoing efforts towards this project will be highlighted.