Wound Healing Modeling Using Partial Differential Equation and Deep Learning

Abstract: The process of wound healing has been an active area of research around the world. The problem is the wounds of different patients heal differently. For example, patients with a background of diabetes may have difficulties in healing [1]. By clearly understanding this process, we can determine the type and quantity of medicine to give to patients with varying types of wounds. In this research, we use a variation of the Alternating Direction Implicit method to solve a partial differential equation that models part of the wound healing process. Wound images are used as the dataset that we analyze. To segment the image's wound, we implement deep learning-based models. We show that the combination of a variant of the Alternating Direction Implicit method and Deep Learning provides a reasonably accurate model for the process of wound healing. To the best of our knowledge, this is the first attempt to combine both numerical PDE and deep learning techniques in an automated system to capture the long-term behavior of wound healing.