Applied Analysis Seminar Simulation of Post-Burned Skin Using Principles from Morphoelasticity

Each year the lives of hundreds of thousands people are heavily impacted by severe burn injuries. Although nowadays clinical technologies allow most patients to survive heavy burn traumas, these burn injuries often come with hypertrophic scars and contractures, which impair the mobility of patients. In order to minimize the impact to the patients, therapies based on principles such as dressings, ointments, splinting and skin grafting (skin transplantation) are applied. In order to optimize treatment, a quantitative description of the underlying biological mechanisms is needed and for this reason, mathematical models have been constructed. In this talk, we present a continuum-based model that is constructed with principles from morphoelasticity. Morphoelasticity is a mathematical formalism that simultaneously deals with elasticity and microstructural changes in the tissue. We will show some mathematical results regarding stability of the model, as well as neural network simulations that reproduce the simulations at very high computational speed.