Of the 80 million scars formed each year, 40-70% will develop into problematic, stiff, thick, painful, itchy and pigmented scars, with an impact on a person's life. Mechanical loads may impact the development of a problematic scar. The application of controlled external mechanical loading (mechanotherapy, through controlled packages of sound waves) can prevent or mitigate these scars. Mathematical modelling of scar formation offers the possibility of predicting which types of loads have a high clinical impact, allowing subsequent clinical trials to be better targeted.
This project aims to develop a reliable mathematical model that simulates surgical scar properties after mechanical loading, so that the condition of the skin on cellular and scar tissue level can be predicted. This model can be used as a tool to assist practitioners in finding the optimal load application in a realistic clinical setting. The research will benefit from and to other modeling studies on skin burn injury and fibrosis in other organs and will be an important step forward for future clinical guidelines on scar (mechano) therapy.
The mathematical model is based on a set of nonlinearly coupled partial differential equations. Due to uncertainty as a result of variations from patient to patient, it is paramount to carry out a sensitity analysis on the mathematical framework. The sensitivity analysis, done through Bayesian variation and principal component analysis, reveals the most important dependencies in the model, and is used to reduce the complexity of the model as much as possible, but retaining the most important features. Hence due to uncertainties, we aim for predictions in a probabilistic sense. Each sample simulation represents the numerical solution of the coupled set of partial differential equations. We rely on numerical methods, such as the finite element method combined with time-integrations to approximate the solution.
As a PhD student on this project, you will conduct research, which entails finite element computer code development, as well as model building and model validation. Furthermore, you will calibrate the developed model to clinical observations from the University of Antwerp. Finally, you will also develop the machine learning-based framework that will be useful for a quick reproduction of the intensive finite element simulations, and write a PhD dissertation. In addition, you will participate in the "Doctoral School of Sciences & Technology" and will make a limited contribution to teaching assignments within the Department of Mathematics.
