Developing a PDE-based model for improved cancer treatment

Cancerous tumours are among the deadliest diseases, causing countless deaths each year due to the rapid growth and invasion of malignant cells into healthy tissues, which damages organs and impairs their functions. To make informed treatment decisions and provide patient-specific therapies, a deeper understanding of tumour evolution is essential. Mathematical models based on Partial Differential Equations (PDEs) are powerful tools for describing tumour behavior, and this project aims to develop a realistic PDE-based cancer model to study tumour progression. Our approach involves creating an efficient numerical algorithm to solve these PDEs on real brain images, incorporating clinically relevant parameters. A key question we will explore is whether our model can guide the development of more effective treatments, which can be reformulated as a PDE-constrained optimization problem. Solving this problem requires advanced numerical methods capable of handling the large-scale, clinically based data typically involved. Ultimately, this project seeks to provide deeper insights into cancer treatment and advance efficient numerical methods for complex, clinically relevant problems. 

Diversity statement

Our research community thrives on the diversity of students and staff which helps to make the University of Dundee a UK university of choice for postgraduate research.  We welcome applications from all talented individuals and are committed to widening access to those who have the ability and potential to benefit from higher education.