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In choosing Loughborough for your research, you’ll work alongside academics who are leaders in their field. You will benefit from comprehensive support and guidance from our Doctoral College, including tailored careers advice, to help you succeed in your research and future career. Find out more.
Project Overview
This research project focuses on the development, computer implementation and analysis of an effective and reliable numerical model to describe the space-time evolution of glioblastoma multiforme (GBM), a form of brain tumour.
Mathematical modelling of GBM is extremely challenging, not only due to the rapid growth of the cells of this tumour, but also their interaction with the brain tissue, which is highly heterogeneous and anisotropic.
Recent promising modelling approaches treat the tumour as a dynamic multiphase mixture of different constituents, and they take into account the availability of oxygen and other chemicals in the brain tissues, as well as the effect of the mechanical stress inside the tumour mass. These models are based on a system of time-dependent nonlinear fourth-order partial differential equations, where the evolution of the tumour volume fraction is described by a Cahn-Hillard-type equation whose mathematical analysis and numerical approximation has not been fully understood yet. The problem is computationally challenging, not only due to the difficulty of the equations to be solved, but also the need of considering complex deformable geometrical domains to realistically describe the tumour and its evolution inside the brain.
This project aims to develop novel algorithms based on operator splitting methods, where the two main equations for the tumour volume fraction and for the concentration of chemicals will be decoupled, linearized, and solved by iterative numerical methods based on suitable families of finite element methods.
Entry requirements:
Applicants should have, or expect to achieve, at least a 2:1 degree (or equivalent international qualification) in mathematics, physics, or a closely related subject. A relevant master’s degree and/or solid experience in one of more of the following will be desirable: numerical methods for partial differential equations, computer programming in, e.g. MATLAB, Python. Applicants must have an enthusiastic attitude towards learning and a commitment to developing high-quality research.
How to apply
All applications should be made online (https://www.lboro.ac.uk/study/apply/research). Under programme name, select ‘Mathematical Sciences’. Please quote the advertised reference number MA/MD-Un1/2022 in your application.
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