Mathematical modelling of glioblastoma  

Project description

Glioblastoma is the most aggressive adult brain tumour. Despite current treatment, the disease invariably returns after surgery, with survival sadly measured in months. Scientific evidence indicates that glioblastoma cells at the tumour’s edge, which infiltrate the healthy brain (termed ‘infiltrative margin’), closely resemble the eventual recurrent tumour. This is a crucial clue, as the glioblastoma infiltrative margin reflects disease which cannot be safely removed by surgery, and which ultimately causes the tumour to return. This project will work will local collaborators in the School of Medicine as well as international partners at the Mayo Clinic (Arizona, USA) to develop predictive models for glioblastoma recurrence.

Existing mathematical models for GBM have been shown to be useful in predicting patient survival based on image-derived model parameters. Complementary approaches to these mechanistic models have included machine learning based radiomics to fuse spatially localized biopsy and spatially resolved MRI data into predictive maps of molecular heterogeneity in unsampled regions. Subsequent model developments have included tissue state transitions in physiological features such as vascularity and hypoxia [1,3], and cellular features such as amplifications in certain driver genes (e.g., EGFR, PDGFRA) [2].

A key research question is whether we can build on this progress to make meaningful predictions of tissue-state transitions that occur prior to tumour recurrence, with the aim to substantially extend the quality and quantity of life for patients. Earlier prediction of tissue transitions preceding recurrence, using mechanistic mathematical models supported by patient data, will permit earlier initiation of second line treatment or patient-tailored experimental therapies post-surgery.

This project will develop mathematical models for glioblastoma growth, building on our improved understanding and ability to characterise heterogeneity using biopsy and imaging data. Models will typically take the form of systems of partial differential equations, although there will be scope to explore alternative formalisms such as individual-based and hybrid models. Model analysis will require a blend of mathematical analysis of reduced submodels (where tractable) and computer simulation, parameter inference and sensitivity analysis. As such, this will require a willingness and enthusiasm to engage with complex biological and mathematical concepts, as well as a signifiant component of computer programming and data analysis.