Queensland University of Technology

Mathematical and computational techniques can improve our understanding of diseases. In this talk, I’ll present ways in which data from cancer patients can be combined with mathematical modelling and used to improve cancer treatments.

Given the variability in individual responses to cancer treatments, agent-based modelling has been a useful technique for accurately capturing cellular behaviours that may lead to stochasticity in patient outcomes. Using a hybrid agent-based model and partial differential equation system, we developed a model for brain cancer (glioblastoma) growth informed by ex-vivo patient samples. Extending the model to capture patient treatment with an oncolytic virus rQNestin, we used our model to propose reasons for treatment failure, which was later confirmed with further patient samples. More recently, we extended this model to investigate the effectiveness of combination treatments (chemotherapy, virotherapy and immunotherapy) informed by individual patient imaging mass cytometry.

This talk hopes to provide examples of ways mathematical and computational modelling can be used to run “virtual” clinical trials with the goal of obtaining more effective treatments for diseases.  

The problem of a bubble moving steadily in a Hele-Shaw cell goes back to Taylor and Saffman in 1959.  It is analogous to the well-known selection problem for Saffman-Taylor fingers in a Hele-Shaw channel.   We apply techniques in exponential asymptotics to study the bubble problem in the limit of vanishing surface tension, confirming previous numerical results, including a previously predicted surface tension scaling law.  Our analysis sheds light on the multiple tips in the shape of the bubbles along solution branches, which appear to be caused by switching on and off exponentially small wavelike contributions across Stokes lines in a conformally mapped plane.