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Cancer is complex disease, in which tumour cells, immune cells and blood vessels interact with each other and the surrounding tissue. These interactions determine how tumours grow and change over time, and whether they will respond to treatment. While significant progress has been made in increasing our understanding of how tumours grow and improving treatment responses, the world-wide burden of cancer continues to increase; there were approximately 20 million diagnoses and 10 million cancer-related deaths in 2020. These statistics highlight the continued need to increase our understanding of how cancers develop, and how existing and emerging treatments should be administered to maximise the therapeutic benefit for individual patients.

Our lab is developing mathematical and computational approaches in order to address the above questions. For example, we are developing mathematical models to understand how tumour and immune cells interact, how they respond to treatment with immunotherapy, and to compare how well different treatments work. We are also using techniques from statistics and mathematics to develop new ways to describe the spatial patterns formed by tumour cells, immune cells and blood vessels. In the longer term, we aim to work out whether this information can be used to make predictions about cancer, such as how the disease will progress and the expected response to treatment.

 

A schematic diagram highlighting the iterative and multidisciplinary nature of mathematical modelling. Experimental data guide the generation of biological hypotheses that can be formalised in mathematical models. Once generated, the mathematical models need to be validated. Model validation involves seeing how closely the model solutions and the experimental data match. If the match is not good, then the hypotheses and models must be revised until qualitative and quantitative agreement is reached. Parameter values can be estimated by fitting the model to the data and the model can then be used to generate experimentally testable predictions.A schematic diagram highlighting the iterative and multidisciplinary nature of mathematical modelling. Experimental data guide the generation of biological hypotheses that can be formalised in mathematical models. Once generated, the mathematical models need to be validated. Model validation involves seeing how closely the model solutions and the experimental data match. If the match is not good, then the hypotheses and models must be revised until qualitative and quantitative agreement is reached. Parameter values can be estimated by fitting the model to the data and the model can then be used to generate experimentally testable predictions.