Mathematical models for angiogenic, metabolic and apoptotic processes in tumours
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This doctoral thesis outlines a body of research within the field of mathematical oncology that focusses on the inclusion of microenvironmental factors in mathematical models for solid tumour behaviour. These models primarily address tumour angiogenesis signalling, tumour metabolism and inducing apoptosis via novel treatment combinations. After a brief introduction in Chapter 1, background material pertinent to cancer biology and treatment is provided in Chapter 2. This chapter details tumour angiogenesis, tumour metabolism and various cancer treatments. This is followed in Chapter 3 by a survey of mathematical models that directly influence my work including summaries of models for relevant tumour entities such as angiogenic growth factors, interstitial fluid pressure, tu- mour metabolism and acidosis. The progression of topics in these two preliminary chapters emulate the ordering of the original research presented in Chapters 4–6. Chapter 4 presents an angiogenic growth factor (AGF) model used to study the impact of transport processes on tumour angiogenic behaviour. The study focusses on a coupled system of diffusion-convection-reaction equations that establish the role of convection in determining relative concentrations of proangiogenic and antiangiogenic growth factors, and hence the angiogenic behaviour, in solid tumours. The effect of various cancer treat- ments, such as chemotherapy and antiangiogenic drugs, that can alter tumour properties are considered through parameter analyses. The angiogenesis that results from angiogenic stimulation provides tumours with an oxygen and nutrient supply required for metabolism. Chapter 5 quantifies the benefit of metabolic symbiosis on tumour ATP production. A diffusion-reaction model of cell metabolism in the hypoxic tissue surrounding a leaky tumour blood vessel is developed that includes both lactate and glucose fuelled respiration along with glycolysis. We can then study the energetic effects of cancer cells’ metabolic behaviour, such as the Warburg effect and metabolic symbiosis. A model coupling these metabolic behaviours with acidosis is also analyzed that includes the effects of extracel- lular buffers. These models can be used to investigate metabolic inhibitor treatments by knocking out specific model parameters and buffering therapies. While treatment effects are considered in the previous chapters via parameter alter- ation, Chapter 6 explicitly models concentrations of molecular inhibitors and chemotherapy nanoparticles. These treatments are coupled to a model for apoptotic protein expression to evaluate strategies for counteracting chemoresistance in triple-negative breast cancer. The protein model is then used to predict cell viability, which indicates the efficacy of schedules for treatment combinations. The model prediction of post-chemotherapy inhibitor outper- forming pre-chemotherapy and simultaneous application is verified by further experiments. Finally, a summary of the contributions to the field of mathematical oncology and suggested future directions are indicated in the final chapter.