Mathematical Modelling of Cancer Growth and Development: Adhesion, Stem Cells and Structure
This thesis has investigated some of the intricacies of the growth and development of a solid tumour. Mathematical models and biological experimentation were used to gain a better understanding of the dual roles that the proto-oncogenic protein β-catenin has in adhesion and transcription, as well as its involvement in the epithelial-mesenchymal transition. Emphasis was placed on the spatial location of β-catenin within cells to determine what function it is performing. A model was also created to explore the hypothesis that multiple forms of β-catenin exist within cells to perform separate functions. The cancer stem cell hypothesis was explored in solid tumour growth, without necrosis and angiogenesis, by the use of a discrete, cell-based model created with the software package CompuCell3D. This was compared to a novel continuum model, which can be used to perform in silico experiments of solid tumours with a stem-progenitor-mature cell structure for a biologically relevant number of cells. Lastly, a cell-based model of a solid, vascularised tumour was created in CompuCell3D to investigate how an age- and size-structured population of cells can affect the overall growth of the tumour. This model was also used to show how the age structure of cells in a solid tumour can affect the efficacy of chemotherapeutic treatments.
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