Towards Hybrid Modeling of Avascular Tumours

This thesis analyses and expands upon an existing multi-physicsagent-based model for avascular tumour growth, in which cell behaviours are determined by a cellular pressure distribution andan oxygen concentration. Two models are developed and included within the avascular tumour model and their effects on the tumour growth patterns are analysed. The development of the two models favours fundamental principles over directly including macro-scalephenomena in order to preserve the simplicity and low computational cost of the original model. The first model includes effects of cell-cell attraction (referred to as the simpleattraction model) and the second model includes effects from the resistance of the surrounding tissue which the tumour expands into(referred to as the external tissue pressure model). Results from the simple attraction model shows that the overall tumour growth is not inhibited, yet the growth pattern is notably altered. Results from the external tissue pressure model suggests that the growth is inhibited, at least for a comparatively very large time scale. Furthermore, computational artefacts from the discretization of the computational domain are found in the longterm growth pattern of the tumour. However, higher values of the model stiffness parameter resulted in an earlier growth inhibition as well as the absence of said computational artefacts. In addition, a useful relation between the final steady state tumour size and an oxygen threshold parameter for cell proliferation was discovered. Finally, the two models are included within a more complex model for tumour growth within the same computational framework. The resulting growth patterns were notably different for the two models, but growth was not inhibited in any of the experiments conducted here