HER2+ breast cancer patients suffer from aggressive tumours that often respond well to treatment compared to HER2- patients. Currently, patients are all treated with the same number of anti-tumour treatments, although the required number to eradicate all tumour cells varies between patients. The goal is thus to have an individualised model based on an MRI before the start of therapy and an MRI after several rounds of therapy that predicts how many treatments are needed to eradicate all tumour cells. In the previous MSc thesis by N. Oudhof, a two-dimensional spatiotemporal mechanically coupled reaction-diffusion model was implemented. This was used to model the number of tumour cells in each position of the breast, where the mechanics are included to simulate the behaviour of the surrounding tissue.

The goal of this thesis is to improve that model by improving the calibration in which the patient-specific parameters are optimised, by taking into account the treatment schedule of the patients and by extending the model to three dimensions. For calibration, the first and second MRI scans are used and a third MRI is used for validation. To simulate the chemotherapy, both the Kety-Tofts model and a Normalised Blood Volume Map are applied, of which the latter appeared the best option. In 2D, four models are implemented: the reaction-diffusion models with and without mechanics and with and without chemotherapy term. These were compared by analysing the predicted and measured tumour densities for a cohort of three HER2+ patients. For 3D, only the basic reaction-diffusion and chemotherapy-incorporated reaction-diffusion models are implemented. The models are compared in terms of mean squared error, global relative error and concordance correlation coefficient. For both 2D and 3D, the models without chemotherapy gave slightly better results in terms of these measures, although the differences between the models were rather small. To determine the required number of therapy rounds, it is however better to use the chemotherapy-incorporated models because they offer more possibilities to simulate different treatment strategies. The computation time of the 3D implementation should be reduced before the mechanics can be included, which will allow conclusions to be drawn on which model is most accurate. Other directions for future improvements include using the second MRI to calculate the chemotherapy concentrations after calibration, adding an immunotherapy term and increasing the number of patients.