Abstract
The focus of this research was to apply mathematical and computational methods for modelling and prediction of tumour volume during the course of radiotherapy. The developed tools could provide valuable information for the optimisation of radiotherapy in the future. Firstly, the feasibility of modelling tumour volume dynamics of individual patients, as measured by computed tomography (CT) imaging, was explored. The main objective was to develop a model that is adequate to describe tumour volume dynamics, and at the same time is not excessively complex as lacking support from clinical data. To this end, various modelling options were explored, and rigorous statistical methods, the Akaike information criterion (AIC) and the corrected Akaike information criterion (AICc), were used for model selection. The models were calibrated to data from two cohorts of non-small cell lung cancer patients, one treated by stereotactic ablative radiotherapy and the other by conventionally fractionated radiotherapy. The results showed that a two-population model with exponential tumour growth is the most appropriate for the data studied as judged by AIC and AICc. Secondly, this model was further equipped with a Bayesian adaption approach in order to predict individual patients’ response to radiotherapy in terms of tumour volume change during the treatment. The main idea was to start from a population-average model, which is subsequently updated, using Bayesian parameter estimation, from an individual’s tumour volume measurement. Therefore the model becomes more and more personalised and so is the prediction. The usefulness of the developed method was demonstrated on clinical data. Finally, attempt was made to link the predicted tumour volume (an important but often secondary treatment outcome indicator) to tumour control probability (one of the primary indicators of treatment outcome), and this model was demonstrated through a simulation study. Overall this research has contributed new methods and results of mathematical modelling for quantitatively analysis and prediction of individual patients’ response to radiotherapy; it represents a significant development that could be used for improved and personalised planning and scheduling of radiotherapy in the future.