Patient selection for proton therapy: a radiobiological fuzzy Markov model incorporating robust plan analysis

While proton therapy can offer increased sparing of healthy tissue compared with X-ray therapy, it can be difficult to predict whether a benefit can be expected for an individual patient. Predictive modelling may aid in this respect. However, the predictions of these models can be affected by uncertainties in radiobiological model parameters and in planned dose. The aim of this work is to present a Markov model that incorporates these uncertainties to compare clinical outcomes for individualised proton and X-ray therapy treatments. A time-inhomogeneous fuzzy Markov model was developed which estimates the response of a patient to a given treatment plan in terms of quality adjusted life years. These are calculated using the dose-dependent probabilities of tumour control and toxicities as transition probabilities in the model. Dose-volume data representing multiple isotropic patient set-up uncertainties and range uncertainties (for proton therapy) are included to model dose delivery uncertainties. The model was retrospectively applied to an example patient as a demonstration. When uncertainty in the radiobiological model parameter was considered, the model predicted that proton therapy would result in an improved clinical outcome compared with X-ray therapy. However, when dose delivery uncertainty was included, there was no difference between the two treatments. By incorporating uncertainties in the predictive modelling calculations, the fuzzy Markov concept was found to be well suited to providing a more holistic comparison of individualised treatment outcomes for proton and X-ray therapy. This may prove to be useful in model-based patient selection strategies.