Handling organ motion in radiotherapy of cancer via Markov chains

This study developed a patient specific mathematical model holding a high potential to cope with patient setup error, internal and physiological organ motion in radiotherapy treatment. The proposed recipe falls into two stages; determining the stationary probability distribution of tumor motion in Markovian sense and then forwarding it as input to covering tumor process in an optimal frame by the knapsack problem, which is well known in operations research. The model is constructed in terms of tumor area, partitioned into small cells, instead of length. The proposed model allows clinicians to add arbitrary extra safety area as corresponding to CTV-to-PTV margin. The method is implemented for a hypothetical prostate cancer and solved by MS Excel. It is undoubtedly needed serious and controlled clinical observations to validate the theoretical model, which is an application of operations research to medicine.