Analysis and comparison of multimodal cancer treatments.

We analyse the sequence in which the three most commonly prescribed cancer treatments--surgery (S), chemotherapy (C) and radiotherapy (R)--should be administered. A system of ordinary differential equations is formulated that captures the various local and systemic effects of the three modes of treatment, as well as the first-order effects of the inter-relationship between the primary tumour and the distant metastatic tumours, including primary tumour shedding and the primary tumour's effect on the rate of angiogenesis in the metastatic tumours. Under a set of stated assumptions on the parameter values, we find the exact cancer cure probability (subject to toxicity constraints) for the six permutation schedules (i.e. SCR, CSR, CRS, SRC, RSC, RCS) and for two novel schedules, SRCR and RSCR, that apply radiotherapy in disjoint, optimally timed portions. We show analytically that SRCR and RSCR are the two best-performing (i.e. highest cure probability) schedules among the eight considered. Further, SRCR is shown to be optimal among all possible schedules, provided a modest condition is satisfied on the delay of initial angiogenesis experienced by the patient's dormant tumours.