Mathematical modelling of objectives in radiation therapy treatment planning

We view radiation therapy treatment planning (RTTP) as a problem of constrained optimization. In this context, the 'optimal' treatment is one that maximizes some objective function subject to the inherent constraints of the problem. We discuss two objective functions which are motivated by biological considerations rather than mathematical expedience. One of these measures the 'goodness' of a treatment in terms of its probability of success. The other measures the degree to which a treatment succeeds in satisfying a system of constraints that are mutually contradictory. We describe how to actually perform the optimization of these objective functions in practice and show some numerical results which demonstrate advantages of these objective functions over their more conventional counterparts.