  A split feasibility formulation for the inverse problem of
intensity-modulated radiation therapy (IMRT) treatment planning with
dose-volume constraints (DVCs) included in the planning algorithm is presented.
It involves a new type of sparsity constraint that enables the inclusion of a
percentage-violation constraint in the model problem and its handling by
continuous (as opposed to integer) methods. We propose an iterative algorithmic
framework for solving such a problem by applying the feasibility-seeking
CQ-algorithm of Byrne combined with the automatic relaxation method (ARM) that
uses cyclic projections. Detailed implementation instructions are furnished.
Functionality of the algorithm was demonstrated through the creation of an
intensity-modulated proton therapy plan for a simple 2D C-shaped geometry and
also for a realistic base-of-skull chordoma treatment site. Monte Carlo
simulations of proton pencil beams of varying energy were conducted to obtain
dose distributions for the 2D test case. A research release of the Pinnacle3
proton treatment planning system was used to extract pencil beam doses for a
clinical base-of-skull chordoma case. In both cases the beamlet doses were
calculated to satisfy dose-volume constraints according to our new algorithm.
Examination of the dose-volume histograms following inverse planning with our
algorithm demonstrated that it performed as intended. The application of our
proposed algorithm to dose-volume constraint inverse planning was successfully
demonstrated. Comparison with optimized dose distributions from the research
release of the Pinnacle3 treatment planning system showed the algorithm could
achieve equivalent or superior results.
