Spread-Out Bragg Peak in Treatment Planning System by Mixed Integer Linear Programming: a Proof of Concept

In this paper we analyze different Mixed Integer Linear Programming (MILP) models in order to produce 1D and 3D Spread-Out Bragg peaks (SOBP) for protons in water. Our techniques do not use much computational resources; in particular, all our experiments have been performed by a standard personal computer. As main result we give the proof of concept that the techniques that we use to create parameterized uniform SOBP can be fruitfully used in Treatment Planning Systems (TPS) for Intensity Modulated Proton Therapy (IMPT). As technical result we show, for the first time to our best knowledge, that there is a trade-off between the minimum number of energies (or layers) to be used to have a SOBP peak within a uniformity tolerance parameter Dt and the same parameter Dt. Minimizing the number of energies also has the advantage of reducing the delivery time using the facilities in operation nowadays.