Combined optimization of spot positions and weights for better FLASH proton therapy

In Intensity Modulated Proton Therapy (IMPT), the weights of individual pencil-beams or spots are optimized to fulfil dosimetric constraints. Theses spots are usually located on a regular lattice and their positions are fixed during optimization. In many cases, the range of spot weights may however be limited, leading sometimes to sub-optimal plan quality. An emblematic use case is the delivery of a plan at ultra-high dose rate (FLASH-RT), for which the spot weights are typically constrained to high values.