Global optimization for spot-based treatment planning

Purpose: Many radiotherapy modalities can deliver concentrated radiation in the form of spots, such as Gamma Knife (GK), GammaPod (GP), intensity-modulated proton therapy, and brachytherapy, and can be generalized as spot-based treatments. These treatments have a great therapeutic advantage of creating potent target dose while sparing the surrounding normal tissues. However, global optimization to determine the spot positions, shapes, and intensities is an intractable combinatorial problem for any real 3D problem. The conventional approach adopts heuristic spot selection and intensity optimization in a sequential manner to mitigate the problem complexity. In this work, we propose a novel framework that enables global optimization of spot-based treatment planning. Methods: The framework is based on kernel decomposition (KD) dose calculation, which models each spot dose as a scaled shift-invariant kernel, with the reference kernels and scales pre-calculated. During optimization, the framework incorporates Fast Fourier Transform (FFT) for objective and derivative evaluations and accommodates all spot candidates in optimization search with a temporal complexity of O(N³log N) as opposed to O(N⁶) complexity in the conventional beamlet framework for volume dimensions of N × N × N. We demonstrated the FFT framework using simulations with different objectives. The framework's planning performance was illustrated using clinical GK and GP cases. Results: Pre-processing involves only a small number of reference kernels and a scale map for the KD model with marginal spatial and temporal overheads. For simulations with 512 × 512 image dimensions, plan optimization finished in ∼2 seconds with FFT, whereas it took 100× longer with the beamlet approach. For clinical cases, the FFT attained solutions within a minute with improved plan quality compared to clinical plans: better conformity and less integral dose because of using a global fine search space for optimal spots. Conclusions: The scaled shift-invariance and FFT framework opens a new paradigm for spot-based treatment planning, as it can substantially reduce both the spatial and temporal complexities. The framework makes global optimization for spot-based treatment planning clinically feasible.