An ultra-high performance parallel (UHPP) framework for complex 4πradiotherapy planning

Purpose. In radiotherapy, dose distribution conformity and compactness are critical to patient outcomes. Advanced techniques like4πradiotherapy leverage non-coplanar beams for superior dosimetry by exploring additional degrees of freedom. However,4πplanning is computationally intensive due to large dose-loading matrices for candidate beams. This work presents an ultra-high performance parallel (UHPP) framework to accelerate high-dimensional treatment planning.Methods. For dose calculation, we developed: (1) a two-step total energy released per unit mass (TERMA) computation module calculating the TERMA array once per beam, enabling reuse across convolution directions; (2) a synchronized dose calculation module based on collapsed-cone convolution superposition (CCCS), arranging rays in dedicated sequences to preserve thread efficiency and minimize memory access; (3) a scattering-based coordinate transformation mapping dose from beamlet to patient Cartesian coordinates, eliminating aliasing without atomic operations. The framework includes CCCS exponential kernel calculation for varying LINAC spectra. For beam orientation optimization, we employed fast iterative shrinkage-thresholding algorithm with group sparsity regularization, accelerated using cuSPARSE library on GPUs. We benchmarked against Monte Carlo (MC) simulations for dose accuracy and compared computational performance to state-of-the-art (SOTA) methods. Plan quality was evaluated across four approaches: UHPP, SOTA, clinical VMAT plans, and MC calculations based on UHPP plans.Results. Compared to MC simulations, UHPP achieved minimum 98% gamma passing rates under 1.5%/1.5 mm criterion for water and slab phantoms, and average 97.35% and 92.18% under 3%/3 mm criterion for pancreas and head-and-neck patients, respectively. UHPP delivered 8.86× and 6.99× speedups in dose calculation and plan optimization while maintaining comparable or superior plan quality. Both UHPP and SOTA consistently produced4πplans outperforming clinical VMAT plans in organ-at-risk sparing and target coverage.Conclusion. The UHPP framework delivers high dose accuracy and substantial computational speedup without sacrificing4πplanning's dosimetric advantages, supporting practical adoption of advanced4πradiotherapy in clinical workflows.