Purpose: The importance of robust proton treatment planning to mitigate the impact of uncertainty is well understood. However, its computational cost grows with the number of uncertainty scenarios, prolonging the treatment planning process. We developed a fast and scalable distributed optimization platform that parallelizes this computation over the scenarios. Methods: We modeled the robust proton treatment planning problem as a weighted least-squares problem. To solve it, we employed an optimization technique called the Alternating Direction Method of Multipliers with Barzilai-Borwein step size (ADMM-BB). We reformulated the problem in such a way as to split the main problem into smaller subproblems, one for each proton therapy uncertainty scenario. The subproblems can be solved in parallel, allowing the computational load to be distributed across multiple processors (e.g., CPU threads/cores). We evaluated ADMM-BB on four head-and-neck proton therapy patients, each with 13 scenarios accounting for 3 mm setup and 3:5% range uncertainties. We then compared the performance of ADMM-BB with projected gradient descent (PGD) applied to the same problem. Results: For each patient, ADMM-BB generated a robust proton treatment plan that satisfied all clinical criteria with comparable or better dosimetric quality than the plan generated by PGD. However, ADMM-BB's total runtime averaged about 6 to 7 times faster. This speedup increased with the number of scenarios. Conclusion: ADMM-BB is a powerful distributed optimization method that leverages parallel processing platforms, such as multi-core CPUs, GPUs, and cloud servers, to accelerate the computationally intensive work of robust proton treatment planning. This results in 1) a shorter treatment planning process and 2) the ability to consider more uncertainty scenarios, which improves plan quality.

翻译：目的：鲁棒质子治疗计划对于降低不确定性的影响具有重要意义，但其计算成本随不确定性场景数量增加而增长，导致治疗计划制定流程延长。我们开发了一种快速且可扩展的分布式优化平台，通过并行化场景计算来解决这一问题。方法：将鲁棒质子治疗计划问题建模为加权最小二乘问题，采用基于Barzilai-Borwein步长的交替方向乘子法（ADMM-BB）进行求解。通过问题重构，将主问题分解为多个子问题，每个子问题对应一种质子治疗不确定性场景。子问题可并行求解，使计算负载分布至多处理器（如CPU线程/核心）。我们基于四例头颈部质子治疗患者对ADMM-BB进行验证，每例患者包含13个场景（涵盖3mm摆位不确定性和3.5%射程不确定性），并将ADMM-BB与投影梯度下降法（PGD）进行性能比较。结果：对每例患者，ADMM-BB生成的鲁棒质子治疗计划均满足全部临床标准，其剂量学质量与PGD计划相当或更优，但总运行时间平均加速6-7倍，且加速比随场景数量增加而提高。结论：ADMM-BB作为一种强大的分布式优化方法，可利用多核CPU、GPU及云服务器等并行处理平台，加速鲁棒质子治疗计划中计算密集型任务。该方法可缩短治疗计划制定流程，同时支持更多不确定性场景的考虑，从而提高计划质量。