The volumetric modulated arc therapy (VMAT) problem is highly non-convex and much more difficult than the fixed-field intensity modulated radiotherapy optimization problem. To solve it efficiently, we propose a sequential convex programming algorithm that solves a sequence of convex optimization problems. Beginning by optimizing the aperture weights of many (72) evenly distributed beams using the beam’s eye view of the target from each direction as the initial aperture shape, the search space is constrained to allowing the leaves to move within a pre-defined step-size. A convex approximation problem is introduced and solved to optimize the leaf positions and the aperture weights within the search space. The algorithm is equipped with both local and global search strategies, whereby a global search is followed by a local search: a large step-size results in a global search with a less accurate convex approximation, followed by a small step-size local search with an accurate convex approximation. The performance of the proposed algorithm is tested on three patients with three different disease sites (paraspinal, prostate and oligometastasis). The algorithm generates VMAT plans comparable to the ideal 72-beam fluence map optimized plans (i.e. IMRT plans before leaf sequencing) in 14 iterations and 36 mins on average. The algorithm is also tested on a small down-sampled prostate case for which we could computationally afford to obtain the ground-truth by solving the non-convex mixed-integer optimization problem exactly. This general algorithm is able to produce results essentially equivalent to the ground-truth but 12 times faster. The algorithm is also scalable and can handle real clinical cases, whereas the ground-truth solution using mixed-integer optimization can only be obtained for highly down-sampled cases.

Each year, approximately 18 million new cancer cases are diagnosed worldwide, and about half must be treated with radiotherapy. A successful treatment requires treatment planning with the customization of penetrating radiation beams to sterilize cancerous cells without harming nearby normal organs and tissues. This process currently involves extensive manual tuning of parameters by an expert planner, making it a time-consuming and labor-intensive process, with quality and immediacy of critical care dependent on the planner’s expertise. To improve the speed, quality, and availability of this highly specialized care, Memorial Sloan Kettering Cancer Center developed and applied advanced optimization tools to this problem (e.g., using hierarchical constrained optimization, convex approximations, and Lagrangian methods). This resulted in both a greatly improved radiotherapy treatment planning process and the generation of reliable and consistent high-quality plans that reflect clinical priorities. These improved techniques have been the foundation of high-quality treatments and have positively impacted over 5,000 patients to date, including numerous patients in severe pain and in urgent need of treatment who might have otherwise required longer hospital stays or undergone unnecessary surgery to control the progression of their disease. We expect that the wide distribution of the system we developed will ultimately impact patient care more broadly, including in resource-constrained countries.

Objective:To propose a novel moment-based loss function for predicting 3D dose distribution for the challenging conventional lung IMRT plans. The moment-based loss function is convex and differentiable and can easily incorporate clinical dose volume histogram (DVH) domain knowledge in any deep learning framework without computational overhead. Approach: We used a large dataset of 360 (240 for training, 50 for validation and 70 for testing) conventional lung patients with 2Gy × 30 fractions to train the deep learning (DL) model using clinically treated plans at our institution. We trained a UNet like CNN architecture using computed tomography (CT), planning target volume (PTV) and organ-at-risk contours (OAR) as input to infer corresponding voxel-wise 3D dose distribution. We evaluated three different loss functions: (1) The popular Mean Absolute Error (MAE) Loss, (2) the recently developed MAE + DVH Loss, and (3) the proposed MAE + Moments Loss. The quality of the predictions was compared using different DVH metrics as well as dose-score and DVH-score, recently introduced by the AAPM knowledge-based planning grand challenge Main results: Model with (MAE + Moment) loss function outperformed the model with MAE loss by significantly improving the DVH-score (11%, p<0.01) while having similar computational cost. It also outperformed the model trained with (MAE+DVH) by significantly improving the computational cost (48%) and the DVH-score (8%, p<0.01)

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