We present a method for handling dose constraints as part of a convex programming framework for inverse treatment planning. Our method uniformly handles mean dose, maximum dose, minimum dose, and dose-volume (i.e., percentile) constraints as part of a convex formulation. Since dose-volume constraints are non-convex, we replace them with a convex restriction. This restriction is, by definition, conservative; to mitigate its impact on the clinical objectives, we develop a two-pass planning algorithm that allows each dose-volume constraint to be met exactly on a second pass by the solver if its corresponding restriction is feasible on the first pass. In another variant, we add slack variables to each dose constraint to prevent the problem from becoming infeasible when the user specifies an incompatible set of constraints or when the constraints are made infeasible by our restriction. Finally, we introduce ConRad, a Python-embedded opensource software package for convex radiation treatment planning. ConRad implements the methods described above and allows users to construct and plan cases through a simple interface. * Anqi Fu and Barıs . Ungun contributed equally to this paper. arXiv:1809.00744v2 [physics.med-ph]

Purpose: To develop a fast optimization method for station parameter optimized radiation therapy (SPORT) and show that SPORT is capable of matching VMAT in both plan quality and delivery efficiency by using three clinical cases of different disease sites. Methods: The angular space from 0• to 360• was divided into 180 station points (SPs). A candidate aperture was assigned to each of the SPs based on the calculation results using a column generation algorithm. The weights of the apertures were then obtained by optimizing the objective function using a state-of-the-art GPU based proximal operator graph solver. To avoid being trapped in a local minimum in beamlet-based aperture selection using the gradient descent algorithm, a stochastic gradient descent was employed here. Apertures with zero or low weight were thrown out. To find out whether there was room to further improve the plan by adding more apertures or SPs, the authors repeated the above procedure with consideration of the existing dose distribution from the last iteration. At the end of the second iteration, the weights of all the apertures were reoptimized, including those of the first iteration. The above procedure was repeated until the plan could not be improved any further. The optimization technique was assessed by using three clinical cases (prostate, head and neck, and brain) with the results compared to that obtained using conventional VMAT in terms of dosimetric properties, treatment time, and total MU. Results: Marked dosimetric quality improvement was demonstrated in the SPORT plans for all three studied cases. For the prostate case, the volume of the 50% prescription dose was decreased by 22% for the rectum and 6% for the bladder. For the head and neck case, SPORT improved the mean dose for the left and right parotids by 15% each. The maximum dose was lowered from 72.7 to 71.7 Gy for the mandible, and from 30.7 to 27.3 Gy for the spinal cord. The mean dose for the pharynx and larynx was reduced by 8% and 6%, respectively. For the brain case, the doses to the eyes, chiasm, and inner ears were all improved. SPORT shortened the treatment time by ∼1 min for the prostate case, ∼0.5 min for brain case, and ∼0.2 min for the head and neck case. Conclusions: The dosimetric quality and delivery efficiency presented here indicate that SPORT is an intriguing alternative treatment modality. With the widespread adoption of digital linac, SPORT should lead to improved patient care in the future. C 2016 American Association of Physicists in Medicine. [http://dx.doi.org/10.1118/1.4960000]

Radiation therapy is widely used in cancer treatment; however, plans necessarily involve tradeoffs between tumor coverage and mitigating damage to healthy tissue. While current hardware can deliver custom-shaped beams from any angle around the patient, choosing (from all possible beams) an optimal set of beams that maximizes tumor coverage while minimizing collateral damage and treatment time is intractable. Furthermore, even though planning algorithms used in practice consider highly restricted sets of candidate beams, the time per run combined with the number of runs required to explore clinical tradeoffs results in planning times of hours to days.We propose a suite of cluster and bound methods that we hypothesize will (a) yield higher quality plans by optimizing over much (i.e., 100-fold) larger sets of candidate beams, and/or (b) reduce planning time by allowing clinicians to search through candidate plans in real time. Our methods hinge on phrasing the treatment planning problem as a convex problem.To handle large scale optimizations, we form and solve compressed approximations to the full problem by clustering beams (i.e., columns of the dose deposition matrix used in the optimization) or voxels (rows of the matrix). Duality theory allows us to bound the error incurred when applying an approximate problem's solution to the full problem. We observe that beam clustering and voxel clustering both yield excellent solutions while enabling a 10-200-fold speedup.

No abstract

Purpose: To develop an ultra‐fast web‐based inverse planning framework for VMAT/IMRT. To achieve high speed, we investigate the use of a simple convex formulation of the inverse treatment planning problem that takes advantage of recent developments in the field of distributed optimization. Methods: A Monte Carlo (MC) dose calculation algorithm was used to calculate the dose matrix (268228 voxels × 360 beams, 96M non‐zeros) for a 360‐aperture, 4‐arc VMAT plan taken from the clinic. We wrote the objective for the inverse treatment planning problem as a sum of convex (piecewise‐linear) penalties on the dose at each voxel in the planning volume. This convex voxel‐separable formulation allowed us to apply a new, open‐source, CPU‐ and GPU‐capable optimization solver (http://foges.github.io/pogs/) to calculate our solutions of optimal beam intensities. In each planning session, after performing one full optimization we accelerated subsequent runs by “warm‐starting”: for run k, the optimal solution from run k‐1 was used as an initial guess. We implemented the treatment planning application as a Python web server running on a standard g2–2xlarge GPU node on Amazon EC2. Results: Our method formed optimal treatment plans in 5–15 seconds. Warm‐start times ranged from 100ms–8s (mean 3s) while sweeping out a 5‐log range of tradeoffs between target coverage and OAR sparing in 1000 total optimizations. Satisfactory plans were reached in 1–10 iterations of the optimization, with total planning time <10 minutes. Dosimetric characteristics such as the DVH curves showed that the resultant plans were comparable or superior to the clinically delivered plan. Conclusion: This work demonstrates the feasibility of high‐quality, low‐latency treatment planning using a convex problem formulation and GPU‐ based convex solver, making it practical to manipulate treatment objectives and view DVH curves and dose‐wash views in nearly real‐time in a web application. Funding support for this work is provided by the Stanford Bio‐X Bowes Graduate Fellowship and NIH Grant 5R01CA176553