Purpose We developed an automated treatment planning system based on a hierarchical goal programming approach. To demonstrate the feasibility of our method, we report the comparison of prostate treatment plans produced from the automated treatment planning system with those produced by a commercial treatment planning system. Methods In our approach, we prioritized the goals of the optimization, and solved one goal at a time. The purpose of prioritization is to ensure that higher priority dose-volume planning goals are not sacrificed to improve lower priority goals. The algorithm has four steps. The first step optimizes dose to the target structures, while sparing key sensitive organs from radiation. In the second step, the algorithm finds the best beamlet weight to reduce toxicity risks to normal tissue while holding the objective function achieved in the first step as a constraint, with a small amount of allowed slip. Likewise, the third and fourth steps introduce lower priority normal tissue goals and beam smoothing. We compared with prostate treatment plans from Memorial Sloan Kettering Cancer Center developed using Eclipse, with a prescription dose of 72 Gy. A combination of liear, quadratic, and gEUD objective functions were used with a modified open source solver code (IPOPT). Results Initial plan results on 3 different cases show that the automated planning system is capable of competing or improving on expert-driven eclipse plans. Compared to the Eclipse planning system, the automated system produced up to 26% less mean dose to rectum and 24% less mean dose to bladder while having the same D95 (after matching) to the target. Conclusion We have demonstrated that Pareto optimal treatment plans can be generated automatically without a trial-and-error process. The solver finds an optimal plan for the given patient, as opposed to database-driven approaches that set parameters based on geometry and population modeling.

Purpose:Systematic and random geometrical shifts of target and normal tissues can lead to delivered doses being significantly worse than planned dose distributions. We developed new methods to make treatment plans robust against geometrical uncertainties.Methods:We used prioritized prescription algorithms as a basis for development. Under the assumption that each structure moves rigidly, a 3‐dimentional vector with a certain probability distribution was used to characterize the position of each structure. One important metric (e.g. mean dose for bladder) was selected to characterize the treatment quality for each structure. An additional optimization step was added to optimize both the mean of each priority Objectives: function as well as the variance values, with respect to the uncertainty probability distributions, while retaining the good quality of the initial optimization results. This method was tested on 10 de‐identified prostate treatment cases.Results:Our optimization algorithm gave very good robust treatment plans consistently for the tested 10 prostate treatment cases, with almost the same robust quality as the traditional CTV‐PTV method on targets but with much lower and more robust doses to sensitive structures, especially on structures very close or overlapping with PTV (the rectum and bladder). The method is computationally efficient: in average the method adds only 3 minutes to the overall optimization time (less than 5 minutes total time on a quad‐core processor.)Conclusion:An optimization algorithm, compatible with prioritized (or lexicographic) optimization, was designed to generate robust treatment plans against motion uncertainties. The method optimizes both the mean and variance values of relevant dose metrics (e.g. bladder mean dose) for all interesting structures. This new algorithm theoretically works for any existing IMRT optimization algorithm and thus has great potential to improve treatment plan robustness.

Purpose: The widely used treatment plan metric Dx (mimimum dose to the hottest x% by volume of the target volume) is simple to interpret and use, but is computationally poorly behaved (non-convex), this impedes its use in computationally efficient intensity-modulated radiotherapy (IMRT) treatment planning algorithms. We therefore searched for surrogate metrics that are concave, computationally efficient, and accurately correlated to Dx values in IMRT treatment plans. Methods: To find concave surrogates of D95—and more generally, Dx values with variable x values—we tested equations containing one or two generalized equivalent uniform dose (gEUD) functions. Fits were obtained by varying gEUD ‘a’ parameter values, as well as the linear equation coefficients. Fitting was performed using a dataset of dose-volume histograms from 498 de-identified head and neck IMRT treatment plans. Fit characteristics were tested using a crossvalidation process. Reported root-mean-square error values were averaged over the cross-validation shuffles. Results: As expected, the two-gEUD formula provided a superior fit, compared to the single-gEUD formula. The best approximation uses two gEUD terms: 16.25 x gEUD[a=0.45] – 15.30 x gEUD[a=1.75] – 0.69. The average root-mean-square error on repeated (70/30) cross validation was 0.94 Gy. In addition, a formula was found that reasonably approximates Dx for x between 80% and 96%. Conclusion: A simple concave function using two gEUD terms was found that correlates well with PTV D95s for these head and neck treatment plans. More generally, a formula was found that represents well the Dx for x values from 80% to 96%, thus providing a computationally efficient formula for use in treatment planning optimization. The formula may need to be adjusted for other institutions with different treatment planning protocols. We conclude that the strategy of replacing Dx values with gEUD-based formulas is promising.

Purpose: To reduce the time and memory requirements of Intensity Modulated Radiation Therapy (IMRT) treatment planning. Methods: We propose a new sampling method, called Computational Boundary Sampling (CBS) for IMRT optimization, which samples all the boundary voxels and a certain percentage of inner voxels of each region of interest (ROI). Within CBS, we developed a grid-based sampling method for choosing inner voxels. In this method, each region is first evenly gridded and then sampling points are randomly selected from each sub-volume. We also developed a supporting theory to quantify the solution quality of CBS. We compared a variant of CBS that always keeps boundary voxels and a variant of CBS that does not. Finally, we quantified the impact of CBS on 10 different anonymized, clinical treatment cases using a prioritized prescription optimization method, including compute time, required memory and objective function values. Results: (1) We have found that the D95 of the targets are generally 4% larger when boundary voxels are included. (2) Grid sampling, compared to completely random sampling, yields more uniformly distributed sampling, with better solution quality, and less variance between independent runs, using the same or less time. (3) We have compared our original IMRT optimization solver without sampling and the solver combined with CBS sampling. The result showed that CBS can reduce the solution time and memory consumption by up to 20x with < 2% change in dosimetric variables. Conclusions: We have proposed a new sampling method (CBS), along with corresponding new techniques including boundary sampling and grid sampling, to improve time and space efficiency of IMRT optimization. A corresponding theory is developed to quantify the error bound. Experimental results have shown that our new methods significantly reduce solution time and memory costs with negligible impact on resulting plan quality.

Purpose/Objective(s)A key unmet need for adaptive radiotherapy treatment planning and improving radiotherapy workflow in general is a method that automatically generates high-quality IMRT plans. Automated treatment planning, if feasible, could also serve as a quality assurance ‘check’ compared to human treatment planning. We compared IMRT treatment plans, generated using hierarchical/prioritized optimization techniques (‘priopt’) and Monte Carlo dosimetry, against clinical Pinnacle treatment plans for definitive prostate treatments.Materials/MethodsSix randomly selected cases were replanned. The workflow consisted of: a fast, water-based dose calculation engine to generate the input beamlet influence matrix; a convex formulation of the treatment planning problem including ‘MOHx’ (mean-of-hottest x%) metrics as closely-correlated substitutes for dose-volume constraints; the MOSEK nonlinear solver; a leaf sequencing algorithm; a final Monte Carlo re-computation step (utilizing a commissioned head model that closely reproduces 6 MV Pinnacle IMRT results from our clinic); all embedded within the research system, CERR. Plans were compared with clinical Pinnacle treatment plans based on a list of planning metrics, and associated goals levels, elicited from the treating physician, including: Target max dose < 110% prescription dose (constraint); Target max dose < 107% prescription dose (preferred); Target D98 > prescription dose; Rectum V40 < 35%; Rectum V65 < 17%; Rectum V70 < 25%; Bladder V40 < 50%; Bladder V65 < 25%; and Bladder V70 < 25%.ResultsMost plan metrics met associated goals for most plans. Priopt plan metrics, averaged over the six cases, were better than Pinnacle for 8/9 metrics based on the simplified dosimetry, and better for 4/9 metrics after leaf-sequencing and final Monte Carlo recalculation. Except for the presence of greater dose heterogeneity allowed in the priopt plans, metric differences were small (usually on the order of a few percent) and seemed unlikely to lead to differing patient outcomes.ConclusionsRemarkably, priopt metrics were very similar to those achieved in the clinic. The results suggest that human planners relying on the Pinnacle system are working at close to optimal levels. The results further suggest that this algorithm could work well as an automated tool that produces high-quality dose distributions, with the caveat that more work needs to be done to slightly reduce the magnitude of hot regions. It therefore appears that this method of automated treatment planning is a good candidate to be further developed for several potential uses, including off-line adaptive re-planning, as a plan quality assurance check, or as a replacement for effort-intensive human planning. Purpose/Objective(s)A key unmet need for adaptive radiotherapy treatment planning and improving radiotherapy workflow in general is a method that automatically generates high-quality IMRT plans. Automated treatment planning, if feasible, could also serve as a quality assurance ‘check’ compared to human treatment planning. We compared IMRT treatment plans, generated using hierarchical/prioritized optimization techniques (‘priopt’) and Monte Carlo dosimetry, against clinical Pinnacle treatment plans for definitive prostate treatments. A key unmet need for adaptive radiotherapy treatment planning and improving radiotherapy workflow in general is a method that automatically generates high-quality IMRT plans. Automated treatment planning, if feasible, could also serve as a quality assurance ‘check’ compared to human treatment planning. We compared IMRT treatment plans, generated using hierarchical/prioritized optimization techniques (‘priopt’) and Monte Carlo dosimetry, against clinical Pinnacle treatment plans for definitive prostate treatments. Materials/MethodsSix randomly selected cases were replanned. The workflow consisted of: a fast, water-based dose calculation engine to generate the input beamlet influence matrix; a convex formulation of the treatment planning problem including ‘MOHx’ (mean-of-hottest x%) metrics as closely-correlated substitutes for dose-volume constraints; the MOSEK nonlinear solver; a leaf sequencing algorithm; a final Monte Carlo re-computation step (utilizing a commissioned head model that closely reproduces 6 MV Pinnacle IMRT results from our clinic); all embedded within the research system, CERR. Plans were compared with clinical Pinnacle treatment plans based on a list of planning metrics, and associated goals levels, elicited from the treating physician, including: Target max dose < 110% prescription dose (constraint); Target max dose < 107% prescription dose (preferred); Target D98 > prescription dose; Rectum V40 < 35%; Rectum V65 < 17%; Rectum V70 < 25%; Bladder V40 < 50%; Bladder V65 < 25%; and Bladder V70 < 25%. Six randomly selected cases were replanned. The workflow consisted of: a fast, water-based dose calculation engine to generate the input beamlet influence matrix; a convex formulation of the treatment planning problem including ‘MOHx’ (mean-of-hottest x%) metrics as closely-correlated substitutes for dose-volume constraints; the MOSEK nonlinear solver; a leaf sequencing algorithm; a final Monte Carlo re-computation step (utilizing a commissioned head model that closely reproduces 6 MV Pinnacle IMRT results from our clinic); all embedded within the research system, CERR. Plans were compared with clinical Pinnacle treatment plans based on a list of planning metrics, and associated goals levels, elicited from the treating physician, including: Target max dose < 110% prescription dose (constraint); Target max dose < 107% prescription dose (preferred); Target D98 > prescription dose; Rectum V40 < 35%; Rectum V65 < 17%; Rectum V70 < 25%; Bladder V40 < 50%; Bladder V65 < 25%; and Bladder V70 < 25%. ResultsMost plan metrics met associated goals for most plans. Priopt plan metrics, averaged over the six cases, were better than Pinnacle for 8/9 metrics based on the simplified dosimetry, and better for 4/9 metrics after leaf-sequencing and final Monte Carlo recalculation. Except for the presence of greater dose heterogeneity allowed in the priopt plans, metric differences were small (usually on the order of a few percent) and seemed unlikely to lead to differing patient outcomes. Most plan metrics met associated goals for most plans. Priopt plan metrics, averaged over the six cases, were better than Pinnacle for 8/9 metrics based on the simplified dosimetry, and better for 4/9 metrics after leaf-sequencing and final Monte Carlo recalculation. Except for the presence of greater dose heterogeneity allowed in the priopt plans, metric differences were small (usually on the order of a few percent) and seemed unlikely to lead to differing patient outcomes. ConclusionsRemarkably, priopt metrics were very similar to those achieved in the clinic. The results suggest that human planners relying on the Pinnacle system are working at close to optimal levels. The results further suggest that this algorithm could work well as an automated tool that produces high-quality dose distributions, with the caveat that more work needs to be done to slightly reduce the magnitude of hot regions. It therefore appears that this method of automated treatment planning is a good candidate to be further developed for several potential uses, including off-line adaptive re-planning, as a plan quality assurance check, or as a replacement for effort-intensive human planning. Remarkably, priopt metrics were very similar to those achieved in the clinic. The results suggest that human planners relying on the Pinnacle system are working at close to optimal levels. The results further suggest that this algorithm could work well as an automated tool that produces high-quality dose distributions, with the caveat that more work needs to be done to slightly reduce the magnitude of hot regions. It therefore appears that this method of automated treatment planning is a good candidate to be further developed for several potential uses, including off-line adaptive re-planning, as a plan quality assurance check, or as a replacement for effort-intensive human planning.

Treatment planning for intensity modulated radiation therapy (IMRT) is challenging due to both the size of the computational problems (thousands of variables and constraints) and the multi-objective, imprecise nature of the goals. We apply hierarchical programming to IMRT treatment planning. In this formulation, treatment planning goals/objectives are ordered in an absolute hierarchy, and the problem is solved from the top-down such that more important goals are optimized in turn. After each objective is optimized, that objective function is converted into a constraint when optimizing lower-priority objectives. We also demonstrate the usefulness of a linear/quadratic formulation, including the use of mean-tail-dose (mean dose to the hottest fraction of a given structure), to facilitate computational efficiency. In contrast to the conventional use of dose-volume constraints (no more than x% volume of a structure should receive more than y dose), the mean-tail-dose formulation ensures convex feasibility spaces and convex objective functions. To widen the search space without seriously degrading higher priority goals, we allowed higher priority constraints to relax or 'slip' a clinically negligible amount during lower priority iterations. This method was developed and tuned for external beam prostate planning and subsequently tested using a suite of 10 patient datasets. In all cases, good dose distributions were generated without individual plan parameter adjustments. It was found that allowance for a small amount of 'slip,' especially in target dose homogeneity, often resulted in improved normal tissue dose burdens. Compared to the conventional IMRT treatment planning objective function formulation using a weighted linear sum of terms representing very different dosimetric goals, this method: (1) is completely automatic, requiring no user intervention, (2) ensures high-priority planning goals are not seriously degraded by lower-priority goals, and (3) ensures that lower priority, yet still important, normal tissue goals are separately pushed as far as possible without seriously impacting higher priority goals.