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Adaptive method for multicriteria optimization of intensity‐modulated proton therapy

PURPOSE
Provide an adaptive multicriteria optimization (MCO) method for intensity-modulated proton therapy (IMPT) utilizing GPU technology. Previously described limitations of MCO such as Pareto approximation and limitation on the number of objectives were addressed.


METHODS
The treatment planning process for IMPT must account for multiple objectives, which requires extensive treatment planning resources. Often a large number of objectives (>10) are required. Hence the need for an MCO algorithm that can handle large number of objectives. The novelty of the MCO method presented here lies on the introduction of the adaptive weighting scheme that can generate a well-distributed and dense representation of the Pareto surface for a large number of objectives in an efficient manner. In our approach the generated Pareto surface is constructed for a set of DVH objectives. The MCO algorithm is based on the augmented weighted Chebychev metric (AWCM) method with an adaptive weighting scheme. This scheme uses the differential evolution (DE) method to generate a set of well-distributed Pareto points. The quality of the Pareto points' distribution in the objective space was assessed quantitatively using the Pareto sampling metric. The MCO algorithm was developed to perform multiple parallel searches to achieve a rapid mapping of the Pareto surface, produce clinically deliverable plans, and was implemented on a GPU cluster. The MCO algorithm was tested on two clinical cases with 10 and 18 objectives. For each case one of the MCO-generated plans was selected for comparison with the clinically generated plan. The MCO plan was randomly selected out of the set of MCO plans that had target coverage similar to the clinically generated plan and the same or better sparing of the organs at risk (OAR). Additionally, a validation study of the AWCM method vs the weighted sum method was performed.


RESULTS
The adaptive MCO algorithm generated Pareto points on the Pareto hypersurface in a fast (2-3 hr) and efficient manner for 2 cases with 10 and 18 objectives. The MCO algorithm generated a dense and well-distributed set of Pareto points on the objective space, and was able to achieve minimization of the Pareto sampling metric. The selected MCO plan showed an improvement of the DVH objectives in comparison to the clinically optimized plan in both cases. For case one, the MCO plan showed a 48% reduction of the 50% dose to OARs and a 16% reduction of the 1% dose to OARs. For case 2, the MCO plan showed a 72% reduction of the 50% dose to OARs and a 42% reduction of the 1% dose to OARs. The comparison of AWCM to WS showed that the AWCM method has a dosimetric advantage over WS for both patient cases.


CONCLUSION
We introduced an adaptive MCO algorithm for IMPT accelerated using GPUs. The algorithm is based on an adaptive method for generating Pareto plans in the objective space. We have shown that the algorithm can provide rapid and efficient mapping of the multicriteria Pareto surface with clinically deliverable plans.