Comparison of linear and nonlinear programming approaches for “worst case dose” and “minmax” robust optimization of intensity‐modulated proton therapy dose distributions

Abstract

Robust optimization of intensity-modulated proton therapy (IMPT) takes uncertainties into account during spot weight optimization and leads to dose distributions that are resilient to uncertainties. Previous studies demonstrated benefits of linear programming (LP) for IMPT in terms of delivery efficiency by considerably reducing the number of spots required for the same quality of plans. However, a reduction in the number of spots may lead to loss of robustness. The purpose of the present study was to evaluate and compare the performance in terms of plan quality and robustness of two robust optimization approaches using LP and nonlinear programming (NLP) models. The so-called “worst case dose” and “minmax” robust optimization approaches and conventional planning target volume (PTV)-based optimization approach were applied to designing IMPT plans for five patients: two with prostate cancer, one with skull-based cancer, and two with head and neck cancer. For each approach, both LP and NLP models were used. Thus, for each case, six sets of IMPT plans were generated and assessed: LP-PTV-based, NLP-PTV-based, LP-worst case dose, NLP-worst case dose, LP-minmax, and NLP-minmax. The four robust optimization methods behaved differently from patient to patient, and no method emerged as superior to the others in terms of nominal plan quality and robustness against uncertainties. The plans generated using LP-based robust optimization were more robust regarding patient setup and range uncertainties than were those generated using NLP-based robust optimization for the prostate cancer patients. However, the robustness of plans generated using NLP-based methods was superior for the skull-based and head and neck cancer patients. Overall, LP-based methods were suitable for the less challenging cancer cases in which all uncertainty scenarios were able to satisfy tight dose constraints, while NLP performed better in more difficult cases in which most uncertainty scenarios were hard to meet tight dose limits. For robust optimization, the worst case dose approach was less sensitive to uncertainties than was the minmax approach for the prostate and skull-based cancer patients, whereas the minmax approach was superior for the head and neck cancer patients. The robustness of the IMPT plans was remarkably better after robust optimization than after PTV-based optimization, and the NLP-PTV-based optimization outperformed the LP-PTV-based optimization regarding robustness of clinical target volume coverage. In addition, plans generated using LP-based methods had notably fewer scanning spots than did those generated using NLP-based methods.

Technical Note: 4D robust optimization in small spot intensity‐modulated proton therapy (IMPT) for distal esophageal carcinoma

“…However, the flexibility of IMPT creates vulnerabilities of plans with increased sensitivity to proton beam range and patient setup uncertainties 10–12 . Additionally, the interplay effect, caused by the interference between the respiration‐related intra‐faction tumor motion and the dynamic delivery of each beamlet, can also result in the deterioration of the IMPT dose distribution 9,13–29 Although robust optimization 9,23–28,30–46 has been proven effective in mitigating the impact of the aforementioned uncertainties, techniques to mitigate the interplay effect are less developed.…”

Dose prescription with spatial uncertainty for peripheral lung SBRT

“…32 Use of a worst-case (minimax) algorithm may enable this to be further investigated. [36][37][38] This type of algorithm focuses on the impact of the worst-case scenario with respect to spatial uncertainty, and can therefore better handle a systematic error. Furthermore, although the dose calculation algorithm used in this study is known to be compatible with current commercial convolution algorithms, the results should be validated more thoroughly with a clinical dose calculation algorithm before implementation of the outcome.…”

Dose Comparison between Eclipse Dose Calculation and Fast Dose Calculator in Single- and Multi-Field Optimization Intensity-Modulated Proton Therapy Plans with Various Multi-Beams for Brain Cancer

“…Therefore, these results reconfirm the importance of beam arrangement in IMPT planning. Further study should now be done to determine, although beam angle optimization [24] and robust optimization techniques [25] may solve a problem of the beam arrangement.…”