Comparison of linear and nonlinear programming approaches for "worst case dose" and "minmax" robust optimization of intensity-modulated proton therapy dose distributions.

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 this 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.

On the interplay effects with proton scanning beams in stage III lung cancer.

PURPOSE: To assess the dosimetric impact of interplay between spot-scanning proton beam and respiratory motion in intensity-modulated proton therapy (IMPT) for stage III lung cancer. METHODS: Eleven patients were sampled from 112 patients with stage III nonsmall cell lung cancer to well represent the distribution of 112 patients in terms of target size and motion. Clinical target volumes (CTVs) and planning target volumes (PTVs) were defined according to the authors' clinical protocol. Uniform and realistic breathing patterns were considered along with regular- and hypofractionation scenarios. The dose contributed by a spot was fully calculated on the computed tomography (CT) images corresponding to the respiratory phase that the spot is delivered, and then accumulated to the reference phase of the 4DCT to generate the dynamic dose that provides an estimation of what might be delivered under the influence of interplay effect. The dynamic dose distributions at different numbers of fractions were compared with the corresponding 4D composite dose which is the equally weighted average of the doses, respectively, computed on respiratory phases of a 4DCT image set. RESULTS: Under regular fractionation, the average and maximum differences in CTV coverage between the 4D composite and dynamic doses after delivery of all 35 fractions were no more than 0.2% and 0.9%, respectively. The maximum differences between the two dose distributions for the maximum dose to the spinal cord, heart V40, esophagus V55, and lung V20 were 1.2 Gy, 0.1%, 0.8%, and 0.4%, respectively. Although relatively large differences in single fraction, correlated with small CTVs relative to motions, were observed, the authors' biological response calculations suggested that this interfractional dose variation may have limited biological impact. Assuming a hypofractionation scenario, the differences between the 4D composite and dynamic doses were well confined even for single fraction. CONCLUSIONS: Despite the presence of interplay effect, the delivered dose may be reliably estimated using the 4D composite dose. In general the interplay effect may not be a primary concern with IMPT for lung cancers for the authors' institution. The described interplay analysis tool may be used to provide additional confidence in treatment delivery.

Evaluation and mitigation of the interplay effects of intensity modulated proton therapy for lung cancer in a clinical setting.

PURPOSE: The primary aim of this study was to evaluate the impact of the interplay effects of intensity modulated proton therapy (IMPT) plans for lung cancer in the clinical setting. The secondary aim was to explore the technique of isolayered rescanning to mitigate these interplay effects. METHODS AND MATERIALS: A single-fraction 4-dimensional (4D) dynamic dose without considering rescanning (1FX dynamic dose) was used as a metric to determine the magnitude of dosimetric degradation caused by 4D interplay effects. The 1FX dynamic dose was calculated by simulating the machine delivery processes of proton spot scanning on a moving patient, described by 4D computed tomography during IMPT delivery. The dose contributed from an individual spot was fully calculated on the respiratory phase that corresponded to the life span of that spot, and the final dose was accumulated to a reference computed tomography phase by use of deformable image registration. The 1FX dynamic dose was compared with the 4D composite dose. Seven patients with various tumor volumes and motions were selected for study. RESULTS: The clinical target volume (CTV) prescription coverage for the 7 patients was 95.04%, 95.38%, 95.39%, 95.24%, 95.65%, 95.90%, and 95.53% when calculated with the 4D composite dose and 89.30%, 94.70%, 85.47%, 94.09%, 79.69%, 91.20%, and 94.19% when calculated with the 1FX dynamic dose. For these 7 patients, the CTV coverage calculated by use of a single-fraction dynamic dose was 95.52%, 95.32%, 96.36%, 95.28%, 94.32%, 95.53%, and 95.78%, with a maximum monitor unit limit value of 0.005. In other words, by increasing the number of delivered spots in each fraction, the degradation of CTV coverage improved up to 14.6%. CONCLUSIONS: A single-fraction 4D dynamic dose without rescanning was validated as a surrogate to evaluate the interplay effects of IMPT for lung cancer in the clinical setting. The interplay effects potentially can be mitigated by increasing the amount of isolayered rescanning in each fraction delivery.