Wenhua Cao

Uncertainty incorporated beam angle optimization for IMPT treatment planning

PURPOSE Beam angle optimization (BAO) by far remains an important and challenging problem in external beam radiation therapy treatment planning. Conventional BAO algorithms discussed in previous studies all focused on photon-based therapies. Impact of BAO on proton therapy is important while proton therapy increasingly receives great interests. This study focuses on potential benefits of BAO on intensity-modulated proton therapy (IMPT) that recently began available to clinical cancer treatment. METHODS The authors have developed a novel uncertainty incorporated BAO algorithm for IMPT treatment planning in that IMPT plan quality is highly sensitive to uncertainties such as proton range and setup errors. A linear programming was used to optimize robust intensity maps to scenario-based uncertainties for an incident beam angle configuration. Unlike conventional intensity-modulated radiation therapy with photons (IMXT), the search space for IMPT treatment beam angles may be relatively small but optimizing an IMPT plan may require higher computational costs due to larger data size. Therefore, a deterministic local neighborhood search algorithm that only needs a very limited number of plan objective evaluations was used to optimize beam angles in IMPT treatment planning. RESULTS Three prostate cancer cases and two skull base chordoma cases were studied to demonstrate the dosimetric advantages and robustness of optimized beam angles from the proposed BAO algorithm. Two- to four-beam plans were optimized for prostate cases, and two- and three-beam plans were optimized for skull base cases. By comparing plans with conventional two parallel-opposed angles, all plans with optimized angles consistently improved sparing at organs at risks, i.e., rectum and femoral heads for prostate, brainstem for skull base, in either nominal dose distribution or uncertainty-based dose distributions. The efficiency of the BAO algorithm was demonstrated by comparing it with alternative methods including simulated annealing and genetic algorithm. The numbers of IMPT plan objective evaluations required were reduced by up to a factor of 5 while the same optimal angle plans were converged in selected comparisons. CONCLUSIONS Uncertainty incorporated BAO may introduce pronounced improvement of IMPT plan quality including dosimetric benefits and robustness over uncertainties, based on the five clinical studies in this paper. In addition, local search algorithms may be more efficient in finding optimal beam angles than global optimization approaches for IMPT BAO.

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.

Radiobiological issues in proton therapy

Abstract Background: The relative biological effectiveness (RBE) for particle therapy is a complex function of particle type, radiation dose, linear energy transfer (LET), cell type, endpoint, etc. In the clinical practice of proton therapy, the RBE is assumed to have a fixed value of 1.1. This assumption, along with the effects of physical uncertainties, may mean that the biologically effective dose distributions received by the patient may be significantly different from what is seen on treatment plans. This may contribute to unforeseen toxicities and/or failure to control the disease. Variability of Proton RBE: It has been shown experimentally that proton RBE varies significantly along the beam path, especially near the end of the particle range. While there is now an increasing acceptance that proton RBE is variable, there is an ongoing debate about whether to change the current clinical practice. Clinical Evidence: A rationale against the change is the uncertainty in the models of variable RBE. Secondly, so far there is no clear clinical evidence of the harm of assuming proton RBE to be 1.1. It is conceivable, however, that the evidence is masked partially by physical uncertainties. It is, therefore, plausible that reduction in uncertainties and their incorporation in the estimation of dose actually delivered may isolate and reveal the variability of RBE in clinical practice. Nevertheless, clinical evidence of RBE variability is slowly emerging as more patients are treated with protons and their response data are analyzed. Modelling and Incorporation of RBE in the Optimization of Proton Therapy: The improvement in the knowledge of RBE could lead to better understanding of outcomes of proton therapy and in the improvement of models to predict RBE. Prospectively, the incorporation of such models in the optimization of intensity-modulated proton therapy could lead to improvements in the therapeutic ratio of proton therapy.

A hybrid framework for optimizing beam angles in radiation therapy planning

The purpose of this paper is twofold: (1) to examine strengths and weaknesses of recently developed optimization methods for selecting radiation treatment beam angles and (2) to propose a simple and easy-to-use hybrid framework that overcomes some of the weaknesses observed with these methods. Six optimization methods—branch and bound (BB), simulated annealing (SA), genetic algorithms (GA), nested partitions (NP), branch and prune (BP), and local neighborhood search (LNS)—were evaluated. Our preliminary test results revealed that (1) one of the major drawbacks of the reported algorithms was the limited ability to find a good solution within a reasonable amount of time in a clinical setting, (2) all heuristic methods require selecting appropriate parameter values, which is a difficult chore, and (3) the LNS algorithm has the ability to identify good solutions only if provided with a good starting point. On the basis of these findings, we propose a unified beam angle selection framework that, through two sequential phases, consistently finds clinically relevant locally optimal solutions. Considering that different users may use different optimization approaches among those mentioned above, the first phase aims to quickly find a good feasible solution using SA, GA, NP, or BP. This solution is then used as a starting point for LNS to find a locally optimal solution. Experimental results using this unified method on five clinical cases show that it not only produces consistently good-quality treatment solutions but also alleviates the effort of selecting an initial set of appropriate parameter values that is required by all of the existing optimization methods.

Linear energy transfer incorporated intensity modulated proton therapy optimization

The purpose of this study was to investigate the feasibility of incorporating linear energy transfer (LET) into the optimization of intensity modulated proton therapy (IMPT) plans. Because increased LET correlates with increased biological effectiveness of protons, high LETs in target volumes and low LETs in critical structures and normal tissues are preferred in an IMPT plan. However, if not explicitly incorporated into the optimization criteria, different IMPT plans may yield similar physical dose distributions but greatly different LET, specifically dose-averaged LET, distributions. Conventionally, the IMPT optimization criteria (or cost function) only includes dose-based objectives in which the relative biological effectiveness (RBE) is assumed to have a constant value of 1.1. In this study, we added LET-based objectives for maximizing LET in target volumes and minimizing LET in critical structures and normal tissues. Due to the fractional programming nature of the resulting model, we used a variable reformulation approach so that the optimization process is computationally equivalent to conventional IMPT optimization. In this study, five brain tumor patients who had been treated with proton therapy at our institution were selected. Two plans were created for each patient based on the proposed LET-incorporated optimization (LETOpt) and the conventional dose-based optimization (DoseOpt). The optimized plans were compared in terms of both dose (assuming a constant RBE of 1.1 as adopted in clinical practice) and LET. Both optimization approaches were able to generate comparable dose distributions. The LET-incorporated optimization achieved not only pronounced reduction of LET values in critical organs, such as brainstem and optic chiasm, but also increased LET in target volumes, compared to the conventional dose-based optimization. However, on occasion, there was a need to tradeoff the acceptability of dose and LET distributions. Our conclusion is that the inclusion of LET-dependent criteria in the IMPT optimization could lead to similar dose distributions as the conventional optimization but superior LET distributions in target volumes and normal tissues. This may have substantial advantages in improving tumor control and reducing normal tissue toxicities.

Improved beam angle arrangement in intensity modulated proton therapy treatment planning for localized prostate cancer.

Purpose: This study investigates potential gains of an improved beam angle arrangement compared to a conventional fixed gantry setup in intensity modulated proton therapy (IMPT) treatment for localized prostate cancer patients based on a proof of principle study. Materials and Methods: Three patients with localized prostate cancer retrospectively selected from our institution were studied. For each patient, IMPT plans were designed using two, three and four beam angles, respectively, obtained from a beam angle optimization algorithm. Those plans were then compared with ones using two lateral parallel-opposed beams according to the conventional planning protocol for localized prostate cancer adopted at our institution. Results: IMPT plans with two optimized angles achieved significant improvements in rectum sparing and moderate improvements in bladder sparing against those with two lateral angles. Plans with three optimized angles further improved rectum sparing significantly over those two-angle plans, whereas four-angle plans found no advantage over three-angle plans. A possible three-beam class solution for localized prostate patients was suggested and demonstrated with preserved dosimetric benefits because individually optimized three-angle solutions were found sharing a very similar pattern. Conclusions: This study has demonstrated the potential of using an improved beam angle arrangement to better exploit the theoretical dosimetric benefits of proton therapy and provided insights of selecting quality beam angles for localized prostate cancer treatment.

Impact of respiratory motion on variable relative biological effectiveness in 4D-dose distributions of proton therapy

Abstract Background: Organ motion during radiation therapy with scanned protons leads to deviations between the planned and the delivered physical dose. Using a constant relative biological effectiveness (RBE) of 1.1 linearly maps these deviations into RBE-weighted dose. However, a constant value cannot account for potential nonlinear variations in RBE suggested by variable RBE models. Here, we study the impact of motion on recalculations of RBE-weighted dose distributions using a phenomenological variable RBE model. Material and methods: 4D-dose calculation including variable RBE was implemented in the open source treatment planning toolkit matRad. Four scenarios were compared for one field and two field proton treatments for a liver cancer patient assuming (α∕β)x = 2 Gy and (α∕β)x = 10 Gy: (A) the optimized static dose distribution with constant RBE, (B) a static recalculation with variable RBE, (C) a 4D-dose recalculation with constant RBE and (D) a 4D-dose recalculation with variable RBE. For (B) and (D), the variable RBE was calculated by the model proposed by McNamara. For (C), the physical dose was accumulated with direct dose mapping; for (D), dose-weighted radio-sensitivity parameters of the linear quadratic model were accumulated to model synergistic irradiation effects on RBE. Results: Dose recalculation with variable RBE led to an elevated biological dose at the end of the proton field, while 4D-dose recalculation exhibited random deviations everywhere in the radiation field depending on the interplay of beam delivery and organ motion. For a single beam treatment assuming (α∕β)x = 2 Gy, D95% was 1.98 Gy (RBE) (A), 2.15 Gy (RBE) (B), 1.81 Gy (RBE) (C) and 1.98 Gy (RBE) (D). The homogeneity index was 1.04 (A), 1.08 (B), 1.23 (C) and 1.25 (D). Conclusion: For the studied liver case, intrafractional motion did not reduce the modulation of the RBE-weighted dose postulated by variable RBE models for proton treatments.

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

&NA; 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.

SU-G-TeP3-01: A New Approach for Calculating Variable Relative Biological Effectiveness in IMPT Optimization

PURPOSE To investigate the impact of a new approach for calculating relative biological effectiveness (RBE) in intensity-modulated proton therapy (IMPT) optimization on RBE-weighted dose distributions. This approach includes the nonlinear RBE for the high linear energy transfer (LET) region, which was revealed by recent experiments at our institution. In addition, this approach utilizes RBE data as a function of LET without using dose-averaged LET in calculating RBE values. METHODS We used a two-piece function for calculating RBE from LET. Within the Bragg peak, RBE is linearly correlated to LET. Beyond the Bragg peak, we use a nonlinear (quadratic) RBE function of LET based on our experimental. The IMPT optimization was devised to incorporate variable RBE by maximizing biological effect (based on the Linear Quadratic model) in tumor and minimizing biological effect in normal tissues. Three glioblastoma patients were retrospectively selected from our institution in this study. For each patient, three optimized IMPT plans were created based on three RBE resolutions, i.e., fixed RBE of 1.1 (RBE-1.1), variable RBE based on linear RBE and LET relationship (RBE-L), and variable RBE based on linear and quadratic relationship (RBE-LQ). The RBE weighted dose distributions of each optimized plan were evaluated in terms of different RBE values, i.e., RBE-1.1, RBE-L and RBE-LQ. RESULTS The RBE weighted doses recalculated from RBE-1.1 based optimized plans demonstrated an increasing pattern from using RBE-1.1, RBE-L to RBE-LQ consistently for all three patients. The variable RBE (RBE-L and RBE-LQ) weighted dose distributions recalculated from RBE-L and RBE-LQ based optimization were more homogenous within the targets and better spared in the critical structures than the ones recalculated from RBE-1.1 based optimization. CONCLUSION We implemented a new approach for RBE calculation and optimization and demonstrated potential benefits of improving tumor coverage and normal sparing in IMPT planning.

SU‐E‐T‐109: An Investigation of Including Variable Relative Biological Effectiveness in Intensity Modulated Proton Therapy Planning Optimization for Head and Neck Cancer Patients

Purpose: The current practice of considering the relative biological effectiveness (RBE) of protons in intensity modulated proton therapy (IMPT) planning is to use a generic RBE value of 1.1. However, RBE is indeed a variable depending on the dose per fraction, the linear energy transfer, tissue parameters, etc. In this study, we investigate the impact of using variable RBE based optimization (vRBE-OPT) on IMPT dose distributions compared by conventional fixed RBE based optimization (fRBE-OPT). Methods: Proton plans of three head and neck cancer patients were included for our study. In order to calculate variable RBE, tissue specific parameters were obtained from the literature and dose averaged LET values were calculated by Monte Carlo simulations. Biological effects were calculated using the linear quadratic model and they were utilized in the variable RBE based optimization. We used a Polak-Ribiere conjugate gradient algorithm to solve the model. In fixed RBE based optimization, we used conventional physical dose optimization to optimize doses weighted by 1.1. IMPT plans for each patient were optimized by both methods (vRBE-OPT and fRBE-OPT). Both variable and fixed RBE weighted dose distributions were calculated for both methods and compared by dosimetric measures. Results: The variable RBE weighted dose distributions were more homogenous within the targets, compared with the fixed RBE weighted dose distributions for the plans created by vRBE-OPT. We observed that there were noticeable deviations between variable and fixed RBE weighted dose distributions if the plan were optimized by fRBE-OPT. For organs at risk sparing, dose distributions from both methods were comparable. Conclusion: Biological dose based optimization rather than conventional physical dose based optimization in IMPT planning may bring benefit in improved tumor control when evaluating biologically equivalent dose, without sacrificing OAR sparing, for head and neck cancer patients. The research is supported in part by National Institutes of Health Grant No. 2U19CA021239-35.