Pseudo beam's-eye-view as applied to beam orientation selection in intensity-modulated radiation therapy

Implementation and evaluation of an iterative-based algorithm for automatic beam angle optimization in breast cancer treatment planning

INTRODUCTION

A beam angle optimization (BAO) algorithm was developed to evaluate its clinical feasibility and investigate the impact of varying BAO constraints on breast cancer treatment plans.

MATERIALS AND METHODS

A two-part study was designed. In part 1, we retrospectively selected 20 patients treated with radiotherapy after breast-conserving surgery. For each patient, BAO plans were designed using beam angles optimized by the BAO algorithm and the same optimization constraints as manual plans. Dosimetric indices were compared between BAO and manual plans. In part 2, fifteen patients with left breast cancer were included. For each patient, three distinct cardiac constraints (mean heart dose < 5 Gy, 3 Gy or 1 Gy) were established during the BAO process to obtain three optimized beam sets which were marked as BAO_H1, BAO_H3, BAO_H5, respectively. These sets of beams were then utilized under identical IMRT constraints for planning. Comparative analysis was conducted among the three groups of plans.

RESULTS

For part 1, no significant differences were observed between BAO plans and manual plans in all dosimetric indices, except for ipsilateral lung V5, where BAO plans performed slightly better than manual plans (35.5% ± 5.6% vs 36.9% ± 4.3%, p = 0.034). For part 2, Stricter BAO heart constraints resulted in more perpendicular beams. However, there was no significant difference between BAO_H1, BAO_H3 and BAO_H5 with the same IMRT constraint in the heart dose. Meanwhile, the left lung dose was increased while the right breast and lung doses were decreased with stricter heart constraints in BAO. When mean heart dose < 5 Gy in IMRT constraint, the mean dose to the right lung was decreased from 0.46 Gy for BAO_H5 to 0.33 Gy for BAO_H1 (p = 0.027).

CONCLUSIONS

The BAO algorithm can achieve quality plans comparable to manual plans. IMRT constraints dominate the final plan dose, while varying BAO constraints alter the trade-off among structures, providing an additional degree of freedom in planning design.

Beam angle optimization for proton therapy via group-sparsity based angle generation method

BACKGROUND

In treatment planning, beam angle optimization (BAO) refers to the selection of a subset with a given number of beam angles from all available angles that provides the best plan quality. BAO is a NP-hard combinatorial problem. Although exhaustive search (ES) can exactly solve BAO by exploring all possible combinations, ES is very time-consuming and practically infeasible.

PURPOSE

To the best of our knowledge, (1) no optimization method has been demonstrated that can provide the exact solution to BAO, and (2) no study has validated an optimization method for solving BAO by benchmarking with the optimal BAO solution (e.g., via ES), both of which will be addressed by this work.

METHODS

This work considers BAO for proton therapy, for example, the selection of 2-4 beam angles for IMPT. The optimal BAO solution is obtained via ES and serves as the ground truth. A new BAO algorithm, namely angle generation (AG) method, is proposed, and demonstrated to provide nearly-exact solutions for BAO in reference to the ES solution. AG iteratively optimizes the angular set via group-sparsity (GS) regularization, until the planning objective does not decrease further.

RESULTS

Since GS alone can also solve BAO, AG was validated and compared with GS for 2-angle brain, 3-angle lung, and 4-angle brain cases, in reference to the optimal BAO solutions obtained by ES: the AG solution had the rank (1/276, 1/2024, 4/10 626), while the GS solution had the rank (42/276, 279/2024, 4328/10 626).

CONCLUSIONS

A new BAO algorithm called AG is proposed and shown to provide substantially improved accuracy for BAO from current methods with nearly-exact solutions to BAO, in reference to the ground truth of optimal BAO solution via ES.

Reflections on beam configuration optimization for intensity-modulated proton therapy

Presumably, intensity-modulated proton radiotherapy (IMPT) is the most powerful form of proton radiotherapy. In the current state of the art, IMPT beam configurations (i.e. the number of beams and their directions) are, in general, chosen subjectively based on prior experience and practicality. Beam configuration optimization (BCO) for IMPT could, in theory, significantly enhance IMPT’s therapeutic potential. However, BCO is complex and highly computer resource-intensive. Some algorithms for BCO have been developed for intensity-modulated photon therapy (IMRT). They are rarely used clinically mainly because the large number of beams typically employed in IMRT renders BCO essentially unnecessary. Moreover, in the newer form of IMRT, volumetric modulated arc therapy, there are no individual static beams. BCO is of greater importance for IMPT because it typically employs a very small number of beams (2-4) and, when the number of beams is small, BCO is critical for improving plan quality. However, the unique properties and requirements of protons, particularly in IMPT, make BCO challenging. Protons are more sensitive than photons to anatomic changes, exhibit variable relative biological effectiveness along their paths, and, as recently discovered, may spare the immune system. Such factors must be considered in IMPT BCO, though doing so would make BCO more resource intensive and make it more challenging to extend BCO algorithms developed for IMRT to IMPT. A limited amount of research in IMPT BCO has been conducted; however, considerable additional work is needed for its further development to make it truly effective and computationally practical. This article aims to provide a review of existing BCO algorithms, most of which were developed for IMRT, and addresses important requirements specific to BCO for IMPT optimization that necessitate the modification of existing approaches or the development of new effective and efficient ones.

Graph neural networks and deep reinforcement learning for simultaneous beam orientation and trajectory optimization of Cyberknife

Objective. Despite the high-quality treatment, the long treatment time of the Cyberknife system is believed to be a drawback. The high flexibility of its robotic arm requires meticulous path-finding algorithms to deliver the prescribed dose in the shortest time.Approach. We proposed a Deep Q-learning based on Graph Neural Networks to find the subset of the beams and the order to traverse them. A complex reward function is defined to minimize the distance covered by the robotic arm while avoiding the selection of close beams. Individual beam scores are also generated based on their effect on the beam intensity and are incorporated in the reward function. Main results. The performance of the presented method is evaluated on three clinical cases suffering from lung cancer. Applying this approach leads to an average of 35% reduction in the treatment time while delivering the prescribed dose provided by the physicians.Significance. Shorter treatment times result in a better treatment experience for individual patients, reduces discomfort and the sides effects of inadvertent movements for them. Additionally, it creates the opportunity to treat a higher number of patients in a given time period at the radiation therapy centers.

Beam Angle Optimization for Double-Scattering Proton Delivery Technique Using an Eclipse Application Programming Interface and Convolutional Neural Network

To automatically identify optimal beam angles for proton therapy configured with the double-scattering delivery technique, a beam angle optimization method based on a convolutional neural network (BAODS-Net) is proposed. Fifty liver plans were used for training in BAODS-Net. To generate a sequence of input data, 25 rays on the eye view of the beam were determined per angle. Each ray collects nine features, including the normalized Hounsfield unit and the position information of eight structures per 2° of gantry angle. The outputs are a set of beam angle ranking scores (S_beam) ranging from 0° to 359°, with a step size of 1°. Based on these input and output designs, BAODS-Net consists of eight convolution layers and four fully connected layers. To evaluate the plan qualities of deep-learning, equi-spaced, and clinical plans, we compared the performances of three types of loss functions and performed K-fold cross-validation (K = 5). For statistical analysis, the volumes V_27Gy and V_30Gy as well as the mean, minimum, and maximum doses were calculated for organs-at-risk by using a paired-samples t-test. As a result, smooth-L1 loss showed the best optimization performance. At the end of the training procedure, the mean squared errors between the reference and predicted S_beam were 0.031, 0.011, and 0.004 for L1, L2, and smooth-L1 loss, respectively. In terms of the plan quality, statistically, Plan_BAO has no significant difference from Plan_Clinic (P >.05). In our test, a deep-learning based beam angle optimization method for proton double-scattering treatments was developed and verified. Using Eclipse API and BAODS-Net, a plan with clinically acceptable quality was created within 5 min.

Automating proton treatment planning with beam angle selection using Bayesian optimization

PURPOSE

To present a fully automated treatment planning process for proton therapy including beam angle selection using a novel Bayesian optimization approach and previously developed constrained hierarchical fluence optimization method.

METHODS

We adapted our in-house automated intensity modulated radiation therapy (IMRT) treatment planning system, which is based on constrained hierarchical optimization and referred to as ECHO (expedited constrained hierarchical optimization), for proton therapy. To couple this to beam angle selection, we propose using a novel Bayesian approach. By integrating ECHO with this Bayesian beam selection approach, we obtain a fully automated treatment planning framework including beam angle selection. Bayesian optimization is a global optimization technique which only needs to search a small fraction of the search space for slowly varying objective functions (i.e., smooth functions). Expedited constrained hierarchical optimization is run for some initial beam angle candidates and the resultant treatment plan for each beam configuration is rated using a clinically relevant treatment score function. Bayesian optimization iteratively predicts the treatment score for not-yet-evaluated candidates to find the best candidate to be optimized next with ECHO. We tested this technique on five head-and-neck (HN) patients with two coplanar beams. In addition, tests were performed with two noncoplanar and three coplanar beams for two patients.

RESULTS

For the two coplanar configurations, the Bayesian optimization found the optimal beam configuration after running ECHO for, at most, 4% of all potential configurations (23 iterations) for all patients (range: 2%-4%). Compared with the beam configurations chosen by the planner, the optimal configurations reduced the mandible maximum dose by 6.6 Gy and high dose to the unspecified normal tissues by 3.8 Gy, on average. For the two noncoplanar and three coplanar beam configurations, the algorithm converged after 45 iterations (examining <1% of all potential configurations).

CONCLUSIONS

A fully automated and efficient treatment planning process for proton therapy, including beam angle optimization was developed. The algorithm automatically generates high-quality plans with optimal beam angle configuration by combining Bayesian optimization and ECHO. As the Bayesian optimization is capable of handling complex nonconvex functions, the treatment score function which is used in the algorithm to evaluate the dose distribution corresponding to each beam configuration can contain any clinically relevant metric.

Comparison of two beam angular optimization algorithms guided by automated multicriterial IMRT

PURPOSE

To compare two beam angle optimization (BAO) algorithms for coplanar and non-coplanar geometries in a multicriterial optimization framework.

METHODS

40 nasopharynx patients were selected for this retrospective planning study. IMRT optimized plans were produced by Erasmus-iCycle multicriterial optimization platform. Two different algorithms, based on a discrete and on a continuous exploration of the space search, algorithm i and B respectively, were used to address BAO. Plan quality evaluation and comparison were performed with SPIDERplan. Statistically significant differences between the plans were also assessed.

RESULTS

For plans using only coplanar incidences, the optimized beam distribution with algorithm i is more asymmetric than with algorithm B. For non-coplanar beam optimization, larger deviations from coplanarity were obtained with algorithm i than with algorithm B. Globally, both algorithms presented near equivalent plan quality scores, with algorithm B presenting a marginally better performance than algorithm i.

CONCLUSION

Almost all plans presented high quality, profiting from multicriterial and beam angular optimization. Although there were not significant differences when average results over the entire sample were considered, a case-by-case analysis revealed important differences for some patients.

Lung IMRT planning with automatic determination of beam angle configurations

Beam angle configuration is a major planning decision in intensity modulated radiation treatment (IMRT) that has a significant impact on dose distributions and thus quality of treatment, especially in complex planning cases such as those for lung cancer treatment. We propose a novel method to automatically determine beam configurations that incorporates noncoplanar beams. We then present a completely automated IMRT planning algorithm that combines the proposed method with a previously reported OAR DVH prediction model. Finally, we validate this completely automatic planning algorithm using a set of challenging lung IMRT cases. A beam efficiency index map is constructed to guide the selection of beam angles. This index takes into account both the dose contributions from individual beams and the combined effect of multiple beams by introducing a beam-spread term. The effect of the beam-spread term on plan quality was studied systematically and the weight of the term to balance PTV dose conformity against OAR avoidance was determined. For validation, complex lung cases with clinical IMRT plans that required the use of one or more noncoplanar beams were re-planned with the proposed automatic planning algorithm. Important dose metrics for the PTV and OARs in the automatic plans were compared with those of the clinical plans. The results are very encouraging. The PTV dose conformity and homogeneity in the automatic plans improved significantly. And all the dose metrics of the automatic plans, except the lung V_{5 Gy}, were statistically better than or comparable with those of the clinical plans. In conclusion, the automatic planning algorithm can incorporate non-coplanar beam configurations in challenging lung cases and can generate plans efficiently with quality closely approximating that of clinical plans.

The Scatter Search Based Algorithm for Beam Angle Optimization in Intensity-Modulated Radiation Therapy

This article introduces a new framework for beam angle optimization (BAO) in intensity-modulated radiation therapy (IMRT) using the Scatter Search Based Algorithm. The potential benefits of plans employing the coplanar optimized beam sets are also examined. In the proposed beam angle selection algorithm, the problem is solved in two steps. Initially, the gantry angles are selected using the Scatter Search Based Algorithm, which is a global optimization method. Then, for each beam configuration, the intensity profile is calculated by the conjugate gradient method to score each beam angle set chosen. A simulated phantom case with obvious optimal beam angles was used to benchmark the validity of the presented algorithm. Two clinical cases (TG-119 phantom and prostate cases) were examined to prepare a dose volume histogram (DVH) and determine the dose distribution to evaluate efficiency of the algorithm. A clinical plan with the optimized beam configuration was compared with an equiangular plan to determine the efficiency of the proposed algorithm. The BAO plans yielded significant improvements in the DVHs and dose distributions compared to the equispaced coplanar beams for each case. The proposed algorithm showed its potential to effectively select the beam direction for IMRT inverse planning at different tumor sites.

A new sparse optimization scheme for simultaneous beam angle and fluence map optimization in radiotherapy planning

[Formula: see text]-minimization-based sparse optimization was employed to solve the beam angle optimization (BAO) in intensity-modulated radiation therapy (IMRT) planning. The technique approximates the exact BAO formulation with efficiently computable convex surrogates, leading to plans that are inferior to those attainable with recently proposed gradient-based greedy schemes. In this paper, we alleviate/reduce the nontrivial inconsistencies between the [Formula: see text]-based formulations and the exact BAO model by proposing a new sparse optimization framework based on the most recent developments in group variable selection. We propose the incorporation of the group-folded concave penalty (gFCP) as a substitution to the [Formula: see text]-minimization framework. The new formulation is then solved by a variation of an existing gradient method. The performance of the proposed scheme is evaluated by both plan quality and the computational efficiency using three IMRT cases: a coplanar prostate case, a coplanar head-and-neck case, and a noncoplanar liver case. Involved in the evaluation are two alternative schemes: the [Formula: see text]-minimization approach and the gradient norm method (GNM). The gFCP-based scheme outperforms both counterpart approaches. In particular, gFCP generates better plans than those obtained using the [Formula: see text]-minimization for all three cases with a comparable computation time. As compared to the GNM, the gFCP improves both the plan quality and computational efficiency. The proposed gFCP-based scheme provides a promising framework for BAO and promises to improve both planning time and plan quality.

Intelligence-guided beam angle optimization in treatment planning of intensity-modulated radiation therapy

An intelligence guided approach based on fuzzy inference system (FIS) was proposed to automate beam angle optimization in treatment planning of intensity-modulated radiation therapy (IMRT). The model of FIS is built on inference rules in describing the relationship between dose quality of IMRT plan and irradiated region of anatomical structure. Dose quality of IMRT plan is quantified by the difference between calculated and constraint doses of the anatomical structures in an IMRT plan. Irradiated region of anatomical structure is characterized by the metric, covered region of interest, which is the region of an anatomical structure under radiation field while beam's eye-view is conform to target volume. Initially, an IMRT plan is created with a single beam. The dose difference is calculated for the input of FIS and the output of FIS is obtained with processing of fuzzy inference. Later, a set of candidate beams is generated for replacing the current beam. This process continues until no candidate beams is found. Then the next beam is added to the IMRT plan and optimized in the same way as the previous beam. The new beam keeps adding to the IMRT plan until the allowed beam number is reached. Two spinal cases were investigated in this study. The preliminary results show that dose quality of IMRT plans achieved by this approach is better than those achieved by the default approach with equally spaced beam setting. It is effective to find the optimal beam combination of IMRT plan with the intelligence-guided approach.

Beam’s-eye-view dosimetrics (BEVD) guided rotational station parameter optimized radiation therapy (SPORT) planning based on reweighted total-variation minimization

Conventional VMAT optimizes aperture shapes and weights at uniformly sampled stations, which is a generalization of the concept of a control point. Recently, rotational station parameter optimized radiation therapy (SPORT) has been proposed to improve the plan quality by inserting beams to the regions that demand additional intensity modulations, thus formulating nonuniform beam sampling. This work presents a new rotational SPORT planning strategy based on reweighted total-variation (TV) minimization (min.), using beam’s-eye-view dosimetrics (BEVD) guided beam selection. The convex programming based reweighted TV min. assures the simplified fluence-map, which facilitates single-aperture selection at each station for single-arc delivery. For the rotational arc treatment planning and non-uniform beam angle setting, the mathematical model needs to be modified by additional penalty term describing the fluence-map similarity and by determination of appropriate angular weighting factors. The proposed algorithm with additional penalty term is capable of achieving more efficient and deliverable plans adaptive to the conventional VMAT and SPORT planning schemes by reducing the dose delivery time about 5 to 10 s in three clinical cases (one prostate and two head-and-neck (HN) cases with a single and multiple targets). The BEVD guided beam selection provides effective and yet easy calculating methodology to select angles for denser, non-uniform angular sampling in SPORT planning. Our BEVD guided SPORT treatment schemes improve the dose sparing to femoral heads in the prostate and brainstem, parotid glands and oral cavity in the two HN cases, where the mean dose reduction of those organs ranges from 0.5 to 2.5 Gy. Also, it increases the conformation number assessing the dose conformity to the target from 0.84, 0.75 and 0.74 to 0.86, 0.79 and 0.80 in the prostate and two HN cases, while preserving the delivery efficiency, relative to conventional single-arc VMAT plans.

Automatic learning-based beam angle selection for thoracic IMRT

PURPOSE

The treatment of thoracic cancer using external beam radiation requires an optimal selection of the radiation beam directions to ensure effective coverage of the target volume and to avoid unnecessary treatment of normal healthy tissues. Intensity modulated radiation therapy (IMRT) planning is a lengthy process, which requires the planner to iterate between choosing beam angles, specifying dose-volume objectives and executing IMRT optimization. In thorax treatment planning, where there are no class solutions for beam placement, beam angle selection is performed manually, based on the planner's clinical experience. The purpose of this work is to propose and study a computationally efficient framework that utilizes machine learning to automatically select treatment beam angles. Such a framework may be helpful for reducing the overall planning workload.

METHODS

The authors introduce an automated beam selection method, based on learning the relationships between beam angles and anatomical features. Using a large set of clinically approved IMRT plans, a random forest regression algorithm is trained to map a multitude of anatomical features into an individual beam score. An optimization scheme is then built to select and adjust the beam angles, considering the learned interbeam dependencies. The validity and quality of the automatically selected beams evaluated using the manually selected beams from the corresponding clinical plans as the ground truth.

RESULTS

The analysis included 149 clinically approved thoracic IMRT plans. For a randomly selected test subset of 27 plans, IMRT plans were generated using automatically selected beams and compared to the clinical plans. The comparison of the predicted and the clinical beam angles demonstrated a good average correspondence between the two (angular distance 16.8° ± 10°, correlation 0.75 ± 0.2). The dose distributions of the semiautomatic and clinical plans were equivalent in terms of primary target volume coverage and organ at risk sparing and were superior over plans produced with fixed sets of common beam angles. The great majority of the automatic plans (93%) were approved as clinically acceptable by three radiation therapy specialists.

CONCLUSIONS

The results demonstrated the feasibility of utilizing a learning-based approach for automatic selection of beam angles in thoracic IMRT planning. The proposed method may assist in reducing the manual planning workload, while sustaining plan quality.

Automated population-based planning for whole brain radiation therapy

Treatment planning for whole‐brain radiation treatment is technically a simple process, but in practice it takes valuable clinical time of repetitive and tedious tasks. This report presents a method that automatically segments the relevant target and normal tissues, and creates a treatment plan in only a few minutes after patient simulation. Segmentation of target and critical structures is performed automatically through morphological operations on the soft tissue and was validated by comparing with manual clinical segmentation using the Dice coefficient and Hausdorff distance. The treatment plan is generated by searching a database of previous cases for patients with similar anatomy. In this search, each database case is ranked in terms of similarity using a customized metric designed for sensitivity by including only geometrical changes that affect the dose distribution. The database case with the best match is automatically modified to replace relevant patient info and isocenter position while maintaining original beam and MLC settings. Fifteen patients with marginally acceptable treatment plans were used to validate the method. In each of these cases the anatomy was accurately segmented, but the beams and MLC settings led to a suboptimal treatment plan by either underdosing the brain or excessively irradiating critical normal tissues. For each case, the anatomy was automatically segmented with the proposed method, and the automated and manual segmentations were then compared. The mean Dice coefficient was 0.97, with a standard deviation of 0.008 for the brain, 0.85±0.009 for the eyes, and 0.67±0.11 for the lens. The mean Euclidian distance was 0.13±0.13 mm for the brain, 0.27±0.31 for the eye, and 2.34±7.23 for the lens. Each case was then subsequently matched against a database of 70 validated treatment plans and the best matching plan (termed autoplanned), was compared retrospectively with the clinical plans in terms of brain coverage and maximum doses to critical structures. Maximum doses were reduced by a maximum of 8.37 Gy for the left eye (mean 2.08), 11.67 for the right eye (1.90) and, respectively, 25.44 (5.59) for the left lens and 24.40 (4.85) for the right lens. Time to generate the autoplan, including the segmentation, was 3−4 min. Automated database‐ based matching is an alternative to classical treatment planning that improves quality while providing a cost‐effective solution to planning through modifying previous validated plans to match a current patient's anatomy.

PACS number: 87.55.D, 87.55.tg, 87.57.nm

Nonisocentric treatment strategy for breast radiation therapy: a proof of concept study

PURPOSE

To propose a nonisocentric treatment strategy as a special form of station parameter optimized radiation therapy, to improve sparing of critical structures while preserving target coverage in breast radiation therapy.

METHODS AND MATERIALS

To minimize the volume of exposed lung and heart in breast irradiation, we propose a novel nonisocentric treatment scheme by strategically placing nonconverging beams with multiple isocenters. As its name suggests, the central axes of these beams do not intersect at a single isocenter as in conventional breast treatment planning. Rather, the isocenter locations and beam directions are carefully selected, in that each beam is only responsible for a certain subvolume of the target, so as to minimize the volume of irradiated normal tissue. When put together, the beams will provide an adequate coverage of the target and expose only a minimal amount of normal tissue to radiation. We apply the nonisocentric planning technique to 2 previously treated clinical cases (breast and chest wall).

RESULTS

The proposed nonisocentric technique substantially improved sparing of the ipsilateral lung. Compared with conventional isocentric plans using 2 tangential beams, the mean lung dose was reduced by 38% and 50% using the proposed technique, and the volume of the ipsilateral lung receiving ≥ 20 Gy was reduced by a factor of approximately 2 and 3 for the breast and chest wall cases, respectively. The improvement in lung sparing is even greater compared with volumetric modulated arc therapy.

CONCLUSIONS

A nonisocentric implementation of station parameter optimized radiation therapy has been proposed for breast radiation therapy. The new treatment scheme overcomes the limitations of existing approaches and affords a useful tool for conformal breast radiation therapy, especially in cases with extreme chest wall curvature.

Prior-knowledge treatment planning for volumetric arc therapy using feature-based database mining

Treatment planning for volumetric arc therapy (VMAT) is a lengthy process that requires many rounds of optimizations to obtain the best treatment settings and optimization constraints for a given patient's geometry. We propose a feature‐selection search engine that explores previously treated cases of similar anatomy, returning the optimal plan configurations and attainable DVH constraints. Using an institutional database of 83 previously treated cases of prostate carcinoma treated with volumetric‐modulated arc therapy, the search procedure first finds the optimal isocenter position with an optimization procedure, then ranks the anatomical similarity as the mean distance between targets. For the best matching plan, the planning information is reformatted to the DICOM format and imported into the treatment planning system to suggest isocenter, arc directions, MLC patterns, and optimization constraints that can be used as starting points in the optimization process. The approach was tested to create prospective treatment plans based on anatomical features that match previously treated cases from the institution database. By starting from a near‐optimal solution and using previous optimization constraints, the best matching test only required simple optimization steps to further decrease target inhomogeneity, ultimately reducing time spend by the therapist in planning arcs' directions and lengths.

PACS number: 87.55.D‐, 87.55.de

An adaptive planning strategy for station parameter optimized radiation therapy (SPORT): Segmentally boosted VMAT

PURPOSE

Conventional volumetric modulated arc therapy (VMAT) discretizes the angular space into equally spaced control points during planning and then optimizes the apertures and weights of the control points. The aperture at an angle in between two control points is obtained through interpolation. This approach tacitly ignores the differential need for intensity modulation of different angles. As such, multiple arcs are often required, which may oversample some angle(s) and undersample others. The purpose of this work is to develop a segmentally boosted VMAT scheme to eliminate the need for multiple arcs in VMAT treatment with improved dose distribution and∕or delivery efficiency.

METHODS

The essence of the new treatment scheme is how to identify the need of individual angles for intensity modulation and to provide the necessary beam intensity modulation for those beam angles that need it. We introduce a "demand metric" at each control point to decide which station or control points need intensity modulation. To boost the modulation at selected stations, additional segments are added in the vicinity of the selected stations. The added segments are then optimized together with the original set of station or control points as a whole. The authors apply the segmentally boosted planning technique to four previously treated clinical cases: two head and neck (HN) cases, one prostate case, and one liver case. The proposed planning technique is compared with conventional one-arc and two-arc VMAT.

RESULTS

The proposed segmentally boosted VMAT technique achieves better critical structure sparing than one-arc VMAT with similar or better target coverage in all four clinical cases. The segmentally boosted VMAT also outperforms two-arc VMAT for the two complicated HN cases, yet with ∼30% reduction in the machine monitor units (MUs) relative to two-arc VMAT, which leads to less leakage∕scatter dose to the patient and can potentially translate into faster dose delivery. For the less challenging prostate and liver cases, similar critical structure sparing as the two-arc VMAT plans was obtained using the segmentally boosted VMAT. The benefit for the two simpler cases is the reduction of MUs and improvement of treatment delivery efficiency.

CONCLUSIONS

Segmentally boosted VMAT achieves better dose conformality and∕or reduced MUs through effective consideration of the need of individual beam angles for intensity modulation. Elimination of the need for multiple arcs in rotational arc therapy while improving the dose distribution should lead to improved workflow and treatment efficacy, thus may have significant implication to radiation oncology practice.

Trajectory optimization for dynamic couch rotation during volumetric modulated arc radiotherapy

Non-coplanar radiation beams are often used in three-dimensional conformal and intensity modulated radiotherapy to reduce dose to organs at risk (OAR) by geometric avoidance. In volumetric modulated arc radiotherapy (VMAT) non-coplanar geometries are generally achieved by applying patient couch rotations to single or multiple full or partial arcs. This paper presents a trajectory optimization method for a non-coplanar technique, dynamic couch rotation during VMAT (DCR–VMAT), which combines ray tracing with a graph search algorithm. Four clinical test cases (partial breast, brain, prostate only, and prostate and pelvic nodes) were used to evaluate the potential OAR sparing for trajectory-optimized DCR–VMAT plans, compared with standard coplanar VMAT. In each case, ray tracing was performed and a cost map reflecting the number of OAR voxels intersected for each potential source position was generated. The least-cost path through the cost map, corresponding to an optimal DCR–VMAT trajectory, was determined using Dijkstra's algorithm. Results show that trajectory optimization can reduce dose to specified OARs for plans otherwise comparable to conventional coplanar VMAT techniques. For the partial breast case, the mean heart dose was reduced by 53%. In the brain case, the maximum lens doses were reduced by 61% (left) and 77% (right) and the globes by 37% (left) and 40% (right). Bowel mean dose was reduced by 15% in the prostate only case. For the prostate and pelvic nodes case, the bowel V50 Gy and V60 Gy were reduced by 9% and 45% respectively. Future work will involve further development of the algorithm and assessment of its performance over a larger number of cases in site-specific cohorts.

Comparison of beam angle selection strategies for intracranial IMRT

PURPOSE

Various strategies to select beneficial beam ensembles for intensity-modulated radiation therapy (IMRT) have been suggested over the years. These beam angle selection (BAS) strategies are usually evaluated against reference configurations applying equispaced coplanar beams but they are not compared to one another. Here, the authors present a meta analysis of four BAS strategies that incorporates fluence optimization (FO) into BAS by combinatorial optimization (CO) and one BAS strategy that decouples FO from BAS, i.e., spherical cluster analysis (SCA). The underlying parameters of the BAS process are investigated and the dosimetric benefits of the BAS strategies are quantified.

METHODS

For three intracranial lesions in proximity to organs at risk (OARs) the authors compare treatment plans applying equispaced coplanar beam ensembles with treatment plans using five different BAS strategies, i.e., four CO techniques and SCA, to establish coplanar and noncoplanar beam ensembles. Treatment plans applying 5, 7, 9, and 11 beams are investigated. For the CO strategies the authors perform BAS runs with a 5°, 10°, 15°, and 20° angular resolution, which corresponds to a minimum of 18 coplanar and a maximum of 1400 noncoplanar candidate beams. In total 272 treatment plans with different BAS settings are generated for every patient. The quality of the treatment plans is compared based on the protection of OARs yet integral dose, target homogeneity, and target conformity are also considered.

RESULTS

It is possible to reduce the average mean and maximum doses in OARs by more than 4 Gy (1 Gy) with optimized noncoplanar (coplanar) beam ensembles found with BAS by CO or SCA. For BAS including FO by CO, the individual algorithm used and the angular resolution in the space of candidate beams does not have a crucial impact on the quality of the resulting treatment plans. All CO algorithms yield similar target conformity and slightly improved target homogeneity in comparison to equispaced coplanar setups. Furthermore, optimized coplanar (noncoplanar) beam ensembles enabled more than a 6% (5%) reduction of the integral dose. For SCA, however, integral dose was increased and target conformity was decreased in comparison to equispaced coplanar setups-especially for a small number of beams.

CONCLUSION

Both BAS strategies incorporating FO by CO and independent BAS strategies excluding FO provide dose savings in OARs for optimized coplanar and especially noncoplanar beam ensembles; they should not be neglected in the clinic.

Characterizing the combinatorial beam angle selection problem

The beam angle selection (BAS) problem in intensity-modulated radiation therapy is often interpreted as a combinatorial optimization problem, i.e. finding the best combination of η beams in a discrete set of candidate beams. It is well established that the combinatorial BAS problem may be solved efficiently with metaheuristics such as simulated annealing or genetic algorithms. However, the underlying parameters of the optimization process, such as the inclusion of non-coplanar candidate beams, the angular resolution in the space of candidate beams, and the number of evaluated beam ensembles as well as the relative performance of different metaheuristics have not yet been systematically investigated. We study these open questions in a meta-analysis of four strategies for combinatorial optimization in order to provide a reference for future research related to the BAS problem in intensity-modulated radiation therapy treatment planning. We introduce a high-performance inverse planning engine for BAS. It performs a full fluence optimization for ≈3600 treatment plans per hour while handling up to 50 GB of dose influence data (≈1400 candidate beams). For three head and neck patients, we compare the relative performance of a genetic, a cross-entropy, a simulated annealing and a naive iterative algorithm. The selection of ensembles with 5, 7, 9 and 11 beams considering either only coplanar or all feasible candidate beams is studied for an angular resolution of 5°, 10°, 15° and 20° in the space of candidate beams. The impact of different convergence criteria is investigated in comparison to a fixed termination after the evaluation of 10 000 beam ensembles. In total, our simulations comprise a full fluence optimization for about 3000 000 treatment plans. All four combinatorial BAS strategies yield significant improvements of the objective function value and of the corresponding dose distributions compared to standard beam configurations with equi-spaced coplanar beams. The genetic and the cross-entropy algorithms showed faster convergence in the very beginning of the optimization but the simulated annealing algorithm eventually arrived at almost the same objective function values. These three strategies typically yield clinically equivalent treatment plans. The iterative algorithm showed the worst convergence properties. The choice of the termination criterion had a stronger influence on the performance of the simulated annealing algorithm than on the performance of the genetic and the cross-entropy algorithms. We advocate to terminate the optimization process after the evaluation of 1000 beam combinations without objective function decrease. For our simulations, this resulted in an average deviation of the objective function from the reference value after 10 000 evaluated beam ensembles of 0.5% for all metaheuristics. On average, there was only a minor improvement when increasing the angular resolution in the space of candidate beam angles from 20° to 5°. However, we observed significant improvements when considering non-coplanar candidate beams for challenging head and neck cases.

Design and development of a new micro-beam treatment planning system: effectiveness of algorithms of optimization and dose calculations and potential of micro-beam treatment

A new treatment planning system (TPS) was designed and developed for a new treatment system, which consisted of a micro-beam-enabled linac with robotics and a real-time tracking system. We also evaluated the effectiveness of the implemented algorithms of optimization and dose calculations in the TPS for the new treatment system. In the TPS, the optimization procedure consisted of the pseudo Beam's-Eye-View method for finding the optimized beam directions and the steepest-descent method for determination of beam intensities. We used the superposition-/convolution-based (SC-based) algorithm and Monte Carlo-based (MC-based) algorithm to calculate dose distributions using CT image data sets. In the SC-based algorithm, dose density scaling was applied for the calculation of inhomogeneous corrections. The MC-based algorithm was implemented with Geant4 toolkit and a phase-based approach using a network-parallel computing. From the evaluation of the TPS, the system can optimize the direction and intensity of individual beams. The accuracy of the dose calculated by the SC-based algorithm was less than 1% on average with the calculation time of 15 s for one beam. However, the MC-based algorithm needed 72 min for one beam using the phase-based approach, even though the MC-based algorithm with the parallel computing could decrease multiple beam calculations and had 18.4 times faster calculation speed using the parallel computing. The SC-based algorithm could be practically acceptable for the dose calculation in terms of the accuracy and computation time. Additionally, we have found a dosimetric advantage of proton Bragg peak-like dose distribution in micro-beam treatment.

A set cover approach to fast beam orientation optimization in intensity modulated radiation therapy for total marrow irradiation

The beam orientation optimization (BOO) problem in intensity modulated radiation therapy (IMRT) treatment planning is a nonlinear problem, and existing methods to obtain solutions to the BOO problem are time consuming due to the complex nature of the objective function and size of the solution space. These issues become even more difficult in total marrow irradiation (TMI), where many more beams must be used to cover a vastly larger treatment area than typical site-specific treatments (e.g., head-and-neck, prostate, etc). These complications result in excessively long computation times to develop IMRT treatment plans for TMI, so we attempt to develop methods that drastically reduce treatment planning time. We transform the BOO problem into the classical set cover problem (SCP) and use existing methods to solve SCP to obtain beam solutions. Although SCP is NP-Hard, our methods obtain beam solutions that result in quality treatments in minutes. We compare our approach to an integer programming solver for the SCP to illustrate the speed advantage of our approach.

Inverse planning for four-dimensional (4D) volumetric modulated arc therapy

PURPOSE

To develop a 4D volumetric modulated arc therapy (VMAT) inverse planning framework.

METHODS

4D VMAT inverse planning aims to derive an aperture and weight modulated arc therapy treatment plan that optimizes the accumulated dose distribution from all gantry angles and breathing phases. Under an assumption that the gantry rotation and patient breathing are synchronized (i.e., there is a functional relationship between the phase of the patient breathing cycle and the beam angle), the authors compute the contribution from different respiration phases through the registration of the phased CT images. The accumulative dose distribution is optimized by iteratively adjusting the aperture shape and weight of each beam through the minimization of the planning objective function. For comparison, traditional 3D VMAT plans are also performed for the two cases and the performance of the proposed technique is demonstrated.

RESULTS

A framework for 4D VMAT inverse planning has been proposed. With the consideration of the extra dimension of time in VMAT, a tighter target margin can be achieved with a full duty cycle, which is otherwise not achievable simultaneously by either 3D VMAT optimization or gated VMAT.

CONCLUSIONS

The 4D VMAT planning formulism proposed here provides useful insight on how the "time" dimension can be exploited in rotational arc therapy to maximally compensate for the intrafraction organ motion.

Spherical cluster analysis for beam angle optimization in intensity-modulated radiation therapy treatment planning

An intuitive heuristic to establish beam configurations for intensity-modulated radiation therapy is introduced as an extension of beam ensemble selection strategies applying scalar scoring functions. It is validated by treatment plan comparisons for three intra-cranial, pancreas, and prostate cases each. Based on a patient specific matrix listing the radiological quality of candidate beam directions individually for every target voxel, a set of locally ideal beam angles is generated. The spherical distribution of locally ideal beam angles is characteristic for every treatment site and patient: ideal beam angles typically cluster around distinct orientations. We interpret the cluster centroids, which are identified with a spherical K-means algorithm, as irradiation angles of an intensity-modulated radiation therapy treatment plan. The fluence profiles are subsequently optimized during a conventional inverse planning process. The average computation time for the pre-optimization of a beam ensemble is six minutes on a state-of-the-art work station. The treatment planning study demonstrates the potential benefit of the proposed beam angle optimization strategy. For the three prostate cases under investigation, the standard treatment plans applying nine coplanar equi-spaced beams and treatment plans applying an optimized non-coplanar nine-beam ensemble yield clinically comparable dose distributions. For symmetric patient geometries, the dose distribution formed by nine equi-spaced coplanar beams cannot be improved significantly. For the three pancreas and intra-cranial cases under investigation, the optimized non-coplanar beam ensembles enable better sparing of organs at risk while guaranteeing equivalent target coverage. Beam angle optimization by spherical cluster analysis shows the biggest impact for target volumes located asymmetrically within the patient and close to organs at risk.

Geometrical pre-planning for conformal radiotherapy

The optimum selection of beams and arcs in conformal techniques is of the outmost importance in modern radiotherapy. In this work we give a description of an analytic method to aid optimum selection, which is based on minimizing the intersection between beams and organs at risk (OAR) and on minimizing the intersection between the beam and the planning target volume (PTV). An arc-selection function that permits selection of irradiation arcs based on individual beam feasibility is introduce. The method simulates the treatment process by defining a computed beam feasibility, for every possible set of gantry-table angles, by taking into account accurately computer intersection volumes between the OAR and beams. The beams are shaped to conform the target using realistic parameters for the treatment process. The results are displayed on a virtual sphere centred at the isocenter with color-coded regions indicating beam feasibility. Arcs selections are performed by searching the map for successive gantry positions at a certain table angle, with feasibility values greater than a user-specified threshold. The accuracy of the method was confirmed by using geometrical regular shapes, as well as real clinical cases.

Direct-aperture optimization applied to selection of beam orientations in intensity-modulated radiation therapy

Direct-aperture optimization (DAO) was applied to iterative beam-orientation selection in intensity-modulated radiation therapy (IMRT), so as to ensure a realistic segmental treatment plan at each iteration. Nested optimization engines dealt separately with gantry angles, couch angles, collimator angles, segment shapes, segment weights and wedge angles. Each optimization engine performed a random search with successively narrowing step sizes. For optimization of segment shapes, the filtered backprojection (FBP) method was first used to determine desired fluence, the fluence map was segmented, and then constrained direct-aperture optimization was used thereafter. Segment shapes were fully optimized when a beam angle was perturbed, and minimally re-optimized otherwise. The algorithm was compared with a previously reported method using FBP alone at each orientation iteration. An example case consisting of a cylindrical phantom with a hemi-annular planning target volume (PTV) showed that for three-field plans, the method performed better than when using FBP alone, but for five or more fields, neither method provided much benefit over equally spaced beams. For a prostate case, improved bladder sparing was achieved through the use of the new algorithm. A plan for partial scalp treatment showed slightly improved PTV coverage and lower irradiated volume of brain with the new method compared to FBP alone. It is concluded that, although the method is computationally intensive and not suitable for searching large unconstrained regions of beam space, it can be used effectively in conjunction with prior class solutions to provide individually optimized IMRT treatment plans.

Automated selection of beam orientations and segmented intensity-modulated radiotherapy (IMRT) for treatment of oesophagus tumors

BACKGROUND AND PURPOSE

For some treatment sites, there is evidence in the literature that five to nine equi-angular input beam directions are enough for generating IMRT plans. For oesophagus cancer, there is a report showing that going from four to nine beams may even result in lower quality plans. In this paper, our previously published algorithm for automated beam angle selection (Cycle) has been extended to include segmented IMRT. For oesophagus cancer patients, we have investigated whether automated orientation selection from a large number of equi-angular input beam directions (up to thirty-six) for IMRT optimisation can result in improved lung sparing.

MATERIALS AND METHODS

CT-data from five oesophagus patients treated recently in our institute were used for this study. For a prescribed mean PTV dose of 55 Gy, Cycle was used in an iterative procedure to minimise the mean lung dose under the following hard constraints: standard deviation for PTV dose inhomogeneity 2% (1,1 Gy), maximum spinal cord dose 45 Gy. Conformal radiotherapy (CFRT) and IMRT plans for a standard four field oesophagus beam configuration were compared with IMRT plans generated by automated selection from nine or thirty-six equi-angular input beam orientations. Comparisons were also made with dose distributions generated with our commercial treatment planning system (TPS), and with observations in the literature.

RESULTS

Using Cycle, automated orientation selection from nine or thirty-six input beam directions resulted in improved lung sparing compared to the four field set-ups. Compared to selection from nine input orientations, selection from thirty-six directions did always result in lower mean lung doses, sometimes with even fewer non-zero weight beams. On average only seven beams with a non-zero weight were enough for obtaining the lowest mean lung dose, yielding clinically feasible plans even in case of thirty-six input directions for the optimisation process. With our commercial TPS we observed the same contra-intuitive, unfavourable results as reported in the literature; nine field equi-angular IMRT plans had substantially higher mean lung doses than plans for the conventional four field set-ups. For all cases, the Cycle plans generated from nine equi-angular input directions were superior compared to similar plans generated with our commercial TPS.

CONCLUSIONS

For the studied oesophagus cancer patients the best plans for IMRT were obtained with Cycle, using automated beam orientation selection from thirty-six input beam directions. The lowest mean lung doses could be obtained with, on average, a selection of only seven beams with non-zero weight.

Dose–volume based ranking of incident beam direction and its utility in facilitating IMRT beam placement

PURPOSE

Beam orientation optimization in intensity-modulated radiation therapy (IMRT) is computationally intensive, and various single beam ranking techniques have been proposed to reduce the search space. Up to this point, none of the existing ranking techniques considers the clinically important dose-volume effects of the involved structures, which may lead to clinically irrelevant angular ranking. The purpose of this work is to develop a clinically sensible angular ranking model with incorporation of dose-volume effects and to show its utility for IMRT beam placement.

METHODS AND MATERIALS

The general consideration in constructing this angular ranking function is that a beamlet/beam is preferable if it can deliver a higher dose to the target without exceeding the tolerance of the sensitive structures located on the path of the beamlet/beam. In the previously proposed dose-based approach, the beamlets are treated independently and, to compute the maximally deliverable dose to the target volume, the intensity of each beamlet is pushed to its maximum intensity without considering the values of other beamlets. When volumetric structures are involved, the complication arises from the fact that there are numerous dose distributions corresponding to the same dose-volume tolerance. In this situation, the beamlets are not independent and an optimization algorithm is required to find the intensity profile that delivers the maximum target dose while satisfying the volumetric constraints. In this study, the behavior of a volumetric organ was modeled by using the equivalent uniform dose (EUD). A constrained sequential quadratic programming algorithm (CFSQP) was used to find the beam profile that delivers the maximum dose to the target volume without violating the EUD constraint or constraints. To assess the utility of the proposed technique, we planned a head-and-neck and abdominal case with and without the guidance of the angular ranking information. The qualities of the two types of IMRT plans were compared quantitatively.

RESULTS

An effective angular ranking model with consideration of volumetric effect has been developed. It is shown that the previously reported dose-based angular ranking represents a special case of the general formalism proposed here. Application of the technique to a abdominal and a head-and-neck IMRT case indicated that the proposed technique is capable of producing clinically sensible angular ranking. In both cases, we found that the IMRT plans obtained under the guidance of EUD-based angular ranking were improved in comparison with that obtained using the conventional uniformly spaced beams.

CONCLUSIONS

The EUD-based function is a general approach for angular ranking and allows us to identify the potentially good and bad angles for clinically complicated cases. The ranking can be used either as a guidance to facilitate the manual beam placement or as prior information to speed up the computer search for the optimal beam configuration. Thus the proposed technique should have positive clinical impact in facilitating the IMRT planning process.

Automatic selection of non-coplanar beam directions for three-dimensional conformal radiotherapy

An algorithm is described, based on ray-tracing and the beam's-eye-view, that exhaustively searches all permitted beam directions. The evaluation of the search is based on a general cost function that can be adapted to the clinical objectives by means of parameters and weighting factors. The approach takes into account the constraints of the linear accelerator by discarding beam directions that are not permitted. A sensitivity analysis was carried out to determine appropriate parameters for different sized organs, and a prostate case was used to benchmark the approach. The algorithm was also applied to two clinical cases (brain and sinus) to test the benefits of the approach compared with manual angle selection. The time to perform a beam direction search was approximately 2 min for the coplanar and 12 min for the non-coplanar beam space. The angles obtained for the prostate case compared well with reports in the literature. For the brain case, the mean dose to the right and left optic nerves was reduced by 12% and 50%, respectively, whilst the target dose uniformity was improved. For the sinus case, the mean doses to the right and left parotid glands were reduced by 54% and 46%, respectively, to the right and left optic nerves by 37% and 62%, respectively, and to the optic chiasm by 39%, whilst the target dose uniformity was also improved. For the clinical cases the plans based on optimized beam directions were simpler and resulted in better sparing of critical structures compared with plans based on manual angle selection. The approach provides a practical alternative to elaborate and time consuming beam angle optimization schemes and is suitable for routine clinical usage.

Development of methods for beam angle optimization for IMRT using an accelerated exhaustive search strategy

PURPOSE

The purpose of this article is to explore the use of the accelerated exhaustive search strategy for developing and validating methods for optimizing beam orientations for intensity-modulated radiation therapy (IMRT). Combining beam-angle optimization (BAO) with intensity distribution optimization is expected to improve the quality of IMRT treatment plans. However, BAO is one of the most difficult problems to solve adequately because of the huge hyperspace of possible beam configurations (e.g., selecting 7 of 36 uniformly spaced coplanar beams would require the intercomparison of 8,347,680 IMRT plans).

METHODS AND MATERIALS

An "influence vector" (IV) approximation technique for high-speed estimation of IMRT dose distributions was used in combination with a fast gradient search algorithm (Newton's method) for IMRT optimization. In the IV approximation, it is assumed that the change in intensity of a ray (or bixel) proportionately changes dose along the ray. Evidence is presented that the IV approximation is valid for BAO. The scatter contribution at points away from the ray is accounted for fully in IMRT optimization after the optimum beam orientation has been determined. IVs for all candidate beam angles are generated before the start of optimization. For all subsets of beams selected from a given pool of beams (e.g., 5 of 24 uniformly spaced beams), the distribution of planning scores for the best and the worst plans, optimum angle distributions, dose distributions, and dose-volume histograms (DVH) were analyzed for one prostate and two lung cancer cases. The results of the exhaustive search technique were used to develop a "multiresolution" search strategy. In this approach, a smaller number of beams (e.g., three) is first used to explore the hyperspace of solutions to determine the most preferred and the least preferred directions. The results of such exploration are then used as a starting point for determining an optimum configuration comprising a larger number of beams (e.g., seven). This two-step process is considerably faster than full exhaustive search. The question to be answered was whether the two methods lead to the same or similar solutions. The results of exhaustive search and multiresolution approaches were also compared with a previously published approach that used beam's-eye-view dosimetrics (BEVD).

RESULTS

The relative ranks of plans optimized by an accurate dose calculation method were highly correlated with those of the plans optimized by the fast calculation method (i.e., using the IV approximation), which suggests that an approximate dose calculation algorithm can be used effectively for ranking of plans during BAO. We found that dose distributions and DVH of many beam configurations within a specified subset from a given pool of beams (e.g., 5 of 18) may be clinically indistinguishable and acceptable. Their optimized IMRT scores fall in a narrow range, although beam configurations and dose distributions may be different. We used the frequency distributions as a function of beam angles for the best 100 and the worst 100 plans to determine the most and the least preferred beam angles. We found that the most and the least preferred angle distributions for 3 of 18 configurations were very similar to those for 5, 6, 7, or 8 of 18 or 24 configurations, but the size of the search space was much smaller for the 3 of 18 case. Using fewer than three beams was discovered to be inadequate. This information was used to select the most preferred angles and eliminate the least preferred ones before searching for the optimum angles for the remaining beams. For the cases we studies, the multiresolution strategy produced very similar results to the full exhaustive search. Based on the observation that the worst plans had at least one parallel-opposed pair of beams and virtually all of the best plans had none, we were able to further reduce the size of the search space dramatically by using a pool of only nonparallel-opposed equispaced beams (i.e., 7 of 19 instead of 7 of 36). Another observation was that the probability of finding an optimum configuration in a smaller beam pool is substantially lower than in a larger pool (e.g., 5 of 18 vs. 5 of 24). The implication of this BAO is not very important when a large number of beams (nine or more) is used and vice versa. Our results showed that the plans with fewer but optimally placed beams could be as good as or better than plans using a larger number of unoptimized or uniformly placed beams.

CONCLUSION

Exhaustive search with fast IMRT algorithms provides a novel and realistic approach to study the characteristics of IMRT dose distributions as a function of beam angles and to design practical BAO strategies for IMRT planning.

Planning quality and delivery efficiency of sMLC delivered IMRT treatment of oropharyngeal cancers evaluated by RTOG H-0022 dosimetric criteria

The time required to deliver intensity‐modulated radiation therapy (IMRT) treatments can be significantly longer than conventional treatments, especially for the segmented multileaf collimator (sMLC) delivery system with a large record and verification (R&V) overhead. In this work, we evaluate the impact of the number of intensity‐modulated beams (IMBs) and the number of intensity levels (ILs) on the quality and delivery efficiency of IMRT plans, generated by the Corvus planning system for sMLC delivery on a Siemens LINAC with the Lantis R&V system. Detailed studies were performed for three image data sets of previously treated oropharyngeal patients. Treatment plans for patient 1 were developed using 5, 7, 9, or 15 evenly spaced axial IMBs as well as one with 7 axial IMBs whose directions were user‐selected, each using ILs of 3, 5, 10, or 20. For patients 2 and 3, plans with 15 IMBs and 20 ILs were not attempted. A total of 42 plans were developed using three oropharyngeal cancer CT image data sets. Plan quality was evaluated by assessing compliance with the Radiation Therapy Oncology Group (RTOG) H‐0022 protocol criteria and the physician's clinical judgment. Plan efficiency was accessed by the number of segments of each plan. We found that for our treatment‐planning and delivery system, an IMRT plan that uses a moderate number of IMBs and ILs, such as 7 or 9 IMBs with 3 or 5 ILs, would appear to be the optimal approach when both quality of the plan and delivery efficiency are considered. Based on this study, we have routinely used 9 IMBs with 3 ILs or 7 IMBs with 5 ILs for head and neck patients. A retrospective comparison indicates that delivery efficiency is improved on the order of 30% compared to plans generated with 9 IMBs with 5 ILs.

PACS number: 87.53.Tf

Feasibility study of beam orientation class-solutions for prostate IMRT

IMRT is being increasingly used for treatment of prostate cancer. In practice, however, the beam orientations used for the treatments are still selected empirically, without any guideline. The purpose of this work was to investigate interpatient variation of the optimal beam configuration and to facilitate intensity modulated radiation therapy (IMRT) prostate treatment planning by proposing a set of beam orientation class-solutions for a range of numbers of incident beams. We used fifteen prostate cases to generate the beam orientation class-solutions. For each patient and a given number of incident beams, a multiobjective optimization engine was employed to provide optimal beam directions. For the fifteen cases considered, the gantry angle of any of the optimized plans were all distributed within a certain range The angular distributions of the optimal beams were analyzed and the most selected directions are identified as optimal directions. The optimal directions for all patients are averaged to obtain the class-solution. The class-solution gantry angles for prostate IMRT were found to be: three beams (0 degrees, 120 degrees, 240 degrees), five beams (35 degrees, 110 degrees, 180 degrees, 250 degrees, 325 degrees), six beams (0 degrees, 60 degrees, 120 degrees, 180 degrees, 240 degrees, 300 degrees), seven beams (25 degrees, 75 degrees, 130 degrees, 180 degrees, 230 degrees, 285 degrees, 335 degrees), eight beams (20 degrees, 70 degrees, 110 degrees, 150 degrees, 200 degrees, 250 degrees, 290 degrees, 340 degrees), and nine beams (20 degrees, 60 degrees, 100 degrees, 140 degrees, 180 degrees, 220 degrees, 260 degrees, 300 degrees, 340 degrees). The level of validity of the class-solutions was tested using an additional clinical prostate case by comparing with the individually optimized beam configurations. The difference between the plans obtained with class-solutions and patient-specific optimizations was found to be clinically insignificant.

A dose calculation method including scatter for IMRT optimization

IMRT optimization is an iterative process in which many dose calculations may be necessary. A fast and accurate dose calculation engine is essential for the optimization program to converge to a reliable solution in a reasonable time. Previously we developed a fast dose calculation method for IMRT optimization based on the table lookup (TLP). The TLP kernel is constructed from the dose distributions computed from an accurate superposition/convolution (SC) algorithm at the beginning. Dose calculations at subsequent iterations are performed by looking up the kernel in memory, therefore are very fast. However, it is assumed by the TLP that the beamlet only deposits doses to the voxels on its path. In this paper, we propose an improved table lookup based dose calculation method that includes the scatter contribution (TLPS). The intensity map for each beam is decomposed into an even and an odd checkbox-type pattern for the construction of the kernel for primary and scatter components. The performance of this algorithm is compared with the methods of SC only and TLP without scatter on a few clinical cases and the advantages of speed and accuracy are demonstrated. This method is especially useful for those optimizations that utilize the IMRT optimization as an inner loop, such as the beam angle optimization.

Selection of beam orientations in intensity-modulated radiation therapy using single-beam indices and integer programming

While the process of IMRT planning involves optimization of the dose distribution, the procedure for selecting the beam inputs for this process continues to be largely trial-and-error. We have developed an integer programming (IP) optimization method to optimize beam orientation using mean organ-at-risk (MOD) data from single-beam plans. Two test cases were selected in which one organ-at-risk (OAR) and four OARs were simulated, respectively, along with a PTV. Beam orientation space was discretized in 10 degrees increments. For each beam orientation, a single-beam plan without intensity modulation and without constraints on OAR dose was generated and normalized to yield a mean PTV dose of 2 Gy and the corresponding MOD was calculated. The degree of OAR sparing was related to the average OAR MODs resulting from the beam orientations utilized with improvements of up to 10% at some dose levels. On the other hand, OAR DVHs in the IMRT plans were insensitive to beam numbers (in the 6-9 range) for similar average single-beam MODs. These MOD data were input to an IP optimization process, which then selected specified numbers of beam angles as inputs to a treatment planning system. Our results show that sets of beam angles with lower average single-beam MODs produce IMRT plans with better OAR sparing than manually selected beam angles. To optimize beam orientations, weights were assigned to each OAR following MOD input to the IP which was subsequently solved using the branch-and-cut algorithm. Seven-beam orientations obtained from solving the IP were applied to the test case with four OARs and the resulting plan with a dose prescription of 63 Gy was compared with an equi-spaced beam plan. The IP selected beams produced dose-volume improvements of up to 40% for OARs proximal to the PTV. Further improvement in the DVH can be obtained by increasing the weights assigned to these OARs but at the expense of the remaining OARs.

An algorithm for systematic selection of beam directions for IMRT

Selection of the number of beams and their directions can be an important problem in radiation therapy, especially when a tumor surrounds a critical organ or is surrounded by multiple critical organs. Beam directions, in this sense, are chosen to not only avoid critical organs, but also to achieve better target dose uniformity. In intensity-modulated radiation therapy (IMRT), optimization of beam directions is further complicated due to the dependence of one beam direction on its corresponding beamlet intensities and the beamlet intensities of all other beam directions. The result is an excessively enlarged search space, even when the number of beams is small (two to three). Until now, only a handful of publications exist regarding beam direction optimization in IMRT. Here, we report a new systematic approach that determines a suitable number of "more optimal" beam directions without optimizing a complicated objective function or resorting to brute force. We start by assuming that beam directions chosen for an N-beam plan are candidates for beam directions in the search for an (N + 1)-beam plan. Knowing that beam directions in an N-beam plan are not always the best choices for the (N + 1)-beam plan, we introduce into the beam direction selection process an analysis of the beamlet weights of every beam direction set sampled. If the relative weights of any particular beam compared to other beams are insignificant and hence have no significant effect on the quality of the treatment plan, then we eliminate this beam from the plan. The algorithm terminates basically when the relative weights of the last beam compared to other beams are insignificant or the replacement of an eliminated beam does not improve the plan. This concept was applied to three two-dimensional phantoms and each plan was compared to a standard equally spaced IMRT plan in terms of dose distributions, dose-volume histograms, and objective function values. The results show improvements in both target dose uniformity and critical organ sparing often with a fewer number of beams than standard equally spaced beam plans.

The physical basis of IMRT and inverse planning

Intensity-modulated radiation therapy (IMRT) can sculpt the high-dose volume around the site of disease with hitherto unachievable precision. Conformal avoidance of normal tissues goes hand in hand with this. Inhomogeneous dose painting is possible. The technique has become a clinical reality and is likely to be the dominant approach this decade for improving the clinical practice of photon therapy. This Series will explore all aspects of the "IMRT chain". Only 15 years ago just a handful of physicists were working on this subject. IMRT has developed so rapidly that its recent past is also its ancient history. This article will review the history of IMRT with just a glance at precursors. The physical basis of IMRT is then described including an attempt to introduce the concepts of convex and concave dose distributions, ill-conditioning, inverse-problem degeneracy, cost functions and complex solutions all with a minimum of technical jargon or mathematics. The many techniques for inverse planning are described and the review concludes with a look forward to the future of image-guided IMRT (IG-IMRT).

Dependence of fluence errors in dynamic IMRT on leaf-positional errors varying with time and leaf number

In d-MLC based IMRT, leaves move along a trajectory that lies within a user-defined tolerance (TOL) about the ideal trajectory specified in a d-MLC sequence file. The MLC controller measures leaf positions multiple times per second and corrects them if they deviate from ideal positions by a value greater than TOL. The magnitude of leaf-positional errors resulting from finite mechanical precision depends on the performance of the MLC motors executing leaf motions and is generally larger if leaves are forced to move at higher speeds. The maximum value of leaf-positional errors can be limited by decreasing TOL. However, due to the inherent time delay in the MLC controller, this may not happen at all times. Furthermore, decreasing the leaf tolerance results in a larger number of beam hold-offs, which, in turn leads, to a longer delivery time and, paradoxically, to higher chances of leaf-positional errors (< or = TOL). On the other end, the magnitude of leaf-positional errors depends on the complexity of the fluence map to be delivered. Recently, it has been shown that it is possible to determine the actual distribution of leaf-positional errors either by the imaging of moving MLC apertures with a digital imager or by analysis of a MLC log file saved by a MLC controller. This leads next to an important question: What is the relation between the distribution of leaf-positional errors and fluence errors. In this work, we introduce an analytical method to determine this relation in dynamic IMRT delivery. We model MLC errors as Random-Leaf Positional (RLP) errors described by a truncated normal distribution defined by two characteristic parameters: a standard deviation sigma and a cut-off value deltax0 (deltaxo approximately TOL). We quantify fluence errors for two cases: (i) deltax0 >> sigma (unrestricted normal distribution) and (ii) deltax0 << sigma (deltax0--limited normal distribution). We show that an average fluence error of an IMRT field is proportional to (i) sigma/ALPO and (ii) deltax0/ALPO, respectively, where ALPO is an Average Leaf Pair Opening (the concept of ALPO was previously introduced by us in Med. Phys. 28, 2220-2226 (2001). Therefore, dose errors associated with RLP errors are larger for fields requiring small leaf gaps. For an N-field IMRT plan, we demonstrate that the total fluence error (if we neglect inhomogeneities and scatter) is proportional to 1/square root of N, where N is the number of fields, which slightly reduces the impact of RLP errors of individual fields on the total fluence error. We tested and applied the analytical apparatus in the context of commercial inverse treatment planning systems used in our clinics (Helios and BrainScan). We determined the actual distribution of leaf-positional errors by studying MLC controller (Varian Mark II and Brainlab Novalis MLCs) log files created by the controller after each field delivery. The analytically derived relationship between fluence error and RLP errors was confirmed by numerical simulations. The equivalence of relative fluence error to relative dose error was verified by a direct dose calculation. We also experimentally verified the truthfulness of fluences derived from the log file data by comparing them to film data.

Algorithm and performance of a clinical IMRT beam-angle optimization system

This paper describes the algorithm and examines the performance of an intensity-modulated radiation therapy (IMRT) beam-angle optimization (BAO) system. In this algorithm successive sets of beam angles are selected from a set of predefined directions using a fast simulated annealing (FSA) algorithm. An IMRT beam-profile optimization is performed on each generated set of beams. The IMRT optimization is accelerated by using a fast dose calculation method that utilizes a precomputed dose kernel. A compact kernel is constructed for each of the predefined beams prior to starting the FSA algorithm. The IMRT optimizations during the BAO are then performed using these kernels in a fast dose calculation engine. This technique allows the IMRT optimization to be performed more than two orders of magnitude faster than a similar optimization that uses a convolution dose calculation engine. Any type of optimization criterion present in the IMRT system can be used in this BAO system. An objective function based on clinically-relevant dose-volume (DV) criteria is used in this study. This facilitates the comparison between a BAO plan and the corresponding plan produced by a planner since the latter is usually optimized using a DV-based objective function. A simple prostate case and a complex head-and-neck (HN) case were used to evaluate the usefulness and performance of this BAO method. For the prostate case we compared the BAO results for three, five and seven coplanar beams with those of the same number of equispaced coplanar beams. For the HN case we compare the BAO results for seven and nine non-coplanar beams with that for nine equispaced coplanar beams. In each case the BAO algorithm was allowed to search up to 1000 different sets of beams. The BAO for the prostate cases were finished in about 1-2 h on a moderate 400 MHz workstation while that for the head-and-neck cases were completed in 13-17 h on a 750 MHz machine. No a priori beam-selection criteria have been used in achieving this performance. In both the prostate and the head-and-neck cases, BAO is shown to provide improvements in plan quality over that of the equispaced beams. The use of DV-based objective function also allows us to study the dependence of the improvement of plan quality offered by BAO on the DV criteria used in the optimization. We found that BAO is especially useful for cases that require strong DV criteria. The main advantages of this BAO system are its speed and its direct link to a clinical IMRT system.

Elimination of importance factors for clinically accurate selection of beam orientations, beam weights and wedge angles in conformal radiation therapy

A method of simultaneously optimizing beam orientations, beam weights, and wedge angles for conformal radiotherapy is presented. This method removes the need for importance factors by optimizing one objective only, subject to a set of rigid constraints. This facilitates the production of inverse solutions which, without trial-and-error modification of importance factors, precisely satisfy the specified constraints. The algorithm minimizes an objective function which is based upon the single objective to be optimized, but which is forced to an artificially high value when the constraints are not met, so that only satisfactory solutions are allowed. Due to the complex nature of the objective function space, including multiple local minima separated by large regions of plateau, a random search technique equivalent to fast simulated annealing is used for producing inverse plans. To illustrate the novel features of the new algorithm, a simulation is first presented, for the case of a cylindrical phantom. The morphology of the objective function space is shown to be significantly different for the new algorithm, compared to that for a conventional quadratic objective function. Clinical cases for prostate and craniopharyngioma are then presented. For the prostate case, the objective is to reduce irradiated rectal volume. Three-field, four-field, and six-field optimizations, with or without orientation optimization, are shown to provide solutions which are consistent with previously reported plans and class solutions. For the craniopharyngioma case, which involves the use of a high-precision stereotactic conformal technique, the objective is to reduce the irradiated volume of normal brain. Practically feasible beam angles are produced which, compared to a standard plan, provide a small but worthwhile sparing of normal brain. The algorithm is thereby shown to be robust and suitable for clinical application.

Plug pattern optimization for gamma knife radiosurgery treatment planning

PURPOSE

To develop a novel dose optimization algorithm for improving the sparing of critical structures during gamma knife radiosurgery by shaping the plug pattern of each individual shot.

METHOD AND MATERIALS

We first use a geometric information (medial axis) aided guided evolutionary simulated annealing (GESA) optimization algorithm to determine the number of shots and isocenter location, size, and weight of each shot. Then we create a plug quality score system that checks the dose contribution to the volume of interest by each plug in the treatment plan. A positive score implies that the corresponding source could be open to improve tumor coverage, whereas a negative score means the source could be blocked for the purpose of sparing normal and critical structures. The plug pattern is then optimized via the GESA algorithm that is integrated with this score system. Weight and position of each shot are also tuned in this procedure.

RESULTS

An acoustic tumor case is used to evaluate our algorithm. Compared to the treatment plan generated without plug patterns, adding an optimized plug pattern into the treatment planning process boosts tumor coverage index from 95.1% to 97.2%, reduces RTOG conformity index from 1.279 to 1.167, lowers Paddick's index from 1.34 to 1.20, and trims the critical structure receiving more than 30% maximum dose from 16 mm(3) to 6 mm(3).

CONCLUSIONS

Automated GESA-based plug pattern optimization of gamma knife radiosurgery frees the treatment planning team from the manual forward planning procedure and provides an optimal treatment plan.