Selection of coplanar or noncoplanar beams using three-dimensional optimization based on maximum beam separation and minimized nontarget irradiation

A data-driven approach to optimal beam/arc angle selection for liver stereotactic body radiation therapy treatment planning

BACKGROUND

Stereotactic body radiation therapy (SBRT) for liver cancer has shown promising therapeutic effects. Effective treatment relies not only on the precise delivery provided by image-guided radiation therapy (IGRT) but also high dose gradient formed around the treatment volume to spare functional liver tissue, which is highly dependent on the beam/arc angle selection. In this study, we aim to develop a decision support model to learn human planner's beam navigation approach for beam angle/arc angle selection for liver SBRT.

METHODS

A total of 27 liver SBRT/HIGRT patients (10 IMRT, 17 VMAT/DCA) were included in this study. A dosimetric budget index was defined for each beam angle/control point considering dose penetration through the patient body and liver tissue. Optimal beam angle setting (beam angles for IMRT and start/terminal angle for VMAT/DCA) was determined by minimizing the loss function defined as the sum of total dosimetric budget index and beam span penalty function. Leave-one-out validation was exercised on all 27 cases while weighting coefficients in the loss function was tuned in nested cross validation. To compare the efficacy of the model, a model plan was generated using automatically generated beam setting while retaining the original optimization constraints in the clinical plan. Model plan was normalized to the same planning target volume (PTV) V100% as the clinical plans. Dosimetric endpoints including PTV D98%, D2%, liver V20Gy and total MU were compared between two plan groups. Wilcoxon Signed-Rank test was performed with the null hypothesis being that no difference exists between two plan groups.

RESULTS

Beam setting prediction was instantaneous. Mean PTV D98% was 91.3% and 91.3% (P=0.566), while mean PTV D2% was 107.9% and 108.1% (P=0.164) for clinical plan and model plan respectively. Liver V20Gy showed no significant difference (P=0.590) with 23.3% for clinical plan and 23.4% for the model plan. Total MU is comparable (P=0.256) between the clinical plan (avg. 2,389.6) and model plan (avg. 2,319.6).

CONCLUSIONS

The evidence driven beam setting model yielded similar plan quality as hand-crafted clinical plan. It is capable of capturing human's knowledge in beam selection decision making. This model could facilitate decision making for beam angle selection while eliminating lengthy trial-and-error process of adjusting beam setting during liver SBRT treatment planning.

Comparison of non-coplanar optimization of static beams and arc trajectories for intensity-modulated treatments of meningioma cases

Two methods for non-coplanar beam direction optimization, one for static beams and another for arc trajectories, were proposed for intracranial tumours. The results of the beam angle optimizations were compared with the beam directions used in the clinical plans. Ten meningioma cases already treated were selected for this retrospective planning study. Algorithms for non-coplanar beam angle optimization (BAO) and arc trajectory optimization (ATO) were used to generate the corresponding plans. A plan quality score, calculated by a graphical method for plan assessment and comparison, was used to guide the beam angle optimization process. For each patient, the clinical plans (CLIN), created with the static beam orientations used for treatment, and coplanar VMAT approximated plans (VMAT) were also generated. To make fair plan comparisons, all plan optimizations were performed in an automated multicriteria calculation engine and the dosimetric plan quality was assessed. BAO and ATO plans presented, on average, moderate global plan score improvements over VMAT and CLIN plans. Nevertheless, while BAO and CLIN plans assured a more efficient OARs sparing, the ATO and VMAT plans presented a higher coverage and conformity of the PTV. Globally, all plans presented high-quality dose distributions. No statistically significant quality differences were found, on average, between BAO, ATO and CLIN plans. However, automated plan solution optimizations (BAO or ATO) may improve plan generation efficiency and standardization. In some individual patients, plan quality improvements were achieved with ATO plans, demonstrating the possible benefits of this automated optimized delivery technique.

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.

Linear accelerator-based radiosurgery is associated with lower incidence of radionecrosis compared with gamma knife for treatment of multiple brain metastases

BACKGROUND

Gamma knife (GK) and linear accelerator (LINAC)-based stereotactic radiosurgery (SRS) both offer excellent local control in the management of multiple brain metastases. The efficacy and toxicity of LINAC and GK SRS have not been directly compared in the modern era. We studied outcomes in patients treated with LINAC SRS and GK at two separate institutions.

METHODS

We identified patients treated with either LINAC or GK who were treated to ≥2 lesions and had available follow up. LINAC patients were treated using single-isocenter multitarget technique. We used Cox regression, Fine and Gray competing risks regression, and nearest neighbor propensity score matching to account for confounders and imbalance between cohorts. Kaplan-Meier curves were used to estimate overall survival and rates of radionecrosis.

RESULTS

We identified 391 patients who were treated in 537 courses to a total 2699 lesions (LINAC: 1014, GK: 1685). After propensity score matching, GK was associated with similar overall survival (HR = 0.86; 95% CI 0.59-1.24; p = 0.41) and higher rate of radionecrosis (HR = 3.83; 95% CI 1.66-8.84; p = 0.002) compared to LINAC. In a secondary propensity score matched analysis comparing radionecrosis in single-fraction LINAC and GK, GK remained associated with higher incidence of radionecrosis (HR = 4.42; 95% CI 1.28-15.29; p = 0.019).

CONCLUSIONS

In this multi-institutional study, we found similar overall survival with lower incidence of radionecrosis in patients treated with LINAC compared to GK SRS. These findings are hypothesis generating and should be validated in an independent cohort.

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.

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.

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.

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.

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.

Optimization of beam angles for intensity modulated radiation therapy treatment planning using genetic algorithm on a distributed computing platform

Planning intensity modulated radiation therapy (IMRT) treatment involves selection of several angle parameters as well as specification of structures and constraints employed in the optimization process. Including these parameters in the combinatorial search space vastly increases the computational burden, and therefore the parameter selection is normally performed manually by a clinician, based on clinical experience. We have investigated the use of a genetic algorithm (GA) and distributed-computing platform to optimize the gantry angle parameters and provide insight into additional structures, which may be necessary, in the dose optimization process to produce optimal IMRT treatment plans. For an IMRT prostate patient, we produced the first generation of 40 samples, each of five gantry angles, by selecting from a uniform random distribution, subject to certain adjacency and opposition constraints. Dose optimization was performed by distributing the 40-plan workload over several machines running a commercial treatment planning system. A score was assigned to each resulting plan, based on how well it satisfied clinically-relevant constraints. The second generation of 40 samples was produced by combining the highest-scoring samples using techniques of crossover and mutation. The process was repeated until the sixth generation, and the results compared with a clinical (equally-spaced) gantry angle configuration. In the sixth generation, 34 of the 40 GA samples achieved better scores than the clinical plan, with the best plan showing an improvement of 84%. Moreover, the resulting configuration of beam angles tended to cluster toward the patient's sides, indicating where the inclusion of additional structures in the dose optimization process may avoid dose hot spots. Additional parameter selection in IMRT leads to a large-scale computational problem. We have demonstrated that the GA combined with a distributed-computing platform can be applied to optimize gantry angle selection within a reasonable amount of time.

Simultaneous beam geometry and intensity map optimization in intensity-modulated radiation therapy

PURPOSE

In current intensity-modulated radiation therapy (IMRT) plan optimization, the focus is on either finding optimal beam angles (or other beam delivery parameters such as field segments, couch angles, gantry angles) or optimal beam intensities. In this article we offer a mixed integer programming (MIP) approach for simultaneously determining an optimal intensity map and optimal beam angles for IMRT delivery. Using this approach, we pursue an experimental study designed to (a) gauge differences in plan quality metrics with respect to different tumor sites and different MIP treatment planning models, and (b) test the concept of critical-normal-tissue-ring--a tissue ring of 5 mm thickness drawn around the planning target volume (PTV)--and its use for designing conformal plans.

METHODS AND MATERIALS

Our treatment planning models use two classes of decision variables to capture the beam configuration and intensities simultaneously. Binary (0/1) variables are used to capture "on" or "off" or "yes" or "no" decisions for each field, and nonnegative continuous variables are used to represent intensities of beamlets. Binary and continuous variables are also used for each voxel to capture dose level and dose deviation from target bounds. Treatment planning models were designed to explicitly incorporate the following planning constraints: (a) upper/lower/mean dose-based constraints, (b) dose-volume and equivalent-uniform-dose (EUD) constraints for critical structures, (c) homogeneity constraints (underdose/overdose) for PTV, (d) coverage constraints for PTV, and (e) maximum number of beams allowed. Within this constrained solution space, five optimization strategies involving clinical objectives were analyzed: optimize total intensity to PTV, optimize total intensity and then optimize conformity, optimize total intensity and then optimize homogeneity, minimize total dose to critical structures, minimize total dose to critical structures and optimize conformity simultaneously. We emphasize that the objectives that include optimizing conformity make use of the critical-normal-tissue-ring. Three tumor sites: head-and-neck, pediatric brain, and prostate are used for comparison.

RESULTS

The critical-normal-tissue-ring acts as a good device for enforcing conformity. Trends in the characteristics and quality of plans resulting from each model were observed. Attempts to reduce dose to critical structures tend to worsen PTV conformity (1.542 to 3.092) and homogeneity (1.223 to 1.984), depending on the relative size and spatial distance of the critical structures to the PTV. When the critical structures are relatively small compared with the PTV (as in the case for the pediatric brain tumor, where each is less than 15% in volume), dose reduction to critical structures is accompanied by much worse scores in conformity (2.482) and homogeneity (1.984). When the critical structures are larger, as in the case of head-and-neck (approximately 50%), the conformity and homogeneity deterioration is less significant (1.542 and 1.239, respectively). There is a clear tradeoff between homogeneity, conformity, and minimum dose to organs at risk (OARs). For head-and-neck and pediatric brain tumor, the model that minimizes total dose to critical structures and optimizes conformity simultaneously offers a compromise among these factors, resulting in reduced critical structure dose with conformal and homogeneous plans. In the prostate case, the tumor is smaller than the two large nearby critical structures, and all models provide very homogeneous PTV dose distribution. However, minimizing dose to critical structures worsens conformity, as it spreads the radiation to the area surrounding the PTV. The maximum dose to the critical structures also increases slightly. Compared with plans used in the clinic which generally have uniformly spaced beam angles, the optimal clinically acceptable plans obtained via the methods herein do not have equispaced beams. The optimal beam angles returned appear to be nonintuitive, and depend on PTV size and geometry and the spatial relationship between the tumor and critical structures.

CONCLUSIONS

The MIP model described allows simultaneous optimization over the space of beamlet fluence weights and beam and couch angles. Based on experiments with tumor data, this approach can return good plans that are clinically acceptable and practical. This work distinguishes itself from recent IMRT research in several ways. First, in previous methods beam angles are selected before intensity map optimization. Herein, we employ 0/1 variables to model the set of candidate beams, and thereby allow the optimization process itself to select optimal beams. Second, instead of incorporating dose-volume criteria within the objective function as in previous work, herein, a combination of discrete and continuous variables associated with each voxel provides a mechanism to strictly enforce dose-volume criteria within the constraints. Third, using the construct of critical-normal-tissue-ring within the objective function can enhance the achievement of conformal plans. Based on the three tumor sites considered, it appears that volume and spatial geometry with respect to the PTV are important factors to consider when selecting objectives to optimize, and in estimating how well suited a particular model is for achieving a specified goal.

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.

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.

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.

Geometrically based optimization for extracranial radiosurgery

For static beam conformal intracranial radiosurgery, geometry of the beam arrangement dominates overall dose distribution. Maximizing beam separation in three dimensions decreases beam overlap, thus maximizing dose conformality and gradient outside of the target volume. Webb proposed arrangements of isotropically convergent beams that could be used as the starting point for a radiotherapy optimization process. We have developed an extracranial radiosurgery optimization method by extending Webb's isotropic beam arrangements to deliverable beam arrangements. This method uses an arrangement of N maximally separated converging vectors within the space available for beam delivery. Each bouquet of isotropic beam vectors is generated by a random sampling process that iteratively maximizes beam separation. Next, beam arrangement is optimized for critical structure avoidance while maintaining minimal overlap between beam entrance and exit pathways. This geometrically optimized beam set can then be used as a template for either conformal beam or intensity modulated extracranial radiosurgery. Preliminary results suggest that using this technique with conformal beam planning provides high plan conformality, a steep dose gradient outside of the tumour volume and acceptable critical structure avoidance in the majority of clinical cases.

The clinical value of non-coplanar photon beams in biologically optimized intensity modulated dose delivery on deep-seated tumours

The aim of the present study is to compare the merits of different radiobiologically optimized treatment techniques using few-field planar and non-coplanar dose delivery on an advanced cancer of the cervix, with rectum and bladder as principal organs at risk. Classically, the rational for using non-coplanar beams is to minimize the overlap of beam entrance and exit regions and to find new beam directions avoiding organs at risk, in order to reduce damage to sensitive normal tissues. Two four-beam configurations have been extensively studied. The first consists of three evenly spaced coplanar beams and a fourth non-coplanar beam. A second tetrahedral-like configuration, with two symmetric non-coplanar beams at the same gantry angle and two coplanar beams, with optimized beam directions, was also tested. The present study shows that when radiobiologically optimized intensity modulated beams are applied to such a geometry, only a marginal increase in the treatment outcome can be achieved by non-coplanar beams compared to the optimal coplanar treatment. The main reason for this result is that the high dose in the beam-overlap regions is already optimally reduced by biologically optimized intensity modulation in the plane. The large number of degrees of freedom already incorporated in the treatment by the use of intensity modulation and radiobiological optimization, leads to the saturation of the benefit acquired by a further increase in the degrees of freedom with non-coplanar beams. In conclusion, the use of coplanar radiobiologically optimized intensity modulation simplifies the dose delivery, reducing the need for non-coplanar beam portals.

Optimization of beam orientations and beam weights for conformal radiotherapy using mixed integer programming

An algorithm for optimizing beam orientations and beam weights for conformal radiotherapy has been developed. The algorithm models the optimization of beam orientations and beam weights as a problem of mixed integer linear programming (MILP), and optimizes the beam orientations and beam weights simultaneously. The application process of the algorithm has four steps: (a) prepare a pool of beam orientation candidates with the consideration of avoiding any patient-gantry collision and avoiding direct irradiation of organs at risk with quite low tolerances (e.g., eyes). (b) Represent each beam orientation candidate with a binary variable, and each beam weight with a continuous variable. (c) Set up an optimization problem according to dose prescriptions and the maximum allowed number of beam orientations. (d) Solve the optimization problem with a ready-to-use MILP solver. After optimization, the candidates with unity binary variables remain in the final beam configuration. The performance of the algorithm was tested with clinical cases. Compared with standard treatment plans, the beam-orientation-optimized plans had better dose distributions in terms of target coverage and avoidance of critical structures. The optimization processes took less than 1 h on a PC with a Pentium IV 2.4 GHz processor.

Non-coplanar beam direction optimization for intensity-modulated radiotherapy

An algorithm for the optimization of the direction of intensity-modulated beams is presented. Although the global optimum dose distribution cannot be predicted, usually a large number of equivalent beam configurations exists. This degeneracy facilitates beam direction optimization (BDO) through a number of possible approximations and because the target set of good beam configurations is very large. Usually, the target volume is accessible through a finite number of paths of little resistance, which are defined by the properties of the objective function and the global optimum dose distribution. Since these paths can be occupied by a finite number of beams, it is reasonable to assume that a minimum number of beams for a configuration that is degenerate to the global optimum exists. Efficiency of the BDO will be characterized by detecting this degeneracy threshold. Beam configurations are altered by adding and deleting beams. A fast exhaustive (up to 3500 non-coplanar orientations) search finds beam directions that improve a configuration. Redundant beams of a configuration can be identified by a fast criterion based on second-order derivative information of the objective function. This offers a fast means of iteratively substituting redundant beams from a configuration. Inferior stationary states can be evaded by adding more beams than the desired number to the current configuration, followed by the subsequent cancellation of superfluous beams. The significance of BDO is examined in a coplanar and a non-coplanar test case. The existence of a threshold number for the minimum configuration and its dependence on the complexity of the problem are shown. BDO outperforms manual configurations and equispaced coplanar beam arrangements in both example cases.

Nontumor integral dose variation in conventional radiotherapy treatment planning

Treatment planning involves selecting delivery parameters that distribute the dose to nontumor tissue in such a way as to minimize the risk of complications. This work studied the relationship between nontumor integral dose (NTID), the fractional energy deposited in nontumor tissue, and a variety of delivery parameters for three clinical cases: nasopharynx, pancreas, and prostate. Integral dose for an organ of uniform density is simply the product of the organ density, volume, and mean dose. For each case, conventional plans were generated with 2, 4, 8, 12 and 36 equally spaced beams. All plans were normalized to the same tumor mean dose (< 3%), which is equivalent to the same tumor integral dose. For the pancreas and prostate cases, the patients were assumed to be uniform density. For the nasopharynx case, bones and air cavities were outlined and each assigned a uniform non-unit density. With four or more beams and clinical margin values, the variation in NTID was < 1% as a function of number of beams. With eight or more beams, the variation was < 0.2%. Reducing the beam margin decreased the NTID because less normal tissue was irradiated. However, the effect of the number of beams on NTID was independent of margin size. Higher energy beams reduced the NTID, as expected, and the effect was independent of the number of beams. With four or more beams, variation in beam direction changed NTID by less than 1.5%. Changing beam weights changed NTID by < 2% for plans with four to eight beams. For the body sites studied, the majority of energy was deposited in nontumor tissue, ranging from 72% in the nasopharynx case to 97% for the prostate case. The NTID decreased with increasing tumor size for similar anatomic sizes and increased with increasing size of anatomical region for similar tumor size. Finally, the effect of heterogeneity-corrected doses on the NTID was found to be < 3% for the nasopharynx case. These data support the hypothesis that the NTID is approximately independent of beam orientation or relative weighting when many beams are used. Optimization, therefore, can only find the best distribution of dose; it cannot reduce the energy imparted. NTID may be useful in establishing an upper bound on the quality of plan that can be achieved by optimization.

A geometry based optimization algorithm for conformal external beam radiotherapy

A geometric solution of the problem of optimal orientation of beams in conformal external radiotherapy is presented. The method uses geometric derived quantities which consider the intersection volume between organs at risk (OAR) and the beam shape. In comparison to previous geometric methods a true 3D volume computation is used which takes into account beam divergence, concave shapes, as well as treatment settings such as individual beam shaping by blocks or multi-leaf collimators. For standard dosimetric cost functions used by dose optimization algorithms a corresponding set of geometric objective functions is proposed. We compare the correlations between geometric and dosimetric cost functions for two clinical cases, a prostate and a head tumour case. A correlation is observed for the prostate case, whereas for the head case it is less pronounced due to the larger part of overlapping volumes between the beams which cannot be considered by the used objectives. In comparison to not-optimized beam directions the dose distribution is significantly better for the beam directions found by the optimization of a geometric multi-objective cost function. An optimal dose distribution can easily be achieved using the geometric model. This is shown by comparing for the two cases the dose-volume histograms (DVH) of manually optimized plans by experienced planners and the DVHs of the geometrically found optimal solutions. In comparison to the manually optimized plans the solutions found by the geometric method significantly reduce the average dose in the OARs and NT, while maintaining the same PTV coverage. The optimization requires only a few seconds and could be used to improve the performance of inverse planning algorithms in radiotherapy for the determination of the optimal direction of beams.

Beam orientation selection for intensity-modulated radiation therapy based on target equivalent uniform dose maximization

PURPOSE

To develop an automated beam-orientation selection procedure for intensity-modulated radiotherapy (IMRT), and to determine if a small number of beams picked by this automated procedure can yield results comparable to a large number of manually placed orientations.

METHODS AND MATERIALS

The automated beam selection procedure maximizes an unconstrained objective function composed of target equivalent uniform dose (EUD) and critical structure dose-volume histogram (DVH) constraints. Beam orientations are selected from a large feasible set of directions through a series of alternating fluence optimization and orientation alteration steps, until convergence to a stable orientation set. The fluence optimization step adjusts fluences to maximize the objective function. The orientation alteration step substitutes beams in the orientation set currently under consideration with beams of the parent set in the immediate angular vicinity; the altered orientation set is deemed current if it produces a higher objective function value in the fluence optimization step.

RESULTS AND CONCLUSIONS

It is demonstrated, for prostate IMRT planning, that a modest number of appropriately selected beam orientations (3 or 5) can provide dose distributions as satisfactory as those produced by a large number of unselected equispaced orientations. Such selected beam orientations can reduce overall treatment time, thus making IMRT more clinically practical.

Dose optimization via index-dose gradient minimization

This paper presents an iterative optimization algorithm based on gradient minimization of index dose, defined as the product of physical dose and a numerical index. Acting as a template the index distribution is designed to represent the dosimetry that meets the dose volume histogram-based optimization objectives. The treatment dosimetry is optimized when the uniformity of the index-dose distribution is maximized. Prior to optimization the user can select all or only some of the beams to be intensity modulated. The remaining unmodulated beams can be either open or wedged photon beams, electron beams, or beams of previous treatments. The optimization result and treatment delivery efficiency can often be enhanced by including not only the IM photon beams but also all suitable fixed-beams available on the linac in the treatment plan. In addition, the doses from previous treatments can also be considered in the optimization of current treatment. Five clinical examples with different complexities in optimization objective are presented. The effects of two nonoptimization variables, beam setup and initial beam weights, on the quality of the dose optimization are also presented. The results are analyzed in terms of isodose distribution, dose volume histograms, and a dose optimization quality factor. The optimization algorithm, implemented in our in-house TPS PLanUNC, has been used in clinical application since 1996. The primary advantages of our optimization algorithm include computational efficiency, intensity modulation selection choice, and performance reliability for a wide range of clinical beam setups and optimization objectives.

Intensity modulation technique using the complementary boost-fields for ethmoid sinus cancer

PURPOSE

To explore a static intensity-modulated radiation therapy (IMRT) technique of a more homogeneous isodose distribution to an irregular-shaped tumour of the ethmoid sinus, with concomitantly sparing the adjacent critical normal organs including the orbit.

METHODS AND MATERIALS

We conducted a static IMRT technique adding 2 or smaller complementary boost-fields to the underdosed volume in the PTV, which resulted from complete blocking of the orbits in all coplanar or non-coplanar main ports of the standard 3-D CRT. The standard 3-D CRT plans (Plan A) and IMRT plans adding complementary boost fields (Plan B) were established for 10 patients with ethmoid sinus cancer. Two sets of different plans for each patient were compared using isodose distribution, dose statistics, and dose volume histogram (DVH) of the planning target volume (PTV) and also using dose statistics and DVH of the adjacent critical structures.

RESULTS

The IMRT plans adding 2 or more complementary boost-fields (Plan B) for each patient demonstrated better coverage and improved dose homogeneity of the PTV compared to the standard 3-D CRT plan (Plan A). Moreover, the radiation doses to adjacent normal tissue organs, such as the orbits, optic nerves, brain stem and optic chiasm were similarly spared in both plans.

CONCLUSION

With concomitantly sparing the surrounding visual pathway structures, our IMRT technique using the complementary boost-fields was quantitatively better than current standard 3-D CRT technique with respect to the dose homogeneity within the PTV. Therefore, we believe that our technique, though still not ideal, is thorough enough to be used routinely in treatment of ethmoid sinus tumour.

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

PURPOSE

To introduce the concept of pseudo beam's-eye-view (pBEV), to establish a framework for computer-assisted beam orientation selection in intensity-modulated radiation therapy (IMRT), and to evaluate the utility of the proposed technique.

METHODS AND MATERIALS

To facilitate the selection of beam orientations for IMRT treatment planning, a scoring of beam direction was introduced. The score function was based on the maximum target dose deliverable by the beam without exceeding the tolerance doses of the critical structures. For the score function calculation, the beam portal at given gantry and couch angles was divided into a grid of beamlets. Each beamlet crossing the target was assigned the maximum intensity that could be used without exceeding the dose tolerances of the organs at risk (OARs) and normal tissue. Thereafter, a score was assigned to the beam according to the target dose delivered. The beams for the treatment were selected among those with the highest scores. In a sense, this technique is similar to the beam's-eye-view approach used in conventional radiation therapy, except that the evaluation by a human is replaced by a score function, and beam modulation is taken into account.

RESULTS

The pBEV technique was tested on two clinical cases: a paraspinal treatment and a nasopharyngeal cancer with both coplanar and noncoplanar beam configurations. The plans generated under the guidance of pBEV for the paraspinal treatment offered superior target dose uniformity and reduced OAR doses. For the nasopharyngeal cancer case, it was also found that the pBEV-selected coplanar and noncoplanar beams significantly improved the target coverage without compromising the sparing of the OARs.

CONCLUSIONS

The pBEV technique developed in this work provides a comprehensive tool for beam orientation selection in IMRT. It is especially valuable for complicated cases, where the target is surrounded by several sensitive structures and where it is difficult to select a set of good beam orientations. The pBEV technique has considerable potential for simplifying the IMRT treatment planning process and for maximizing the technical capacity of IMRT.

Isotropic beam bouquets for shaped beam linear accelerator radiosurgery

In stereotactic radiosurgery and radiotherapy treatment planning, the steepest dose gradient is obtained by using beam arrangements with maximal beam separation. We propose a treatment plan optimization method that optimizes beam directions from the starting point of a set of isotropically convergent beams, as suggested by Webb. The optimization process then individually steers each beam to the best position, based on beam's-eye-view (BEV) critical structure overlaps with the target projection and the target's projected cross sectional area at each beam position. This final optimized beam arrangement maintains a large angular separation between adjacent beams while conformally avoiding critical structures. As shown by a radiosurgery plan, this optimization method improves the critical structure sparing properties of an unoptimized isotropic beam bouquet, while maintaining the same degree of dose conformity and dose gradient. This method provides a simple means of designing static beam radiosurgery plans with conformality indices that are within established guidelines for radiosurgery planning, and with dose gradients that approach those achieved in conventional radiosurgery planning.

Computer-assisted selection of coplanar beam orientations in intensity-modulated radiation therapy

In intensity-modulated radiation therapy (IMRT), the incident beam orientations are often determined by a trial and error search. The conventional beam's-eye view (BEV) tool becomes less helpful in IMRT because it is frequently required that beams go through organs at risk (OARs) in order to achieve a compromise between the dosimetric objectives of the planning target volume (PTV) and the OARs. In this paper, we report a beam's-eye view dosimetrics (BEVD) technique to assist in the selection of beam orientations in IMRT. In our method, each beam portal is divided into a grid of beamlets. A score function is introduced to measure the 'goodness' of each beamlet at a given gantry angle. The score is determined by the maximum PTV dose deliverable by the beamlet without exceeding the tolerance doses of the OARs and normal tissue located in the path of the beamlet. The overall score of the gantry angle is given by a sum of the scores of all beamlets. For a given patient. the score function is evaluated for each possible beam orientation. The directions with the highest scores are then selected as the candidates for beam placement. This procedure is similar to the BEV approach used in conventional radiation therapy, except that the evaluation by a human is replaced by a score function to take into account the intensity modulation. This technique allows one to select beam orientations without the excessive computing overhead of computer optimization of beam orientation. It also provides useful insight into the problem of selection of beam orientation and is especially valuable for complicated cases where the PTV is surrounded by several sensitive structures and where it is difficult to select a set of 'good' beam orientations. Several two-dimensional (2D) model cases were used to test the proposed technique. The plans obtained using the BEVD-selected beam orientations were compared with the plans obtained using equiangular spaced beams. For all the model cases investigated, the use of BEVD-selected beam orientations improved the dose distributions significantly. These examples indicate that the technique has considerable potential for simplifying the IMRT treatment planning process and allows for better utilization of the technical capacity of IMRT.

Role of beam orientation optimization in intensity-modulated radiation therapy

PURPOSE

To investigate the role of beam orientation optimization in intensity-modulated radiation therapy (IMRT) and to examine the potential benefits of noncoplanar intensity-modulated beams.

METHODS AND MATERIALS

A beam orientation optimization algorithm was implemented. For this purpose, system variables were divided into two groups: beam position (gantry and table angles) and beam profile (beamlet weights). Simulated annealing was used for beam orientation optimization and the simultaneous iterative inverse treatment planning algorithm (SIITP) for beam intensity profile optimization. Three clinical cases were studied: a localized prostate cancer, a nasopharyngeal cancer, and a paraspinal tumor. Nine fields were used for all treatments. For each case, 3 types of treatment plan optimization were performed: (1) beam intensity profiles were optimized for 9 equiangular spaced coplanar beams; (2) orientations and intensity profiles were optimized for 9 coplanar beams; (3) orientations and intensity profiles were optimized for 9 noncoplanar beams.

RESULTS

For the localized prostate case, all 3 types of optimization described above resulted in dose distributions of a similar quality. For the nasopharynx case, optimized noncoplanar beams provided a significant gain in the gross tumor volume coverage. For the paraspinal case, orientation optimization using noncoplanar beams resulted in better kidney sparing and improved gross tumor volume coverage.

CONCLUSION

The sensitivity of an IMRT treatment plan with respect to the selection of beam orientations varies from site to site. For some cases, the choice of beam orientations is important even when the number of beams is as large as 9. Noncoplanar beams provide an additional degree of freedom for IMRT treatment optimization and may allow for notable improvement in the quality of some complicated plans.

Optimization of radiosurgery treatment planning via mixed integer programming

An automated optimization algorithm based on mixed integer programming techniques is presented for generating high-quality treatment plans for LINAC radiosurgery treatment. The physical planning in radiosurgery treatment involves selecting among a large collection of beams with different physical parameters an optimal beam configuration (geometries and intensities) to deliver the clinically prescribed radiation dose to the tumor volume while sparing the nearby critical structure and normal tissue. The proposed mixed integer programming models incorporate strict dose restrictions on tumor volume, and constraints on the desired number of beams, isocenters, couch angles, and gantry angles. The model seeks to deliver full prescription dose coverage and uniform radiation dose to the tumor volume while minimizing the excess radiation to the periphery normal tissue. In particular, it ensures that proximal normal tissues receive minimal dose via rapid dose fall-off. Preliminary numerical tests on a single patient case indicate that this approach can produce exceptionally high-quality plans in a fraction of the time required using the procedure currently employed by clinicians. The resulting plans provide highly uniform prescription dose to the tumor volume while drastically reducing the irradiation received by the proximal critical normal tissue.

The development of target-eye-view maps for selection of coplanar or noncoplanar beams in conformal radiotherapy treatment planning

Three-dimensional conformal radiotherapy allows the use of tightly conformed, multiple coplanar or noncoplanar beams. However, visualizing the spatial relationships between the target volume and adjacent critical structures is not always obvious or intuitive. Tools such as beam's eye view (BEV) have aided in this process and been very useful. In this study, a target-eye-view (TEV) map is developed as a functional extension of BEVs. The TEV map for a critical structure is created by checking the BEVs for all gantries and table rotations. For each possible BEV, the amount of overlap between the planning target volume (PTV) and the organ at risk (OAR) is determined. This information is presented in a Mercator spherical map, where the color tone indicates the amount of overlap between the PTV and the OAR. A composite TEV map is then created by summing the TEV grading scores for all OARs. The composite map shows beam orientations with the most overlap being light and the least overlap being dark, thus simplifying the selection of appropriate beam angles. The accuracy of the TEV maps has been confirmed separately with corresponding BEVs generated by a three-dimensional treatment planning system.

Constrained customization of non-coplanar beam orientations in radiotherapy of brain tumours

A methodology for the constrained customization of non-coplanar beam orientations in radiotherapy treatment planning has been developed and tested on a cohort of five patients with tumours of the brain. The methodology employed a combination of single and multibeam cost functions to produce customized beam orientations. The single-beam cost function was used to reduce the search space for the multibeam cost function, which was minimized using a fast simulated annealing algorithm. The scheme aims to produce well-spaced, customized beam orientations for each patient that produce low dose to organs at risk (OARs). The customized plans were compared with standard plans containing the number and orientation of beams chosen by a human planner. The beam orientation constraint-customized plans employed the same number of treatment beams as the standard plan but with beam orientations chosen by the constrained-customization scheme. Improvements from beam orientation constraint-customization were studied in isolation by customizing the beam weights of both plans using a dose-based downhill simplex algorithm. The results show that beam orientation constraint-customization reduced the maximum dose to the orbits by an average of 18.8 (+/-3.8, ISD)% and to the optic nerves by 11.4 (+/-4.8, ISD)% with no degradation of the planning target volume (PTV) dose distribution. The mean doses, averaged over the patient cohort, were reduced by 4.2 (+/-1.1, ISD)% and 12.4 (+/-3.1, ISD)% for the orbits and optic nerves respectively. In conclusion, the beam orientation constraint-customization can reduce the dose to OARs, for few-beam treatment plans, when compared with standard treatment plans developed by a human planner.

[Progress in dosage optimization for stereotactic radiosurgery]

Stereotactic radiosurgery is a technique for treatment of intracranial lesions requiring high precision in all steps--from image acquisition to final irradiation. One of most difficult steps is the treatment planning phase, consisting of determination of irradiation parameters sufficient to cover the target volume by avoiding sensitive volumes. A manual and empirical definition can be very long and difficult, especially in the case of complex target volumes situated in sensitive zones. As in conventional radiotherapy, stereotactic radiosurgery has taken advantages from dosimetric optimization. The question is: "What is the configuration of irradiation parameters used in order to obtain the treatment plan by satisfying defined constraints?". The purpose of this article is to summarize optimization methods used in radiosurgery and to describe the technical alternatives proposed for this treatment as well as the possibilities of plan evaluation between different techniques. This purpose will be illustrated by the optimization methodology used in the Center Oscar Lambret of Lille, France for the radiosurgical treatment with linear accelerator.