A case study comparing the relative benefit of optimizing beam weights, wedge angles, beam orientations and tomotherapy in stereotactic radiotherapy of the brain

Knowledge-light adaptation approaches in case-based reasoning for radiotherapy treatment planning

OBJECTIVE

Radiotherapy treatment planning aims at delivering a sufficient radiation dose to cancerous tumour cells while sparing healthy organs in the tumour-surrounding area. It is a time-consuming trial-and-error process that requires the expertise of a group of medical experts including oncologists and medical physicists and can take from 2 to 3h to a few days. Our objective is to improve the performance of our previously built case-based reasoning (CBR) system for brain tumour radiotherapy treatment planning. In this system, a treatment plan for a new patient is retrieved from a case base containing patient cases treated in the past and their treatment plans. However, this system does not perform any adaptation, which is needed to account for any difference between the new and retrieved cases. Generally, the adaptation phase is considered to be intrinsically knowledge-intensive and domain-dependent. Therefore, an adaptation often requires a large amount of domain-specific knowledge, which can be difficult to acquire and often is not readily available. In this study, we investigate approaches to adaptation that do not require much domain knowledge, referred to as knowledge-light adaptation.

METHODOLOGY

We developed two adaptation approaches: adaptation based on machine-learning tools and adaptation-guided retrieval. They were used to adapt the beam number and beam angles suggested in the retrieved case. Two machine-learning tools, neural networks and naive Bayes classifier, were used in the adaptation to learn how the difference in attribute values between the retrieved and new cases affects the output of these two cases. The adaptation-guided retrieval takes into consideration not only the similarity between the new and retrieved cases, but also how to adapt the retrieved case.

RESULTS

The research was carried out in collaboration with medical physicists at the Nottingham University Hospitals NHS Trust, City Hospital Campus, UK. All experiments were performed using real-world brain cancer patient cases treated with three-dimensional (3D)-conformal radiotherapy. Neural networks-based adaptation improved the success rate of the CBR system with no adaptation by 12%. However, naive Bayes classifier did not improve the current retrieval results as it did not consider the interplay among attributes. The adaptation-guided retrieval of the case for beam number improved the success rate of the CBR system by 29%. However, it did not demonstrate good performance for the beam angle adaptation. Its success rate was 29% versus 39% when no adaptation was performed.

CONCLUSIONS

The obtained empirical results demonstrate that the proposed adaptation methods improve the performance of the existing CBR system in recommending the number of beams to use. However, we also conclude that to be effective, the proposed adaptation of beam angles requires a large number of relevant cases in the case base.

Beam geometry selection using sequential beam addition

PURPOSE

The selection of optimal beam geometry has been of interest since the inception of conformal radiotherapy. The authors report on sequential beam addition, a simple beam geometry selection method, for intensity modulated radiation therapy.

METHODS

The sequential beam addition algorithm (SBA) requires definition of an objective function (score) and a set of candidate beam geometries (pool). In the first iteration, the optimal score is determined for each beam in the pool and the beam with the best score selected. In the next iteration, the optimal score is calculated for each beam remaining in the pool combined with the beam selected in the first iteration, and the best scoring beam is selected. The process is repeated until the desired number of beams is reached. The authors selected three treatment sites, breast, lung, and brain, and determined beam arrangements for up to 11 beams from a pool comprised of 25 equiangular transverse beams. For the brain, arrangements were additionally selected from a pool of 22 noncoplanar beams. Scores were determined for geometries comprised equiangular transverse beams (EQA), as well as two tangential beams for the breast case.

RESULTS

In all cases, SBA resulted in scores superior to EQA. The breast case had the strongest dependence on beam geometry, for which only the 7-beam EQA geometry had a score better than the two tangential beams, whereas all SBA geometries with more than two beams were superior. In the lung case, EQA and SBA scores monotonically improved with increasing number of beams; however, SBA required fewer beams to achieve scores equivalent to EQA. For the brain case, SBA with a coplanar pool was equivalent to EQA, while the noncoplanar pool resulted in slightly better scores; however, the dose-volume histograms demonstrated that the differences were not clinically significant.

CONCLUSIONS

For situations in which beam geometry has a significant effect on the objective function, SBA can identify arrangements equivalent to equiangular geometries but using fewer beams. Furthermore, SBA provides the value of the objective function as the number of beams is increased, allowing the planner to select the minimal beam number that achieves the clinical goals. The method is simple to implement and could readily be incorporated into an existing optimization system.

Guaranteed epsilon-optimal treatment plans with the minimum number of beams for stereotactic body radiation therapy

Stereotactic body radiation therapy (SBRT) is characterized by delivering a high amount of dose in a short period of time. In SBRT the dose is delivered using open fields (e.g., beam's-eye-view) known as 'apertures'. Mathematical methods can be used for optimizing treatment planning for delivery of sufficient dose to the cancerous cells while keeping the dose to surrounding organs at risk (OARs) minimal. Two important elements of a treatment plan are quality and delivery time. Quality of a plan is measured based on the target coverage and dose to OARs. Delivery time heavily depends on the number of beams used in the plan as the setup times for different beam directions constitute a large portion of the delivery time. Therefore the ideal plan, in which all potential beams can be used, will be associated with a long impractical delivery time. We use the dose to OARs in the ideal plan to find the plan with the minimum number of beams which is guaranteed to be epsilon-optimal (i.e., a predetermined maximum deviation from the ideal plan is guaranteed). Since the treatment plan optimization is inherently a multi-criteria-optimization problem, the planner can navigate the ideal dose distribution Pareto surface and select a plan of desired target coverage versus OARs sparing, and then use the proposed technique to reduce the number of beams while guaranteeing epsilon-optimality. We use mixed integer programming (MIP) for optimization. To reduce the computation time for the resultant MIP, we use two heuristics: a beam elimination scheme and a family of heuristic cuts, known as 'neighbor cuts', based on the concept of 'adjacent beams'. We show the effectiveness of the proposed technique on two clinical cases, a liver and a lung case. Based on our technique we propose an algorithm for fast generation of epsilon-optimal plans.

Multibeam tomotherapy: a new treatment unit devised for multileaf collimation, intensity-modulated radiation therapy

A fully integrated system for treatment planning, application, and verification for automated multileaf collimator (MLC) based, intensity-modulated, image-guided, and adaptive radiation therapy (IMRT, IGRT and ART, respectively) is proposed. Patient comfort, which was the major development goal, will be achieved through a new unit design and short treatment times. Our device for photon beam therapy will consist of a new dual energy linac with five fixed treatment heads positioned evenly along one plane but one electron beam generator only. A minimum of moving parts increases technical reliability and reduces motion times to a minimum. Motion is allowed solely for the MLCs, the robotic patient table, and the small angle gantry rotation of +/- 36 degrees. Besides sophisticated electron beam guidance, this compact setup can be built using existing modules. The flattening-filter-free treatment heads are characterized by reduced beam-on time and contain apertures restricted in one dimension to the area of maximum primary fluence output. In the case of longer targets, this leads to a topographic intensity modulation, thanks to the combination of "step and shoot" MLC delivery and discrete patient couch motion. Owing to the limited number of beam directions, this multislice cone beam serial tomotherapy is referred to as "multibeam tomotherapy." Every patient slice is irradiated by one treatment head at any given moment but for one subfield only. The electron beam is then guided to the next head ready for delivery, while the other heads are preparing their leaves for the next segment. The "Multifocal MLC-positioning" algorithm was programmed to enable treatment planning and optimize treatment time. We developed an overlap strategy for the longitudinally adjacent fields of every beam direction, in doing so minimizing the field match problem and the effects of possible table step errors. Clinical case studies show for the same or better planning target volume coverage, better organ-at-risk sparing, and comparable mean integral dose to the normal tissue a reduction in treatment time by more than 50% to only a few minutes in comparison to high-quality 3-D conformal and IMRT treatments. As a result, it will be possible to incorporate features for better patient positioning and image guidance, while sustaining reasonable overall treatment times at the same time. The virtual multibeam tomotherapy design study TOM'5-CT contains a dedicated electron beam CT (TOM'AGE) and an objective optical topometric patient positioning system (TOPOS). Thanks to the wide gantry bore of 120 cm and slim gantry depths of 70 cm, patients can be treated very comfortably, in all cases tumor-isocentrically, as well as with noncoplanar beam arrangements as in stereotactic radiosurgery with a couch rotation of up to +/- 54 degrees. The TOM'5 treatment unit on which this theoretical concept is based has a stand-alone depth of 40 cm and an outer diameter of 245 cm; the focus-isocenter distance of the heads is 100 cm with a field size of 40 cm x 7 cm and 0.5 cm leaves, which operate perpendicular to the axis of table motion.

A telerobotic haptic system for minimally invasive stereotactic neurosurgery

Medical robotics and computer assisted surgery are feasible and promising applications of robotic technology, whose main goals are surgical augmentation, information enhancement and improved surgical action. Neurosurgery probably presents the most major challenges, and can considerably benefit from the introduction of computers and robots to guide surgical procedures. This paper presents an innovative master-slave haptic robotic system for minimally invasive neurosurgery, which can help surgeons overcome human shortcomings and perform more accurate, repeatable, and reliable stereotactic neurosurgery. The system, named LANS, consists of a slave mechatronic actuator and a haptic master. The slave is designed to move linearly a laser pointer, a biopsy needle or a low-energy X-ray emitter along a pre-planned axis. The tool insertion into the brain is guided by the surgeon through the haptic master which also provides force feedback to the operator. Not only can the haptic master reproduce the contact force between the surgical tool and the treated tissue, but it can also produce virtual forces aimed at assisting surgeons during the operations. Experiments have been conducted to prove the soundness and accuracy of the overall system mechanical design and to assess the effectiveness of the control schemes synthesized for the master and the slave.

Comparison of linac based fractionated stereotactic radiotherapy and tomotherapy treatment plans for skull-base tumors

BACKGROUND AND PURPOSE

To compare and evaluate helical tomotherapy and linac based fractionated stereotactic radiotherapy (FSRT) techniques in the treatment of skull-base tumors.

PATIENTS AND METHODS

Ten patients diagnosed with skull-base tumors, originally planned for optically guided FSRT to prescribed doses of 50.4-54 Gy were replanned for treatment with clinically deliverable helical tomotherapy. All original CT scans, MR-CT fusion defined target and normal structure contours, and PTV margins were used for helical tomotherapy planning. Linac based plans utilized one of the following FSRT planning techniques: non-coplanar or coplanar intensity modulated radiation therapy (IMRT), multiple non-coplanar conformal arcs, and non-coplanar conformal radiation therapy (CRT). These plans were used as the standard to which the subsequent tomotherapy plans were compared, using the following criteria: prescription isodose to target volume (PITV) ratios, an inhomogeneity index (II), equivalent uniform dose (EUD) for PTV volumes, mean normalized total doses (NTDmean) for critical structures, and size of 10, 20, and 30 Gy isodose volumes.

RESULTS

Use of both linac based FSRT techniques and helical tomotherapy generated highly conformal treatment plans. Tomotherapy plans, which are predominantly coplanar in nature, compared to non-coplanar linac based plans exhibited increased PITV ratios, variable change in II, similar EUD values, and generally comparable NTD(mean) values for organs at risk. When compared to non-coplanar field arrangements, deliverable (as opposed to idealized) tomotherapy plans also resulted in 13-540% increases in low dose isodose volumes. All criteria except for the II, which was generally improved with tomotherapy, were found to be similar when coplanar linac based plans were compared to helical tomotherapy plans.

CONCLUSIONS

Results show a distinct advantage in using non-coplanar beam arrangements for treatment of skull-base tumors. In the case where disease spreads far inferiorly, limiting the ability to use non-coplanar arrangements, helical tomotherapy can be used to generate a comparable treatment plan, with potentially superior homogeneity.

A simple and reliable index for scoring rival stereotactic radiosurgery plans

PURPOSE

A simple and robust index for ranking rival stereotactic radiosurgery plans is presented.

METHODS

The radiosurgery plan score index, CGI (Conformity/Gradient Index), is an average of a conformity score and a gradient score. Computation of the CGI score is simple, requiring only three pieces of data: (1) the total volume irradiated to the prescription isodose level, (2) the volume of the target, and (3) the total volume irradiated at half of the prescription isodose level. The overall CGI Index is a simple function of these three pieces of data.

RESULTS

When multiple sets of rival stereotactic radiosurgery plans were ranked with respect to this single score index, the resulting plan rankings closely matched the plan rankings according to biologic indices (calculated nontarget brain normal tissue complication probabilities).

CONCLUSIONS

The CGI is a simple and fast plan evaluation tool that can assist the radiosurgery planner in evaluating and optimizing multiple candidate radiosurgery plans.

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.

Configuration space analysis of common cost functions in radiotherapy beam-weight optimization algorithms

The successful implementation of downhill search engines in radiotherapy optimization algorithms depends on the absence of local minima in the search space. Such techniques are much faster than stochastic optimization methods but may become trapped in local minima if they exist. A technique known as 'configuration space analysis' was applied to examine the search space of cost functions used in radiotherapy beam-weight optimization algorithms. A downhill-simplex beam-weight optimization algorithm was run repeatedly to produce a frequency distribution of final cost values. By plotting the frequency distribution as a function of final cost, the existence of local minima can be determined. Common cost functions such as the quadratic deviation of dose to the planning target volume (PTV), integral dose to organs-at-risk (OARs), dose-threshold and dose-volume constraints for OARs were studied. Combinations of the cost functions were also considered. The simple cost function terms such as the quadratic PTV dose and integral dose to OAR cost function terms are not susceptible to local minima. In contrast, dose-threshold and dose-volume OAR constraint cost function terms are able to produce local minima in the example case studied.

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.

Simultaneous optimization of beam orientations and beam weights in conformal radiotherapy

A methodology for the concurrent optimization of beam orientations and beam weights in conformal radiotherapy treatment planning has been developed and tested on a cohort of five patients. The algorithm is based on a beam-weight optimization scheme with a downhill simplex optimization engine. The use of random voxels in the dose calculation provides much of the required speed up in the optimization process, and allows the simultaneous optimization of beam orientations and beam weights in a reasonable time. In the implementation of the beam-weight optimization algorithm just 10% of the original patient voxels are used for the dose calculation and cost function evaluation. A fast simulated annealing algorithm controls the optimization of the beam arrangement. The optimization algorithm was able to produce clinically acceptable plans for the five patients in the cohort study. The algorithm equalized the dose to the optic nerves compared to the standard plans and reduced the mean dose to the brain stem by an average of 4.4% (+/- 1.9, 1 SD), p value = 0.007. The dose distribution to the PTV was not compromised by developing beam arrangements via the optimization algorithm. In conclusion, the simultaneous optimization of beam orientations and beam weights has been developed to be routinely used in a realistic time. The results of optimization in a small cohort study show that the optimization can reliably produce clinically acceptable dose distributions and may be able to improve dose distributions compared to those from a human planner.

A geometrically based method for automated radiosurgery planning

PURPOSE

A geometrically based method of multiple isocenter linear accelerator radiosurgery treatment planning optimization was developed, based on a target's solid shape.

METHODS AND MATERIALS

Our method uses an edge detection process to determine the optimal sphere packing arrangement with which to cover the planning target. The sphere packing arrangement is converted into a radiosurgery treatment plan by substituting the isocenter locations and collimator sizes for the spheres.

RESULTS

This method is demonstrated on a set of 5 irregularly shaped phantom targets, as well as a set of 10 clinical example cases ranging from simple to very complex in planning difficulty. Using a prototype implementation of the method and standard dosimetric radiosurgery treatment planning tools, feasible treatment plans were developed for each target. The treatment plans generated for the phantom targets showed excellent dose conformity and acceptable dose homogeneity within the target volume. The algorithm was able to generate a radiosurgery plan conforming to the Radiation Therapy Oncology Group (RTOG) guidelines on radiosurgery for every clinical and phantom target examined.

CONCLUSIONS

This automated planning method can serve as a valuable tool to assist treatment planners in rapidly and consistently designing conformal multiple isocenter radiosurgery treatment plans.

Optimum beam configurations in tomographic intensity modulated radiation therapy

We review and extend the theory of tomographic dose reconstruction for intensity modulated radiotherapy (IMRT). We derive the basis for a saturation with beam number of dose conformation, and provide an analysis which ranks particular beam orientations in terms of the contribution to the delivered dose. Preferred beam directions are found which effectively reduce the number of beams necessary to achieve a given level of dose conformation. The analysis is a new application of the tomographic projection-slice theorem to the problem of beam orientation determination. The effects of the beam front filter and the positivity constraint arising from the tomographic approach are analysed, and modifications of the beam front filter for small beam numbers are suggested. The theory is applied to simple geometric shapes in two dimensions. A Gaussian ellipse, where analytical results are obtained, and simple hard-edged convex prescribed dose shapes are examined to illustrate beam selection based on the beam overlap metric. More complex concave prescribed dose shapes which contain a sensitive organ are also analysed and for low beam numbers are found to have preferred beam directions.

Comparison of intensity-modulated tomotherapy with stereotactically guided conformal radiotherapy for brain tumors

PURPOSE

Intensity-modulated radiotherapy (IMRT) offers the potential to more closely conform dose distributions to the target, and spare organs at risk (OAR). Its clinical value is still being defined. The present study aims to compare IMRT with stereotactically guided conformal radiotherapy (SCRT) for patients with medium size convex-shaped brain tumors.

METHODS AND MATERIALS

Five patients planned with SCRT were replanned with the IMRT-tomotherapy method using the Peacock system (Nomos Corporation). The planning target volume (PTV) and relevant OAR were assessed, and compared relative to SCRT plans using dose statistics, dose-volume histograms (DVH), and the Radiation Therapy Oncology Group (RTOG) stereotactic radiosurgery criteria.

RESULTS

The median and mean PTV were 78 cm3 and 85 cm3 respectively (range 62-119 cm3). The differences in PTV doses for the whole group (Peacock-SCRT +/-1 SD) were 2%+/-1.8 (minimum PTV), and 0.1%+/-1.9 (maximum PTV). The PTV homogeneity achieved by Peacock was 12.1%+/-1.7 compared to 13.9%+/-1.3 with SCRT. Using RTOG guidelines, Peacock plans provided acceptable PTV coverage for all 5/5 plans compared to minor coverage deviations in 4/5 SCRT plans; acceptable homogeneity index for both plans (Peacock = 1.1 vs. SCRT = 1.2); and comparable conformity index (1.4 each). As a consequence of the transaxial method of arc delivery, the optic nerves received mean and maximum doses that were 11.1 to 11.6%, and 10.3 to 15.2% higher respectively with Peacock plan. The maximum optic lens, and brainstem dose were 3.1 to 4.8% higher, and 0.6% lower respectively with Peacock plan. However, all doses remained below the tolerance threshold (5 Gy for lens, and 50 Gy for optic nerves) and were clinically acceptable.

CONCLUSIONS

The Peacock method provided improved PTV coverage, albeit small, in this group of convex tumors. Although the OAR doses were higher using the Peacock plans, all doses remained within the clinically defined threshold and were clinically acceptable. Further improvements may be expected using other methods of IMRT planning that do not limit the treatment delivery to transaxial arcs. Each IMRT system needs to be individually assessed as the paradigm utilized may provide different outcomes.

A simple model for examining issues in radiotherapy optimization

Convolution/superposition software has been used to produce a library of photon pencil beam dose matrices. This library of pencil beams is designed to serve as a tool for both education and investigation in the field of radiotherapy optimization. The elegance of this pencil beam model stems from its cylindrical symmetry. Because of the symmetry, the dose distribution for a pencil beam from any arbitrary angle can be determined through a simple rotation of a pre-computed dose matrix. Rapid dose calculations can thus be performed while maintaining the accuracy of a convolution/superposition based dose computation. The pencil beam data sets have been made publicly available. It is hoped that the data sets will facilitate a comparison of a variety of optimization and delivery approaches. This paper will present a number of studies designed to demonstrate the usefulness of the pencil beam data sets. These studies include an examination of the extent to which a treatment plan can be improved through either an increase in the number of beam angles and/or a decrease in the collimator size. A few insights into the significance of heterogeneity corrections for treatment planning for intensity modulated radiotherapy will also be presented.

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.