Improvements in prostate radiotherapy from the customization of beam directions

An uncertainty-incorporated method for fast beam angle selection in intensity-modulated proton therapy

Aim

We propose a novel metric called ψ - score to rank the Intensity Modulated Proton Therapy (IMPT) beams in the order of their optimality and robustness. The beams ranked based on this metric were accordingly chosen for IMPT optimization. The objective of this work is to study the effectiveness of the proposed method in various clinical cases.

Methods and Materials

We have used Pinnacle TPS (Philips Medical System V 16.2) for performing the optimization. To validate our approach, we have applied it in four clinical cases: Lung, Pancreas, Prostate+Node and Prostate. Basically, for all clinical cases, four set of plans were created using Multi field optimization (MFO) and Robust Optimization (RO) with same clinical objectives, namely (1) Conventional angle plan without Robust Optimization (CA Plan), (2) Suitable angle Plan without Robust Optimization (SA Plan), (3) Conventional angle plan with Robust Optimization (CA-RO Plan), (4) Suitable angle Plan with Robust Optimization (SA-RO Plan). Initial plan was generated with 20 equiangular beams starting from the gantry angle of 0°. In the corresponding SA Plan and SA-RO Plan, the beam angles were obtained using the guidance provided by ψ - score.

Results

All CA plans were compared against the SA plans in terms of Dose distribution, Dose volume histogram (DVH) and percentage of dose difference. The results obtained from the clinical cases indicate that the plan quality is considerably improved without significantly compromising the robustness when the beam angles are optimized using the proposed method. It takes approximately 10-15 min to find the suitable beam angles without Robust Optimization (RO), while it takes approximately 20-30 min to find the suitable beam angles with RO. However, the inclusion of RO in BAO did not result in a change in the final beam angles for anatomies other than lung.

Conclusion

The results obtained in different anatomic sites demonstrate the usefulness of our approach in improving the plan quality by determining optimal beam angles in IMPT.

Comparing Multi-Objective Local Search Algorithms for the Beam Angle Selection Problem

In intensity-modulated radiation therapy, treatment planners aim to irradiate the tumour according to a medical prescription while sparing surrounding organs at risk as much as possible. Although this problem is inherently a multi-objective optimisation (MO) problem, most of the models in the literature are single-objective ones. For this reason, a large number of single-objective algorithms have been proposed in the literature to solve such single-objective models rather than multi-objective ones. Further, a difficulty that one has to face when solving the MO version of the problem is that the algorithms take too long before converging to a set of (approximately) non-dominated points. In this paper, we propose and compare three different strategies, namely random PLS (rPLS), judgement-function-guided PLS (jPLS) and neighbour-first PLS (nPLS), to accelerate a previously proposed Pareto local search (PLS) algorithm to solve the beam angle selection problem in IMRT. A distinctive feature of these strategies when compared to the PLS algorithms in the literature is that they do not evaluate their entire neighbourhood before performing the dominance analysis. The rPLS algorithm randomly chooses the next non-dominated solution in the archive and it is used as a baseline for the other implemented algorithms. The jPLS algorithm first chooses the non-dominated solution in the archive that has the best objective function value. Finally, the nPLS algorithm first chooses the solutions that are within the neighbourhood of the current solution. All these strategies prevent us from evaluating a large set of BACs, without any major impairment in the obtained solutions’ quality. We apply our algorithms to a prostate case and compare the obtained results to those obtained by the PLS from the literature. The results show that algorithms proposed in this paper reach a similar performance than PLS and require fewer function evaluations.

A fast optimization approach for treatment planning of volumetric modulated arc therapy

Background

Volumetric modulated arc therapy (VMAT) is widely used in clinical practice. It not only significantly reduces treatment time, but also produces high-quality treatment plans. Current optimization approaches heavily rely on stochastic algorithms which are time-consuming and less repeatable. In this study, a novel approach is proposed to provide a high-efficient optimization algorithm for VMAT treatment planning.

Methods

A progressive sampling strategy is employed for beam arrangement of VMAT planning. The initial beams with equal-space are added to the plan in a coarse sampling resolution. Fluence-map optimization and leaf-sequencing are performed for these beams. Then, the coefficients of fluence-maps optimization algorithm are adjusted according to the known fluence maps of these beams. In the next round the sampling resolution is doubled and more beams are added. This process continues until the total number of beams arrived. The performance of VMAT optimization algorithm was evaluated using three clinical cases and compared to those of a commercial planning system.

Results

The dosimetric quality of VMAT plans is equal to or better than the corresponding IMRT plans for three clinical cases. The maximum dose to critical organs is reduced considerably for VMAT plans comparing to those of IMRT plans, especially in the head and neck case. The total number of segments and monitor units are reduced for VMAT plans. For three clinical cases, VMAT optimization takes < 5 min accomplished using proposed approach and is 3–4 times less than that of the commercial system.

Conclusions

The proposed VMAT optimization algorithm is able to produce high-quality VMAT plans efficiently and consistently. It presents a new way to accelerate current optimization process of VMAT planning.

Non-coplanar trajectories to improve organ at risk sparing in volumetric modulated arc therapy for primary brain tumors

BACKGROUND AND PURPOSE

To evaluate non-coplanar volumetric modulated arc radiotherapy (VMAT) trajectories for organ at risk (OAR) sparing in primary brain tumor radiotherapy.

MATERIALS AND METHODS

Fifteen patients were planned using coplanar VMAT and compared against non-coplanar VMAT plans for three trajectory optimization techniques. A geometric heuristic technique (GH) combined beam scoring and Dijkstra's algorithm to minimize the importance-weighted sum of OAR volumes irradiated. Fluence optimization was used to perform a local search around coplanar and GH trajectories, producing fluence-based local search (FBLS) and FBLS+GH trajectories respectively.

RESULTS

GH, FBLS, and FBLS+GH trajectories reduced doses to the contralateral globe, optic nerve, hippocampus, temporal lobe, and cochlea. However, FBLS increased dose to the ipsilateral lens, optic nerve and globe. Compared to GH, FBLS+GH increased dose to the ipsilateral temporal lobe and hippocampus, contralateral optics, and the brainstem and body. GH and FBLS+GH trajectories reduced bilateral hippocampi normal tissue complication probability (p=0.028 and p=0.043, respectively). All techniques reduced PTV conformity; GH and FBLS+GH trajectories reduced homogeneity but less so for FBLS+GH.

CONCLUSIONS

The geometric heuristic technique best spared OARs and reduced normal tissue complication probability, however incorporating fluence information into non-coplanar trajectory optimization maintained PTV homogeneity.

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.

Determination of optimal number of beams in direct machine parameter optimization-based intensity modulated radiotherapy for head and neck cases

This paper aims to introduce an algorithm called “sensitivity-based beam number selection (SBBNS)” for fully automated and case-specific determination of an optimal number of equispaced beams in intensity-modulated radiotherapy (IMRT). We tested the algorithm in five head and neck cases of varying complexity. We used direct machine parameter optimization method coupled with Auto Plan feature available in Pinnacle TPS (Version 9.10.0) for optimization. The Pearson correlation test shows a correlation of 0.88 between predicted and actual optimal number of beams, which indicates that SBBNS method is capable of predicting optimal number of beams for head and neck cases with reasonable accuracy. The major advantage of the algorithm is that it intrinsically takes into account various case- and machine-specific factors for the determination of optimal number. The study demonstrates that the algorithm can be effectively applied to IMRT scenarios to determine case specific and optimal number of beams for head and neck cases.

Automated population-based planning for whole brain radiation therapy

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

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

Experimental assessment of gold nanoparticle-mediated dose enhancement in radiation therapy beams using electron spin resonance dosimetry

In this work, we aim to experimentally assess increments of dose due to nanoparticle-radiation interactions via electron spin resonance (ESR) dosimetry performed with a biological-equivalent sensitive material.We employed 2-Methyl-Alanine (2MA) in powder form to compose the radiation sensitive medium embedding gold nanoparticles (AuNPs) 5 nm in diameter. Dosimeters manufactured with 0.1% w/w of AuNPs or no nanoparticles were irradiated with clinically utilized 250 kVp orthovoltage or 6 MV linac x-rays in dosimetric conditions. Amplitude peak-to-peak (App) at the central ESR spectral line was used for dosimetry. Dose-response curves were obtained for samples with or without nanoparticles and each energy beam. Dose increments due to nanoparticles were analyzed in terms of absolute dose enhancements (DEs), calculated as App ratios for each dose/beam condition, or relative dose enhancement factors (DEFs) calculated as the slopes of the dose-response curves.Dose enhancements were observed to present an amplified behavior for small doses (between 0.1-0.5 Gy), with this effect being more prominent with the kV beam. For doses between 0.5-5 Gy, dose-independent trends were observed for both beams, stable around (2.1   ±   0.7) and (1.3   ±   0.4) for kV and MV beams, respectively. We found DEFs of (1.62   ±   0.04) or (1.27   ±   0.03) for the same beams. Additionally, we measured no interference between AuNPs and the ESR apparatus, including the excitation microwaves, the magnetic fields and the paramagnetic radicals.2MA was demonstrated to be a feasible paramagnetic radiation-sensitive material for dosimetry in the presence of AuNPs, and ESR dosimetry a powerful experimental method for further verifications of increments in nanoparticle-mediated doses of biological interest. Ultimately, gold nanoparticles can cause significant and detectable dose enhancements in biological-like samples irradiated at both kilo or megavoltage beams.

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

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

PACS number: 87.55.D‐, 87.55.de

Trajectory optimization for dynamic couch rotation during volumetric modulated arc radiotherapy

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

An experimental investigation on the effect of beam angle optimization on the reduction of beam numbers in IMRT of head and neck tumors

In static intensity-modulated radiation therapy (IMRT), the fundamental factors that determine the quality of a plan are the number of beams and their angles. The objective of this study is to investigate the effect of beam angle optimization (BAO) on the beam number in IMRT. We used six head and neck cases to carry out the study. Basically the methodology uses a parameter called "Beam Intensity Profile Perturbation Score" (BIPPS) to determine the suitable beam angles in IMRT. We used two set of plans in which one set contains plans with equispaced beam configuration starting from beam numbers 3 to 18, and another set contains plans with optimal beam angles chosen using the in-house BAO algorithm. We used quadratic dose-based single criteria objective function as a measure of the quality of a plan. The objective function scores obtained for equispaced beam plans and optimal beam angle plans for six head and neck cases were plotted against the beam numbers in a single graphical plot for effective comparison. It is observed that the optimization of beam angles reduces the beam numbers required to produce clini-cally acceptable dose distribution in IMRT of head and neck tumors. Especially N0.1 (represents the beam number at which the objective function reaches a value of 0.1) is considerably reduced by beam angle optimization in almost all the cases included in the study. We believe that the experimental findings of this study will be helpful in understanding the interplay between beam angle optimization and beam number selection process in IMRT which, in turn, can be used to improve the performance of BAO algorithms and beam number selection process in IMRT.

A self-adaptive case-based reasoning system for dose planning in prostate cancer radiotherapy

PURPOSE

Prostate cancer is the most common cancer in the male population. Radiotherapy is often used in the treatment for prostate cancer. In radiotherapy treatment, the oncologist makes a trade-off between the risk and benefit of the radiation, i.e., the task is to deliver a high dose to the prostate cancer cells and minimize side effects of the treatment. The aim of our research is to develop a software system that will assist the oncologist in planning new treatments.

METHODS

A nonlinear case-based reasoning system is developed to capture the expertise and experience of oncologists in treating previous patients. Importance (weights) of different clinical parameters in the dose planning is determined by the oncologist based on their past experience, and is highly subjective. The weights are usually fixed in the system. In this research, the weights are updated automatically each time after generating a treatment plan for a new patient using a group based simulated annealing approach.

RESULTS

The developed approach is analyzed on the real data set collected from the Nottingham University Hospitals NHS Trust, City Hospital Campus, UK. Extensive experiments show that the dose plan suggested by the proposed method is coherent with the dose plan prescribed by an experienced oncologist or even better.

CONCLUSIONS

The developed case-based reasoning system enables the use of knowledge and experience gained by the oncologist in treating new patients. This system may play a vital role to assist the oncologist in making a better decision in less computational time; it utilizes the success rate of the previously treated patients and it can also be used in teaching and training processes.

Intensity modulated radiation therapy with field rotation--a time-varying fractionation study

This paper proposes a novel mathematical approach to the beam selection problem in intensity modulated radiation therapy (IMRT) planning. The approach allows more beams to be used over the course of therapy while limiting the number of beams required in any one session. In the proposed field rotation method, several sets of beams are interchanged throughout the treatment to allow a wider selection of beam angles than would be possible with fixed beam orientations. The choice of beamlet intensities and the number of identical fractions for each set are determined by a mixed integer linear program that controls jointly for the distribution per fraction and the cumulative dose distribution delivered to targets and critical structures. Trials showed the method allowed substantial increases in the dose objective and/or sparing of normal tissues while maintaining cumulative and fraction size limits. Trials for a head and neck site showed gains of 25%-35% in the objective (average tumor dose) and for a thoracic site gains were 7%-13%, depending on how strict the fraction size limits were set. The objective did not rise for a prostate site significantly, but the tolerance limits on normal tissues could be strengthened with the use of multiple beam sets.

Inverse planning for IMRT with nonuniform beam profiles using total-variation regularization (TVR)

PURPOSE

Radiation therapy with high dose rate and flattening filter-free (FFF) beams has the potential advantage of greatly reduced treatment time and out-of-field dose. Current inverse planning algorithms are, however, not customized for beams with nonuniform incident profiles and the resultant IMRT plans are often inefficient in delivery. The authors propose a total-variation regularization (TVR)-based formalism by taking the inherent shapes of incident beam profiles into account.

METHODS

A novel TVR-based inverse planning formalism is established for IMRT with nonuniform beam profiles. The authors introduce a TVR term into the objective function, which encourages piecewise constant fluence in the nonuniform FFF fluence domain. The proposed algorithm is applied to lung and prostate and head and neck cases and its performance is evaluated by comparing the resulting plans to those obtained using a conventional beamlet-based optimization (BBO).

RESULTS

For the prostate case, the authors' algorithm produces acceptable dose distributions with only 21 segments, while the conventional BBO requires 114 segments. For the lung case and the head and neck case, the proposed method generates similar coverage of target volume and sparing of the organs-at-risk as compared to BBO, but with a markedly reduced segment number.

CONCLUSIONS

TVR-based optimization in nonflat beam domain provides an effective way to maximally leverage the technical capacity of radiation therapy with FFF fields. The technique can generate effective IMRT plans with improved dose delivery efficiency without significant deterioration of the dose distribution.

An algorithm for fast beam angle selection in intensity modulated radiotherapy

PURPOSE

This article aims to introduce a novel algorithm for fast beam angle selection in intensity modulated radiotherapy (IMRT).

METHODS

The algorithm models the optimization problem as a beam angle ranking problem and chooses suitable beam angles according to their rank. A new parameter called "beam intensity profile perturbation score (BIPPS)" is used for ranking the beam angles. The BIPPS-based beam angle ranking implicitly accounts for the dose-volume effects of the involved structures. A simulated phantom case with obvious optimal beam angles is used to verify the validity of the presented technique. In addition, the efficiency of the algorithm was examined in three clinical cases (prostate, pancreas, and head and neck) in terms of DVH and dose distribution. In all cases, the judgment of the algorithm's efficiency was based on the comparison between plans with equidistant beams (equal-angle-plan) and plans with beams obtained using the algorithm (suitable-angle-plan).

RESULTS

It is observed from the study that the beam angle ranking function over BIPPS instantly picks up a suitable set of beam angles for a specific case. It takes only about 15 min for choosing the suitable beam angles even for the most complicated cases. The DVHs and dose distributions confirm that the proposed algorithm can efficiently reduce the mean or maximum dose to OARs, while guaranteeing the target coverage and dose uniformity. On the average, about 17% reduction in the mean dose to critical organs, such as rectum, bladder, kidneys and parotids, is observed. Also, about 12% (averaged) reduction in the maximum dose to critical organs (spinal cord) is observed in the clinical cases presented in this study.

CONCLUSIONS

This study demonstrates that the algorithm can be effectively applied to IMRT scenarios to get fast and case specific beam angle configurations.

Geometrical pre-planning for conformal radiotherapy

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

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.

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

BACKGROUND AND PURPOSE

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

MATERIALS AND METHODS

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

RESULTS

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

CONCLUSIONS

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

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

PURPOSE

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

METHODS AND MATERIALS

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

RESULTS

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

CONCLUSIONS

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

A particle swarm optimization algorithm for beam angle selection in intensity-modulated radiotherapy planning

Automatic beam angle selection is an important but challenging problem for intensity-modulated radiation therapy (IMRT) planning. Though many efforts have been made, it is still not very satisfactory in clinical IMRT practice because of overextensive computation of the inverse problem. In this paper, a new technique named BASPSO (Beam Angle Selection with a Particle Swarm Optimization algorithm) is presented to improve the efficiency of the beam angle optimization problem. Originally developed as a tool for simulating social behaviour, the particle swarm optimization (PSO) algorithm is a relatively new population-based evolutionary optimization technique first introduced by Kennedy and Eberhart in 1995. In the proposed BASPSO, the beam angles are optimized using PSO by treating each beam configuration as a particle (individual), and the beam intensity maps for each beam configuration are optimized using the conjugate gradient (CG) algorithm. These two optimization processes are implemented iteratively. The performance of each individual is evaluated by a fitness value calculated with a physical objective function. A population of these individuals is evolved by cooperation and competition among the individuals themselves through generations. The optimization results of a simulated case with known optimal beam angles and two clinical cases (a prostate case and a head-and-neck case) show that PSO is valid and efficient and can speed up the beam angle optimization process. Furthermore, the performance comparisons based on the preliminary results indicate that, as a whole, the PSO-based algorithm seems to outperform, or at least compete with, the GA-based algorithm in computation time and robustness. In conclusion, the reported work suggested that the introduced PSO algorithm could act as a new promising solution to the beam angle optimization problem and potentially other optimization problems in IMRT, though further studies need to be investigated.

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.

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.

Automatic beam angle selection in IMRT planning using genetic algorithm

The selection of suitable beam angles in external beam radiotherapy is at present generally based upon the experience of the human planner. The requirement to automatically select beam angles is particularly highlighted in intensity-modulated radiation therapy (IMRT), in which a smaller number of modulated beams is hoped to be used, in comparison with conformal radiotherapy. It has been proved by many researchers that the selection of suitable beam angles is most valuable for a plan with a small number of beams (< or = 5). In this paper an efficient method is presented to investigate how to improve the dose distributions by selecting suitable coplanar beam angles. In our automatic beam angle selection (ABAS) algorithm, the optimal coplanar beam angles correspond to the lowest objective function value of the dose distributions calculated using the intensity-modulated maps of this group of candidate beams. Due to the complexity of the problem and the large search space involved, the selection of beam angles and the optimization of intensity maps are treated as two separate processes and implemented iteratively. A genetic algorithm (GA) incorporated with an immunity operation is used to select suitable beam angles, and a conjugate gradient (CG) method is used to quickly optimize intensity maps for each selected beam combination based on a dose-based objective function. A pencil-beam-based three-dimensional (3D) full scatter convolution (FSC) algorithm is employed for the dose calculation. Two simulated cases with obvious optimal beam angles are used to verify the validity of the presented technique, and a more complicated case simulating a prostate tumour and two clinical cases are employed to test the efficiency of ABAS. The results show that ABAS is valid and efficient and can improve the dose distributions within a clinically acceptable computation time.

Multiobjective evolutionary optimization of the number of beams, their orientations and weights for intensity-modulated radiation therapy

We propose a hybrid multiobjective (MO) evolutionary optimization algorithm (MOEA) for intensity-modulated radiotherapy inverse planning and apply it to optimize the number of incident beams, their orientations and intensity profiles. The algorithm produces a set of efficient solutions, which represent different clinical trade-offs and contains information such as variety of dose distributions and dose-volume histograms. No importance factors are required and solutions can be obtained in regions not accessible by conventional weighted sum approaches. The application of the algorithm using a test case, a prostate and a head and neck tumour case is shown. The results are compared with MO inverse planning using a gradient-based optimization algorithm.

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.

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.

[Optimization criteria in intensity-modulated radiotherapy]

The present paper provides an overview on the inverse treatment planning for the assessment of intensity-modulated fields. The problem is to find the optimal dose distribution for given attributes of the irradiated tissue. The attributes of the optimal dose distribution are delineated by an objective function. In practice, models are used that evaluate the physical dose distribution, either directly or through their radiobiological effects. In the simplest case, the squared deviation of the achieved dose distribution is minimized to the prescribed dose distribution. For organs structured in parallel, it is common to introduce dose-volume constraints. Another approach is to optimize a value for the probability of complication-free tumor control. The complication probability for normal tissue, in turn, is a rather complex function. However, using the relative seriality, a simple model can be devised with a certain approximation. Other models of "effective dose" are also presented.

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.

Automated beam angle and weight selection in radiotherapy treatment planning applied to pancreas tumors

PURPOSE

To extend and investigate the clinical value of a recently developed algorithm for automatic beam angle and beam weight selection, for irradiation of pancreas tumors.

METHODS AND MATERIALS

The algorithm aims at generation of acceptable treatment plans, i.e., delivering the prescribed tumor dose while strictly obeying the imposed hard constraints for organs at risk and target. Extensions were made to minimize the beam number and/or to escalate the tumor dose. For 5 pancreas patients, the clinical value and the potential for beam number reduction and dose escalation were investigated. Comparisons were made with clinical plans and equiangular plans.

RESULTS

Compared to clinical plans, the generated plans with the same number of beams yielded a substantial reduction in the dose to critical tissues. Using the algorithm, an escalated tumor dose of 58 Gy could be achieved for two cases. Maximum dose escalations required a minimum of 3 to 4 beam orientations. For 13 CT slices and an in-slice resolution of 0.5 cm, the total calculation times were 23-55 min, including precalculation of 180 input dose distributions (15 min).

CONCLUSIONS

The algorithm yielded acceptable treatment plans with clinically feasible numbers of beams, even for escalated tumor doses. Generated plans were superior to the clinically applied plans and to equiangular setups. Calculation times were clinically acceptable. The algorithm is now increasingly used in clinical routine.

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.

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.

Speed versus accuracy in a fast convolution photon dose calculation for conformal radiotherapy

A convolution dose calculation for megavoltage photon beams is described and the compromise between speed and accuracy examined. The algorithm is suitable for treatment planning optimization, where the need is for a fast, flexible method requiring minimal beam data but providing an accurate result. The algorithm uses a simple tabular beam model, together with a discrete scatter kernel. These beam parameters are fitted either to a measured dose distribution, or to a dose distribution calculated using a more accurate dose calculation algorithm. The calculation is then applied to pelvic and thoracic conformal plans, and the results compared with those provided by a commercial radiotherapy treatment planning system (Pinnacle3, Philips Radiation Oncology Systems, Milpitas, CA), which has been verified against measurements. The calculation takes around 4 s to compute a 100 x 100 mm field, and agreement of the dose-volume histograms with the commercial treatment planning system is to within 5% dose or 8% volume. Use of a grid resolution coarser than 5 x 5 x 5 mm is found to be inaccurate, whereas calculating primary dose on a coarse grid and interpolating is found to increase speed without significantly reducing accuracy. Kernel resolution influences the speed and accuracy, but using 12 discrete points provides a fast result with a limited error. Thus, the algorithm is suitable for optimization applications.

Intensity modulated versus non-intensity modulated radiotherapy in the treatment of the left breast and upper internal mammary lymph node chain: a comparative planning study

BACKGROUND AND PURPOSE

To compare and evaluate intensity modulated (IMRT) and non-intensity modulated radiotherapy techniques in the treatment of the left breast and upper internal mammary lymph node chain.

MATERIALS AND METHODS

The breast, upper internal mammary chain (IMC), heart and lungs were delineated on a computed tomography (CT)-scan for 12 patients. Three different treatment plans were created: (1) tangential photon fields with oblique IMC electron-photon fields with manually optimized beam weights and wedges, (2) wide split tangential photon fields with a heart block and computer optimized wedge angles, and (3) IMRT tangential photon fields. For the IMRT technique, an inverse planning program (KonRad) generated the intensity profiles and a clinical three-dimensional treatment planning system (U-MPlan) optimized the segment weights. U-MPlan calculated the dose distribution for all three techniques. The normal tissue complication probabilities (NTCPs) for the organs at risk (ORs) were calculated for comparison.

RESULTS

The average root mean square deviation of the differential dose-volume histogram of the breast planning target volume was 4.6, 3.9 and 3.5% and the average mean dose to the IMC was 97.2, 108.0 and 99.6% for the oblique electron, wide split tangent and IMRT techniques, respectively. The average NTCP for the ORs (i.e. heart and lungs) were comparable between the oblique electron and IMRT techniques (<or=0.7%). The wide split tangent technique resulted in higher NTCP values (>or=2%) for the ORs.

CONCLUSIONS

The lowest NTCP values were found with the oblique electron and the IMRT techniques. The IMRT technique had the best breast and IMC target coverage.

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.

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.

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.

Constrained treatment planning using sequential beam selection

In this paper an algorithm is described for automated treatment plan generation. The algorithm aims at delivery of the prescribed dose to the target volume without violation of constraints for target, organs at risk and the surrounding normal tissue. Pre-calculated dose distributions for all candidate orientations are used as input. Treatment beams are selected in a sequential way. A score function designed for beam selection is used for the simultaneous selection of beam orientations and weights. In order to determine the optimum choice for the orientation and the corresponding weight of each new beam, the score function is first redefined to account for the dose distribution of the previously selected beams. Addition of more beams to the plan is stopped when the target dose is reached or when no additional dose can be delivered without violating a constraint. In the latter case the score function is modified by importance factor changes to enforce better sparing of the organ with the limiting constraint and the algorithm is run again.

Beam orientation optimization in intensity-modulated radiation treatment planning

Beam direction optimization is an important problem in radiation therapy. In intensity modulated radiation therapy (IMRT), the difficulty for computer optimization of the beam directions arises from the fact that they are coupled with the intensity profiles of the incident beams. In order to obtain the optimal incident beam directions using iterative or stochastic methods, the beam profiles ought to be optimized after every change of beam configuration. In this paper we report an effective algorithm to optimize gantry angles for IMRT. In our calculation the gantry angles and the beam profiles (beamlet weights) were treated as two separate groups of variables. The gantry angles were sampled according to a simulated annealing algorithm. For each sampled beam configuration, beam profile calculation was done using a fast filtered backprojection (FBP) method. Simulated annealing was also used for beam profile optimization to examine the performance of the FBP for beam orientation optimization. Relative importance factors were incorporated into the objective function to control the relative importance of the target and the sensitive structures. Minimization of the objective function resulted in the best possible beam orientations and beam profiles judged by the given objective function. The algorithm was applied to several model problems and the results showed that the approach has potential for IMRT applications.

An evaluation of three-field coplanar plans for conformal radiotherapy of prostate cancer

BACKGROUND AND PURPOSE

A series of coplanar three-field configurations for two different clinical treatment volumes, prostate only (PO) and prostate plus seminal vesicles (PSV) were studied to determine the optimal three-field plan arrangement for prostate radiotherapy.

MATERIALS AND METHODS

A variety of conformal three-field 6 MV plans prescribed to both 64 and 74 Gy were created for PO and PSV volumes in each of ten patients. For description, the orientation of each sequential beam was named in a clockwise fashion. Plans included series with arrangements of 0 degrees, 60-150 degrees, 210-300 degrees; 0 degrees, 90 degrees, 225-255 degrees; 90 degrees, 210-240 degrees, 300-330 degrees and a four-field (4F) box plan for comparison. Six-hundred and eighty plans were compared using the rectal volume irradiated to greater than 50% (V(50)), 80% (V(80)), and 90% (V(90)) of the prescribed dose, normal tissue complications (NTCP) for rectum, bladder, and femoral heads (FH), and tumour control probabilities (TCP). FH tolerance was set at 52 Gy to 10% volume.

RESULTS

In comparing the 34 different three-field configurations for each of the PO and PSV groups, the greatest rectal sparing was achieved by a three-field plan with gantry angles of 0 degrees, 90 degrees, 270 degrees (PO: rectal V(80)=22.8+/-5.5% (1S.D.), V(90)=18.4+/-5.7%, and PSV: rectal V(80)=41.9+/-5.8%, V(90)=35.5+/-5.9%). This also improved on the 4F-box plan (PO: rectal V(80)=26.0+/-5.8%, V(90)=21.4+/-5.2%, P<0.001; and PSV: rectal V(80)=47.3+/-5.5%, V(90)=41.6+/-5.1%, P<0.001). The worst rectal sparing was seen with the 0 degrees, 120 degrees, 240 degrees plan (PO: rectal V(80)=35.2+/-8.0%, V(90)=30.3+/-7.1%, P<0.001; and PSV: rectal V(80)=65.7+/-9.0%, V(90)=58.8+/-8.8%, P<0.001). In the PO group, the increase in predicted rectal NTCP with dose escalation from 64 to 74 Gy was 3.3% using the 0 degrees, 90 degrees, 270 degrees plan, 4.7% with the 4F-box plan, and 6.9% with the 0 degrees, 120 degrees, 240 degrees plan. In the PSV group, dose escalation increased the predicted rectal NTCP by 7.9, 10.1 and 15.7% for the 0 degrees, 90 degrees, 270 degrees plan, 4F-box plan, and 0 degrees, 120 degrees, 240 degrees plan, respectively.

CONCLUSIONS

For both PO and PSV volumes, the three-field plan which afforded the greatest rectal sparing with acceptable bladder and femoral head doses was the 0 degrees, 90 degrees, 270 degrees plan. This plan also improved on the 4F-box. The increase in predicted rectal NTCP when escalating dose from 64 to 74 Gy was smaller using this plan compared to either the three-field 0 degrees, 120 degrees, 240 degrees plan or the 4F-box plan.

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.

Optimization of coplanar six-field techniques for conformal radiotherapy of the prostate

PURPOSE

To determine the optimal coplanar treatment technique for six-field conformal radiotherapy of prostate only (PO) or prostate plus seminal vesicles (PSV).

METHODS AND MATERIALS

A series of 6-MV six-field coplanar treatment plans were created for PO and PSV volumes in 10 patients prescribed to both 64 and 74 Gy. All plans consisted of laterally-symmetric anterior oblique, lateral, and posterior oblique fields. The posterior oblique fields were varied through 20-45 degrees relative to the lateral fields, and for each of these angles, the anterior oblique fields were varied through 25-65 degrees relative to lateral. The plans were compared by means of rectal volumes irradiated to 80% or more of the prescribed dose (V80); normal tissue complication probability (NTCP) for rectum, bladder, and femoral heads; and tumor control probability (TCP). Femoral head tolerance was designated as 52 Gy to no more than 10% volume.

RESULTS

For the PO group, anterior oblique fields at 50 degrees from lateral and posterior oblique fields at 25 degrees from lateral produced the lowest V80, together with femoral head doses which were appropriate for most patients (V80 = 24.4+/-5.3% [1 SD]). Compared to a commonly-used six-field (reference) plan with both anterior and posterior oblique fields at 35 degrees from lateral (V80 = 26.3+/-5.9%), this represented an improvement (p = 0.001). For the PSV group, the optimal anterior and posterior oblique fields were at 65 degrees and 30 degrees from lateral, respectively (V80 = 47.5+/-6.3%). Relative to the reference plan (V80 = 49.4+/-5.6%), this was a marginal improvement (p = 0.07).

CONCLUSION

The optimized six-field plans provide increased rectal sparing at both standard and escalated doses. Moreover, the gain in TCP resulting from dose escalation can be achieved with a smaller increase in rectal NTCP using the optimized six-field plans.

Clinical implementation of wedge filter optimization in three-dimensional radiotherapy treatment planning

BACKGROUND AND PURPOSE

To describe a wedge filter optimization technique which automatically chooses the beam weights and wedge filters and to demonstrate the implementation of the algorithm in clinical three-dimensional (3D) radiotherapy treatment planning.

MATERIAL AND METHODS

Given the incident directions and beam energies of J beams, the dose distribution is a function of the beam weights, wedge angles, and wedge orientations. Instead of decomposing an incident field into a superposition of an open and two nominal wedged fields and then optimizing their weights, the algorithm optimizes the objective function with respect to the beam weights, wedge angles and wedge orientations directly. A salient feature of the algorithm is that no planner intervention was required in the selection of wedge filters during the optimization process. A dose-based objective function which incorporated the relative importance of structures was adopted in this work. The objective function was minimized by the method of simulated annealing. The technique was demonstrated by using a phantom study and two clinical cases.

RESULTS

For the phantom case, the classical wedge pair result was obtained, providing a useful test of the algorithm. Dose distributions and dose volume histograms for the target and surrounding organs were presented for the two clinical cases. It was also shown that dose homogeneity to the target could be compromised by increasing the relative importance factors to the surrounding organs.

CONCLUSIONS

A 3D wedge filter optimization algorithm has been developed. The technique has the potential to fully automate the 3D radiotherapy treatment planning process. In addition, treatment planning time and efforts were significantly reduced.

Beam-orientation customization using an artificial neural network

A methodology for the constrained customization of coplanar beam orientations in radiotherapy treatment planning using an artificial neural network (ANN) has been developed. The geometry of the patients, with cancer of the prostate, was modelled by reducing the external contour, planning target volume (PTV) and organs at risk (OARs) to a set of cuboids. The coordinates and size of the cuboids were given to the ANN as inputs. A previously developed beam-orientation constrained-customization (BOCC) scheme employing a conventional computer algorithm was used to determine the customized beam orientations in a training set containing 45 patient datasets. Twelve patient datasets not involved in the training of the artificial neural network were used to test whether the ANN was able to map the inputs to customized beam orientations. Improvements from the customized beam orientations were compared with standard treatment plans with fixed gantry angles and plans produced from the BOCC scheme. The ANN produced customized beam orientations within 5 degrees of the BOCC scheme in 62.5% of cases. The average difference in the beam orientations produced by the ANN and the BOCC scheme was 7.7 degrees (+/-1.7, 1 SD). Compared with the standard treatment plans, the BOCC scheme produced plans with an increase in the average tumour control probability (TCP) of 5.7% (+/-1.4, 1 SD) whilst the ANN generated plans increased the average TCP by 3.9% (+/-1.3, 1 SD). Both figures refer to the TCP at a fixed rectal normal tissue complication probability (NTCP) of 1%. In conclusion, even using a very simple model for the geometry of the patient, an ANN was able to produce beam orientations that were similar to those produced by a conventional computer algorithm.

A comparison of coplanar four-field techniques for conformal radiotherapy of the prostate

BACKGROUND AND PURPOSE

Conformal radiotherapy of the prostate is an increasingly common technique, but the optimal choice of beam configuration remains unclear. This study systematically compares a number of coplanar treatment plans for four-field irradiation of two different clinical treatment volumes: prostate only (PO) and the prostate plus seminal vesicles (PSV).

MATERIALS AND METHODS

A variety of four-field coplanar treatment plans were created for PO and PSV volumes in each of ten patients. Plans included a four-field 'box' plan, a symmetric plan having bilateral anterior and posterior oblique fields, a plan with anterior oblique and lateral fields, a series of asymmetric plans, and a three-field plan having anterior and bilateral fields for comparison. Doses of 64 and 74 Gy were prescribed to the isocentre. Plans were compared using the volume of rectum irradiated to greater than 50% (V50), 80% (V80) and 90% (V90) of the prescribed dose. Tumour control probabilities (TCP) and normal tissue complication probabilities (NTCP) for the rectum, bladder and femoral heads were also evaluated. Femoral head dose was limited such that less than 10% of each femoral head received 70% of the prescribed dose.

RESULTS

For the PO group, the optimal plan consisted of anterior oblique and lateral fields (Rectal V80 = 23.8+/-5.0% (1 SD)), while the box technique (V80 = 26.0+/-5.8%) was less advantageous in terms of rectal sparing (P = 0.001). Similar results were obtained for the PSV group (Rectal V80 = 43.9+/-5.0% and 47.3+/-5.5% for the two plan types, respectively, P = 0.001). The three-field plan was comparable to the optimal four-field plan but gave higher superficial body dose. With dose escalation from 64 to 74 Gy, the mean TCP for the optimal plan rose from 52.0+/-2.8% to 74.1+/-2.0%. Meanwhile, rectal NTCP for the optimal plan rose by 3.5% (PO) or 8.4% (PSV), compared to 4.7% (PO) or 10.1% (PSV) for the box plan.

CONCLUSIONS

For PO volumes, a plan with gantry angles of 35 degrees, 90 degrees, 270 degrees and 325 degrees offers a high level of rectal sparing and acceptable dose to the femoral heads for all patients, while for PSV volumes, the corresponding plan has gantry angles of 20 degrees, 90 degrees , 270 degrees and 340 degrees. Using these plans, the gain in TCP resulting from dose escalation can be achieved with a smaller increase in anticipated rectal NTCP.

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.