Constrained treatment planning using sequential beam selection

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

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

Fully automated noncoplanar radiation therapy treatment planning

PURPOSE

To perform fully automated noncoplanar (NC) treatment planning, we propose a method called NC-POPS to produce NC plans using the Pareto optimal projection search (POPS) algorithm.

METHODS

NC radiation therapy treatment planning has the potential to improve dosimetric quality as compared to traditional coplanar techniques. Likewise, automated treatment planning algorithms can reduce a planner's active treatment planning time and remove inter-planner variability. Our NC-POPS algorithm extends the original POPS algorithm to the NC setting with potential applications to both intensity-modulated radiation therapy (IMRT) and volumetric modulated arc therapy (VMAT). The proposed algorithm consists of two main parts: (1) NC beam angle optimization (BAO) and (2) fully automated inverse planning using the POPS algorithm.

RESULTS

We evaluate the performance of NC-POPS by comparing between various NC and coplanar configurations. To evaluate plan quality, we compute the homogeneity index (HI), conformity index (CI), and dose-volume histogram statistics for various organs-at-risk (OARs). As compared to the evaluated coplanar baseline methods, the proposed NC-POPS method achieves significantly better OAR sparing, comparable or better dose conformity, and similar dose homogeneity.

CONCLUSIONS

Our proposed NC-POPS algorithm provides a modular approach for fully automated treatment planning of NC IMRT cases with the potential to substantially improve treatment planning workflow and plan quality.

Recent developments in non-coplanar radiotherapy

This paper gives an overview of recent developments in non-coplanar intensity modulated radiotherapy (IMRT) and volumetric modulated arc therapy (VMAT). Modern linear accelerators are capable of automating motion around multiple axes, allowing efficient delivery of highly non-coplanar radiotherapy techniques. Novel techniques developed for C-arm and non-standard linac geometries, methods of optimization, and clinical applications are reviewed. The additional degrees of freedom are shown to increase the therapeutic ratio, either through dose escalation to the target or dose reduction to functionally important organs at risk, by multiple research groups. Although significant work is still needed to translate these new non-coplanar radiotherapy techniques into the clinic, clinical implementation should be prioritized. Recent developments in non-coplanar radiotherapy demonstrate that it continues to have a place in modern cancer treatment.

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

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

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.

Comparison of beam angle selection strategies for intracranial IMRT

PURPOSE

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

METHODS

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

RESULTS

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

CONCLUSION

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

Integrated multicriterial optimization of beam angles and intensity profiles for coplanar and noncoplanar head and neck IMRT and implications for VMAT

PURPOSE

To quantify improved salivary gland sparing for head and neck cancer patients using intensity-modulated radiotherapy (IMRT) plans based on integrated computerized optimization of beam orientations and intensity profiles. To assess if optimized nonzero couch angles also improve VMAT plans.

METHODS

Our in-house developed algorithm iCycle was used for automated generation of multicriterial optimized plans with optimized beam orientations and intensity profiles, and plans with optimized profiles for preselected beam arrangements. For 20 patients, five IMRT plans, based on one "wish-list," were compared: (i) and (ii) seven- and nine-beam equiangular coplanar plans (iCycle(7equi), iCycle(9equi)), (iii) and (iv) nine-beam plans with optimized coplanar and noncoplanar beam orientations (iCycle(copl), iCycle(noncopl)), and (v) a nine-beam coplanar plan with optimized gantry angles and one optimized couch rotation (iCycle(couch)). VMAT plans without and with this optimized couch rotation were evaluated.

RESULTS

iCycle(noncopl) resulted in the best salivary gland sparing, while iCycle(couch) yielded similar results for 18 patients. For iCycle(7equi), submandibular gland NTCP values were on average 5% higher. iCycle(9equi) performed better than iCycle(7equi). iCycle(copl) showed further improvement. Application of the optimized couch angle from iCycle(couch) also improved NTCP values in VMAT plans.

CONCLUSIONS

iCycle allows objective comparison of competing planning strategies. Integrated optimization of beam profiles and angles can significantly improve normal tissue sparing, yielding optimal results for iCycle(noncopl).

On the beam direction search space in computerized non-coplanar beam angle optimization for IMRT-prostate SBRT

In a recent paper, we have published a new algorithm, designated 'iCycle', for fully automated multi-criterial optimization of beam angles and intensity profiles. In this study, we have used this algorithm to investigate the relationship between plan quality and the extent of the beam direction search space, i.e. the set of candidate beam directions that may be selected for generating an optimal plan. For a group of ten prostate cancer patients, optimal IMRT plans were made for stereotactic body radiation therapy (SBRT), mimicking high dose rate brachytherapy dosimetry. Plans were generated for five different beam direction input sets: a coplanar (CP) set and four non-coplanar (NCP) sets. For CP treatments, the search space consisted of 72 orientations (5° separations). The NCP CyberKnife (CK) space contained all directions available in the robotic CK treatment unit. The fully non-coplanar (F-NCP) set facilitated the highest possible degree of freedom in selecting optimal directions. CK(+) and CK(++) were subsets of F-NCP to investigate some aspects of the CK space. For each input set, plans were generated with up to 30 selected beam directions. Generated plans were clinically acceptable, according to an assessment of our clinicians. Convergence in plan quality occurred only after around 20 included beams. For individual patients, variations in PTV dose delivery between the five generated plans were minimal, as aimed for (average spread in V(95): 0.4%). This allowed plan comparisons based on organ at risk (OAR) doses, with the rectum considered most important. Plans generated with the NCP search spaces had improved OAR sparing compared to the CP search space, especially for the rectum. OAR sparing was best with the F-NCP, with reductions in rectum D(Mean), V(40Gy), V(60Gy) and D(2%) compared to CP of 25%, 35%, 37% and 8%, respectively. Reduced rectum sparing with the CK search space compared to F-NCP could be largely compensated by expanding CK with beams with relatively large direction components along the superior-inferior axis (CK(++)). Addition of posterior beams (CK(++) → F-NCP) did not lead to further improvements in OAR sparing. Plans with 25 beams clearly performed better than 11-beam plans. For CP plans, an increase from 11 to 25 involved beams resulted in reductions in rectum D(Mean), V(40Gy), V(60Gy) and D(2%) of 39%, 57%, 64% and 13%, respectively.

iCycle: Integrated, multicriterial beam angle, and profile optimization for generation of coplanar and noncoplanar IMRT plans

PURPOSE

To introduce iCycle, a novel algorithm for integrated, multicriterial optimization of beam angles, and intensity modulated radiotherapy (IMRT) profiles.

METHODS

A multicriterial plan optimization with iCycle is based on a prescription called wish-list, containing hard constraints and objectives with ascribed priorities. Priorities are ordinal parameters used for relative importance ranking of the objectives. The higher an objective priority is, the higher the probability that the corresponding objective will be met. Beam directions are selected from an input set of candidate directions. Input sets can be restricted, e.g., to allow only generation of coplanar plans, or to avoid collisions between patient/couch and the gantry in a noncoplanar setup. Obtaining clinically feasible calculation times was an important design criterium for development of iCycle. This could be realized by sequentially adding beams to the treatment plan in an iterative procedure. Each iteration loop starts with selection of the optimal direction to be added. Then, a Pareto-optimal IMRT plan is generated for the (fixed) beam setup that includes all so far selected directions, using a previously published algorithm for multicriterial optimization of fluence profiles for a fixed beam arrangement Breedveld et al. [Phys. Med. Biol. 54, 7199-7209 (2009)]. To select the next direction, each not yet selected candidate direction is temporarily added to the plan and an optimization problem, derived from the Lagrangian obtained from the just performed optimization for establishing the Pareto-optimal plan, is solved. For each patient, a single one-beam, two-beam, three-beam, etc. Pareto-optimal plan is generated until addition of beams does no longer result in significant plan quality improvement. Plan generation with iCycle is fully automated.

RESULTS

Performance and characteristics of iCycle are demonstrated by generating plans for a maxillary sinus case, a cervical cancer patient, and a liver patient treated with SBRT. Plans generated with beam angle optimization did better meet the clinical goals than equiangular or manually selected configurations. For the maxillary sinus and liver cases, significant improvements for noncoplanar setups were seen. The cervix case showed that also in IMRT with coplanar setups, beam angle optimization with iCycle may improve plan quality. Computation times for coplanar plans were around 1-2 h and for noncoplanar plans 4-7 h, depending on the number of beams and the complexity of the site.

CONCLUSIONS

Integrated beam angle and profile optimization with iCycle may result in significant improvements in treatment plan quality. Due to automation, the plan generation workload is minimal. Clinical application has started.

Automated non-coplanar beam direction optimization improves IMRT in SBRT of liver metastasis

PURPOSE

To investigate whether automatically optimized coplanar, or non-coplanar beam setups improve intensity modulated radiotherapy (IMRT) treatment plans for stereotactic body radiotherapy (SBRT) of liver tumors, compared to a reference equi-angular IMRT plan.

METHODS

For a group of 13 liver patients, an in-house developed beam selection algorithm (Cycle) was used for generation of 3D-CRT plans with either optimized coplanar-, or non-coplanar beam setups. These 10 field, coplanar and non-coplanar setups, and an 11 field, equi-angular coplanar reference setup were then used as input for generation of IMRT plans. For all plans, the PTV dose was maximized in an iterative procedure by increasing the prescribed PTV dose in small steps until further increase was prevented by constraint violation(s).

RESULTS

For optimized non-coplanar setups, D(PTV, max) increased by on average 30% (range 8-64%) compared to the corresponding reference IMRT plan. Similar increases were observed for D(PTV, 99%) and gEUD(a). For optimized coplanar setups, mean PTV dose increases were only approximately 4%. After re-scaling all plans to the clinically applied dose, optimized non-coplanar configurations resulted in the best sparing of organs at risk (healthy liver, spinal cord, bowel).

CONCLUSION

Compared to an equi-angular beam setup, computer optimized non-coplanar setups do result in substantial improvements in IMRT plans for SBRT of liver tumors.

Simultaneous tumour dose escalation and liver sparing in Stereotactic Body Radiation Therapy (SBRT) for liver tumours due to CTV-to-PTV margin reduction

PURPOSE

To quantify potential benefits of CTV-to-PTV margin reduction for SBRT of liver tumours, as allowed by enhanced treatment precision.

MATERIALS AND METHODS

For 14 patients plans were generated for the clinical margin and for 3 tighter margins. An in-house developed algorithm was used to optimise beam directions, shapes, and weights for generation of the plan with the highest isocenter dose (D(iso)), while keeping the minimum PTV dose at least 65%xD(iso) and strictly adhering to all imposed hard OAR constraints. Each plan contains 10 optimal beam directions, automatically selected from up to 252 coplanar and non-coplanar input directions.

RESULTS

Apart from the expected tumour dose escalation (D(iso), EUD(PTV), gEUD(PTV)) with decreasing margin, a simultaneous improved sparing of the normal liver (D33%, D50%, D(mean)) was also observed. The smaller the margin was, the bigger both effects were. For renormalized plans with D(iso) equal to the clinical value (3x19.2Gy), and a margin reduction of 50% (2.5mm laterally, 5mm longitudinally), normal liver D33% and D50% reduced on average by 22% (maximum 38%), and 26% (maximum 47%), respectively.

CONCLUSIONS

Using an algorithm for beam direction, shape and weight optimisation, large increases in the therapeutic ratio of liver plans could be obtained for reduced margins.

PTV dose prescription strategies for SBRT of metastatic liver tumours

PURPOSE

Recently we have demonstrated that our in-house developed algorithm for automated plan generation for fully non-coplanar SBRT of liver patients (designated Cycle) yields plans that are superior to conventionally generated plans of experienced dosimetrists. Here we use Cycle in the comparison of plans with prescription isodoses of 65% or 80% of the isocentre dose.

METHODS

Plans were generated using CT-data of 15 previously treated patients. For each patient, both for the 65%- and the 80% strategy, Cycle was used to generate a plan with the maximum isocentre dose, D(isoc), while strictly obeying a set of hard constraints for the organs at risk (OAR). Plans for the two strategies were compared using D(isoc), D(PTV,99%) (the minimum dose delivered to 99% of the PTV), and the generalised equivalent uniform dose, gEUD(PTV)(a), for several values of the parameter a. Moreover, for the OARs, the distance to the constraint values was analysed.

RESULTS

The 65% strategy resulted in treatment plans with a higher D(isoc) (average 17.6%, range 7.6-31.1%) than the 80% strategy, at the cost of a somewhat lower D(PTV,99%) (average -2.0%, range -9.6% to 9.3%). On average, voxels with a dose in the 65% strategy, lower than the minimum PTV dose in the 80% strategy, were within 0.2cm from the PTV surface. For a-10, the 65% strategy yielded on average a significantly (P<0.01) higher gEUD(PTV)(a) than the 80% strategy, whereas for highly negative a-values the 80% approach was slightly better, although not significantly. Large variations between patients were observed. Generally, for the OAR the approach to the constraint levels was similar for the two strategies.

CONCLUSION

On average, PTV dose delivery is superior with the 65% strategy. However, apart from the isocentre dose, for each applied PTV dose parameter at least one patient would have been better off with the 80% dose prescription strategy.

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

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

Computer optimization of noncoplanar beam setups improves stereotactic treatment of liver tumors

PURPOSE

To investigate whether computer-optimized fully noncoplanar beam setups may improve treatment plans for the stereotactic treatment of liver tumors.

METHODS

An algorithm for automated beam orientation and weight selection (Cycle) was extended for noncoplanar stereotactic treatments. For 8 liver patients previously treated in our clinic using a prescription isodose of 65%, Cycle was used to generate noncoplanar and coplanar plans with the highest achievable minimum planning target volume (PTV) dose for the clinically delivered isocenter and mean liver doses, while not violating the clinically applied hard planning constraints. The clinical and the optimized coplanar and noncoplanar plans were compared, with respect to D(PTV,99%), the dose received by 99% of the PTV, the PTV generalized equivalent uniform dose (gEUD), and the compliance with the clinical constraints.

RESULTS

For each patient, the ratio between D(PTV,99%) and D(isoc), and the gEUD(-5) and gEUD(-20) values of the optimized noncoplanar plan were higher than for the clinical plan with an average increase of respectively 18.8% (range, 7.8-24.0%), 6.4 Gy (range, 3.4-11.8 Gy), and 10.3 Gy (range, 6.7-12.5). D(PTV,99%)/D(isoc), gEUD(-5), and gEUD(-20) of the optimized noncoplanar plan was always higher than for the optimized coplanar plan with an average increase of, respectively, 4.5% (range, 0.2-9.7%), 2.7 Gy (range, 0.6-9.7 Gy), and 3.4 Gy (range, 0.6-9.9 Gy). All plans were within the imposed hard constraints. On average, the organs at risk were better spared with the optimized noncoplanar plan than with the optimized coplanar plan and the clinical plan.

CONCLUSIONS

The use of automatically generated, fully noncoplanar beam setups results in plans that are favorable compared with coplanar techniques. Because of the automation, we found that the planning workload can be decreased from 1 to 2 days to 1 to 2 h.

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

BACKGROUND AND PURPOSE

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

MATERIALS AND METHODS

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

RESULTS

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

CONCLUSIONS

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

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

PURPOSE

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

METHODS AND MATERIALS

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

RESULTS

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

CONCLUSIONS

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

Automatic 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.

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.

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.

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.

Investigation of the added value of high-energy electrons in intensity-modulated radiotherapy: four clinical cases

PURPOSE

Intensity-modulated radiotherapy (IMRT) with photon beams is currently pursued in many clinics. Theoretically, inclusion of intensity- and energy-modulated high-energy electron beams (15-50 MeV) offers additional possibilities to improve radiotherapy treatments of deep-seated tumors. In this study the added value of high-energy electron beams in IMRT treatments was investigated.

METHODS AND MATERIALS

In a comparative treatment planning study, conventional treatment plans and various types of IMRT plans were constructed for four clinical cases (cancer of the bladder, pancreas, chordoma of the sacrum, and breast). The conventional plans were used for the actual treatment of the patients. The IMRT plans were optimized using the Orbit optimization code (Löf et al., 2000) with a radiobiologic objective function. The IMRT plans were either photon or combined electron and photon beam plans, with or without dose homogeneity constraints assuming standard or increased radiosensitivities of organs at risk.

RESULTS

Large improvements in expected treatment outcome are found using IMRT plans compared to conventional plans, but differences in tumor control probability (TCP) and normal tissue complication probabilities (NTCP) values between IMRT plans with and without electrons are small. However, the use of electrons improves the dose-volume histograms for organs at risk, especially at lower dose levels (e.g., 0-40 Gy).

CONCLUSIONS

This preliminary study indicates that addition of higher energy electrons to IMRT can only marginally improve treatment outcome for the selected cases. The dose-volume histograms of organs at risk show improvements for IMRT with higher energy electrons, which may reduce tumor induction but does not substantially reduce NTCP.