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

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.

Beam selection for stereotactic ablative radiotherapy using Cyberknife with multileaf collimation

The Cyberknife system (Accuray Inc., Sunnyvale, CA) enables radiotherapy using stereotactic ablative body radiotherapy (SABR) with a large number of non-coplanar beam orientations. Recently, a multileaf collimator has also been available to allow flexibility in field shaping. This work aims to evaluate the quality of treatment plans obtainable with the multileaf collimator. Specifically, the aim is to find a subset of beam orientations from a predetermined set of candidate directions, such that the treatment quality is maintained but the treatment time is reduced. An evolutionary algorithm is used to successively refine a randomly selected starting set of beam orientations. By using an efficient computational framework, clinically useful solutions can be found in several hours. It is found that 15 beam orientations are able to provide treatment quality which approaches that of the candidate beam set of 110 beam orientations, but with approximately half of the estimated treatment time. Choice of an efficient subset of beam orientations offers the possibility to improve the patient experience and maximise the number of patients treated.

OUT-OF-FIELD DOSE MEASUREMENTS FOR 3D CONFORMAL AND INTENSITY MODULATED RADIOTHERAPY OF A PAEDIATRIC BRAIN TUMOUR

The purpose of this study was to measure out-of-field organ doses in clinical conditions in anthropomorphic paediatric phantoms which received a simulated treatment of a brain tumour with intensity modulated radiotherapy (IMRT) and 3D conformal radiotherapy (3D CRT). Organ doses measured with radiophotoluminescent and thermoluminescent dosemeters were on average 1.6 and 3.0 times higher for the 5 y-old than for the 10 y-old phantom for IMRT and 3D CRT, respectively. A larger 5-y to 10-y organ dose ratio for 3D CRT can be explained because the use of a mechanical wedge for the 5-y-old 3D CRT phantom treatment increased out-of-field doses. Due to different configurations of the radiation fields, for both phantoms, the IMRT technique resulted in a higher non-target brain dose and higher eye doses but lower thyroid doses compared to 3D CRT. For 3D CRT (which used a non-coplanar field configuration), eye doses were 3-6% and for IMRT (which used a coplanar field configuration) 27-30% of the treatment dose, respectively. For thyroid and more distant organs, doses were less than 1% of the treatment dose. Comparison of measured doses and doses calculated by the treatment planning system (TPS) showed that the TPS underestimated out-of-field doses both for IMRT and 3D CRT.

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.

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

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

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.

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

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

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

BACKGROUND AND PURPOSE

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

MATERIALS AND METHODS

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

RESULTS

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

CONCLUSIONS

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

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

PURPOSE

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

METHODS AND MATERIALS

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

RESULTS

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

CONCLUSIONS

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

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

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

Feasibility study of beam orientation class-solutions for prostate IMRT

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

Determining optimal two-beam axial orientations for heart sparing in left-sided breast cancer patients

BACKGROUND AND PURPOSE

The optimal intensity fluence profile of a beam depends on the profiles of other beams but most optimizations assume fixed beam orientations, a priori. Breast cancer radiotherapy attempts to cover the target and to spare critical structures such as the heart and lungs. The study aims are (1) to determine and document the optimal two-beam orientation that best spares the heart for left-sided breast cancer patients and (2) to investigate the influence of the treatment technique (i.e., conformal versus intensity modulation) on the optimal objective cost function.

MATERIAL AND METHODS

Ten left-sided breast cancer patients were planned using a conformal (3DCRT) and a simplified intensity modulated (sIMRT) technique using predefined segments and different two-beam orientations. Optimal segment weights were determined exhaustively for all axial two-beam combinations, in 5 degree increments, by minimizing a quadratic objective cost function. The resulting objective cost function was analyzed with respect to target geometry and treatment technique.

RESULTS

The sIMRT plans are generally less sensitive to beam orientation compared to 3DCRT plans. Optimal two-beam orientations for 3DCRT and sIMRT plans exist and they correspond to a hinge angle of approximately 188 degrees and 160 degrees or 210 degrees (the latter is bimodal), respectively.

CONCLUSIONS

The optimization software is a useful tool that can test many different beam combinations and estimate their associated objective cost values. Afterwards, the most promising beam orientations could be re-optimized under the TPS to fine-tune and verify the dose distributions. Optimal uniform two-beam orientations for the breast consist of opposing tangential medial and lateral beams. Optimal nonuniform two-beam orientations for left-sided breast cancers are bimodal, containing hinge angles around 160 degrees and 210 degrees. Nonuniform beam techniques are less sensitive to beam orientation compared to uniform beam techniques and result in significantly improved heart sparing but at a cost of slightly compromised planning target volume coverage.

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

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

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.

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.

A geometry based optimization algorithm for conformal external beam radiotherapy

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

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

PURPOSE

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

METHODS AND MATERIALS

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

RESULTS AND CONCLUSIONS

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

Incorporating prior knowledge into beam orientation optimization in IMRT

PURPOSE

Selection of beam configuration in currently available intensity-modulated radiotherapy (IMRT) treatment planning systems is still based on trial-and-error search. Computer beam orientation optimization has the potential to improve the situation, but its practical implementation is hindered by the excessive computing time associated with the calculation. The purpose of this work is to provide an effective means to speed up the beam orientation optimization by incorporating a priori geometric and dosimetric knowledge of the system and to demonstrate the utility of the new algorithm for beam placement in IMRT.

METHODS AND MATERIALS

Beam orientation optimization was performed in two steps. First, the quality of each possible beam orientation was evaluated using beam's-eye-view dosimetrics (BEVD) developed in our previous study. A simulated annealing algorithm was then employed to search for the optimal set of beam orientations, taking into account the BEVD scores of different incident beam directions. During the calculation, sampling of gantry angles was weighted according to the BEVD score computed before the optimization. A beam direction with a higher BEVD score had a higher probability of being included in the trial configuration, and vice versa. The inclusion of the BEVD weighting in the stochastic beam angle sampling process made it possible to avoid spending valuable computing time unnecessarily at "bad" beam angles. An iterative inverse treatment planning algorithm was used for beam intensity profile optimization during the optimization process. The BEVD-guided beam orientation optimization was applied to an IMRT treatment of paraspinal tumor. The advantage of the new optimization algorithm was demonstrated by comparing the calculation with the conventional scheme without the BEVD weighting in the beam sampling.

RESULTS

The BEVD tool provided useful guidance for the selection of the potentially good directions for the beams to incident and was used to guide the search for the optimal beam configuration. The BEVD-guided sampling improved both optimization speed and convergence of the calculation. A comparison of several five-field IMRT treatment plans obtained with and without BEVD guidance indicated that the computational efficiency was increased by a factor of approximately 10.

CONCLUSION

Incorporation of BEVD information allows for development of a more robust tool for beam orientation optimization in IMRT planning. It enables us to more effectively use the angular degree of freedom in IMRT without paying the excessive computing overhead and brings us one step closer to the goal of automated selection of beam orientations in a clinical environment.

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

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

Role of beam orientation optimization in intensity-modulated radiation therapy

PURPOSE

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

METHODS AND MATERIALS

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

RESULTS

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

CONCLUSION

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

A mixed-encoding genetic algorithm with beam constraint for conformal radiotherapy treatment planning

In this paper we propose a new hierarchical evolutionary algorithm that combines binary encoding and floating-point encoding to automatically select the beam directions and determine the weights of the selected beams. With traditional optimization methods the beam directions are fixed a priori by the operator in recognition of the fact that computer selection of beam directions is a difficult problem. In this investigation, we used a hybrid-encoding scheme. The binary encoding part of each chromosome was used to select the beam directions, and its corresponding floating-point encoding part of the same chromosome was used to determine the weights of those selected beams. Before beginning the optimization process, we set a constraint on the number of the beam directions we wanted in the final solution. We present three examples to verify this method. These examples differ with each other in tumor sites, problem sizes, and optimization parameters. Three-dimensional optimization results and statistical data showed that this method is feasible. We think this method can be easily extended to solve more complex target problems (such as nonconvex target problems).

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 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.