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

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.

A fast deep learning approach for beam orientation optimization for prostate cancer treated with intensity-modulated radiation therapy

PURPOSE

Beam orientation selection, whether manual or protocol-based, is the current clinical standard in radiation therapy treatment planning, but it is tedious and can yield suboptimal results. Many algorithms have been designed to optimize beam orientation selection because of its impact on treatment plan quality, but these algorithms suffer from slow calculation of the dose influence matrices of all candidate beams. We propose a fast beam orientation selection method, based on deep learning neural networks (DNN), capable of developing a plan comparable to those developed by the state-of-the-art column generation (CG) method. Our model's novelty lies in its supervised learning structure (using CG to teach the network), DNN architecture, and ability to learn from anatomical features to predict dosimetrically suitable beam orientations without using dosimetric information from the candidate beams. This may save hours of computation.

METHODS

A supervised DNN is trained to mimic the CG algorithm, which iteratively chooses beam orientations one-by-one by calculating beam fitness values based on Karush-Kush-Tucker optimality conditions at each iteration. The DNN learns to predict these values. The dataset contains 70 prostate cancer patients - 50 training, 7 validation, and 13 test patients - to develop and test the model. Each patient's data contains 6 contours: PTV, body, bladder, rectum, and left and right femoral heads. Column generation was implemented with a GPU-based Chambolle-Pock algorithm, a first-order primal-dual proximal-class algorithm, to create 6270 plans. The DNN trained over 400 epochs, each with 2500 steps and a batch size of 1, using the Adam optimizer at a learning rate of 1 × 10-5 and a sixfold cross-validation technique.

RESULTS

The average and standard deviation of training, validation, and testing loss functions among the six folds were 0.62 ± 0.09%, 1.04 ± 0.06%, and 1.44 ± 0.11%, respectively. Using CG and supervised DNN, we generated two sets of plans for each scenario in the test set. The proposed method took at most 1.5 s to select a set of five beam orientations and 300 s to calculate the dose influence matrices for 5 beams and finally 20 s to solve the fluence map optimization (FMO). However, CG needed around 15 h to calculate the dose influence matrices of all beams and at least 400 s to solve both the beam orientation selection and FMO problems. The differences in the dose coverage of PTV between plans generated by CG and by DNN were 0.2%. The average dose differences received by organs at risk were between 1 and 6 percent: Bladder had the smallest average difference in dose received (0.956 ± 1.184%), then Rectum (2.44 ± 2.11%), Left Femoral Head (6.03 ± 5.86%), and Right Femoral Head (5.885 ± 5.515%). The dose received by Body had an average difference of 0.10 ± 0.1% between the generated treatment plans.

CONCLUSIONS

We developed a fast beam orientation selection method based on a DNN that selects beam orientations in seconds and is therefore suitable for clinical routines. In the training phase of the proposed method, the model learns the suitable beam orientations based on patients' anatomical features and omits time intensive calculations of dose influence matrices for all possible candidate beams. Solving the FMO to get the final treatment plan requires calculating dose influence matrices only for the selected beams.

New Developments in Intensity Modulated Radiation Therapy

As intensity modulated radiation therapy (IMRT) becomes routine clinical practice, its advantages and limitations are better understood. With these new understandings, some new developments have emerged in an effort to alleviate the limitations of the current IMRT practice. This article describes a few of these efforts made at the University of Maryland, including: i) improving IMRT efficiency with direct aperture optimization; ii) broadening the scope of optimization to include the mode of delivery and beam angles; and iii) new planning methods for intensity modulated arc therapy (IMAT).

Spherical cluster analysis for beam angle optimization in intensity-modulated radiation therapy treatment planning

An intuitive heuristic to establish beam configurations for intensity-modulated radiation therapy is introduced as an extension of beam ensemble selection strategies applying scalar scoring functions. It is validated by treatment plan comparisons for three intra-cranial, pancreas, and prostate cases each. Based on a patient specific matrix listing the radiological quality of candidate beam directions individually for every target voxel, a set of locally ideal beam angles is generated. The spherical distribution of locally ideal beam angles is characteristic for every treatment site and patient: ideal beam angles typically cluster around distinct orientations. We interpret the cluster centroids, which are identified with a spherical K-means algorithm, as irradiation angles of an intensity-modulated radiation therapy treatment plan. The fluence profiles are subsequently optimized during a conventional inverse planning process. The average computation time for the pre-optimization of a beam ensemble is six minutes on a state-of-the-art work station. The treatment planning study demonstrates the potential benefit of the proposed beam angle optimization strategy. For the three prostate cases under investigation, the standard treatment plans applying nine coplanar equi-spaced beams and treatment plans applying an optimized non-coplanar nine-beam ensemble yield clinically comparable dose distributions. For symmetric patient geometries, the dose distribution formed by nine equi-spaced coplanar beams cannot be improved significantly. For the three pancreas and intra-cranial cases under investigation, the optimized non-coplanar beam ensembles enable better sparing of organs at risk while guaranteeing equivalent target coverage. Beam angle optimization by spherical cluster analysis shows the biggest impact for target volumes located asymmetrically within the patient and close to organs at risk.

Geometrical pre-planning for conformal radiotherapy

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

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.

Escalated median dose for pituitary macroadenomas using intensity-modulated radiation therapy

Three-dimensional conformal radiotherapy (3D CRT) has become an established treatment for pituitary macroadenomas. This study is an investigation into the possible dosimetric advantages of intensity-modulated radiotherapy for such critically located tumors. Three consecutive patients with pituitary macroadenoma previously treated with 3D CRT were replanned with inverse-planned IMRT using Helax-TMS (V.6.0, Helax AB, Uppsala, Sweden. Fusion of computed tomography (CT) with postoperative magnetic resonance imaging (MRI) was performed within the planning system to define the gross tumor volume (GTV), planning target volume (PTV), and normal structures including the optic chiasm. Dose-volume histograms (DVHs) for the 3D CRT plans were then compared with those of the corresponding prospective IMRT plans. Both techniques maintained critical structure doses below tolerance levels while maintaining a minimum dose of 45 Gy to 100% of the PTV. While IMRT plans deliver consistently more heterogeneous dose distributions to the PTV, the median PTV dose is elevated in the IMRT plans compared with the 3D CRT plans. For critically located tumors like these pituitary macroadenomas, IMRT allows escalation of the median dose to the tumor without an accompanying loss in critical structure sparing or creating unacceptable cold spots within the PTV.

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

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

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.

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.

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.

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

PURPOSE

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

METHODS AND MATERIALS

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

RESULTS

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

CONCLUSIONS

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

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.