Computerized triplet beam orientation optimization for MRI-guided Co-60 radiotherapy.

The intensity modulated radiation therapy (IMRT) treatment planning problem consists of several subproblems which are typically solved sequentially. We seek to combine two of the subproblems: the beam orientation optimization (BOO) problem and the fluence map optimization (FMO) problem. The BOO problem is the problem of selecting the beam orientations to deliver radiation to the patient. The FMO problem is the problem of determining the amount of radiation intensity, or fluence, of each beamlet in each beam. The solution to the FMO problem measures the quality of a beam set, but the majority of previous BOO studies rely on heuristics and approximations to gauge the quality of the beam set. In contrast with these studies, we use an exact measure of the treatment plan quality attainable using a given beam set, which ensures convergence to a global optimum in the case of our simulated annealing algorithm and a local optimum in the case of our local search algorithm. We have also developed a new neighborhood structure that allows for faster convergence using our simulated annealing and local search algorithms, thus reducing the amount of time required to obtain a good solution. Finally, we show empirically that we can generate clinically acceptable treatment plans that require fewer beams than in current practice. This may reduce the length of treatment time, which is an important clinical consideration in IMRT.

In this study, we perform a scientific comparative analysis of using 60Co beams in intensity-modulated radiation therapy (IMRT). In particular, we evaluate the treatment plan quality obtained with (i) 6 MV, 18 MV and 60Co IMRT; (ii) different numbers of static multileaf collimator (MLC) delivered 60Co beams and (iii) a helical tomotherapy 60Co beam geometry. We employ a convex fluence map optimization (FMO) model, which allows for the comparison of plan quality between different beam energies and configurations for a given case. A total of 25 clinical patient cases that each contain volumetric CT studies, primary and secondary delineated targets, and contoured structures were studied: 5 head-and-neck (H&N), 5 prostate, 5 central nervous system (CNS), 5 breast and 5 lung cases. The DICOM plan data were anonymized and exported to the University of Florida optimized radiation therapy (UFORT) treatment planning system. The FMO problem was solved for each case for 5–71 equidistant beams as well as a helical geometry for H&N, prostate, CNS and lung cases, and for 3–7 equidistant beams in the upper hemisphere for breast cases, all with 6 MV, 18 MV and 60Co dose models. In all cases, 95% of the target volumes received at least the prescribed dose with clinical sparing criteria for critical organs being met for all structures that were not wholly or partially contained within the target volume. Improvements in critical organ sparing were found with an increasing number of equidistant 60Co beams, yet were marginal above 9 beams for H&N, prostate, CNS and lung. Breast cases produced similar plans for 3–7 beams. A helical 60Co beam geometry achieved similar plan quality as static plans with 11 equidistant 60Co beams. Furthermore, 18 MV plans were initially found not to provide the same target coverage as 6 MV and 60Co plans; however, adjusting the trade-offs in the optimization model allowed equivalent target coverage for 18 MV. For plans with comparable target coverage, critical structure sparing was best achieved with 6 MV beams followed closely by 60Co beams, with 18 MV beams requiring significantly increased dose to critical structures. In this paper, we report in detail on a representative set of results from these experiments. The results of the investigation demonstrate the potential for IMRT radiotherapy employing commercially available 60Co sources and a double-focused MLC. Increasing the number of equidistant beams beyond 9 was not observed to significantly improve target coverage or critical organ sparing and static plans were found to produce comparable plans to those obtained using a helical tomotherapy treatment delivery when optimized using the same well-tuned convex FMO model. While previous studies have shown that 18 MV plans are equivalent to 6 MV for prostate IMRT, we found that the 18 MV beams actually required more fluence to provide similar quality target coverage.

The fluence map optimization (FMO) problem is one of the most studied problems in intensity-modulated radiation therapy treatment planning. Although many approaches have shown to yield good solutions to the FMO problem, the optimal solutions obtained ensure that the resulting treatment is the best possible with respect to the weighting parameters of the formulation used. Since the ‘optimal’ weighting scheme is unknown, the choice of the weight parameters is typically a long trial-and-error process until a satisfactory solution is achieved. Moreover, for selecting the best irradiating directions, it is not clear how traditional trial-and-error parameter tuning should be incorporated or managed. A two-stage programming approach is proposed to reduce the dependency of the optimal solutions on the weight parameters and simultaneously improve the overall plan quality. This approach is yet another step towards automated generation of treatment plans which will result in breakthrough developments in radiation therapy care.

Radiation therapy is one of the main treatment modalities for cancer. The objective of radiation therapy is to eliminate all cancer cells by delivering a prescribed dose of radiation to the tumor volume while sparing at the same time the surrounding tissues. Intensity-modulated radiation therapy (IMRT) is a sophisticated technologically-driven type of radiation therapy where non-uniform radiation fields are used to irradiate the patient from different beam angle directions. Appropriate selection of beam irradiation directions – beam angle optimization (BAO) problem – enhance the quality of the treatment plan. The BAO problem is a very difficult global non-convex optimization problem for which there are few or none commercial solutions. Typically, the BAO procedure is driven by the outcome of the fluence map optimization (FMO) problem – the problem of calculating the most adequate radiation intensities. However, functions used for modeling the FMO problem have little clinical meaning. Typically, selection/validation of treatment plans is done considering a set of dosimetric measures. In this study, we propose a treatment plan global score, based on dosimetric criteria and its relative importance, as alternative plan’s quality measure to drive the BAO procedure. For the clinical case of nasopharyngeal tumor, the use of a global score to drive the BAO procedure lead to higher quality treatment plans. For similar target coverage, an improved organ sparing was obtained.

We consider the problem of intensity-modulated radiation therapy (IMRT) treatment planning using direct aperture optimization. While this problem has been relatively well studied in recent years, most approaches employ a heuristic approach to the generation of apertures. In contrast, we use an exact approach that explicitly formulates the fluence map optimization (FMO) problem as a convex optimization problem in terms of all multileaf collimator (MLC) deliverable apertures and their associated intensities. However, the number of deliverable apertures, and therefore the number of decision variables and constraints in the new problem formulation, is typically enormous. To overcome this, we use an iterative approach that employs a subproblem whose optimal solution either provides a suitable aperture to add to a given pool of allowable apertures or concludes that the current solution is optimal. We are able to handle standard consecutiveness, interdigitation and connectedness constraints that may be imposed by the particular MLC system used, as well as jaws-only delivery. Our approach has the additional advantage that it can explicitly account for transmission of dose through the part of an aperture that is blocked by the MLC system, yielding a more precise assessment of the treatment plan than what is possible using a traditional beamlet-based FMO problem. Finally, we develop and test two stopping rules that can be used to identify treatment plans of high clinical quality that are deliverable very efficiently. Tests on clinical head-and-neck cancer cases showed the efficacy of our approach, yielding treatment plans comparable in quality to plans obtained by the traditional method with a reduction of more than 75% in the number of apertures and a reduction of more than 50% in beam-on time, with only a modest increase in computational effort. The results also show that delivery efficiency is very insensitive to the addition of traditional MLC constraints; however, jaws-only treatment requires about a doubling in beam-on time and number of apertures used. Finally, we showed the importance of accounting for transmission effects when assessing or, preferably, optimizing treatment plan quality.

Dosimetric comparison of left-sided whole-breast irradiation with 3DCRT, forward-planned IMRT, inverse-planned IMRT, helical tomotherapy, and volumetric arc therapy

To evaluate dosimetric differences of IMRT lung plans generated from RayStation× Multi-Criteria Optimization (MCO) and Pinnacle Direct Machine Parameters Optimization (DMPO) Methods: Five patients previously treated with plans from Pinnacle v9.0 using DMPO algorithm were re-planned on RayStation v2.4.8.180 using MCO Pareto plans with same dose constraints, beam angles and objectives. The prescription was 60 Gy to 95% of PTV. Planning outcomes such as D95 (95% of volume receiving the prescribed dose), D2, D1 for PTV, D33 and mean dose for heart, V20 (volume receives at least 20 Gy) and mean dose for lung, max dose for cord were reported for evaluation according to our clinical protocols. The conformity of the prescription isodose volume to PTV was evaluated as conformity index (CI). Planning time was also observed. The mean volume of PTV was 356 ± 141 cm3 . The D95 of PTV with RayStation was improved and more uniform compared to plans from Pinnacle (59.4 ± 0.2 vs. 59.2 ± 0.8 Gy), respectively. D2 and D1 of PTV were lower with RayStation plans. Mean dose and V20 of total lung were lower for all RayStation plans with max dose of cord, and D33 and mean dose of heart following the same trend. CI was better with RayStation compared to Pinnacle (1.09 ± 0.06 vs. 1.16 ± 0.11). Planning time was faster with RayStation from Pinnacle (few minutes. vs. minimum of 20 minutes, approximately). MCO planning automatically generates a set of Pareto optimized solutions for given objectives to allow tradeoffs between targets and critical organs. RayStation can achieve better uniform tumor coverage with fewer hot spots while sparing more critical structures. MCO Pareto based IMRT plans is helpful in determining the best optimized dosimetry with shorter planning time.

We present a novel linear programming (LP) based approach for efficiently solving the intensity modulated radiation therapy (IMRT) fluence-map optimization (FMO) problem to global optimality. Our model overcomes the apparent limitations of a linear-programming approach by approximating any convex objective function by a piecewise linear convex function. This approach allows us to retain the flexibility offered by general convex objective functions, while allowing us to formulate the FMO problem as a LP problem. In addition, a novel type of partial-volume constraint that bounds the tail averages of the differential dose–volume histograms of structures is imposed while retaining linearity as an alternative approach to improve dose homogeneity in the target volumes, and to attempt to spare as many critical structures as possible. The goal of this work is to develop a very rapid global optimization approach that finds high quality dose distributions. Implementation of this model has demonstrated excellent results. We found globally optimal solutions for eight 7-beam head-and-neck cases in less than 3 min of computational time on a single processor personal computer without the use of partial-volume constraints. Adding such constraints increased the running times by a factor of 2–3, but improved the sparing of critical structures. All cases demonstrated excellent target coverage (>95%), target homogeneity (<10% overdosing and <7% underdosing) and organ sparing using at least one of the two models.

We developed a fluence map prediction method that directly generates fluence maps for a given desired dose distribution without optimization for volumetric modulated arc therapy (VMAT) planning. The prediction consists of two steps. First, projections of the desired dose are calculated and then inversely mapped to fluence maps in the phantom geometry by a deep neural network. Second, a plan scaling technique is applied to scale fluence maps from phantom to patient geometry. We evaluated the performance of the proposed fluence map prediction method for 102 head and neck (H&N) and 14 prostate cancer VMAT plans by comparing the patient doses calculated from the predicted fluence maps with the given desired dose distributions. The mean dose differences were 1.42% ± 0.37%, 1.53% ± 0.44% and 1.25% ± 0.44% for the planning target volume (PTV), the region from the PTV boundary to the 50% isodose line, and the region from the 50% to the 20% isodose line, respectively. The gamma passing rate was 98.06% ± 2.64% with the 3 mm/3% criterion. The prediction time for a single VMAT plan was less than one second. In conclusion, we developed an inverse mapping-based method that predicts fluence maps for desired dose distributions with high accuracy. Our method is effectively an optimization-free inverse planning approach, which was orders of magnitude faster than fluence map optimization. Combining the proposed method with leaf sequencing has the potential to dramatically speed up VMAT treatment planning.

Conventional beam orientation optimization (BOO) algorithms for IMRT assume that the same set of beam angles is used for all treatment fractions. In this paper we present a BOO formulation based on group sparsity that simultaneously optimizes non-coplanar beam angles for all fractions, yielding a fraction-variant (FV) treatment plan. Beam angles are selected by solving a multi-fraction fluence map optimization problem involving 500-700 candidate beams per fraction, with an additional group sparsity term that encourages most candidate beams to be inactive. The optimization problem is solved using the fast iterative shrinkage-thresholding algorithm. Our FV BOO algorithm is used to create five-fraction treatment plans for digital phantom, prostate, and lung cases as well as a 30-fraction plan for a head and neck case. A homogeneous PTV dose coverage is maintained in all fractions. The treatment plans are compared with fraction-invariant plans that use a fixed set of beam angles for all fractions. The FV plans reduced OAR mean dose and D2 values on average by 3.3% and 3.8% of the prescription dose, respectively. Notably, mean OAR dose was reduced by 14.3% of prescription dose (rectum), 11.6% (penile bulb), 10.7% (seminal vesicle), 5.5% (right femur), 3.5% (bladder), 4.0% (normal left lung), 15.5% (cochleas), and 5.2% (chiasm). D2 was reduced by 14.9% of prescription dose (right femur), 8.2% (penile bulb), 12.7% (proximal bronchus), 4.1% (normal left lung), 15.2% (cochleas), 10.1% (orbits), 9.1% (chiasm), 8.7% (brainstem), and 7.1% (parotids). Meanwhile, PTV homogeneity defined as D95/D5 improved from .92 to .95 (digital phantom), from .95 to .98 (prostate case), and from .94 to .97 (lung case), and remained constant for the head and neck case. Moreover, the FV plans are dosimetrically similar to conventional plans that use twice as many beams per fraction. Thus, FV BOO offers the potential to reduce delivery time for non-coplanar IMRT.

Previous diffusion tensor imaging (DTI) studies have mainly focused on dose-dependent white matter (WM) alterations 1month to 1year after radiation therapy (RT) with a tract-average method. However, WM alterations immediately after RT are subtle, resulting in early WM alterations that cannot be detected by tract-average methods. Therefore, we performed a study with an along-tract method in patients with brain metastases to explore the early dose-response pattern of WM alterations after RT. Sixteen patients with brain metastases underwent DTI before and 1-3days after brain RT. DTI metrics, such as fractional anisotropy (FA), axial diffusivity (AD), radial diffusivity (RD) and mean diffusivity (MD), were calculated. Along-tract statistics were then used to resample WM fibre streamlines and generate a WM skeleton fibre tract. DTI metric alterations (post_RT-pre_RT DTI metrics) and the planned doses (max or mean doses) were mapped to 18 WM tracts. A linear fixed model was performed to analyse the main effect of dose on DTI metric alterations. AD alterations in the left hemispheric uncinated fasciculus (UNC_L) were associated with max doses, in which decreased AD alterations were associated with higher doses. Our findings may provide pathological insight into early dose-dependent WM alterations and may contribute to the development of max dose-constrained RT techniques to protect brain microstructure in the UNC_L.

Intensity modulated radiation therapy (IMRT) inverse planning using total-variation (TV) regularization has been proposed to reduce the complexity of fluence maps and facilitate dose delivery. Conventionally, the optimization problem with L-1 norm is solved with quadratic programming (QP), which is time consuming and memory expensive due to the second-order Newton update. This study proposes to use a new algorithm, template for first-order conic solver (TFOCS), for fast and memory-efficient optimization in IMRT inverse planning. The TFOCS utilizes dual-variable updates and first-order approaches for TV minimization without the need to compute and store the enlarged Hessian matrix required for Newton update in the QP technique. To evaluate the effectiveness and efficiency of the proposed method, two clinical cases were used for IMRT inverse planning: a head and neck case and a prostate case. For comparison, the conventional QP-based method for the TV form was adopted to solve the fluence map optimization problem in the above two cases. The convergence criteria and algorithm parameters were selected to achieve similar dose conformity for a fair comparison between the two methods. Compared with conventional QP-based approach, the proposed TFOCS-based method shows a remarkable improvement in computational efficiency for fluence map optimization, while maintaining the conformal dose distribution. Compared with QP-based algorithms, the computational speed using TFOCS for fluence optimization is increased by a factor of 4 to 6, and at the same time the memory requirement is reduced by a factor of 3 to 4. Therefore, TFOCS provides an effective, fast and memory-efficient method for IMRT inverse planning. The unique features of the approach should be particularly important in inverse planning involving a large number of beams, such as in VMAT and dense angularly sampled and sparse intensity modulated radiation therapy (DASSIM-RT).

The intensity-modulated radiation therapy (IMRT) treatment planning is usually a sequential process where initially a given number of beam directions are selected followed by the fluence map optimization (FMO) considering those beam directions. The beam angle optimization (BAO) problem consists on the selection of appropriate radiation incidence directions in radiation therapy treatment planning and may be decisive for the quality of the treatment plan, both for appropriate tumor coverage and for enhancement of better organs sparing. This selection must be based on the optimal value of the FMO problem otherwise the resulting beam angle set has no guarantee of optimality and has questionable reliability. Pattern search methods (PSM) have been used successfully to address the BAO problem driven by the optimal fluence value of the FMO problem. PSM are iterative methods generating a sequence of non-increasing iterates such that iterate progression is solely based on a finite number of function evaluations in each iteration, without explicit or implicit use of derivatives. Typically, in IMRT optimization, the quality of the solutions obtained is not simply related to the final value of an objective function but rather judged by dose-volume histograms or considering a set of physical dose metrics. These dose metrics can be simply described as obtaining a minimum prescribed dose for the target volumes (the regions that have to be irradiated) and a maximum or mean tolerance dose values for the remaining surrounding structures (the regions that should be spared). The goal of this paper is to present a non-descent PSM that can be guided both by an objective function formulation of the FMO problem and by physical dose metrics. Four retrospective treated cases of head-and-neck tumors at the Portuguese Institute of Oncology of Coimbra are used to discuss the benefits of non-descent PSM for the optimization of the BAO problem.

The advent of automated beam orientation and fluence optimization enables more complex intensity modulated radiation therapy (IMRT) planning using an increasing number of fields to exploit the expanded solution space. This has created a challenge in converting complex fluences to robust multileaf collimator (MLC) segments for delivery. A novel method to regularize the fluence map and simplify MLC segments is introduced to maximize delivery efficiency, accuracy, and plan quality. In this work, we implemented a novel approach to regularize optimized fluences in the dose domain. The treatment planning problem was formulated in an optimization framework to minimize the segmentation-induced dose distribution degradation subject to a total variation regularization to encourage piecewise smoothness in fluence maps. The optimization problem was solved using a first-order primal-dual algorithm known as the Chambolle-Pock algorithm. Plans for 2 GBM, 2 head and neck, and 2 lung patients were created using 20 automatically selected and optimized noncoplanar beams. The fluence was first regularized using Chambolle-Pock and then stratified into equal steps, and the MLC segments were calculated using a previously described level reducing method. Isolated apertures with sizes smaller than preset thresholds of 1-3 bixels, which are square units of an IMRT fluence map from MLC discretization, were removed from the MLC segments. Performance of the dose domain regularized (DDR) fluences was compared to direct stratification and direct MLC segmentation (DMS) of the fluences using level reduction without dose domain fluence regularization. For all six cases, the DDR method increased the average planning target volume dose homogeneity (D95/D5) from 0.814 to 0.878 while maintaining equivalent dose to organs at risk (OARs). Regularized fluences were more robust to MLC sequencing, particularly to the stratification and small aperture removal. The maximum and mean aperture sizes using the DDR were consistently larger than those from DMS for all tested number of segments. The fluence map to MLC segmentation conversion problem was formulated as a secondary optimization problem in the dose domain to minimize the smoothness-regularized dose discrepancy. The large scale optimization problem was solved using a primal-dual algorithm that transformed complicated fluences into maps that were more robust to the MLC segmentation and sequencing, affording fewer and larger segments with minimal degradation to dose distribution.

We present a spatiotemporally integrated formulation of the optimal fractionation problem using the standard log-linear-quadratic survival model. Our objective is to choose a fluence map and a number of fractions to maximize the biological effect of tumor dose averaged over its voxels subject to maximum dose, mean dose, and dose-volume constraints for various normal tissues. Constraints are expressed in biologically effective dose equivalents. We propose an efficient convex programming method to approximately solve the resulting computationally difficult model. Through extensive computer simulations on 10 head-and-neck and prostate cancer test cases with a broad range of radiobiological parameters, we compare the biological effect on tumors obtained by our integrated approach relative to that from two other models. The first is a traditional intensity modulated radiation therapy (IMRT) fluence map optimization model that does not optimize the number of fractions. The second assumes that a fluence map is available a priori from a traditional IMRT optimization model and then optimizes the number of fractions, thus separating the spatial and temporal components. The improvements in tumor biological effect over IMRT were 9%–52%, with an average of 22% for head-and-neck, and 53%–108%, with an average of 69% for prostate. The improvements in tumor biological effect over the spatiotemporally separated model were 15%–45%, with an average of 27%, and 17%–23%, with an average of 21%, for head-and-neck and prostate, respectively. This suggests that integrated optimization of the fluence map and the number of fractions could improve treatment efficacy, as measured within the linear-quadratic framework.