Accounting for the tongue-and-groove effect using a robust direct aperture optimization approach.

PURPOSE: Traditionally, the tongue-and-groove effect due to the multileaf collimator architecture in intensity-modulated radiation therapy (IMRT) has typically been deferred to the leaf sequencing stage. The authors propose a new direct aperture optimization method for IMRT treatment planning that explicitly incorporates dose calculation inaccuracies due to the tongue-and-groove effect into the treatment plan optimization stage. METHODS: The authors avoid having to accurately estimate the dosimetric effects of the tongue-and-groove architecture by using lower and upper bounds on the dose distribution delivered to the patient. They then develop a model that yields a treatment plan that is robust with respect to the corresponding dose calculation inaccuracies. RESULTS: Tests on a set of ten clinical head-and-neck cancer cases demonstrate the effectiveness of the new method in developing robust treatment plans with tight dose distributions in targets and critical structures. This is contrasted with the very loose bounds on the dose distribution that are obtained by solving a traditional treatment plan optimization model that ignores tongue-and-groove effects in the treatment planning stage. CONCLUSIONS: A robust direct aperture optimization approach is proposed to account for the dosimetric inaccuracies caused by the tongue-and-groove effect. The experiments validate the ability of the proposed approach in designing robust treatment plans regardless of the exact consequences of the tongue-and-groove architecture.

3D tumor localization through real-time volumetric x-ray imaging for lung cancer radiotherapy.

PURPOSE: To evaluate an algorithm for real-time 3D tumor localization from a single x-ray projection image for lung cancer radiotherapy. METHODS: Recently, we have developed an algorithm for reconstructing volumetric images and extracting 3D tumor motion information from a single x-ray projection [Li et al., Med. Phys. 37, 2822-2826 (2010)]. We have demonstrated its feasibility using a digital respiratory phantom with regular breathing patterns. In this work, we present a detailed description and a comprehensive evaluation of the improved algorithm. The algorithm was improved by incorporating respiratory motion prediction. The accuracy and efficiency of using this algorithm for 3D tumor localization were then evaluated on (1) a digital respiratory phantom, (2) a physical respiratory phantom, and (3) five lung cancer patients. These evaluation cases include both regular and irregular breathing patterns that are different from the training dataset. RESULTS: For the digital respiratory phantom with regular and irregular breathing, the average 3D tumor localization error is less than 1 mm which does not seem to be affected by amplitude change, period change, or baseline shift. On an NVIDIA Tesla C1060 graphic processing unit (GPU) card, the average computation time for 3D tumor localization from each projection ranges between 0.19 and 0.26 s, for both regular and irregular breathing, which is about a 10% improvement over previously reported results. For the physical respiratory phantom, an average tumor localization error below 1 mm was achieved with an average computation time of 0.13 and 0.16 s on the same graphic processing unit (GPU) card, for regular and irregular breathing, respectively. For the five lung cancer patients, the average tumor localization error is below 2 mm in both the axial and tangential directions. The average computation time on the same GPU card ranges between 0.26 and 0.34 s. CONCLUSIONS: Through a comprehensive evaluation of our algorithm, we have established its accuracy in 3D tumor localization to be on the order of 1 mm on average and 2 mm at 95 percentile for both digital and physical phantoms, and within 2 mm on average and 4 mm at 95 percentile for lung cancer patients. The results also indicate that the accuracy is not affected by the breathing pattern, be it regular or irregular. High computational efficiency can be achieved on GPU, requiring 0.1-0.3 s for each x-ray projection.

GPU-based fast low-dose cone beam CT reconstruction via total variation.

X-ray imaging dose from serial Cone-beam CT (CBCT) scans raises a clinical concern in most image guided radiation therapy procedures. The goal of this paper is to develop a fast GPU-based algorithm to reconstruct high quality CBCT images from undersampled and noisy projection data so as to lower the imaging dose. The CBCT is reconstructed by minimizing an energy functional consisting of a data fidelity term and a total variation regularization term. We develop a GPU-friendly version of a forward-backward splitting algorithm to solve this problem. A multi-grid technique is also employed. We test our CBCT reconstruction algorithm on a digital phantom and a head-and-neck patient case. The performance under low mAs is also validated using physical phantoms. It is found that 40 x-ray projections are sufficient to reconstruct CBCT images with satisfactory quality for clinical purposes. Phantom experiments indicate that CBCT images can be successfully reconstructed under 0.1 mAs/projection. Comparing with the widely used head-and-neck scanning protocol of about 360 projections with 0.4 mAs/projection, an overall 36 times dose reduction has been achieved. The reconstruction time is about 130 sec on an NVIDIA Tesla C1060 GPU card, which is estimated ∼ 100 times faster than similar regularized iterative reconstruction approaches.

Ultrafast treatment plan optimization for volumetric modulated arc therapy (VMAT).

PURPOSE: To develop a novel aperture-based algorithm for volumetric modulated are therapy (VMAT) treatment plan optimization with high quality and high efficiency. METHODS: The VMAT optimization problem is formulated as a large-scale convex programming problem solved by a column generation approach. The authors consider a cost function consisting two terms, the first enforcing a desired dose distribution and the second guaranteeing a smooth dose rate variation between successive gantry angles. A gantry rotation is discretized into 180 beam angles and for each beam angle, only one MLC aperture is allowed. The apertures are generated one by one in a sequential way. At each iteration of the column generation method, a deliverable MLC aperture is generated for one of the unoccupied beam angles by solving a subproblem with the consideration of MLC mechanic constraints. A subsequent master problem is then solved to determine the dose rate at all currently generated apertures by minimizing the cost function. When all 180 beam angles are occupied, the optimization completes, yielding a set of deliverable apertures and associated dose rates that produce a high quality plan. RESULTS: The algorithm was preliminarily tested on five prostate and five head-and-neck clinical cases, each with one full gantry rotation without any couch/collimator rotations. High quality VMAT plans have been generated for all ten cases with extremely high efficiency. It takes only 5-8 min on CPU (MATLAB code on an Intel Xeon 2.27 GHz CPU) and 18-31 s on GPU (CUDA code on an NVIDIA Tesla C1060 GPU card) to generate such plans. CONCLUSIONS: The authors have developed an aperture-based VMAT optimization algorithm which can generate clinically deliverable high quality treatment plans at very high efficiency.

Real-time volumetric image reconstruction and 3D tumor localization based on a single x-ray projection image for lung cancer radiotherapy.

PURPOSE: To develop an algorithm for real-time volumetric image reconstruction and 3D tumor localization based on a single x-ray projection image for lung cancer radiotherapy. METHODS: Given a set of volumetric images of a patient at N breathing phases as the training data, deformable image registration was performed between a reference phase and the other N-1 phases, resulting in N-1 deformation vector fields (DVFs). These DVFs can be represented efficiently by a few eigenvectors and coefficients obtained from principal component analysis (PCA). By varying the PCA coefficients, new DVFs can be generated, which, when applied on the reference image, lead to new volumetric images. A volumetric image can then be reconstructed from a single projection image by optimizing the PCA coefficients such that its computed projection matches the measured one. The 3D location of the tumor can be derived by applying the inverted DVF on its position in the reference image. The algorithm was implemented on graphics processing units (GPUs) to achieve real-time efficiency. The training data were generated using a realistic and dynamic mathematical phantom with ten breathing phases. The testing data were 360 cone beam projections corresponding to one gantry rotation, simulated using the same phantom with a 50% increase in breathing amplitude. RESULTS: The average relative image intensity error of the reconstructed volumetric images is 6.9% +/- 2.4%. The average 3D tumor localization error is 0.8 +/- 0.5 mm. On an NVIDIA Tesla C1060 GPU card, the average computation time for reconstructing a volumetric image from each projection is 0.24 s (range: 0.17 and 0.35 s). CONCLUSIONS: The authors have shown the feasibility of reconstructing volumetric images and localizing tumor positions in 3D in near real-time from a single x-ray image.

Comparative analysis of 60Co intensity-modulated radiation therapy.

In this study, we perform a scientific comparative analysis of using (60)Co beams in intensity-modulated radiation therapy (IMRT). In particular, we evaluate the treatment plan quality obtained with (i) 6 MV, 18 MV and (60)Co IMRT; (ii) different numbers of static multileaf collimator (MLC) delivered (60)Co beams and (iii) a helical tomotherapy (60)Co 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 (60)Co 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 (60)Co 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 (60)Co beam geometry achieved similar plan quality as static plans with 11 equidistant (60)Co beams. Furthermore, 18 MV plans were initially found not to provide the same target coverage as 6 MV and (60)Co 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 (60)Co 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 (60)Co 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.

An exact approach to direct aperture optimization in IMRT treatment planning.

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.

Optimization approaches to volumetric modulated arc therapy planning.

Volumetric modulated arc therapy (VMAT) has found widespread clinical application in recent years. A large number of treatment planning studies have evaluated the potential for VMAT for different disease sites based on the currently available commercial implementations of VMAT planning. In contrast, literature on the underlying mathematical optimization methods used in treatment planning is scarce. VMAT planning represents a challenging large scale optimization problem. In contrast to fluence map optimization in intensity-modulated radiotherapy planning for static beams, VMAT planning represents a nonconvex optimization problem. In this paper, the authors review the state-of-the-art in VMAT planning from an algorithmic perspective. Different approaches to VMAT optimization, including arc sequencing methods, extensions of direct aperture optimization, and direct optimization of leaf trajectories are reviewed. Their advantages and limitations are outlined and recommendations for improvements are discussed.

Beam orientation optimization for intensity modulated radiation therapy using adaptive l(2,1)-minimization.

Beam orientation optimization (BOO) is a key component in the process of intensity modulated radiation therapy treatment planning. It determines to what degree one can achieve a good treatment plan in the subsequent plan optimization process. In this paper, we have developed a BOO algorithm via adaptive l(2, 1)-minimization. Specifically, we introduce a sparsity objective function term into our model which contains weighting factors for each beam angle adaptively adjusted during the optimization process. Such an objective function favors a small number of beam angles. By optimizing a total objective function consisting of a dosimetric term and the sparsity term, we are able to identify unimportant beam angles and gradually remove them without largely sacrificing the dosimetric objective. In one typical prostate case, the convergence property of our algorithm, as well as how beam angles are selected during the optimization process, is demonstrated. Fluence map optimization (FMO) is then performed based on the optimized beam angles. The resulting plan quality is presented and is found to be better than that of equiangular beam orientations. We have further systematically validated our algorithm in the contexts of 5-9 coplanar beams for five prostate cases and one head and neck case. For each case, the final FMO objective function value is used to compare the optimized beam orientations with the equiangular ones. It is found that, in the majority of cases tested, our BOO algorithm leads to beam configurations which attain lower FMO objective function values than those of corresponding equiangular cases, indicating the effectiveness of our BOO algorithm. Superior plan qualities are also demonstrated by comparing DVH curves between BOO plans and equiangular plans.

GPU-based ultra-fast direct aperture optimization for online adaptive radiation therapy.

Online adaptive radiation therapy (ART) has great promise to significantly reduce normal tissue toxicity and/or improve tumor control through real-time treatment adaptations based on the current patient anatomy. However, the major technical obstacle for clinical realization of online ART, namely the inability to achieve real-time efficiency in treatment re-planning, has yet to be solved. To overcome this challenge, this paper presents our work on the implementation of an intensity-modulated radiation therapy (IMRT) direct aperture optimization (DAO) algorithm on the graphics processing unit (GPU) based on our previous work on the CPU. We formulate the DAO problem as a large-scale convex programming problem, and use an exact method called the column generation approach to deal with its extremely large dimensionality on the GPU. Five 9-field prostate and five 5-field head-and-neck IMRT clinical cases with 5 x 5 mm(2) beamlet size and 2.5 x 2.5 x 2.5 mm(3) voxel size were tested to evaluate our algorithm on the GPU. It takes only 0.7-3.8 s for our implementation to generate high-quality treatment plans on an NVIDIA Tesla C1060 GPU card. Our work has therefore solved a major problem in developing ultra-fast (re-)planning technologies for online ART.

Single-projection based volumetric image reconstruction and 3D tumor localization in real time for lung cancer radiotherapy.

We have developed an algorithm for real-time volumetric image reconstruction and 3D tumor localization based on a single x-ray projection image. We first parameterize the deformation vector fields (DVF) of lung motion by principal component analysis (PCA). Then we optimize the DVF applied to a reference image by adapting the PCA coefficients such that the simulated projection of the reconstructed image matches the measured projection. The algorithm was tested on a digital phantom as well as patient data. The average relative image reconstruction error and 3D tumor localization error for the phantom is 7.5% and 0.9 mm, respectively. The tumor localization error for patient is approximately 2 mm. The computation time of reconstructing one volumetric image from each projection is around 0.2 and 0.3 seconds for phantom and patient, respectively, on an NVIDIA C1060 GPU. Clinical application can potentially lead to accurate 3D tumor tracking from a single imager.

GPU-based ultra-fast dose calculation using a finite size pencil beam model.

Online adaptive radiation therapy (ART) is an attractive concept that promises the ability to deliver an optimal treatment in response to the inter-fraction variability in patient anatomy. However, it has yet to be realized due to technical limitations. Fast dose deposit coefficient calculation is a critical component of the online planning process that is required for plan optimization of intensity-modulated radiation therapy (IMRT). Computer graphics processing units (GPUs) are well suited to provide the requisite fast performance for the data-parallel nature of dose calculation. In this work, we develop a dose calculation engine based on a finite-size pencil beam (FSPB) algorithm and a GPU parallel computing framework. The developed framework can accommodate any FSPB model. We test our implementation in the case of a water phantom and the case of a prostate cancer patient with varying beamlet and voxel sizes. All testing scenarios achieved speedup ranging from 200 to 400 times when using a NVIDIA Tesla C1060 card in comparison with a 2.27 GHz Intel Xeon CPU. The computational time for calculating dose deposition coefficients for a nine-field prostate IMRT plan with this new framework is less than 1 s. This indicates that the GPU-based FSPB algorithm is well suited for online re-planning for adaptive radiotherapy.

GPU-based ultrafast IMRT plan optimization.

The widespread adoption of on-board volumetric imaging in cancer radiotherapy has stimulated research efforts to develop online adaptive radiotherapy techniques to handle the inter-fraction variation of the patient's geometry. Such efforts face major technical challenges to perform treatment planning in real time. To overcome this challenge, we are developing a supercomputing online re-planning environment (SCORE) at the University of California, San Diego (UCSD). As part of the SCORE project, this paper presents our work on the implementation of an intensity-modulated radiation therapy (IMRT) optimization algorithm on graphics processing units (GPUs). We adopt a penalty-based quadratic optimization model, which is solved by using a gradient projection method with Armijo's line search rule. Our optimization algorithm has been implemented in CUDA for parallel GPU computing as well as in C for serial CPU computing for comparison purpose. A prostate IMRT case with various beamlet and voxel sizes was used to evaluate our implementation. On an NVIDIA Tesla C1060 GPU card, we have achieved speedup factors of 20-40 without losing accuracy, compared to the results from an Intel Xeon 2.27 GHz CPU. For a specific nine-field prostate IMRT case with 5 x 5 mm(2) beamlet size and 2.5 x 2.5 x 2.5 mm(3) voxel size, our GPU implementation takes only 2.8 s to generate an optimal IMRT plan. Our work has therefore solved a major problem in developing online re-planning technologies for adaptive radiotherapy.