Search for IMRT inverse plans with piecewise constant fluence maps using compressed sensing techniques

Improving the efficiency of small animal 3D-printed compensator IMRT with beamlet intensity total variation regularization

PURPOSE

There is growing interest in the use of modern 3D printing technology to implement intensity-modulated radiation therapy (IMRT) on the preclinical scale that is analogous to clinical IMRT. However, current 3D-printed IMRT methods suffer from complex modulation patterns leading to long delivery times, excess filament usage, and less accurate compensator fabrication. In this work, we have developed a total variation regularization (TVR) approach to address these issues.

METHODS

TVR-IMRT was used to optimize the beamlet intensity map, which was then converted to a thickness of the corresponding compensator attenuation region in copper-doped polylactic acid (PLA) filament. IMRT and TVR-IMRT heart and lung plans were generated for two different mice using three, five, or seven gantry angles. The total compensator thickness, total variation of compensator beamlet thicknesses, total variation of beamlet intensities, and exposure time were compared. The individual field doses and composite dose were delivered to film for one plan and gamma analysis was performed.

RESULTS

In total, 12 mice heart and lung plans were generated for both IMRT and TVR-IMRT cases. Across all cases, it was found that TVR-IMRT reduced the total variation of compensator beamlet thicknesses and beamlet intensities by 54 ± 4 % $54\pm 4\%$ and 50 ± 3 % $50\pm 3\%$ on average when compared to standard 3D-printed compensator IMRT. On average, the total mass of compensator material consumed and radiation beam-on time were reduced by 45 ± 6 % $45\pm 6\%$ and 24 ± 4 % $24\pm 4\%$ , respectively, whereas dose metrics remained comparable. Heart plan compensators were printed and delivered to film and subsequent gamma analysis performed for each of the single fields as well as the composite dose. For the composite delivery, a passing rate of 89.1% for IMRT and 95.4% for TVR-IMRT was achieved for a 3 % / 0.3 $3\%/0.3$ mm criterion.

CONCLUSIONS

TVR can be applied to small animal IMRT beamlet intensities to produce fluence maps and subsequent 3D-printed compensator patterns with significantly less complexity while still maintaining similar dose conformity to traditional IMRT. This can simplify/accelerate the 3D printing process, reduce the amount of filament required, and reduce overall beam-on time to deliver a plan.

Z-Index Parameterization for Volumetric CT Image Reconstruction via 3-D Dictionary Learning

Despite the rapid developments of X-ray cone-beam CT (CBCT), image noise still remains a major issue for the low dose CBCT. To suppress the noise effectively while retain the structures well for low dose CBCT image, in this paper, a sparse constraint based on the 3-D dictionary is incorporated into a regularized iterative reconstruction framework, defining the 3-D dictionary learning (3-DDL) method. In addition, by analyzing the sparsity level curve associated with different regularization parameters, a new adaptive parameter selection strategy is proposed to facilitate our 3-DDL method. To justify the proposed method, we first analyze the distributions of the representation coefficients associated with the 3-D dictionary and the conventional 2-D dictionary to compare their efficiencies in representing volumetric images. Then, multiple real data experiments are conducted for performance validation. Based on these results, we found: 1) the 3-D dictionary-based sparse coefficients have three orders narrower Laplacian distribution compared with the 2-D dictionary, suggesting the higher representation efficiencies of the 3-D dictionary; 2) the sparsity level curve demonstrates a clear Z-shape, and hence referred to as Z-curve, in this paper; 3) the parameter associated with the maximum curvature point of the Z-curve suggests a nice parameter choice, which could be adaptively located with the proposed Z-index parameterization (ZIP) method; 4) the proposed 3-DDL algorithm equipped with the ZIP method could deliver reconstructions with the lowest root mean squared errors and the highest structural similarity index compared with the competing methods; 5) similar noise performance as the regular dose FDK reconstruction regarding the standard deviation metric could be achieved with the proposed method using (1/2)/(1/4)/(1/8) dose level projections. The contrast-noise ratio is improved by ~2.5/3.5 times with respect to two different cases under the (1/8) dose level compared with the low dose FDK reconstruction. The proposed method is expected to reduce the radiation dose by a factor of 8 for CBCT, considering the voted strongly discriminated low contrast tissues.

Deterministic direct aperture optimization using multiphase piecewise constant segmentation

PURPOSE

Direct aperture optimization (DAO) attempts to incorporate machine constraints in the inverse optimization to eliminate the post-processing steps in fluence map optimization (FMO) that degrade plan quality. Current commercial DAO methods utilize a stochastic or greedy approach to search a small aperture solution space. In this study, we propose a novel deterministic direct aperture optimization that integrates the segmentation of fluence map in the optimization problem using the multiphase piecewise constant Mumford-Shah formulation.

METHODS

The Mumford-Shah based direct aperture optimization problem was formulated to include an L2-norm dose fidelity term to penalize differences between the projected dose and the prescribed dose, an anisotropic total variation term to promote piecewise continuity in the fluence maps, and the multiphase piecewise constant Mumford-Shah function to partition the fluence into pairwise discrete segments. A proximal-class, first-order primal-dual solver was implemented to solve the large scale optimization problem, and an alternating module strategy was implemented to update fluence and delivery segments. Three patients of varying complexity-one glioblastoma multiforme (GBM) patient, one lung (LNG) patient, and one bilateral head and neck (H&N) patient with 3 PTVs-were selected to test the new DAO method. For each patient, 20 non-coplanar beams were first selected using column generation, followed by the Mumford-Shah based DAO (DAO_MS ). For comparison, a popular and successful approach to DAO known as simulated annealing-a stochastic approach-was replicated. The simulated annealing DAO (DAO_SA ) plans were then created using the same beam angles and maximum number of segments per beam. PTV coverage, PTV homogeneity D95D5, and OAR sparing were assessed for each plan. In addition, high dose spillage, defined as the 50% isodose volume divided by the tumor volume, as well as conformity, defined as the van't Riet conformation number, were evaluated.

RESULTS

DAO_MS achieved essentially the same OAR doses compared with the DAO_SA plans for the GBM case. The average difference of OAR D_max and D_mean between the two plans were within 0.05% of the plan prescription dose. The lung case showed slightly improved critical structure sparing using the DAO_MS approach, where the average OAR D_max and D_mean were reduced by 3.67% and 1.08%, respectively, of the prescription dose. The DAO_MS plan substantially improved OAR dose sparing for the H&N patient, where the average OAR D_max and D_mean were reduced by over 10% of the prescription dose. The DAO_MS and DAO_SA plans were comparable for the GBM and LNG PTV coverage, while the DAO_MS plan substantially improved the H&N PTV coverage, increasing D99 by 6.98% of the prescription dose. For the GBM and LNG patients, the DAO_MS and DAO_SA plans had comparable high dose spillage but slightly worse conformity with the DAO_MS approach. For the H&N plan, DAO_MS was considerably superior in high dose spillage and conformity to the DAO_SA . The deterministic approach is able to solve the DAO problem substantially faster than the simulated annealing approach, with a 9.5- to 40-fold decrease in total solve time, depending on the patient case.

CONCLUSIONS

A novel deterministic direct aperture optimization formulation was developed and evaluated. It combines fluence map optimization and the multiphase piecewise constant Mumford-Shah segmentation into a unified framework, and the resulting optimization problem can be solved efficiently. Compared to the widely and commercially used simulated annealing DAO approach, it showed comparable dosimetry behavior for simple plans, and substantially improved OAR sparing, PTV coverage, PTV homogeneity, high dose spillage, and conformity for the more complex head and neck plan.

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

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

Use of proximal operator graph solver for radiation therapy inverse treatment planning

PURPOSE

Most radiation therapy optimization problems can be formulated as an unconstrained problem and solved efficiently by quasi-Newton methods such as the Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm. However, several next generation planning techniques such as total variation regularization- based optimization and MV+kV optimization, involve constrained or mixed-norm optimization, and cannot be solved by quasi-Newton methods. Using standard optimization algorithms on such problems often leads to prohibitively long optimization times and large memory requirements. This work investigates the use of a recently developed proximal operator graph solver (POGS) in solving such radiation therapy optimization problems.

METHODS

Radiation therapy inverse treatment planning was formulated as a graph form problem, and the proximal operators of POGS for quadratic optimization were derived. POGS was exploited for the first time to impose hard dose constraints along with soft constraints in the objective function. The solver was applied to several clinical treatment sites (TG119, liver, prostate, and head&neck), and the results were compared to the solutions obtained by other commercial and non-commercial optimizers.

RESULTS

For inverse planning optimization with nonnegativity box constraints on beamlet intensity, the speed of POGS can compete with that of LBFGSB in some situations. For constrained and mixed-norm optimization, POGS is about one or two orders of magnitude faster than the other solvers while requiring less computer memory.

CONCLUSIONS

POGS was used for solving inverse treatment planning problems involving constrained or mixed-norm formulation on several example sites. This approach was found to improve upon standard solvers in terms of computation speed and memory usage, and is capable of solving traditionally difficult problems, such as total variation regularization-based optimization and combined MV+kV optimization.

Application programming in C# environment with recorded user software interactions and its application in autopilot of VMAT/IMRT treatment planning

An autopilot scheme of volumetric‐modulated arc therapy (VMAT)/intensity‐modulated radiation therapy (IMRT) planning with the guidance of prior knowledge is established with recorded interactions between a planner and a commercial treatment planning system (TPS). Microsoft (MS) Visual Studio Coded UI is applied to record some common planner‐TPS interactions as subroutines. The TPS used in this study is a Windows‐based Eclipse system. The interactions of our application program with Eclipse TPS are realized through a series of subroutines obtained by prerecording the mouse clicks or keyboard strokes of a planner in operating the TPS. A strategy to autopilot Eclipse VMAT/IMRT plan selection process is developed as a specific example of the proposed “scripting” method. The autopiloted planning is navigated by a decision function constructed with a reference plan that has the same prescription and similar anatomy with the case at hand. The calculation proceeds by alternating between the Eclipse optimization and the outer‐loop optimization independent of the Eclipse. In the C# program, the dosimetric characteristics of a reference treatment plan are used to assess and modify the Eclipse planning parameters and to guide the search for a clinically sensible treatment plan. The approach is applied to plan a head and neck (HN) VMAT case and a prostate IMRT case. Our study demonstrated the feasibility of application programming method in C# environment with recorded interactions of planner‐TPS. The process mimics a planner's planning process and automatically provides clinically sensible treatment plans that would otherwise require a large amount of manual trial and error of a planner. The proposed technique enables us to harness a commercial TPS by application programming via the use of recorded human computer interactions and provides an effective tool to greatly facilitate the treatment planning process.

PACS number(s): 87.55.D‐, 87.55.kd, 87.55.de

Robust fluence map optimization via alternating direction method of multipliers with empirical parameter optimization

For the treatment planning during intensity modulated radiation therapy (IMRT) or volumetric modulated arc therapy (VMAT), beam fluence maps can be first optimized via fluence map optimization (FMO) under the given dose prescriptions and constraints to conformally deliver the radiation dose to the targets while sparing the organs-at-risk, and then segmented into deliverable MLC apertures via leaf or arc sequencing algorithms. This work is to develop an efficient algorithm for FMO based on alternating direction method of multipliers (ADMM). Here we consider FMO with the least-square cost function and non-negative fluence constraints, and its solution algorithm is based on ADMM, which is efficient and simple-to-implement. In addition, an empirical method for optimizing the ADMM parameter is developed to improve the robustness of the ADMM algorithm. The ADMM based FMO solver was benchmarked with the quadratic programming method based on the interior-point (IP) method using the CORT dataset. The comparison results suggested the ADMM solver had a similar plan quality with slightly smaller total objective function value than IP. A simple-to-implement ADMM based FMO solver with empirical parameter optimization is proposed for IMRT or VMAT.

Common-mask guided image reconstruction (c-MGIR) for enhanced 4D cone-beam computed tomography

Compared to 3D cone beam computed tomography (3D CBCT), the image quality of commercially available four-dimensional (4D) CBCT is severely impaired due to the insufficient amount of projection data available for each phase. Since the traditional Feldkamp-Davis-Kress (FDK)-based algorithm is infeasible for reconstructing high quality 4D CBCT images with limited projections, investigators had developed several compress-sensing (CS) based algorithms to improve image quality. The aim of this study is to develop a novel algorithm which can provide better image quality than the FDK and other CS based algorithms with limited projections. We named this algorithm 'the common mask guided image reconstruction' (c-MGIR).In c-MGIR, the unknown CBCT volume is mathematically modeled as a combination of phase-specific motion vectors and phase-independent static vectors. The common-mask matrix, which is the key concept behind the c-MGIR algorithm, separates the common static part across all phase images from the possible moving part in each phase image. The moving part and the static part of the volumes were then alternatively updated by solving two sub-minimization problems iteratively. As the novel mathematical transformation allows the static volume and moving volumes to be updated (during each iteration) with global projections and 'well' solved static volume respectively, the algorithm was able to reduce the noise and under-sampling artifact (an issue faced by other algorithms) to the maximum extent. To evaluate the performance of our proposed c-MGIR, we utilized imaging data from both numerical phantoms and a lung cancer patient. The qualities of the images reconstructed with c-MGIR were compared with (1) standard FDK algorithm, (2) conventional total variation (CTV) based algorithm, (3) prior image constrained compressed sensing (PICCS) algorithm, and (4) motion-map constrained image reconstruction (MCIR) algorithm, respectively. To improve the efficiency of the algorithm, the code was implemented with a graphic processing unit for parallel processing purposes.Root mean square error (RMSE) between the ground truth and reconstructed volumes of the numerical phantom were in the descending order of FDK, CTV, PICCS, MCIR, and c-MGIR for all phases. Specifically, the means and the standard deviations of the RMSE of FDK, CTV, PICCS, MCIR and c-MGIR for all phases were 42.64  ±  6.5%, 3.63  ±  0.83%, 1.31%  ±  0.09%, 0.86%  ±  0.11% and 0.52 %  ±  0.02%, respectively. The image quality of the patient case also indicated the superiority of c-MGIR compared to other algorithms.The results indicated that clinically viable 4D CBCT images can be reconstructed while requiring no more projection data than a typical clinical 3D CBCT scan. This makes c-MGIR a potential online reconstruction algorithm for 4D CBCT, which can provide much better image quality than other available algorithms, while requiring less dose and potentially less scanning time.

Total-variation regularization based inverse planning for intensity modulated arc therapy

Intensity modulated arc therapy (IMAT) delivers conformal dose distributions through continuous gantry rotation with constant or variable speed while modulating the field aperture shape and weight. The enlarged angular space and machine delivery constraints make inverse planning of IMAT more intractable as compared to its counterpart of fixed gantry IMRT. Currently, IMAT inverse planning is being done using two extreme methods: the first one computes in beamlet domain with a subsequent arc leaf sequencing, and the second proceeds in machine parameter domain with entire emphasis placed on a pre-determined delivery method without exploring potentially better alternative delivery schemes. Towards truly optimizing the IMAT treatment on a patient specific basis, in this work we propose a total-variation based inverse planning framework for IMAT, which takes advantage of the useful features of the above two existing approaches while avoiding their shortcomings. A quadratic optimization algorithm has been implemented to demonstrate the performance and advantage of the proposed approach. Applications of the technique to a prostate case and a head and neck case indicate that the algorithm is capable of generating IMAT plans with patient specific numbers of arcs efficiently. Superior dose distributions and delivery time are achieved with a maximum number of apertures of three for each field. As compared to conventional beamlet-based algorithms, our method regularizes the field modulation complexity during optimization, and permits us to obtain the best possible plan with a pre-set modulation complexity of fluences. As illustrated in both prostate and head-and-neck case studies, the proposed method produces more favorable dose distributions than the segment-based algorithms, by optimally accommodating the clinical need of intensity modulation levels for each individual field. On a more fundamental level, our formulation preserves the convexity of optimization and makes the search of the global optimal solution possible with a deterministic method.

Toward a planning scheme for emission guided radiation therapy (EGRT): FDG based tumor tracking in a metastatic breast cancer patient

PURPOSE

Emission guided radiation therapy (EGRT) is a new modality that uses PET emissions in real-time for direct tumor tracking during radiation delivery. Radiation beamlets are delivered along positron emission tomography (PET) lines of response (LORs) by a fast rotating ring therapy unit consisting of a linear accelerator (Linac) and PET detectors. The feasibility of tumor tracking and a primitive modulation method to compensate for attenuation have been demonstrated using a 4D digital phantom in our prior work. However, the essential capability of achieving dose modulation as in conventional intensity modulated radiation therapy (IMRT) treatments remains absent. In this work, the authors develop a planning scheme for EGRT to accomplish sophisticated intensity modulation based on an IMRT plan while preserving tumor tracking.

METHODS

The planning scheme utilizes a precomputed LOR response probability distribution to achieve desired IMRT planning modulation with effects of inhomogeneous attenuation and nonuniform background activity distribution accounted for. Evaluation studies are performed on a 4D digital patient with a simulated lung tumor and a clinical patient who has a moving breast cancer metastasis in the lung. The Linac dose delivery is simulated using a voxel-based Monte Carlo algorithm. The IMRT plan is optimized for a planning target volume (PTV) that encompasses the tumor motion using the MOSEK package and a Pinnacle3™ workstation (Philips Healthcare, Fitchburg, WI) for digital and clinical patients, respectively. To obtain the emission data for both patients, the Geant4 application for tomographic emission (GATE) package and a commercial PET scanner are used. As a comparison, 3D and helical IMRT treatments covering the same PTV based on the same IMRT plan are simulated.

RESULTS

3D and helical IMRT treatments show similar dose distribution. In the digital patient case, compared with the 3D IMRT treatment, EGRT achieves a 15.1% relative increase in dose to 95% of the gross tumor volume (GTV) and a 31.8% increase to 50% of the GTV. In the patient case, EGRT yields a 15.2% relative increase in dose to 95% of the GTV and a 20.7% increase to 50% of the GTV. The organs at risk (OARs) doses are kept similar or lower for EGRT in both cases. Tumor tracking is observed in the presence of planning modulation in all EGRT treatments.

CONCLUSIONS

As compared to conventional IMRT treatments, the proposed EGRT planning scheme allows an escalated target dose while keeping dose to the OARs within the same planning limits. With the capabilities of incorporating planning modulation and accurate tumor tracking, EGRT has the potential to greatly improve targeting in radiation therapy and enable a practical and effective implementation of 4D radiation therapy for planning and delivery.

Improving IMRT delivery efficiency with reweighted L1-minimization for inverse planning

PURPOSE

This study presents an improved technique to further simplify the fluence-map in intensity modulated radiation therapy (IMRT) inverse planning, thereby reducing plan complexity and improving delivery efficiency, while maintaining the plan quality.

METHODS

First-order total-variation (TV) minimization (min.) based on L1-norm has been proposed to reduce the complexity of fluence-map in IMRT by generating sparse fluence-map variations. However, with stronger dose sparing to the critical structures, the inevitable increase in the fluence-map complexity can lead to inefficient dose delivery. Theoretically, L0-min. is the ideal solution for the sparse signal recovery problem, yet practically intractable due to its nonconvexity of the objective function. As an alternative, the authors use the iteratively reweighted L1-min. technique to incorporate the benefits of the L0-norm into the tractability of L1-min. The weight multiplied to each element is inversely related to the magnitude of the corresponding element, which is iteratively updated by the reweighting process. The proposed penalizing process combined with TV min. further improves sparsity in the fluence-map variations, hence ultimately enhancing the delivery efficiency. To validate the proposed method, this work compares three treatment plans obtained from quadratic min. (generally used in clinic IMRT), conventional TV min., and our proposed reweighted TV min. techniques, implemented by a large-scale L1-solver (template for first-order conic solver), for five patient clinical data. Criteria such as conformation number (CN), modulation index (MI), and estimated treatment time are employed to assess the relationship between the plan quality and delivery efficiency.

RESULTS

The proposed method yields simpler fluence-maps than the quadratic and conventional TV based techniques. To attain a given CN and dose sparing to the critical organs for 5 clinical cases, the proposed method reduces the number of segments by 10-15 and 30-35, relative to TV min. and quadratic min. based plans, while MIs decreases by about 20%-30% and 40%-60% over the plans by two existing techniques, respectively. With such conditions, the total treatment time of the plans obtained from our proposed method can be reduced by 12-30 s and 30-80 s mainly due to greatly shorter multileaf collimator (MLC) traveling time in IMRT step-and-shoot delivery.

CONCLUSIONS

The reweighted L1-minimization technique provides a promising solution to simplify the fluence-map variations in IMRT inverse planning. It improves the delivery efficiency by reducing the entire segments and treatment time, while maintaining the plan quality in terms of target conformity and critical structure sparing.

Fast compressed sensing-based CBCT reconstruction using Barzilai-Borwein formulation for application to on-line IGRT

PURPOSE

Compressed sensing theory has enabled an accurate, low-dose cone-beam computed tomography (CBCT) reconstruction using a minimal number of noisy projections. However, the reconstruction time remains a significant challenge for practical implementation in the clinic. In this work, we propose a novel gradient projection algorithm, based on the Gradient-Projection-Barzilai-Borwein formulation (GP-BB), that handles the total variation (TV)-norm regularization-based least squares problem for the CBCT reconstruction in a highly efficient manner, with speed acceptable for routine use in the clinic.

METHODS

CBCT is reconstructed by minimizing an energy function consisting of a data fidelity term and a TV-norm regularization term. Both terms are simultaneously minimized by calculating the gradient projection of the energy function with the step size determined using an approximate Hessian calculation at each iteration, based on the Barzilai-Borwein formulation. To speed up the process, a multiresolution optimization is used. In addition, the entire algorithm was designed to run with a single graphics processing unit (GPU) card. To evaluate the performance, the Shepp-Logan numerical phantom, the CatPhan 600 physical phantom, and a clinically-treated head-and-neck patient were acquired from the TrueBeam™ system (Varian Medical Systems, Palo Alto, CA). For each scan, in total, 364 projections were acquired in a 200° rotation. The imager has 1024 × 768 pixels with 0.388 × 0.388-mm resolution. This was down-sampled to 512 × 384 pixels with 0.776 × 0.776-mm resolution for reconstruction. Evenly spaced angles were subsampled and used for varying the number of projections for the image reconstruction. To assess the performance of our GP-BB algorithm, we have implemented and compared with three compressed sensing-type algorithms, the two of which are popular and published (forward-backward splitting techniques), and the other one with a basic line-search technique. In addition, the conventional Feldkamp-Davis-Kress (FDK) reconstruction of the clinical patient data is compared as well.

RESULTS

In comparison with the other compressed sensing-type algorithms, our algorithm showed convergence in ≤30 iterations whereas other published algorithms need at least 50 iterations in order to reconstruct the Shepp-Logan phantom image. With the CatPhan phantom, the GP-BB algorithm achieved a clinically-reasonable image with 40 projections in 12 iterations, in less than 12.6 s. This is at least an order of magnitude faster in reconstruction time compared with the most recent reports utilizing GPU technology given the same input projections. For the head-and-neck clinical scan, clinically-reasonable images were obtained from 120 projections in 34-78 s converging in 12-30 iterations. In this reconstruction range (i.e., 120 projections) the image quality is visually similar to or better than the conventional FDK reconstructed images using 364 projections. This represents a dose reduction of nearly 67% (120∕364 projections) while maintaining a reasonable speed in clinical implementation.

CONCLUSIONS

In this paper, we proposed a novel, fast, low-dose CBCT reconstruction algorithm using the Barzilai-Borwein step-size calculation. A clinically viable head-and-neck image can be obtained within ∼34-78 s while simultaneously cutting the dose by approximately 67%. This makes our GP-BB algorithm potentially useful in an on-line image-guided radiation therapy (IGRT).

Multicriteria optimization for volumetric-modulated arc therapy by decomposition into a fluence-based relaxation and a segment weight-based restriction

PURPOSE

To develop a method for inverse volumetric-modulated arc therapy (VMAT) planning that combines multicriteria optimization (MCO) with direct machine parameter optimization. The ultimate goal is to provide an efficient and intuitive method for generating high quality VMAT plans.

METHODS

Multicriteria radiation therapy treatment planning amounts to approximating the relevant treatment options by a discrete set of plans, and selecting the combination thereof that strikes the best possible balance between conflicting objectives. This approach is applied to two decompositions of the inverse VMAT planning problem: a fluence-based relaxation considered at a coarsened gantry angle spacing and under a regularizing penalty on fluence modulation, and a segment weight-based restriction in a neighborhood of the solution to the relaxed problem. The two considered variable domains are interconnected by direct machine parameter optimization toward reproducing the dose-volume histogram of the fluence-based solution.

RESULTS

The dose distribution quality of plans generated by the proposed MCO method was assessed by direct comparison with benchmark plans generated by a conventional VMAT planning method. The results for four patient cases (prostate, pancreas, lung, and head and neck) are highly comparable between the MCO plans and the benchmark plans: Discrepancies between studied dose-volume statistics for organs at risk were-with the exception of the kidneys of the pancreas case-within 1 Gy or 1 percentage point. Target coverage of the MCO plans was comparable with that of the benchmark plans, but with a small tendency toward a shift from conformity to homogeneity.

CONCLUSIONS

MCO allows tradeoffs between conflicting objectives encountered in VMAT planning to be explored in an interactive manner through search over a continuous representation of the relevant treatment options. Treatment plans selected from such a representation are of comparable dose distribution quality to conventionally optimized VMAT plans.

Emission guided radiation therapy for lung and prostate cancers: a feasibility study on a digital patient

PURPOSE

Accurate tumor tracking remains a challenge in current radiation therapy. Many strategies including image guided radiation therapy alleviate the problem to certain extents. The authors propose a new modality called emission guided radiation therapy (EGRT) to accurately and directly track the tumor based on its biological signature. This work is to demonstrate the feasibility of EGRT under two clinical scenarios using a 4D digital patient model.

METHODS

EGRT uses lines of response (LOR's) from positron emission events to direct beamlets of therapeutic radiation through the emission sites inside a tumor. This is accomplished by a radiation delivery system consisting of a Linac and positron emission tomography (PET) detectors on a fast rotating closed-ring gantry. During the treatment of radiotracer-administrated cancer patients, PET detectors collect LOR's from tumor uptake sites and the Linac responds in nearly real-time with beamlets of radiation along the same LOR paths. Moving tumors are therefore treated with a high targeting accuracy. Based on the EGRT concept, the authors design a treatment method with additional modulation algorithms including attenuation correction and an integrated boost scheme. Performance is evaluated using simulations of a lung tumor case with 3D motion and a prostate tumor case with setup errors. The emission process is simulated by Geant4 Application for Tomographic Emission package (GATE) and Linac dose delivery is simulated using a voxel-based Monte Carlo algorithm (VMC++).

RESULTS

In the lung case with attenuation correction, compared to a conventional helical treatment, EGRT achieves a 41% relative increase in dose to 95% of the gross tumor volume (GTV) and a 55% increase to 50% of the GTV. All dose distributions are normalized for the same dose to the lung. In the prostate case with the integrated boost and no setup error, EGRT yields a 19% and 55% relative dose increase to 95% and 50% of the GTV, respectively, when all methods are normalized for the same dose to the rectum. In the prostate case with integrated boost where setup error is present, EGRT contributes a 21% and 52% relative dose increase to 95% and 50% of the GTV, respectively.

CONCLUSIONS

As a new radiation therapy modality with inherent tumor tracking, EGRT has the potential to substantially improve targeting in radiation therapy in the presence of intrafractional and interfractional motion.

Dose optimization with first-order total-variation minimization for dense angularly sampled and sparse intensity modulated radiation therapy (DASSIM-RT)

PURPOSE

A new treatment scheme coined as dense angularly sampled and sparse intensity modulated radiation therapy (DASSIM-RT) has recently been proposed to bridge the gap between IMRT and VMAT. By increasing the angular sampling of radiation beams while eliminating dispensable segments of the incident fields, DASSIM-RT is capable of providing improved conformity in dose distributions while maintaining high delivery efficiency. The fact that DASSIM-RT utilizes a large number of incident beams represents a major computational challenge for the clinical applications of this powerful treatment scheme. The purpose of this work is to provide a practical solution to the DASSIM-RT inverse planning problem.

METHODS

The inverse planning problem is formulated as a fluence-map optimization problem with total-variation (TV) minimization. A newly released L1-solver, template for first-order conic solver (TFOCS), was adopted in this work. TFOCS achieves faster convergence with less memory usage as compared with conventional quadratic programming (QP) for the TV form through the effective use of conic forms, dual-variable updates, and optimal first-order approaches. As such, it is tailored to specifically address the computational challenges of large-scale optimization in DASSIM-RT inverse planning. Two clinical cases (a prostate and a head and neck case) are used to evaluate the effectiveness and efficiency of the proposed planning technique. DASSIM-RT plans with 15 and 30 beams are compared with conventional IMRT plans with 7 beams in terms of plan quality and delivery efficiency, which are quantified by conformation number (CN), the total number of segments and modulation index, respectively. For optimization efficiency, the QP-based approach was compared with the proposed algorithm for the DASSIM-RT plans with 15 beams for both cases.

RESULTS

Plan quality improves with an increasing number of incident beams, while the total number of segments is maintained to be about the same in both cases. For the prostate patient, the conformation number to the target was 0.7509, 0.7565, and 0.7611 with 80 segments for IMRT with 7 beams, and DASSIM-RT with 15 and 30 beams, respectively. For the head and neck (HN) patient with a complicated target shape, conformation numbers of the three treatment plans were 0.7554, 0.7758, and 0.7819 with 75 segments for all beam configurations. With respect to the dose sparing to the critical structures, the organs such as the femoral heads in the prostate case and the brainstem and spinal cord in the HN case were better protected with DASSIM-RT. For both cases, the delivery efficiency has been greatly improved as the beam angular sampling increases with the similar or better conformal dose distribution. Compared with conventional quadratic programming approaches, first-order TFOCS-based optimization achieves far faster convergence and smaller memory requirements in DASSIM-RT.

CONCLUSIONS

The new optimization algorithm TFOCS provides a practical and timely solution to the DASSIM-RT or other inverse planning problem requiring large memory space. The new treatment scheme is shown to outperform conventional IMRT in terms of dose conformity to both the targetand the critical structures, while maintaining high delivery efficiency.

Accelerated barrier optimization compressed sensing (ABOCS) reconstruction for cone-beam CT: phantom studies

PURPOSE

Recent advances in compressed sensing (CS) enable accurate CT image reconstruction from highly undersampled and noisy projection measurements, due to the sparsifiable feature of most CT images using total variation (TV). These novel reconstruction methods have demonstrated advantages in clinical applications where radiation dose reduction is critical, such as onboard cone-beam CT (CBCT) imaging in radiation therapy. The image reconstruction using CS is formulated as either a constrained problem to minimize the TV objective within a small and fixed data fidelity error, or an unconstrained problem to minimize the data fidelity error with TV regularization. However, the conventional solutions to the above two formulations are either computationally inefficient or involved with inconsistent regularization parameter tuning, which significantly limit the clinical use of CS-based iterative reconstruction. In this paper, we propose an optimization algorithm for CS reconstruction which overcomes the above two drawbacks.

METHODS

The data fidelity tolerance of CS reconstruction can be well estimated based on the measured data, as most of the projection errors are from Poisson noise after effective data correction for scatter and beam-hardening effects. We therefore adopt the TV optimization framework with a data fidelity constraint. To accelerate the convergence, we first convert such a constrained optimization using a logarithmic barrier method into a form similar to that of the conventional TV regularization based reconstruction but with an automatically adjusted penalty weight. The problem is then solved efficiently by gradient projection with an adaptive Barzilai-Borwein step-size selection scheme. The proposed algorithm is referred to as accelerated barrier optimization for CS (ABOCS), and evaluated using both digital and physical phantom studies.

RESULTS

ABOCS directly estimates the data fidelity tolerance from the raw projection data. Therefore, as demonstrated in both digital Shepp-Logan and physical head phantom studies, consistent reconstruction performances are achieved using the same algorithm parameters on scans with different noise levels and∕or on different objects. On the contrary, the penalty weight in a TV regularization based method needs to be fine-tuned in a large range (up to seven times) to maintain the reconstructed image quality. The improvement of ABOCS on computational efficiency is demonstrated in the comparisons with adaptive-steepest-descent-projection-onto-convex-sets (ASD-POCS), an existing CS reconstruction algorithm also using constrained optimization. ASD-POCS alternatively minimizes the TV objective using adaptive steepest descent (ASD) and the data fidelity error using projection onto convex sets (POCS). For similar image qualities of the Shepp-Logan phantom, ABOCS requires less computation time than ASD-POCS in MATLAB by more than one order of magnitude.

CONCLUSIONS

We propose ABOCS for CBCT reconstruction. As compared to other published CS-based algorithms, our method has attractive features of fast convergence and consistent parameter settings for different datasets. These advantages have been demonstrated on phantom studies.

Faster STORM using compressed sensing

In super-resolution microscopy methods based on single-molecule switching, the rate of accumulating single-molecule activation events often limits the time resolution. Here we developed a sparse-signal recovery technique using compressed sensing to analyze images with highly overlapping fluorescent spots. This method allows an activated fluorophore density an order of magnitude higher than what conventional single-molecule fitting methods can handle. Using this method, we demonstrated imaging microtubule dynamics in living cells with a time resolution of 3 s.

Bridging the gap between IMRT and VMAT: dense angularly sampled and sparse intensity modulated radiation therapy

PURPOSE

To propose an alternative radiation therapy (RT) planning and delivery scheme with optimal angular beam sampling and intrabeam modulation for improved dose distribution while maintaining high delivery efficiency.

METHODS

In the proposed approach, coined as dense angularly sampled and sparse intensity modulated RT (DASSIM-RT), a large number of beam angles are used to increase the angular sampling, leading to potentially more conformal dose distributions as compared to conventional IMRT. At the same time, intensity modulation of the incident beams is simplified to eliminate the dispensable segments, compensating the increase in delivery time caused by the increased number of beams and facilitating the plan delivery. In a sense, the proposed approach shifts and transforms, in an optimal fashion, some of the beam segments in conventional IMRT to the added beams. For newly available digital accelerators, the DASSIM-RT delivery can be made very efficient by concatenating the beams so that they can be delivered sequentially without operator's intervention. Different from VMAT, the level of intensity modulation in DASSIS-RT is field specific and optimized to meet the need of each beam direction. Three clinical cases (a head and neck (HN) case, a pancreas case, and a lung case) are used to evaluate the proposed RT scheme. DASSIM-RT, VMAT, and conventional IMRT plans are compared quantitatively in terms of the conformality index (CI) and delivery efficiency.

RESULTS

Plan quality improves generally with the number and intensity modulation of the incident beams. For a fixed number of beams or fixed level of intensity modulation, the improvement saturates after the intensity modulation or number of beams reaches to a certain level. An interplay between the two variables is observed and the saturation point depends on the values of both variables. For all the cases studied here, the CI of DASSIM-RT with 15 beams and 5 intensity levels (0.90, 0.79, and 0.84 for the HN, pancreas, and lung cases, respectively) is similar with that of conventional IMRT with seven beams and ten intensity levels (0.88, 0.79, and 0.83) and is higher than that of single-arc VMAT (0.75, 0.75, and 0.82). It is also found that the DASSIM-RT plans generally have better sparing of organs-at-risk than IMRT plans. It is estimated that the dose delivery time of DASSIM-RT with 15 beams and 5 intensity levels is about 4.5, 4.4, and 4.2 min for the HN, pancreas, and lung case, respectively, similar to that of IMRT plans with 7 beams and 10 intensity levels.

CONCLUSION

DASSIS-RT bridges the gap between IMRT and VMAT and allows optimal sampling of angular space and intrabeam modulation, thus it provides improved conformity in dose distributions while maintaining high delivery efficiency.

Inverse planning for IMRT with nonuniform beam profiles using total-variation regularization (TVR)

PURPOSE

Radiation therapy with high dose rate and flattening filter-free (FFF) beams has the potential advantage of greatly reduced treatment time and out-of-field dose. Current inverse planning algorithms are, however, not customized for beams with nonuniform incident profiles and the resultant IMRT plans are often inefficient in delivery. The authors propose a total-variation regularization (TVR)-based formalism by taking the inherent shapes of incident beam profiles into account.

METHODS

A novel TVR-based inverse planning formalism is established for IMRT with nonuniform beam profiles. The authors introduce a TVR term into the objective function, which encourages piecewise constant fluence in the nonuniform FFF fluence domain. The proposed algorithm is applied to lung and prostate and head and neck cases and its performance is evaluated by comparing the resulting plans to those obtained using a conventional beamlet-based optimization (BBO).

RESULTS

For the prostate case, the authors' algorithm produces acceptable dose distributions with only 21 segments, while the conventional BBO requires 114 segments. For the lung case and the head and neck case, the proposed method generates similar coverage of target volume and sparing of the organs-at-risk as compared to BBO, but with a markedly reduced segment number.

CONCLUSIONS

TVR-based optimization in nonflat beam domain provides an effective way to maximally leverage the technical capacity of radiation therapy with FFF fields. The technique can generate effective IMRT plans with improved dose delivery efficiency without significant deterioration of the dose distribution.

Toward truly optimal IMRT dose distribution: inverse planning with voxel-specific penalty

PURPOSE

To establish an inverse planning framework with adjustable voxel penalty for more conformal IMRT dose distribution as well as improved interactive controllability over the regional dose distribution of the resultant plan.

MATERIALS AND METHOD

In the proposed coarse-to-fine planning scheme, a conventional inverse planning with organ specific parameters is first performed. The voxel penalty scheme is then "switched on" by allowing the prescription dose to change on an individual voxel scale according to the deviation of the actual voxel dose from the ideally desired dose. The rationale here is intuitive: when the dose at a voxel does not meet its ideal dose, it simply implies that this voxel is not competitive enough when compared with the ones that have met their planning goal. In this case, increasing the penalty of the voxel by varying the prescription can boost its competitiveness and thus improve its dose. After the prescription adjustment, the plan is re-optimized. The dose adjustment/re-optimization procedure is repeated until the resultant dose distribution cannot be improved anymore. The prescription adjustment on a finer scale can be accomplished either automatically or manually. In the latter case, the regions/voxels where a dose improvement is needed are selected visually, unlike in the automatic case where the selection is done purely based on the difference of the actual dose at a given voxel and its ideal prescription. The performance of the proposed method is evaluated using a head and neck and a prostate case.

RESULTS

An inverse planning framework with the voxel-specific penalty is established. By adjusting voxel prescriptions iteratively to boost the region where large mismatch between the actual calculated and desired doses occurs, substantial improvements can be achieved in the final dose distribution. The proposed method is applied to a head and neck case and a prostate case. For the former case, a significant reduction in the maximum dose to the brainstem is achieved while the PTV dose coverage is greatly improved. The doses to other organs at risk are also reduced, ranging from 10% to 30%. For the prostate case, the use of the voxel penalty scheme also results in vast improvements to the final dose distribution. The PTV experiences improved dose uniformity and the mean dose to the rectum and bladder is reduced by as much as 15%.

CONCLUSION

Introduction of the spatially non-uniform and adjustable prescription provides room for further improvements of currently achievable dose distributions and equips the planner with an effective tool to modify IMRT dose distributions interactively. The technique is easily implementable in any existing inverse planning platform, which should facilitate clinical IMRT planning process and, in future, off-line/on-line adaptive IMRT.

Clinical development of a failure detection-based online repositioning strategy for prostate IMRT--experiments, simulation, and dosimetry study

PURPOSE

To implement and evaluate clinic-ready adaptive imaging protocols for online patient repositioning (motion tracking) during prostate IMRT using treatment beam imaging supplemented by minimal, as-needed use of on-board kV.

METHODS

The authors examine the two-step decision-making strategy: (1) Use cine-MV imaging and online-updated characterization of prostate motion to detect target motion that is potentially beyond a predefined threshold and (2) use paired MV-kV 3D localization to determine overthreshold displacement and, if needed, reposition the patient. Two levels of clinical implementation were evaluated: (1) Field-by-field based motion correction for present-day linacs and (2) instantaneous repositioning for new-generation linacs with capabilities of simultaneous MV-kV imaging and remote automatic couch control during treatment delivery. Experiments were performed on a Varian Trilogy linac in clinical mode using a 4D motion phantom programed with prostate motion trajectories taken from patient data. Dosimetric impact was examined using a 2D ion chamber array. Simulations were done for 536 trajectories from 17 patients.

RESULTS

Despite the loss of marker detection efficiency caused by the MLC leaves sometimes obscuring the field at the marker's projected position on the MV imager, the field-by-field correction halved (from 23% to 10%) the mean percentage of time that target displacement exceeded a 3 mm threshold, as compared to no intervention. This was achieved at minimal cost in additional imaging (average of one MV-kV pair per two to three treatment fractions) and with a very small number of repositionings (once every four to five fractions). Also with low kV usage (approximation 2/fraction), the instantaneous repositioning approach reduced overthreshold time by more than 75% (23% to 5%) even with severe MLC blockage as often encountered in current IMRT and could reduce the overthreshold time tenfold (to < 2%) if the MLC blockage problem were relieved. The information acquired for repositioning using combined MV-kV images was found to have submillimeter accuracy.

CONCLUSIONS

This work demonstrated with a current clinical setup that substantial reduction of adverse targeting effects of intrafraction prostate motion can be realized. The proposed adaptive imaging strategy incurs minimal imaging dose to the patient as compared to other stereoscopic imaging techniques.

A unified framework for 3D radiation therapy and IMRT planning: plan optimization in the beamlet domain by constraining or regularizing the fluence map variations

The purpose of this work is to demonstrate that physical constraints on fluence gradients in 3D radiation therapy (RT) planning can be incorporated into beamlet optimization explicitly by direct constraint on the spatial variation of the fluence maps or implicitly by using total-variation regularization (TVR). The former method forces the fluence to vary in accordance with the known form of a wedged field and latter encourages the fluence to take the known form of the wedged field by requiring the derivatives of the fluence maps to be piece-wise constant. The performances of the proposed methods are evaluated by using a brain cancer case and a head and neck case. It is found that both approaches are capable of providing clinically sensible 3D RT solutions with monotonically varying fluence maps. For currently available 3D RT delivery schemes based on the use of customized physical or dynamic wedges, constrained optimization seems to be more useful because the optimized fields are directly deliverable. Working in the beamlet domain provides a natural way to model the spatial variation of the beam fluence. The proposed methods take advantage of the fact that 3D RT is a special form of intensity-modulated radiation therapy (IMRT) and finds the optimal plan by searching for fields with a certain type of spatial variation. The approach provides a unified framework for 3D CRT and IMRT plan optimization.