Justin C. Park

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).

Liver motion during cone beam computed tomography guided stereotactic body radiation therapy

PURPOSE Understanding motion characteristics of liver such as, interfractional and intrafractional motion variability, difference in motion within different locations in the organ, and their complex relationship with the breathing cycles are particularly important for image-guided liver SBRT. The purpose of this study was to investigate such motion characteristics based on fiducial markers tracked with the x-ray projections of the CBCT scans, taken immediately prior to the treatments. METHODS Twenty liver SBRT patients were analyzed. Each patient had three fiducial markers (2 × 5-mm gold) percutaneously implanted around the gross tumor. The prescription ranged from 2 to 8 fractions per patient. The CBCT projections data for each fraction (∼650 projections∕scan), for each patient, were analyzed and the 2D positions of the markers were extracted using an in-house algorithm. In total, >55 000 x-ray projections were analyzed from 85 CBCT scans. From the 2D extracted positions, a 3D motion trajectory of the markers was constructed, from each CBCT scans, resulting in left-right (LR), anterior-posterior (AP), and cranio-caudal (CC) location information of the markers with >55 000 data points. The authors then analyzed the interfraction and intrafraction liver motion variability, within different locations in the organ, and as a function of the breathing cycle. The authors also compared the motion characteristics against the planning 4DCT and the RPM™ (Varian Medical Systems, Palo Alto, CA) breathing traces. Variations in the appropriate gating window (defined as the percent of the maximum range at which 50% of the marker positions are contained), between fractions were calculated as well. RESULTS The range of motion for the 20 patients were 3.0 ± 2.0 mm, 5.1 ± 3.1 mm, and 17.9 ± 5.1 mm in the planning 4DCT, and 2.8 ± 1.6 mm, 5.3 ± 3.1 mm, and 16.5 ± 5.7 mm in the treatment CBCT, for LR, AP, and CC directions, respectively. The range of respiratory period was 3.9 ± 0.7 and 4.2 ± 0.8 s during the 4DCT simulation and the CBCT scans, respectively. The authors found that breathing-induced AP and CC motions are highly correlated. That is, all markers moved cranially also moved posteriorly and vice versa, irrespective of the location. The LR motion had a more variable relationship with the AP∕CC motions, and appeared random with respect to the location. That is, when the markers moved toward cranial-posterior direction, 58% of the markers moved to the patient-right, 22% of the markers moved to the patient-left, and 20% of the markers had minimal∕none motion. The absolute difference in the motion magnitude between the markers, in different locations within the liver, had a positive correlation with the absolute distance between the markers (R(2) = 0.69, linear-fit). The interfractional gating window varied significantly for some patients, with the largest having 29.4%-56.4% range between fractions. CONCLUSIONS This study analyzed the liver motion characteristics of 20 patients undergoing SBRT. A large variation in motion was observed, interfractionally and intrafractionally, and that as the distance between the markers increased, the difference in the absolute range of motion also increased. This suggests that marker(s) in closest proximity to the target be used.

Patient-specific motion artifacts in 4DCT

PURPOSE Four-dimensional computed tomography (4DCT) has enhanced images of the thorax and upper abdomen during respiration, but intraphase residual motion artifacts will persist in cine-mode scanning. In this study, the source and magnitude of projection artifacts due to intraphase target motion is investigated. METHODS A theoretical model of geometric uncertainty due to partial projection artifacts in cine-mode 4DCT was derived based on ideal periodic motion. Predicted artifacts were compared to measured errors with a rigid lung phantom attached to a programmable motion platform. Ideal periodic motion and actual patient breathing patterns were used as input for phantom motion. Reconstructed target dimensions were measured along the direction of motion and compared to the actual, known dimensions. RESULTS Artifacts due to intraphase residual motion in cine-mode 4DCT range from a few mm up to a few cm on a given scanner, and can be predicted based on target motion and CT gantry rotation time. Errors in ITV and GTV dimensions were accurately characterized by the theoretical uncertainty at all phases when sinusoidal motion was considered, and in 96% of 300 measurements when patient breathing patterns were used as motion input. When peak-to-peak motion of 1.5 cm is combined with a breathing period of 4 s and gantry rotation time of 1 s, errors due to partial projection artifacts can be greater than 1 cm near midventilation and are a few mm in the inhale and exhale phases. Incorporation of such uncertainty into margin design should be considered in addition to other uncertainties. CONCLUSIONS Artifacts due to intraphase residual motion exist in 4DCT, even for ideal breathing motions (e.g., sine waves). It was determined that these motion artifacts depend on patient-specific tumor motion and CT gantry rotation speed. Thus, if the patient-specific motion parameters are known (i.e., amplitude and period), a patient-specific margin can and should be designed to compensate for this uncertainty.

Four-dimensional cone-beam computed tomography and digital tomosynthesis reconstructions using respiratory signals extracted from transcutaneously inserted metal markers for liver SBRT.

PURPOSE Respiration-induced intrafraction target motion is a concern in liver cancer radiotherapy, especially in stereotactic body radiotherapy (SBRT), and therefore, verification of its motion is necessary. An effective means to localize the liver cancer is to insert metal fiducial markers to or near the tumor with simultaneous imaging using cone-beam computed tomography (CBCT). Utilizing the fiducial markers, the authors have demonstrated a method to generate breath-induced motion signal of liver for reconstructing 4D digital tomosynthesis (4DDTS) and 4DCBCT images based on phasewise and/or amplitudewise sorting of projection data. METHODS The marker extraction algorithm is based on template matching of a prior known marker image and has been coded to optimally extract marker positions in CBCT projections from the On-Board Imager (Varian Medical Systems, Palo Alto, CA). To validate the algorithm, multiple projection images of moving thorax phantom and five patient cases were examined. Upon extraction of the motion signals from the markers, 4D image sorting and image reconstructions were subsequently performed. In the case of incomplete signals due to projections with missing markers, the authors have implemented signal profiling to replace the missing portion. RESULTS The proposed marker extraction algorithm was shown to be very robust and accurate in the phantom and patient cases examined. The maximum discrepancy of the algorithm predicted marker location versus operator selected location was < 1.2 mm, with the overall average of 0.51 +/- 0.15 mm, for 500 projections. The resulting 4DDTS and 4DCBCT images showed clear reduction in motion-induced blur of the markers and the anatomy for an effective image guidance. The signal profiling method was useful in replacing missing signals. CONCLUSIONS The authors have successfully demonstrated that motion tracking of fiducial markers and the subsequent 4D reconstruction of CBCT and DTS are possible. Due to the significant reduction in motion-induced image blur, it is anticipated that such technology will be useful in image-guided liver SBRT treatments.

Ultra-Fast Digital Tomosynthesis Reconstruction Using General-Purpose GPU Programming for Image-Guided Radiation Therapy

The purpose of this work is to demonstrate an ultra-fast reconstruction technique for digital tomosynthesis (DTS) imaging based on the algorithm proposed by Feldkamp, Davis, and Kress (FDK) using standard general-purpose graphics processing unit (GPGPU) programming interface. To this end, the FDK-based DTS algorithm was programmed “in-house” with C language with utilization of 1) GPU and 2) central processing unit (CPU) cards. The GPU card consisted of 480 processing cores (2 × 240 dual chip) with 1,242 MHz processing clock speed and 1,792 MB memory space. In terms of CPU hardware, we used 2.68 GHz clock speed, 12.0 GB DDR3 RAM, on a 64-bit OS. The performance of proposed algorithm was tested on twenty-five patient cases (5 lung, 5 liver, 10 prostate, and 5 head-and-neck) scanned either with a full-fan or half-fan mode on our cone-beam computed tomography (CBCT) system. For the full-fan scans, the projections from 157.5°–202.5° (45°-scan) were used to reconstruct coronal DTS slices, whereas for the half-fan scans, the projections from both 157.5°–202.5° and 337.5°–22.5° (2 × 45°-scan) were used to reconstruct larger FOV coronal DTS slices. For this study, we chose 45°-scan angle that contained ~80 projections for the full-fan and ~160 projections with 2 × 45°-scan angle for the half-fan mode, each with 1024 × 768 pixels with 32-bit precision. Absolute pixel value differences, profiles, and contrast-to-noise ratio (CNR) calculations were performed to compare and evaluate the images reconstructed using GPU- and CPU-based implementations. The time dependence on the reconstruction volume was also tested with (512 × 512) × 16, 32, 64, 128, and 256 slices. In the end, the GPU-based implementation achieved, at most, 1.3 and 2.5 seconds to complete full reconstruction of 512 × 512 × 256 volume, for the full-fan and half-fan modes, respectively. In turn, this meant that our implementation can process > 13 projections-per-second (pps) and > 18 pps for the full-fan and half-fan modes, respectively. Since commercial CBCT system nominally acquires 11 pps (with 1 gantry-revolution-per-minute), our GPU-based implementation is sufficient to handle the incoming projections data as they are acquired and reconstruct the entire volume immediately after completing the scan. In addition, on increasing the number of slices (hence volume) to be reconstructed from 16 to 256, only minimal increases in reconstruction time were observed for the GPU-based implementation where from 0.73 to 1.27 seconds and 1.42 to 2.47 seconds increase were observed for the full-fan and half-fan modes, respectively. This resulted in speed improvement of up to 87 times compared with the CPU-based implementation (for 256 slices case), with visually identical images and small pixel-value discrepancies (< 6.3%), and CNR differences (< 2.3%). With this achievement, we have shown that time allocation for DTS image reconstruction is virtually eliminated and that clinical implementation of this approach has become quite appealing. In addition, with the speed achievement, further image processing and real-time applications that was prohibited prior due to time restrictions can now be tempered with.

Dynamic modulated brachytherapy (DMBT) for rectal cancer

PURPOSE All forms of past and current high-dose-rate brachytherapy utilize immobile applicators during treatment delivery. The only moving part is the source itself. This paradigm misses an important degree of freedom that, if explored, can in some instances produce previously unachievable dose conformality; that is, the dynamic motion of the applicator itself during treatment delivery. Monte Carlo and treatment planning simulations were used to illustrate the potential benefits of moving applicators for rectal cancer applications in particular. This concept is termed dynamic modulated brachytherapy (DMBT). METHODS The DMBT system uses a high-density, 18.0 g∕cm(3), 45 mm long tungsten alloy shield, cylindrical in shape, with a small window on one side to encapsulate a (192)Ir source, to create collimation that results in a highly directional beam profile. This shield can be dynamically translated and rotated, using an attached robotic arm, during treatment to create a volumetric modulated arc therapy-type delivery, but from inside the rectal cavity. Monte Carlo simulations and planning optimization algorithms were developed inhouse to evaluate the effectiveness of this new approach using 36 clinical treatment plans comprised of 13 patients each treated using the intracavitary mold applicator (ICMA, Nucletron, The Netherlands) to quantify the potential clinical benefit. The prescription dose was 10 Gy∕fx and the group had an average clinical target volume of 9.0 ± 3.5 cm(3). Ideal phantom geometries were used to evaluate the impact of various shield dimensions and designs on the resulting plan quality. RESULTS Simulations of ideal phantom geometries found that shields as small as 10 mm in diameter can produce high quality plans. For the clinical patient cases, compared to the ICMA, for equal prescription tumor coverage, the DMBT plans provided >30% decrease in D(5) (high dose volume) resulting in a ∼40% decrease in dose heterogeneity index. In addition, mean dose and D(98) showed a reduction (typically 40%-60%) on all critical structures evaluated. However, for a 10 Gy prescribed dose there was an increase in total treatment time on average from 7.6 to 20.8 min for a source with an air-kerma strength of 40.25 kU (10 Ci). CONCLUSIONS Dosimetric properties of a novel DMBT system have been described and evaluated. Comparison with the ICMA commercial applicator has shown it to be a prospective step forward in high-dose-rate brachytherapy (192)Ir technology. Dynamic motion of an applicator during treatment, for any applicator and site in general, can provide additional degrees of freedom that, if properly considered, can potentially increase the plan quality significantly.

Motion-map constrained image reconstruction (MCIR): Application to four-dimensional cone-beam computed tomography

PURPOSE Utilization of respiratory correlated four-dimensional cone-beam computed tomography (4DCBCT) has enabled verification of internal target motion and volume immediately prior to treatment. However, with current standard CBCT scan, 4DCBCT poses challenge for reconstruction due to the fact that multiple phase binning leads to insufficient number of projection data to reconstruct and thus cause streaking artifacts. The purpose of this study is to develop a novel 4DCBCT reconstruction algorithm framework called motion-map constrained image reconstruction (MCIR), that allows reconstruction of high quality and high phase resolution 4DCBCT images with no more than the imaging dose as well as projections used in a standard free breathing 3DCBCT (FB-3DCBCT) scan. METHODS The unknown 4DCBCT volume at each phase was mathematically modeled as a combination of FB-3DCBCT and phase-specific update vector which has an associated motion-map matrix. The motion-map matrix, which is the key innovation of the MCIR algorithm, was defined as the matrix that distinguishes voxels that are moving from stationary ones. This 4DCBCT model was then reconstructed with compressed sensing (CS) reconstruction framework such that the voxels with high motion would be aggressively updated by the phase-wise sorted projections and the voxels with less motion would be minimally updated to preserve the FB-3DCBCT. To evaluate the performance of our proposed MCIR algorithm, we evaluated both numerical phantoms and a lung cancer patient. The results were then compared with the (1) clinical FB-3DCBCT reconstructed using the FDK, (2) 4DCBCT reconstructed using the FDK, and (3) 4DCBCT reconstructed using the well-known prior image constrained compressed sensing (PICCS). RESULTS Examination of the MCIR algorithm showed that high phase-resolved 4DCBCT with sets of up to 20 phases using a typical FB-3DCBCT scan could be reconstructed without compromising the image quality. Moreover, in comparison with other published algorithms, the image quality of the MCIR algorithm is shown to be excellent. CONCLUSIONS This work demonstrates the potential for providing high-quality 4DCBCT during on-line image-guided radiation therapy (IGRT), without increasing the imaging dose. The results showed that (at least) 20 phase images could be reconstructed using the same projections data, used to reconstruct a single FB-3DCBCT, without streak artifacts that are caused by insufficient projections.

Development of a fast Monte Carlo dose calculation system for online adaptive radiation therapy quality assurance

Online adaptive radiation therapy (ART) based on real-time magnetic resonance imaging represents a paradigm-changing treatment scheme. However, conventional quality assurance (QA) methods based on phantom measurements are not feasible with the patient on the treatment couch. The purpose of this work is to develop a fast Monte Carlo system for validating online re-optimized tri-60Co IMRT adaptive plans with both high accuracy and speed. The Monte Carlo system is based on dose planning method (DPM) code with further simplification of electron transport and consideration of external magnetic fields. A vendor-provided head model was incorporated into the code. Both GPU acceleration and variance reduction were implemented. Additionally, to facilitate real-time decision support, a C++ GUI was developed for visualizing 3D dose distributions and performing various analyses in an online adaptive setting. A thoroughly validated Monte Carlo code (gPENELOPE) was used to benchmark the new system, named GPU-accelerated DPM with variance reduction (gDPMvr). The comparison using 15 clinical IMRT plans demonstrated that gDPMvr typically runs 43 times faster with only 0.5% loss in accuracy. Moreover, gDPMvr reached 1% local dose uncertainty within 2.3 min on average, and thus is well-suited for ART QA.

SU‐E‐J‐14: A Novel, Fast, Variable Step Size Gradient Method for Solving Simultaneous Algebraic Reconstruction Technique (SART)‐Type Reconstructions: An Example Application to CBCT

Purpose: To develop a fast‐converging SART‐type algorithm and show clinical feasibility in CBCTreconstructions by combining the algorithmic enhancements with a parallel computing hardware (GPU). Methods: SART reconstructs a volumetric image by iteratively conducting volume projection and correction backprojection. However, this reconstruction problem can also be cast as a least squares problem for minimizing the volume projection errors with respect to the scanner projection data. This way, SART can be viewed as equivalent to a gradient method for minimizing the quadratic objective function f(x), with a fixed step‐size. Novelty in this work is that we implemented a simple yet much faster algorithm by computing a unique step‐size at each iteration. We applied this variable step‐size (VS)‐SART algorithm to numerical and physical phantoms for reconstruction. Furthermore, we accelerated the reconstruction by implementing the algorithm on NVIDIA GTX 295 GPU card. CBCT projections of CatPhan phantom were acquired from the Varian TrueBeam system. Results: We first compared SART and VS‐SART using Shepp‐Logan numerical phantom with 180 parallel‐beam projections. As the iterations progress, f(x) is asymptotically minimized for both algorithms but VS‐SART is found to converge much faster. Therefore, for a fixed number of iterations, VS‐SART commands superior image quality. In addition, compared with the FDK algorithm with 364 projections, our VS‐SART algorithm produces visibly equivalent quality CBCTimage for CatPhan phantom with only 120 projections, in 12 iterations completed in 33 seconds. This is a factor of three dose reduction while maintaining the reconstruction time acceptable. Conclusions: By approaching SART reconstruction problem from a gradient method perspective, we enhanced the reconstruction speed significantly (i.e., less number of iterations). In addition, with GPU acceleration, the overall reconstruction time is achieved within a clinically viable range. We anticipate that the VS‐SART algorithm can be applied to CT,PET, and SPECT also.

Variable step size methods for solving simultaneous algebraic reconstruction technique (SART)-type CBCT reconstructions

Compared to analytical reconstruction by Feldkamp-Davis-Kress (FDK), simultaneous algebraic reconstruction technique (SART) offers a higher degree of flexibility in input measurements and often produces superior quality images. Due to the iterative nature of the algorithm, however, SART requires intense computations which have prevented its use in clinical practice. In this paper, we developed a fast-converging SART-type algorithm and showed its clinical feasibility in CBCT reconstructions. Inspired by the quasi-orthogonal nature of the x-ray projections in CBCT, we implement a simple yet much faster algorithm by computing Barzilai and Borwein step size at each iteration. We applied this variable step-size (VS)-SART algorithm to numerical and physical phantoms as well as cancer patients for reconstruction. By connecting the SART algebraic problem to the statistical weighted least squares problem, we enhanced the reconstruction speed significantly (i.e., less number of iterations). We further accelerated the reconstruction speed of algorithms by using the parallel computing power of GPU.