A GPU-based finite-size pencil beam algorithm with 3D-density correction for radiotherapy dose calculation

Spectral CT image reconstruction using a constrained optimization approach-An algorithm for AAPM 2022 spectral CT grand challenge and beyond

BACKGROUND

CT reconstruction is of essential importance in medical imaging. In 2022, the American Association of Physicists in Medicine (AAPM) sponsored a Grand Challenge to investigate the challenging inverse problem of spectral CT reconstruction, with the aim of achieving the most accurate reconstruction results. The authors of this paper participated in the challenge and won as a runner-up team.

PURPOSE

This paper reports details of our PROSPECT algorithm (Prior-based Restricted-variable Optimization for SPEctral CT) and follow-up studies regarding the algorithm's accuracy and enhancement of its convergence speed.

METHODS

We formulated the reconstruction task as an optimization problem. PROSPECT employed a one-step backward iterative scheme to solve this optimization problem by allowing estimation of and correction for the difference between the actual polychromatic projection model and the monochromatic model used in the optimization problem. PROSPECT incorporated various forms of prior information derived by analyzing training data provided by the Grand Challenge to reduce the number of unknown variables. We investigated the impact of projection data precision on the resulting solution accuracy and improved convergence speed of the PROSPECT algorithm by incorporating a beam-hardening correction (BHC) step in the iterative process. We also studied the algorithm's performance under noisy projection data.

RESULTS

Prior knowledge allowed a reduction of the number of unknown variables by85.9 % $85.9\%$ . PROSPECT algorithm achieved the average root of mean square error (RMSE) of3.3 × 10 - 6 $3.3\,\times \,10^{-6}$ in the test data set provided by the Grand Challenge. Performing the reconstruction with the same algorithm but using double-precision projection data reduced RMSE to1.2 × 10 - 11 $1.2\,\times \,10^{-11}$ . Including the BHC step in the PROSPECT algorithm accelerated the iteration process with a 40% reduction in computation time.

CONCLUSIONS

PROSPECT algorithm achieved a high degree of accuracy and computational efficiency.

Internet-based computer technology on radiotherapy

Recent rapid development of Internet-based computer technologies has made possible many novel applications in radiation dose delivery. However, translational speed of applying these new technologies in radiotherapy could hardly catch up due to the complex commissioning process and quality assurance protocol. Implementing novel Internet-based technology in radiotherapy requires corresponding design of algorithm and infrastructure of the application, set up of related clinical policies, purchase and development of software and hardware, computer programming and debugging, and national to international collaboration. Although such implementation processes are time consuming, some recent computer advancements in the radiation dose delivery are still noticeable. In this review, we will present the background and concept of some recent Internet-based computer technologies such as cloud computing, big data processing and machine learning, followed by their potential applications in radiotherapy, such as treatment planning and dose delivery. We will also discuss the current progress of these applications and their impacts on radiotherapy. We will explore and evaluate the expected benefits and challenges in implementation as well.

An Approach in Radiation Therapy Treatment Planning: A Fast, GPU-Based Monte Carlo Method

An accurate and fast radiation dose calculation is essential for successful radiation radiotherapy. The aim of this study was to implement a new graphic processing unit (GPU) based radiation therapy treatment planning for accurate and fast dose calculation in radiotherapy centers. A program was written for parallel running based on GPU. The code validation was performed by EGSnrc/DOSXYZnrc. Moreover, a semi-automatic, rotary, asymmetric phantom was designed and produced using a bone, the lung, and the soft tissue equivalent materials. All measurements were performed using a Mapcheck dosimeter. The accuracy of the code was validated using the experimental data, which was obtained from the anthropomorphic phantom as the gold standard. The findings showed that, compared with those of DOSXYZnrc in the virtual phantom and for most of the voxels (>95%), <3% dose-difference or 3 mm distance-to-agreement (DTA) was found. Moreover, considering the anthropomorphic phantom, compared to the Mapcheck dose measurements, <5% dose-difference or 5 mm DTA was observed. Fast calculation speed and high accuracy of GPU-based Monte Carlo method in dose calculation may be useful in routine radiation therapy centers as the core and main component of a treatment planning verification system.

A method to reconstruct and apply 3D primary fluence for treatment delivery verification

Motivation

In this study, a method is reported to perform IMRT and VMAT treatment delivery verification using 3D volumetric primary beam fluences reconstructed directly from planned beam parameters and treatment delivery records. The goals of this paper are to demonstrate that 1) 3D beam fluences can be reconstructed efficiently, 2) quality assurance (QA) based on the reconstructed 3D fluences is capable of detecting additional treatment delivery errors, particularly for VMAT plans, beyond those identifiable by other existing treatment delivery verification methods, and 3) QA results based on 3D fluence calculation (3DFC) are correlated with QA results based on physical phantom measurements and radiation dose recalculations.

Methods

Using beam parameters extracted from DICOM plan files and treatment delivery log files, 3D volumetric primary fluences are reconstructed by forward‐projecting the beam apertures, defined by the MLC leaf positions and modulated by beam MU values, at all gantry angles using first‐order ray tracing. Treatment delivery verifications are performed by comparing 3D fluences reconstructed using beam parameters in delivery log files against those reconstructed from treatment plans. Passing rates are then determined using both voxel intensity differences and a 3D gamma analysis. QA sensitivity to various sources of errors is defined as the observed differences in passing rates. Correlations between passing rates obtained from QA derived from both 3D fluence calculations and physical measurements are investigated prospectively using 20 clinical treatment plans with artificially introduced machine delivery errors.

Results

Studies with artificially introduced errors show that common treatment delivery problems including gantry angle errors, MU errors, jaw position errors, collimator rotation errors, and MLC leaf position errors were detectable at less than normal machine tolerances. The reported 3DFC QA method has greater sensitivity than measurement‐based QA methods. Statistical analysis‐based Spearman's correlations shows that the 3DFC QA passing rates are significantly correlated with passing rates of physical phantom measurement‐based QA methods.

Conclusion

Among measurement‐less treatment delivery verification methods, the reported 3DFC method is less demanding than those based on full dose re‐calculations, and more comprehensive than those that solely checks beam parameters in treatment log files. With QA passing rates correlating to measurement‐based passing rates, the 3DFC QA results could be useful for complementing the physical phantom measurements, or verifying treatment deliveries when physical measurements are not available. For the past 4+ years, the reported method has been implemented at authors’ institution 1) as a complementary metric to physical phantom measurements for pretreatment, patient‐specific QA of IMRT and VMAT plans, and 2) as an important part of the log file‐based automated verification of daily patient treatment deliveries. It has been demonstrated to be useful in catching both treatment plan data transfer errors and treatment delivery problems.

Automatic metastatic brain tumor segmentation for stereotactic radiosurgery applications

The objective of this study is to develop an automatic segmentation strategy for efficient and accurate metastatic brain tumor delineation on contrast-enhanced T1-weighted (T1c) magnetic resonance images (MRI) for stereotactic radiosurgery (SRS) applications. The proposed four-step automatic brain metastases segmentation strategy is comprised of pre-processing, initial contouring, contour evolution, and contour triage. First, T1c brain images are preprocessed to remove the skull. Second, an initial tumor contour is created using a multi-scaled adaptive threshold-based bounding box and a super-voxel clustering technique. Third, the initial contours are evolved to the tumor boundary using a regional active contour technique. Fourth, all detected false-positive contours are removed with geometric characterization. The segmentation process was validated on a realistic virtual phantom containing Gaussian or Rician noise. For each type of noise distribution, five different noise levels were tested. Twenty-one cases from the multimodal brain tumor image segmentation (BRATS) challenge dataset and fifteen clinical metastases cases were also included in validation. Segmentation performance was quantified by the Dice coefficient (DC), normalized mutual information (NMI), structural similarity (SSIM), Hausdorff distance (HD), mean value of surface-to-surface distance (MSSD) and standard deviation of surface-to-surface distance (SDSSD). In the numerical phantom study, the evaluation yielded a DC of 0.98  ±  0.01, an NMI of 0.97  ±  0.01, an SSIM of 0.999  ±  0.001, an HD of 2.2  ±  0.8 mm, an MSSD of 0.1  ±  0.1 mm, and an SDSSD of 0.3  ±  0.1 mm. The validation on the BRATS data resulted in a DC of 0.89  ±  0.08, which outperform the BRATS challenge algorithms. Evaluation on clinical datasets gave a DC of 0.86  ±  0.09, an NMI of 0.80  ±  0.11, an SSIM of 0.999  ±  0.001, an HD of 8.8  ±  12.6 mm, an MSSD of 1.5  ±  3.2 mm, and an SDSSD of 1.8  ±  3.4 mm when comparing to the physician drawn ground truth. The result indicated that the developed automatic segmentation strategy yielded accurate brain tumor delineation and presented as a useful clinical tool for SRS applications.

An Automated Treatment Plan Quality Control Tool for Intensity-Modulated Radiation Therapy Using a Voxel-Weighting Factor-Based Re-Optimization Algorithm

Intensity-modulated radiation therapy (IMRT) currently plays an important role in radiotherapy, but its treatment plan quality can vary significantly among institutions and planners. Treatment plan quality control (QC) is a necessary component for individual clinics to ensure that patients receive treatments with high therapeutic gain ratios. The voxel-weighting factor-based plan re-optimization mechanism has been proved able to explore a larger Pareto surface (solution domain) and therefore increase the possibility of finding an optimal treatment plan. In this study, we incorporated additional modules into an in-house developed voxel weighting factor-based re-optimization algorithm, which was enhanced as a highly automated and accurate IMRT plan QC tool (TPS-QC tool). After importing an under-assessment plan, the TPS-QC tool was able to generate a QC report within 2 minutes. This QC report contains the plan quality determination as well as information supporting the determination. Finally, the IMRT plan quality can be controlled by approving quality-passed plans and replacing quality-failed plans using the TPS-QC tool. The feasibility and accuracy of the proposed TPS-QC tool were evaluated using 25 clinically approved cervical cancer patient IMRT plans and 5 manually created poor-quality IMRT plans. The results showed high consistency between the QC report quality determinations and the actual plan quality. In the 25 clinically approved cases that the TPS-QC tool identified as passed, a greater difference could be observed for dosimetric endpoints for organs at risk (OAR) than for planning target volume (PTV), implying that better dose sparing could be achieved in OAR than in PTV. In addition, the dose-volume histogram (DVH) curves of the TPS-QC tool re-optimized plans satisfied the dosimetric criteria more frequently than did the under-assessment plans. In addition, the criteria for unsatisfied dosimetric endpoints in the 5 poor-quality plans could typically be satisfied when the TPS-QC tool generated re-optimized plans without sacrificing other dosimetric endpoints. In addition to its feasibility and accuracy, the proposed TPS-QC tool is also user-friendly and easy to operate, both of which are necessary characteristics for clinical use.

Adaptive beamlet-based finite-size pencil beam dose calculation for independent verification of IMRT and VMAT

PURPOSE

The use of sophisticated dose calculation procedure in modern radiation therapy treatment planning is inevitable in order to account for complex treatment fields created by multileaf collimators (MLCs). As a consequence, independent volumetric dose verification is time consuming, which affects the efficiency of clinical workflow. In this study, the authors present an efficient adaptive beamlet-based finite-size pencil beam (AB-FSPB) dose calculation algorithm that minimizes the computational procedure while preserving the accuracy.

METHODS

The computational time of finite-size pencil beam (FSPB) algorithm is proportional to the number of infinitesimal and identical beamlets that constitute an arbitrary field shape. In AB-FSPB, dose distribution from each beamlet is mathematically modeled such that the sizes of beamlets to represent an arbitrary field shape no longer need to be infinitesimal nor identical. As a result, it is possible to represent an arbitrary field shape with combinations of different sized and minimal number of beamlets. In addition, the authors included the model parameters to consider MLC for its rounded edge and transmission.

RESULTS

Root mean square error (RMSE) between treatment planning system and conventional FSPB on a 10 × 10 cm(2) square field using 10 × 10, 2.5 × 2.5, and 0.5 × 0.5 cm(2) beamlet sizes were 4.90%, 3.19%, and 2.87%, respectively, compared with RMSE of 1.10%, 1.11%, and 1.14% for AB-FSPB. This finding holds true for a larger square field size of 25 × 25 cm(2), where RMSE for 25 × 25, 2.5 × 2.5, and 0.5 × 0.5 cm(2) beamlet sizes were 5.41%, 4.76%, and 3.54% in FSPB, respectively, compared with RMSE of 0.86%, 0.83%, and 0.88% for AB-FSPB. It was found that AB-FSPB could successfully account for the MLC transmissions without major discrepancy. The algorithm was also graphical processing unit (GPU) compatible to maximize its computational speed. For an intensity modulated radiation therapy (∼12 segments) and a volumetric modulated arc therapy fields (∼90 control points) with a 3D grid size of 2.0 × 2.0 × 2.0 mm(3), dose was computed within 3-5 and 10-15 s timeframe, respectively.

CONCLUSIONS

The authors have developed an efficient adaptive beamlet-based pencil beam dose calculation algorithm. The fast computation nature along with GPU compatibility has shown better performance than conventional FSPB. This enables the implementation of AB-FSPB in the clinical environment for independent volumetric dose verification.

Reconstructing cone-beam CT with spatially varying qualities for adaptive radiotherapy: a proof-of-principle study

With the aim of maximally reducing imaging dose while meeting requirements for adaptive radiation therapy (ART), we propose in this paper a new cone beam CT (CBCT) acquisition and reconstruction method that delivers images with a low noise level inside a region of interest (ROI) and a relatively high noise level outside the ROI. The acquired projection images include two groups: densely sampled projections at a low exposure with a large field of view (FOV) and sparsely sampled projections at a high exposure with a small FOV corresponding to the ROI. A new algorithm combining the conventional filtered back-projection algorithm and the tight-frame iterative reconstruction algorithm is also designed to reconstruct the CBCT based on these projection data. We have validated our method on a simulated head-and-neck (HN) patient case, a semi-real experiment conducted on a HN cancer patient under a full-fan scan mode, as well as a Catphan phantom under a half-fan scan mode. Relative root-mean-square errors (RRMSEs) of less than 3% for the entire image and ~1% within the ROI compared to the ground truth have been observed. These numbers demonstrate the ability of our proposed method to reconstruct high-quality images inside the ROI. As for the part outside ROI, although the images are relatively noisy, it can still provide sufficient information for radiation dose calculations in ART. Dose distributions calculated on our CBCT image and on a standard CBCT image are in agreement, with a mean relative difference of 0.082% inside the ROI and 0.038% outside the ROI. Compared with the standard clinical CBCT scheme, an imaging dose reduction of approximately 3-6 times inside the ROI was achieved, as well as an 8 times outside the ROI. Regarding computational efficiency, it takes 1-3 min to reconstruct a CBCT image depending on the number of projections used. These results indicate that the proposed method has the potential for application in ART.

GPU-based high-performance computing for radiation therapy

Recent developments in radiotherapy therapy demand high computation powers to solve challenging problems in a timely fashion in a clinical environment. The graphics processing unit (GPU), as an emerging high-performance computing platform, has been introduced to radiotherapy. It is particularly attractive due to its high computational power, small size, and low cost for facility deployment and maintenance. Over the past few years, GPU-based high-performance computing in radiotherapy has experienced rapid developments. A tremendous amount of study has been conducted, in which large acceleration factors compared with the conventional CPU platform have been observed. In this paper, we will first give a brief introduction to the GPU hardware structure and programming model. We will then review the current applications of GPU in major imaging-related and therapy-related problems encountered in radiotherapy. A comparison of GPU with other platforms will also be presented.

Automatic treatment plan re-optimization for adaptive radiotherapy guided with the initial plan DVHs

Adaptive radiation therapy (ART) can reduce normal tissue toxicity and/or improve tumor control through treatment adaptations based on the current patient anatomy. Developing an efficient and effective re-planning algorithm is an important step toward the clinical realization of ART. For the re-planning process, manual trial-and-error approach to fine-tune planning parameters is time-consuming and is usually considered unpractical, especially for online ART. It is desirable to automate this step to yield a plan of acceptable quality with minimal interventions. In ART, prior information in the original plan is available, such as dose-volume histogram (DVH), which can be employed to facilitate the automatic re-planning process. The goal of this work is to develop an automatic re-planning algorithm to generate a plan with similar, or possibly better, DVH curves compared with the clinically delivered original plan. Specifically, our algorithm iterates the following two loops. An inner loop is the traditional fluence map optimization, in which we optimize a quadratic objective function penalizing the deviation of the dose received by each voxel from its prescribed or threshold dose with a set of fixed voxel weighting factors. In outer loop, the voxel weighting factors in the objective function are adjusted according to the deviation of the current DVH curves from those in the original plan. The process is repeated until the DVH curves are acceptable or maximum iteration step is reached. The whole algorithm is implemented on GPU for high efficiency. The feasibility of our algorithm has been demonstrated with three head-and-neck cancer IMRT cases, each having an initial planning CT scan and another treatment CT scan acquired in the middle of treatment course. Compared with the DVH curves in the original plan, the DVH curves in the resulting plan using our algorithm with 30 iterations are better for almost all structures. The re-optimization process takes about 30 s using our in-house optimization engine.

A GPU tool for efficient, accurate, and realistic simulation of cone beam CT projections

PURPOSE

Simulation of x-ray projection images plays an important role in cone beam CT (CBCT) related research projects, such as the design of reconstruction algorithms or scanners. A projection image contains primary signal, scatter signal, and noise. It is computationally demanding to perform accurate and realistic computations for all of these components. In this work, the authors develop a package on graphics processing unit (GPU), called gDRR, for the accurate and efficient computations of x-ray projection images in CBCT under clinically realistic conditions.

METHODS

The primary signal is computed by a trilinear ray-tracing algorithm. A Monte Carlo (MC) simulation is then performed, yielding the primary signal and the scatter signal, both with noise. A denoising process specifically designed for Poisson noise removal is applied to obtain a smooth scatter signal. The noise component is then obtained by combining the difference between the MC primary and the ray-tracing primary signals, and the difference between the MC simulated scatter and the denoised scatter signals. Finally, a calibration step converts the calculated noise signal into a realistic one by scaling its amplitude according to a specified mAs level. The computations of gDRR include a number of realistic features, e.g., a bowtie filter, a polyenergetic spectrum, and detector response. The implementation is fine-tuned for a GPU platform to yield high computational efficiency.

RESULTS

For a typical CBCT projection with a polyenergetic spectrum, the calculation time for the primary signal using the ray-tracing algorithms is 1.2-2.3 s, while the MC simulations take 28.1-95.3 s, depending on the voxel size. Computation time for all other steps is negligible. The ray-tracing primary signal matches well with the primary part of the MC simulation result. The MC simulated scatter signal using gDRR is in agreement with EGSnrc results with a relative difference of 3.8%. A noise calibration process is conducted to calibrate gDRR against a real CBCT scanner. The calculated projections are accurate and realistic, such that beam-hardening artifacts and scatter artifacts can be reproduced using the simulated projections. The noise amplitudes in the CBCT images reconstructed from the simulated projections also agree with those in the measured images at corresponding mAs levels.

CONCLUSIONS

A GPU computational tool, gDRR, has been developed for the accurate and efficient simulations of x-ray projections of CBCT with realistic configurations.

Four-dimensional cone beam CT reconstruction and enhancement using a temporal nonlocal means method

PURPOSE

Four-dimensional cone beam computed tomography (4D-CBCT) has been developed to provide respiratory phase-resolved volumetric imaging in image guided radiation therapy. Conventionally, it is reconstructed by first sorting the x-ray projections into multiple respiratory phase bins according to a breathing signal extracted either from the projection images or some external surrogates, and then reconstructing a 3D CBCT image in each phase bin independently using FDK algorithm. This method requires adequate number of projections for each phase, which can be achieved using a low gantry rotation or multiple gantry rotations. Inadequate number of projections in each phase bin results in low quality 4D-CBCT images with obvious streaking artifacts. 4D-CBCT images at different breathing phases share a lot of redundant information, because they represent the same anatomy captured at slightly different temporal points. Taking this redundancy along the temporal dimension into account can in principle facilitate the reconstruction in the situation of inadequate number of projection images. In this work, the authors propose two novel 4D-CBCT algorithms: an iterative reconstruction algorithm and an enhancement algorithm, utilizing a temporal nonlocal means (TNLM) method.

METHODS

The authors define a TNLM energy term for a given set of 4D-CBCT images. Minimization of this term favors those 4D-CBCT images such that any anatomical features at one spatial point at one phase can be found in a nearby spatial point at neighboring phases. 4D-CBCT reconstruction is achieved by minimizing a total energy containing a data fidelity term and the TNLM energy term. As for the image enhancement, 4D-CBCT images generated by the FDK algorithm are enhanced by minimizing the TNLM function while keeping the enhanced images close to the FDK results. A forward-backward splitting algorithm and a Gauss-Jacobi iteration method are employed to solve the problems. The algorithms implementation on GPU is designed to avoid redundant and uncoalesced memory access, in order to ensure a high computational efficiency. Our algorithms have been tested on a digital NURBS-based cardiac-torso phantom and a clinical patient case.

RESULTS

The reconstruction algorithm and the enhancement algorithm generate visually similar 4D-CBCT images, both better than the FDK results. Quantitative evaluations indicate that, compared with the FDK results, our reconstruction method improves contrast-to-noise-ratio (CNR) by a factor of 2.56-3.13 and our enhancement method increases the CNR by 2.75-3.33 times. The enhancement method also removes over 80% of the streak artifacts from the FDK results. The total computation time is 509-683 s for the reconstruction algorithm and 524-540 s for the enhancement algorithm on an NVIDIA Tesla C1060 GPU card.

CONCLUSIONS

By innovatively taking the temporal redundancy among 4D-CBCT images into consideration, the proposed algorithms can produce high quality 4D-CBCT images with much less streak artifacts than the FDK results, in the situation of inadequate number of projections.

A new column-generation-based algorithm for VMAT treatment plan optimization

We study the treatment plan optimization problem for volumetric modulated arc therapy (VMAT). We propose a new column-generation-based algorithm that takes into account bounds on the gantry speed and dose rate, as well as an upper bound on the rate of change of the gantry speed, in addition to MLC constraints. The algorithm iteratively adds one aperture at each control point along the treatment arc. In each iteration, a restricted problem optimizing intensities at previously selected apertures is solved, and its solution is used to formulate a pricing problem, which selects an aperture at another control point that is compatible with previously selected apertures and leads to the largest rate of improvement in the objective function value of the restricted problem. Once a complete set of apertures is obtained, their intensities are optimized and the gantry speeds and dose rates are adjusted to minimize treatment time while satisfying all machine restrictions. Comparisons of treatment plans obtained by our algorithm to idealized IMRT plans of 177 beams on five clinical prostate cancer cases demonstrate high quality with respect to clinical dose-volume criteria. For all cases, our algorithm yields treatment plans that can be delivered in around 2 min. Implementation on a graphic processing unit enables us to finish the optimization of a VMAT plan in 25-55 s.

GPU-based fast Monte Carlo simulation for radiotherapy dose calculation

Monte Carlo (MC) simulation is commonly considered to be the most accurate dose calculation method in radiotherapy. However, its efficiency still requires improvement for many routine clinical applications. In this paper, we present our recent progress toward the development of a graphics processing unit (GPU)-based MC dose calculation package, gDPM v2.0. It utilizes the parallel computation ability of a GPU to achieve high efficiency, while maintaining the same particle transport physics as in the original dose planning method (DPM) code and hence the same level of simulation accuracy. In GPU computing, divergence of execution paths between threads can considerably reduce the efficiency. Since photons and electrons undergo different physics and hence attain different execution paths, we use a simulation scheme where photon transport and electron transport are separated to partially relieve the thread divergence issue. A high-performance random number generator and a hardware linear interpolation are also utilized. We have also developed various components to handle the fluence map and linac geometry, so that gDPM can be used to compute dose distributions for realistic IMRT or VMAT treatment plans. Our gDPM package is tested for its accuracy and efficiency in both phantoms and realistic patient cases. In all cases, the average relative uncertainties are less than 1%. A statistical t-test is performed and the dose difference between the CPU and the GPU results is not found to be statistically significant in over 96% of the high dose region and over 97% of the entire region. Speed-up factors of 69.1 ∼ 87.2 have been observed using an NVIDIA Tesla C2050 GPU card against a 2.27 GHz Intel Xeon CPU processor. For realistic IMRT and VMAT plans, MC dose calculation can be completed with less than 1% standard deviation in 36.1 ∼ 39.6 s using gDPM.