M Folkerts

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.

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

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

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.

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

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

Towards the clinical implementation of iterative low-dose cone-beam CT reconstruction in image-guided radiation therapy: Cone/ring artifact correction and multiple GPU implementation

PURPOSE Compressed sensing (CS)-based iterative reconstruction (IR) techniques are able to reconstruct cone-beam CT (CBCT) images from undersampled noisy data, allowing for imaging dose reduction. However, there are a few practical concerns preventing the clinical implementation of these techniques. On the image quality side, data truncation along the superior-inferior direction under the cone-beam geometry produces severe cone artifacts in the reconstructed images. Ring artifacts are also seen in the half-fan scan mode. On the reconstruction efficiency side, the long computation time hinders clinical use in image-guided radiation therapy (IGRT). METHODS Image quality improvement methods are proposed to mitigate the cone and ring image artifacts in IR. The basic idea is to use weighting factors in the IR data fidelity term to improve projection data consistency with the reconstructed volume. In order to improve the computational efficiency, a multiple graphics processing units (GPUs)-based CS-IR system was developed. The parallelization scheme, detailed analyses of computation time at each step, their relationship with image resolution, and the acceleration factors were studied. The whole system was evaluated in various phantom and patient cases. RESULTS Ring artifacts can be mitigated by properly designing a weighting factor as a function of the spatial location on the detector. As for the cone artifact, without applying a correction method, it contaminated 13 out of 80 slices in a head-neck case (full-fan). Contamination was even more severe in a pelvis case under half-fan mode, where 36 out of 80 slices were affected, leading to poorer soft tissue delineation and reduced superior-inferior coverage. The proposed method effectively corrects those contaminated slices with mean intensity differences compared to FDK results decreasing from ∼497 and ∼293 HU to ∼39 and ∼27 HU for the full-fan and half-fan cases, respectively. In terms of efficiency boost, an overall 3.1 × speedup factor has been achieved with four GPU cards compared to a single GPU-based reconstruction. The total computation time is ∼30 s for typical clinical cases. CONCLUSIONS The authors have developed a low-dose CBCT IR system for IGRT. By incorporating data consistency-based weighting factors in the IR model, cone/ring artifacts can be mitigated. A boost in computational efficiency is achieved by multi-GPU implementation.

A hybrid reconstruction algorithm for fast and accurate 4D cone‐beam CT imaging

PURPOSE 4D cone beam CT (4D-CBCT) has been utilized in radiation therapy to provide 4D image guidance in lung and upper abdomen area. However, clinical application of 4D-CBCT is currently limited due to the long scan time and low image quality. The purpose of this paper is to develop a new 4D-CBCT reconstruction method that restores volumetric images based on the 1-min scan data acquired with a standard 3D-CBCT protocol. METHODS The model optimizes a deformation vector field that deforms a patient-specific planning CT (p-CT), so that the calculated 4D-CBCT projections match measurements. A forward-backward splitting (FBS) method is invented to solve the optimization problem. It splits the original problem into two well-studied subproblems, i.e., image reconstruction and deformable image registration. By iteratively solving the two subproblems, FBS gradually yields correct deformation information, while maintaining high image quality. The whole workflow is implemented on a graphic-processing-unit to improve efficiency. Comprehensive evaluations have been conducted on a moving phantom and three real patient cases regarding the accuracy and quality of the reconstructed images, as well as the algorithm robustness and efficiency. RESULTS The proposed algorithm reconstructs 4D-CBCT images from highly under-sampled projection data acquired with 1-min scans. Regarding the anatomical structure location accuracy, 0.204 mm average differences and 0.484 mm maximum difference are found for the phantom case, and the maximum differences of 0.3-0.5 mm for patients 1-3 are observed. As for the image quality, intensity errors below 5 and 20 HU compared to the planning CT are achieved for the phantom and the patient cases, respectively. Signal-noise-ratio values are improved by 12.74 and 5.12 times compared to results from FDK algorithm using the 1-min data and 4-min data, respectively. The computation time of the algorithm on a NVIDIA GTX590 card is 1-1.5 min per phase. CONCLUSIONS High-quality 4D-CBCT imaging based on the clinically standard 1-min 3D CBCT scanning protocol is feasible via the proposed hybrid reconstruction algorithm.

A GPU OpenCL based cross-platform Monte Carlo dose calculation engine (goMC).

Monte Carlo (MC) simulation has been recognized as the most accurate dose calculation method for radiotherapy. However, the extremely long computation time impedes its clinical application. Recently, a lot of effort has been made to realize fast MC dose calculation on graphic processing units (GPUs). However, most of the GPU-based MC dose engines have been developed under NVidias CUDA environment. This limits the code portability to other platforms, hindering the introduction of GPU-based MC simulations to clinical practice. The objective of this paper is to develop a GPU OpenCL based cross-platform MC dose engine named goMC with coupled photon-electron simulation for external photon and electron radiotherapy in the MeV energy range. Compared to our previously developed GPU-based MC code named gDPM (Jia et al 2012 Phys. Med. Biol. 57 7783-97), goMC has two major differences. First, it was developed under the OpenCL environment for high code portability and hence could be run not only on different GPU cards but also on CPU platforms. Second, we adopted the electron transport model used in EGSnrc MC package and PENELOPEs random hinge method in our new dose engine, instead of the dose planning method employed in gDPM. Dose distributions were calculated for a 15 MeV electron beam and a 6 MV photon beam in a homogenous water phantom, a water-bone-lung-water slab phantom and a half-slab phantom. Satisfactory agreement between the two MC dose engines goMC and gDPM was observed in all cases. The average dose differences in the regions that received a dose higher than 10% of the maximum dose were 0.48-0.53% for the electron beam cases and 0.15-0.17% for the photon beam cases. In terms of efficiency, goMC was ~4-16% slower than gDPM when running on the same NVidia TITAN card for all the cases we tested, due to both the different electron transport models and the different development environments. The code portability of our new dose engine goMC was validated by successfully running it on a variety of different computing devices including an NVidia GPU card, two AMD GPU cards and an Intel CPU processor. Computational efficiency among these platforms was compared.

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

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

SU‐E‐I‐35: A GPU Optimized DRR Algorithm

Purpose: To develop and evaluate a new DRR algorithm on GPU and compare its accuracy and efficiency to two other commonly used DRR algorithms. Methods: We developed a new fixed grid algorithm optimized for GPU. This new algorithm first rotates and re‐samples CT data layer by layer and then traces rays through voxel slabs perpendicular to the projection axis. We also implemented the fixed stride algorithm and Siddons incremental algorithm on GPU. We compared the accuracy of each algorithm to a ground truth that was generated by sampling 1024 evenly spaced ray paths per pixel using Siddons incremental algorithm. We then computed the relative error for 36 equally spaced projections in a full rotation about the SI axis for 5 different voxel resolutions (ranging from 512 to 32 cubed). We compared the efficiency of each algorithm by simulating 360 projections, one per degree, of a clinically sized phantom (512×512×128) in a full rotation about the SI axis. Both tests simulated common CBCT geometry with a 40.0×30.0 cm, 1024×768 pixel detector. XCAT phantoms were used in all tests. Results: We found that all three DRR algorithms attain small error as a function of decreasing voxel size ranging from 10% at 16.0 mm/voxel to less than 0.2% at 1.0 mm/voxel. We also found the average projection time for the fixed grid algorithm is 21.8 ms/projection, 40% faster than Siddons incremental algorithm which had an average projection time of 36.5 ms. The fixed stride algorithm is 18% faster than Siddons incremental algorithm with an average projection time of 28.7 ms. Conclusion: By specifically designing a DRR algorithm for GPU, we were able to improve the computation efficiency without losing accuracy. This work will be useful for computational tasks requiring frequent rendering of DRR projections.

An analytic linear accelerator source model for GPU-based Monte Carlo dose calculations

Recently, there has been a lot of research interest in developing fast Monte Carlo (MC) dose calculation methods on graphics processing unit (GPU) platforms. A good linear accelerator (linac) source model is critical for both accuracy and efficiency considerations. In principle, an analytical source model should be more preferred for GPU-based MC dose engines than a phase-space file-based model, in that data loading and CPU-GPU data transfer can be avoided. In this paper, we presented an analytical field-independent source model specifically developed for GPU-based MC dose calculations, associated with a GPU-friendly sampling scheme. A key concept called phase-space-ring (PSR) was proposed. Each PSR contained a group of particles that were of the same type, close in energy and reside in a narrow ring on the phase-space plane located just above the upper jaws. The model parameterized the probability densities of particle location, direction and energy for each primary photon PSR, scattered photon PSR and electron PSR. Models of one 2D Gaussian distribution or multiple Gaussian components were employed to represent the particle direction distributions of these PSRs. A method was developed to analyze a reference phase-space file and derive corresponding model parameters. To efficiently use our model in MC dose calculations on GPU, we proposed a GPU-friendly sampling strategy, which ensured that the particles sampled and transported simultaneously are of the same type and close in energy to alleviate GPU thread divergences. To test the accuracy of our model, dose distributions of a set of open fields in a water phantom were calculated using our source model and compared to those calculated using the reference phase-space files. For the high dose gradient regions, the average distance-to-agreement (DTA) was within 1 mm and the maximum DTA within 2 mm. For relatively low dose gradient regions, the root-mean-square (RMS) dose difference was within 1.1% and the maximum dose difference within 1.7%. The maximum relative difference of output factors was within 0.5%. Over 98.5% passing rate was achieved in 3D gamma-index tests with 2%/2 mm criteria in both an IMRT prostate patient case and a head-and-neck case. These results demonstrated the efficacy of our model in terms of accurately representing a reference phase-space file. We have also tested the efficiency gain of our source model over our previously developed phase-space-let file source model. The overall efficiency of dose calculation was found to be improved by ~1.3-2.2 times in water and patient cases using our analytical model.