High-throughput, accurate Monte Carlo simulation on CPU hardware for PET applications

In ion beam therapy, Positron Emission Tomography (PET) imaging can be applied to provide a consistency check of the delivered treatment with respect to the treatment plan. Treatment verification relies on the comparison between a PET distribution measured during or after treatment delivery (“measured PET”) and a PET simulation calculated on the basis of the treatment plan (“expected PET”). The method is challenged by the poor image quality of the measured PET, which may result in a low sensitivity to detectable mismatches between planned and applied treatment. In this work we propose the application of a motion-aware 4D Maximum Likelihood (ML) reconstruction strategy for PET-based treatment verification in ion beam therapy. This approach is specifically tested on simulated clinical-like scenarios, as well as on a real clinical dataset. The measured PET and the expected PET are interpreted as two different motion states of a 4D PET dataset. The idea is to estimate the deformation field mapping the expected PET onto the measured PET as a measure of mismatches. An enhanced measured PET is therefore obtained by warping the expected PET according to the estimated motion field. Clinical-like scenarios were reproduced by means of Monte Carlo simulations corresponding to a hypo-fractionated carbon ion treatment of liver tumour. The measured PET was attributed to different simulations introducing positioning mismatches by means of rigid translations, to be compared to the reference expected PET simulation without mismatch. Real clinical dataset include PET data acquired shortly after treatment at a dedicated PET-CT scanner installed at HIT (Heidelberg Ion beam Therapy Center, Germany), in comparison to the corresponding expected PET coming from Monte Carlo simulations. The accuracy of mismatch estimation and the robustness to noise are shown.

Purpose: To present a Monte Carlo (MC) x‐ray transport simulation code that uses a massively parallel graphics processing units (GPU) to generate medical images of voxelized patient models and estimate organ doses. Methods: We updated MC‐GPU, a CUDA‐based open‐source code for the simulation of radiographic projections and CT, to include the capability to tally 3D dose distributions. Since electrons are not transported, deposited doses are assumed to be equivalent to photon KERMA. The validity of this assumption was investigated by comparing it with the general‐purpose MC code PENELOPE in the simulation of a posterior‐anterior chest examination with 1010, 60‐keV x rays and a realistic female phantom with 1‐mm voxels. The stability of the simulation in a 480‐core GPU was also benchmarked using a sequential execution in a single CPU core. A utility to post‐process the voxel doses and report average and peak organ doses and effective dose for the procedure (and their uncertainty) has been developed. Results: The accuracy of the dose values generated by MC‐GPU was successfully validated. Average relative differences in the doses from PENELOPE and MC‐GPU executed in CPU and GPU were below 2%, in the expected range for statistical fluctuations. The simulation speeds were 46554 x rays/s with PENELOPE (electron transport disabled), 158216 x rays/s with MC‐GPU in a CPU, and 5124867 x rays/s in a GPU (simulation time in the GPU: 32.5 minutes, 32‐fold speedup compared to the CPU). The average and peak doses in breast and skin were estimated as 1.1 and 3.4 eV/g, and 1.7 and 15.6 eV/g per history respectively. Conclusion: The presented code can estimate organ doses 110 times faster than a general‐purpose MC code with comparable accuracy. A multi‐GPU execution of MC‐GPU has the potential to provide accurate organ doses in a CT scan in near real‐time.

To develop and evaluate a fast and accurate Monte Carlo simulation (MCS) based scatter correction for PET/MR imaging, based on Geant4 using graphical processing units (GPUs). The GPU implementation by Bert et al. [1] including the photon tracking within a voxelized volume was extended with the modeling of the detection process in the Siemens MR-BrainPET. Using NVIDIA’s CUDA photon pairs undergo several kernel functions in parallel, from their generation according to the activity distribution up to their detection in the scanner. Subsequently, coincidences are sorted and stored in list-mode. The new GPU implementation (GeForce GTX690) was validated by comparison with Gate v6.2 on a single CPU (Intel Core i7, 3.4GHz), showing a speedup factor of 135. The use of multiple GPUs can further increase this acceleration. For Compton scatter correction the reconstructed emission image, the patient MR-derived attenuation map and a CT-derived attenuation template of the MR coils are used as input for the simulation. The resulting simulated projection data are scaled to the normalized measured projection data. Thus, the often unstable fit to the distribution tails, necessary for single scatter simulation (SSS)[2], is circumvented. The scaled simulated scatter distribution is then incorporated in the reconstruction. The proposed scatter correction methodology was evaluated and compared to the SSS approach using sphere phantom measurements. Finally, the effect on patient data was investigated. Phantom results suggest an improved contrast with our new MC-based scatter correction, especially for measurements including the MR coils, where the contrast recovery was improved by 10-14%. First patient images also show improved grey/white matter contrast. Table 1 Comparison of recovery coefficients after scatter correction based on MCS and SSS. MC-based scatter correction shows improved recovery coefficients for the hot spheres. Figure 1 Assessment of image quality according to NEMA NU 2-2007. Images show the phantom with a hot spheres/background ratio of 8:1 measured with MR head coils inside the BrainPET scanner. Figure 2 Comparison of reconstructed FDG images using the scatter estimate provided by the vendor’s SSS (left) and our MCS method (right). Images were reconstructed using the vendor provided 3D OP-OSEM algorithm with 2 subsets and 32 iterations. The new GPU-accelerated MCS allows for fast and accurate estimation of scattered coincidences in PET studies using the Siemens MR-BrainPET with a major speed-up compared to standard MCS and superior image quality compared with the standard correction based on SSS.

Purpose: Positron emission tomography (PET) using open dual ring geometry was investigated as an on‐board system for functional imaging and PET marker tracking, specifically with tomotherapy. The open dual ring PET would allow measurement of both inter and intra‐fractional variation, improving the delineation of tumor volume at any stage in the radiation treatment delivery process. We compare results from data obtained with ray tracing to data from Monte Carlo simulations. This study demonstrates that depth of information (DOI) along the z axis of the crystal is required to reduce artifact from DOI blurring due to long axial PET geometry. Methods: PET design was accomplished via Monte Carlo simulations with GATE, the Geant4 Application for Emission Tomography. Images were reconstructed using Software for Image Reconstruction (STIR) with a fully 3D OSEM. Investigation of whether the image blurring is the result of DOI was carried out by scaling axially the PET design to one half and one forth the original proposed open PET. Image reconstruction with varying the ring difference or level of obliqueness of the accepted lines of response (LORs) for reconstruction also indicates the role of the DOI blurring. Results: Monte Carlo simulations of the open PET geometry indicate that the prominent physical factor that degrades image quality is the DOI. When comparing the Monte Carlo simulation for a phantom with four hot sources and cold background in air (reducing the effect of attenuation, randoms, and scatter) to that of the ray tracing simulations, we can visualize the degradation in the image quality. The reason is that GATE simulates the depth information but does not correct for DOI blurring, but STIR generated data assumes all LORs interact at the crystal surface. Conclusions: Onboard open PET with Tomotherapy must include DOI detectors to correct for the observed blurring.

Large-scale simulations on multiple Graphics Processing Units (GPUs) for the direct simulation Monte Carlo method

Positron emission tomography (PET) images suffer from a noticeable amount of statistical noise. In order to reduce the noise, a post smoothing process is usually adopted in the conventional PET systems. However, its performance is limited because the process is mostly based on a Gaussian random noise which is quite distinct from the noise of PET images. It has been reported that noise variance of each voxel is proportional to the square of the mean value in a PET image reconstructed by expectation-maximization (EM). In addition, we also observe that the variance varies with the spatial sensitivity distribution in a PET system. Based on those properties, we determine a unique formula representing a relationship between the mean and variance for a given PET system. Meanwhile, a block matching 3D (or 4D) algorithm is known as the state of the art in Gaussian noise reduction. To effectively apply it for noise reduction of PET images, we first perform a noise characteristic conversion from the PET image noise to Gaussian random noise using a pre-determined relationship. We then apply a block matching 4D (BM4D) algorithm and reconvert the result. Using the Monte Carlo simulation, we demonstrate that proposed algorithm can effectively reduce the noise in the whole image region while minimizing the image resolution degradation.

GPU accelerated MCMC for modeling terrorist activity

In radiation transport calculations, the effects of material temperature on neutron/nucleus interactions must be taken into account through Doppler broadening adjustments to the microscopic cross section data. Historically, Monte Carlo transport simulations have accounted for this temperature dependence by interpolating among precalculated Doppler broadened cross sections at a variety of temperatures. More recently, there has been much interest in on-the-fly Doppler broadening methods, where reference data is broadened on-demand during particle transport to any temperature. Unfortunately, Doppler broadening operations are expensive on traditional central processing unit (CPU) architectures, making on-the-fly Doppler broadening unaffordable without approximations or complex data preprocessing. This work considers the use of graphics processing unit (GPU)s, which excel at parallel data processing, for on-the-fly Doppler broadening in continuous-energy Monte Carlo simulations. Two methods are considered for the broadening operations – a GPU implementation of the standard SIGMA1 algorithm and a novel vectorized algorithm that leverages the convolution properties of the broadening operation in an attempt to expose additional parallelism. Numerical results demonstrate that similar cross section lookup throughput is obtained for on-the-fly broadening on a GPU as cross section lookup throughput with precomputed data on a CPU, implying that offloading Doppler broadening operations to a GPU may enable on-the-fly temperature treatment of cross sections without a noticeable reduction in cross section processing performance in Monte Carlo transport codes.

Purpose: For microdosimetric calculation event-by-event Monte Carlo (MC) simulation is considered the most accurate, but it is very time-consuming. In this work we present an event-by-event MC simulation of low energy electron and proton for accelerated microdosimetric MC simulations on a graphic processing unit (GPU). Methods: The MC simulation of particle was implemented in C and executed on a multi-core CPU, and a commercially available general purpose GPU using the compute unified device architecture (CUDA). Additionally, a hybrid implementation scheme was realized by employing OpenMP and CUDA so that both GPU and multi-core CPU were utilized simultaneously. The two implementation schemes have been tested and compared with the sequential single threaded MC simulation on the CPU. A calculation time comparison was established on the speed-up for a set of benchmarking cases of electron and proton. Results: Dosimetric results were obtained with both the parallel and serial MC codes. A GPU over CPU speed-up of 67.2 and 19.2 times was achieved for 300 eV and 2 keV electron tracks respectively. For proton tracks, the GPU-based code was approximately 5 times faster than the CPU-single-thread code. By incorporating a multi-core CPU and running the MC code simultaneously on the GPU and CPU, an increase of 2%-7% and 20% in the speedup was noticed for electrons and protons tracks respectively. A good dosimetric agreement between the CPU- and GPU-based MC methods was observed for both electrons and proton. Conclusions: A GPU-based MC method for microdosimetric calculations of low energy electron and proton has been presented. The results indicate the capability of our GPU-based implementation for accelerated MC simulations of both electron and proton without loss of accuracy. Lastly, the potential of a hybrid approach by utilizing simultaneously a GPU and a multi-core CPU for further acceleration of MC microdosimetric calculations has been demonstrated.

Positron emission tomography (PET) is one of the most promising techniques for hadron therapy monitoring. This method uses imaging of the annihilation photons resulting from positron emitting isotopes produced during patient irradiation in hadron therapy. In order to maximize the sensitivity, in-beam PET is the preferred option, which requires a partial ring configuration. The usage of partial ring PET systems causes image artefacts and low quality images due to incomplete data. The inclusion of Time-of-flight (TO F) information into the reconstruction algorithm provides better image quality for PET systems. Therefore, a PET system with very good time and spatial resolution is necessary for hadron therapy monitoring. The Resistive-Plate-Chambers (RPCs), providing very good time and spatial resolution might be used for the quality control of hadron therapy. However, they have lower sensitivity than crystal-based systems. The objective of this study is the comparison of the performance of two TOF-PET systems, a RPC-based PET system currently under investigation by the TERA group and a commercially available crystal-based PET system, with respect to their feasibility of being applied to monitor cancer treatment with ion- and proton-beams. Various Monte-Carlo simulations were performed using GATE to evaluate the performance of both systems following NEMA protocols. Furthermore, a set of sources emulating the annihilation photons from β+-emitters produced after proton pencil beam irradiation on a PMMA target were obtained. These sources were employed to study the capability to reproduce the proton beam path and the distal edge position. Finally, we calculated the activity distribution produced by carbon ions on the basis of one field of a real treatment plan. The results obtained indicate that a RPC-based system has five times lower sensitivity, similar spatial resolution and about two times higher scatter fraction compared to the crystal-based system. The low sensitivity obtained by the RPC-based system is not sufficient to determine range deviations.

Clinical Application of In-Room Positron Emission Tomography for In Vivo Treatment Monitoring in Proton Radiation Therapy

Network Function Virtualization (NFV) replaces the hardware that supports packet processing in network operation from specific- by general-purpose ones, reducing costs and bringing more flexibility and agility to the network operation. However, this shift can cause performance losses due to the non-optimal packet processing capabilities of the general-purpose hardware. Moreover, supporting the line rate of optical network channels with Virtualized Network Functions (VNFs) is a challenging task. This work analyzes the benefits of using Graphics Processing Units (GPUs) to support the execution of a Deep Packet Inspection (DPI) VNF towards supporting the line rate of an optical channel. The use of GPUs in VNFs has a great potential to increase throughput, but the delay incurred might be an issue for some functions. Our simulation was performed using an Intrusion Detection Systems (IDS) which performs DPI deployed as a VNF under real-world traffic scaled to high bit rates. Results show that the packet processing speedup achieved by using GPUs can reach up to 19 times, at the expense of a higher packet delay.

In positron emission tomography (PET), 3D iterative image reconstruction methods have a huge computational burden. In this paper, we developed a list-mode image reconstruction method using graphics processing units (GPUs). Efficiency of acceleration for GPU implementation largely depends on the method chosen, where a reduced number of conditional statements and a reduced memory size are required. On the other hand, accurate system models are required to improve the quality of reconstructed images. Various accurate system models for conventional CPU implementation have been proposed, but these models basically require many conditional statements and huge memory size. Therefore, we developed a new system model which matches GPU implementation better. In this model, the detector response functions, which vary depending on each line of response (LOR), are pre-computed in CPUs and modeled by sixth-order polynomial functions in order to reduce the memory size occupied in GPUs. Each element of a system matrix is obtained on-the-fly in GPUs by calculating the distance between an LOR and a voxel. Therefore the developed system model enables efficient GPU implementation of the accurate system modeling with a reduced number of conditional statements and a reduced memory size. We applied the developed method to a small OpenPET prototype, in which 4-layered depth-of-interaction (DOI) detectors were used. For image reconstruction, we used the dynamic row-action maximum likelihood algorithm (DRAMA). Compared with a conventional model for GPU implementation, in which DRFs are given as a Gaussian function of fixed width, we saw no remarkable difference for DOI data, but for non-DOI data the proposed model outperformed the conventional at the peripheral region of the field-of-view. The proposed model had almost the same calculation time as the conventional model did. For further acceleration, we tried parallel GPU implementation, and we obtained 3.8-fold acceleration by using 4 GPUs.

Recently, hierarchical cascading accelerated with graphics processing units (GPUs) has proven efficient for accelerating 3D periodic finite-element method (FEM) analysis of acoustic wave devices. However, the limited memory available in GPUs severely restricts the accuracy of the simulations; moreover, numerical libraries are not fully matured yet. This paper considers two techniques to circumvent these limitations. Firstly, to extend the size of the problems that can be handled, the use of GPUs can be limited to isolated cascading operations. While the related data transfer between RAM and GPUs hinders the efficiency of GPUs, significant acceleration is still achieved as compared to CPU-based implementation. Secondly, a GPU-friendly alternative is presented for the reduction of FEM system matrices to B-matrices. Examples of simulations of 3D periodic TCSAW, IHP, and XBAR arrays are provided.

Graphical Processing Units (GPU) have become a vital source for data processing in many advanced or intelligent technologies. They have proven to be faster and more efficient than the Central Processing Unit (CPU) in computing large data sets. The automotive industry has adopted GPUs for Advanced Driver Assistance Systems (ADAS), but other systems like electric vehicles and autonomous vehicles will also employ GPUs soon. Although GPUs are faster at computing large data sets, a substantial increase in core temperature is challenging during the process. This review paper primarily focuses on active and passive cooling methods for GPUs in the automotive industry. The paper commences by addressing the role and need for GPUs in the automotive industry and explores the challenges they face and the factors that lead to an increase in temperature. The paper further reviews various cooling methods that original equipment manufacturers (OEM) use in the automotive industry. The outcomes of the review are a detailed understanding of the use of GPUs in automotive, a brief interpretation of heating issues in GPUs and what causes them, a comprehensive understanding of the cooling methods used to reduce the core temperature, and a perception of an anticipated technology to resolve the heating problem.