An efficient quasi-Monte Carlo method with forced fixed detection for photon scatter simulation in CT

Detected scattered photons can cause cupping and streak artifacts, significantly degrading the quality of CT images. For fast and accurate estimation of scatter intensities resulting from photon interactions with a phantom, we first transform the path probability of photons interacting with the phantom into a high-dimensional integral. Secondly, we develope a new efficient algorithm called gQMCFFD, which combines graphics processing unit(GPU)-based quasi-Monte Carlo (QMC) with forced fixed detection to approximate this integral. QMC uses low discrepancy sequences for simulation and is deterministic versions of Monte Carlo. Numerical experiments show that the results are in excellent agreement and the efficiency improvement factors are 4 ∼ 46 times in all simulations by gQMCFFD with comparison to GPU-based Monte Carlo methods. And by combining gQMCFFD with sparse matrix method, the simulation time is reduced to 2 seconds in a single projection angle and the relative difference is 3.53%.

Quasi-Monte Carlo method for calculating X-ray scatter in CT

In this paper we transform the trajectories of X-ray as it interacts with a phantom into a high-dimensional integration problem and give the integral formula for the probability of photons emitted from the X-ray source through the phantom to reach the detector. We propose a superior algorithm called gQMCFRD, which combines GPU-based quasi-Monte Carlo (gQMC) method with forced random detection (FRD) technique to simulate this integral. QMC simulation is deterministic versions of Monte Carlo (MC) simulation, which uses deterministic low discrepancy points (such as Sobol' points) instead of the random points. By using the QMC and FRD technique, the gQMCFRD greatly increases the simulation convergence rate and efficiency. We benchmark gQMCFRD, GPU based MC tool (gMCDRR), which performs conventional simulations, a GPU-based Metropolis MC tool (gMMC), which uses the Metropolis-Hasting algorithm to sample the entire photon path from the X-ray source to the detector and gMCFRD, that uses random points for sampling against PENELOPE subroutines: MC-GPU. The results are in excellent agreement and the Efficiency Improvement Factor range 27 ∼ 37 (or 1.09 ∼ 1.16, or 0.12 ∼ 0.15, or 3.62 ∼ 3.70) by gQMCFRD (or gMCDRR, or gMMC, or gMCFRD) with comparison to MC-GPU in all cases. It shows that gQMCFRD is more effective in these cases.

Fast GPU-based Monte Carlo code for SPECT/CT reconstructions generates improved 177Lu images

Background

Full Monte Carlo (MC)-based SPECT reconstructions have a strong potential for correcting for image degrading factors, but the reconstruction times are long. The objective of this study was to develop a highly parallel Monte Carlo code for fast, ordered subset expectation maximum (OSEM) reconstructions of SPECT/CT images. The MC code was written in the Compute Unified Device Architecture language for a computer with four graphics processing units (GPUs) (GeForce GTX Titan X, Nvidia, USA). This enabled simulations of parallel photon emissions from the voxels matrix (128³ or 256³). Each computed tomography (CT) number was converted to attenuation coefficients for photo absorption, coherent scattering, and incoherent scattering. For photon scattering, the deflection angle was determined by the differential scattering cross sections. An angular response function was developed and used to model the accepted angles for photon interaction with the crystal, and a detector scattering kernel was used for modeling the photon scattering in the detector. Predefined energy and spatial resolution kernels for the crystal were used. The MC code was implemented in the OSEM reconstruction of clinical and phantom ¹⁷⁷Lu SPECT/CT images. The Jaszczak image quality phantom was used to evaluate the performance of the MC reconstruction in comparison with attenuated corrected (AC) OSEM reconstructions and attenuated corrected OSEM reconstructions with resolution recovery corrections (RRC).

Result

The performance of the MC code was 3200 million photons/s. The required number of photons emitted per voxel to obtain a sufficiently low noise level in the simulated image was 200 for a 128³ voxel matrix. With this number of emitted photons/voxel, the MC-based OSEM reconstruction with ten subsets was performed within 20 s/iteration. The images converged after around six iterations. Therefore, the reconstruction time was around 3 min. The activity recovery for the spheres in the Jaszczak phantom was clearly improved with MC-based OSEM reconstruction, e.g., the activity recovery was 88% for the largest sphere, while it was 66% for AC-OSEM and 79% for RRC-OSEM.

Conclusion

The GPU-based MC code generated an MC-based SPECT/CT reconstruction within a few minutes, and reconstructed patient images of ¹⁷⁷Lu-DOTATATE treatments revealed clearly improved resolution and contrast.

A parallel computational model for GATE simulations

GATE/Geant4 Monte Carlo simulations are computationally demanding applications, requiring thousands of processor hours to produce realistic results. The classical strategy of distributing the simulation of individual events does not apply efficiently for Positron Emission Tomography (PET) experiments, because it requires a centralized coincidence processing and large communication overheads. We propose a parallel computational model for GATE that handles event generation and coincidence processing in a simple and efficient way by decentralizing event generation and processing but maintaining a centralized event and time coordinator. The model is implemented with the inclusion of a new set of factory classes that can run the same executable in sequential or parallel mode. A Mann-Whitney test shows that the output produced by this parallel model in terms of number of tallies is equivalent (but not equal) to its sequential counterpart. Computational performance evaluation shows that the software is scalable and well balanced.

A detector response function design in pinhole SPECT including geometrical calibration

Clinical single photon emission computed tomography (SPECT) equipped with pinhole collimators have a magnification factor that results in high spatial resolution images for small animal imaging. Using Monte Carlo simulations to model the acquisition process and the propagation of the photons from their point of emission to their detection point then integrating the model into an iterative reconstruction algorithm improves the signal-to-noise ratio, the contrast and the spatial resolution in the reconstructed images. However, pinhole SPECT systems are known to be very sensitive to geometrical misalignments. Geometrical misalignments are defined as the radial or axial shift of the collimator pinhole and/or twist and tilt of the detector heads and are introduced in the system each time the collimation device is changed (pinhole to parallel holes or vice versa). In this work, we present a flexible detector response function table (DRFT) design that takes into account the geometrical misalignments and avoids performing new Monte Carlo simulations for each exam in order to calculate a geometrical study-dependent system matrix. The utilization of the DRFT for the calculation of the system matrix speeds up its computation time by two orders of magnitude making it acceptable for preclinical and clinical applications.

Implementation of angular response function modeling in SPECT simulations with GATE

Among Monte Carlo simulation codes in medical imaging, the GATE simulation platform is widely used today given its flexibility and accuracy, despite long run times, which in SPECT simulations are mostly spent in tracking photons through the collimators. In this work, a tabulated model of the collimator/detector response was implemented within the GATE framework to significantly reduce the simulation times in SPECT. This implementation uses the angular response function (ARF) model. The performance of the implemented ARF approach has been compared to standard SPECT GATE simulations in terms of the ARF tables' accuracy, overall SPECT system performance and run times. Considering the simulation of the Siemens Symbia T SPECT system using high-energy collimators, differences of less than 1% were measured between the ARF-based and the standard GATE-based simulations, while considering the same noise level in the projections, acceleration factors of up to 180 were obtained when simulating a planar 364 keV source seen with the same SPECT system. The ARF-based and the standard GATE simulation results also agreed very well when considering a four-head SPECT simulation of a realistic Jaszczak phantom filled with iodine-131, with a resulting acceleration factor of 100. In conclusion, the implementation of an ARF-based model of collimator/detector response for SPECT simulations within GATE significantly reduces the simulation run times without compromising accuracy.