Reconstruction of multi-animal PET acquisitions with anisotropically variant PSF

Among other factors such as random, attenuation and scatter corrections, uniform spatial resolution is key to performing accurate quantitative studies in Positron emission tomography (PET). Particularly in preclinical PET studies involving simultaneous acquisition of multiple animals, the degradation of image resolution due to the depth of interaction (DOI) effect far from the center of the Field of View (FOV) becomes a significant concern. In this work, we incorporated a spatially-variant resolution model into a real time iterative reconstruction code to obtain accurate images of multi-animal acquisition. We estimated the spatially variant point spread function (SV-PSF) across the FOV using measurements and Monte Carlo (MC) simulations. The SV-PSF obtained was implemented in a GPU-based Ordered subset expectation maximization (OSEM) reconstruction code, which includes scatter, attenuation and random corrections. The method was evaluated with acquisitions from two preclinical PET/CT scanners of the SEDECAL Argus family: a Derenzo phantom placed 2 cm off center in the 4R-SuperArgus, and a multi-animal study with 4 mice in the 6R-SuperArgus. The SV-PSF reconstructions showed uniform spatial resolution without significant increase in reconstruction time, with superior image quality compared to the uniform PSF model.

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

Monte Carlo simulations (MCS) represent a fundamental approach to modelling the photon interactions in Positron Emission Tomography (PET). A variety of PET-dedicated MCS tools are available to assist and improve PET imaging applications. Of these, GATE has evolved into one of the most popular software for PET MCS because of its accuracy and flexibility. However, simulations are extremely time-consuming. The use of graphics processing units (GPU) has been proposed as a solution to this, with reported acceleration factors about 400-800. These factors refer to GATE benchmarks performed on a single CPU core. Consequently, CPU-based MCS can also be easily accelerated by one order of magnitude or beyond when exploiting multi-threading on powerful CPUs. Thus, CPU-based implementations become competitive when further optimisations can be achieved. In this context, we have developed a novel, CPU-based software called the PET Physics Simulator (PPS), which combines several efficient methods to significantly boost the performance. PPS flexibly applies GEANT4 cross-sections as a pre-calculated database, thus obtaining results equivalent to GATE. This is demonstrated for an elaborated PET scanner with 3-layer block detectors. All code optimisations yield an acceleration factor of  20 (single core). Multi-threading on a high-end CPU workstation (96 cores) further accelerates the PPS by a factor of 80. This results in a total speed-up factor of 1600, which outperforms comparable GPU-based MCS by a factor of  2. Optionally, the proposed method of coincidence multiplexing can further enhance the throughput by an additonal factor of 15. The combination of all optimisations corresponds to an acceleration factor of  24000. In this way, the PPS can simulate complex PET detector systems with an effective throughput of photon pairs in less than 10 milliseconds.

Evaluation of quantitative, efficient image reconstruction for VersaPET, a compact PET system

PURPOSE

Previously we developed a high-resolution positron emission tomography (PET) system-VersaPET-characterized by a block geometry with relatively large axial and transaxial interblock gaps and a compact geometry susceptible to parallax blurring effects. In this work, we report the qualitative and quantitative evaluation of a graphic processing unit (GPU)-accelerated maximum-likelihood by expectation-maximization (MLEM) image reconstruction framework for VersaPET which features accurate system geometry and projection space point-spread-function (PSF) modeling.

METHODS

We combined the ray-tracing module from software for tomographic image reconstruction (STIR), an open-source PET image reconstruction package, with VersaPET's exact block geometry for the geometric system matrix. Point-spread-function modeling of crystal penetration and scattering was achieved by a custom Monte-Carlo simulation for projection space blurring in all dimensions. We also parallelized the reconstruction in GPU taking advantage of the system's symmetry for PSF computation. To investigate the effects of PSF width, we generated and studied multiple kernels between one that reflects the true LYSO density in the MC simulation and another that reflects geometry only (no PSF). GATE simulations of hot and cold-sphere phantoms with spheres of different sizes, real microDerenzo phantom, and human blood vessel data were used to characterize the quantitative and qualitative performances of the reconstruction.

RESULTS

Reconstruction with an accurate system geometry effectively improved image quality compared to STIR (version 3.0) which assumes an idealized system geometry. Reconstructions of GATE-simulated hot-sphere phantom data showed that all PSF kernels achieved superior performance in contrast recovery and bias reduction compared to using no PSF, but may introduce edge artifact and lumped background noise pattern depending on the width of PSF kernels. Cold-sphere phantom simulation results also indicated improvement in contrast recovery and quantification with PSF modeling (compared to no PSF) for 5 and 10 mm cold spheres. Real microDerenzo phantom images with the PSF kernel that reflects the true LYSO density showed degraded resolving power of small sectors that could be resolved more clearly by underestimated PSF kernels, which is consistent with recent literature despite differences in scanner geometries and in approaches to system model estimation. The human vessel results resemble those of the hot-sphere phantom simulation with the PSF kernel that reflects the true LYSO density achieving the highest peak in the time activity curve (TAC) and similar lumped noise pattern.

CONCLUSIONS

We fully evaluated a practical MLEM reconstruction framework that we developed for VersaPET in terms of qualitative and quantitative performance. Different PSF kernels may be adopted for improving the results of specific imaging tasks but the underlying reasons for the variation in optimal kernel for the real and simulation studies requires further study.

Resolution modeling in projection space using a factorized multi-block detector response function for PET image reconstruction

Positron emission tomography (PET) images usually suffer from limited resolution and statistical uncertainties. However, a technique known as resolution modeling (RM) can be used to improve image quality by accurately modeling the system's detection process within the iterative reconstruction. In this study, we present an accurate RM method in projection space based on a simulated multi-block detector response function (DRF) and evaluate it on the Siemens hybrid MR-BrainPET system. The DRF is obtained using GATE simulations that consider nearly all the possible annihilation photons from the field-of-view (FOV). Intrinsically, the multi-block DRF allows the block crosstalk to be modeled. The RM blurring kernel is further generated by factorizing the blurring matrix of one line-of-response (LOR) into two independent detector responses, which can then be addressed with the DRF. Such a kernel is shift-variant in 4D projection space without any distance or angle compression, and is integrated into the image reconstruction for the BrainPET insert with single instruction multiple data (SIMD) and multi-thread support. Evaluation of simulations and measured data demonstrate that the reconstruction with RM yields significantly improved resolutions and reduced mean squared error (MSE) values at different locations of the FOV, compared with reconstruction without RM. Furthermore, the shift-variant RM kernel models the varying blurring intensity for different LORs due to the depth-of-interaction (DOI) dependencies, thus avoiding severe edge artifacts in the images. Additionally, compared to RM in single-block mode, the multi-block mode shows significantly improved resolution and edge recovery at locations beyond 10 cm from the center of BrainPET insert in the transverse plane. However, the differences have been observed to be low for patient data between single-block and multi-block mode RM, due to the brain size and location as well as the geometry of the BrainPET insert. In conclusion, the RM method proposed in this study can yield better reconstructed images in terms of resolution and MSE value, compared to conventional reconstruction without RM.

Improved Woodcock tracking on Monte Carlo simulations for medical applications

This paper presents a new variance reduction technique called super voxel Woodcock (SVW), which combines Woodcock tracking technique with the super voxel concept, used in computer graphics. It consists in grouping the voxels of the volume in a super voxel grid (pre-processing step) by associating to each of the super voxels a local value of the most attenuate medium which will later serve to the interaction distances sampling. SVW allows reducing the sampling of the particle path while a high-density material is present within the simulated phantom. In order to evaluate the performance of the SVW method compare to both standard and Woodcock tracking methods, algorithms were implemented within the same GPU MCS framework GGEMS. This method improves the performance of the standard Woodcock method by a factor of 4.5 and 4.3 for x-ray imaging application and intraoperative radiotherapy respectively. The proposed SVW method did not introduce any bias on the simulations.

PET performance evaluation of MADPET4: a small animal PET insert for a 7 T MRI scanner

MADPET4 is the first small animal PET insert with two layers of individually read out crystals in combination with silicon photomultiplier technology. It has a novel detector arrangement, in which all crystals face the center of field of view transaxially. In this work, the PET performance of MADPET4 was evaluated and compared to other preclinical PET scanners using the NEMA NU 4 measurements, followed by imaging a mouse-size hot-rod resolution phantom and two in vivo simultaneous PET/MRI scans in a 7 T MRI scanner. The insert had a peak sensitivity of 0.49%, using an energy threshold of 350 keV. A uniform transaxial resolution was obtained up to 15 mm radial offset from the axial center, using filtered back-projection with single-slice rebinning. The measured average radial and tangential resolutions (FWHM) were 1.38 mm and 1.39 mm, respectively. The 1.2 mm rods were separable in the hot-rod phantom using an iterative image reconstruction algorithm. The scatter fraction was 7.3% and peak noise equivalent count rate was 15.5 kcps at 65.1 MBq of activity. The FDG uptake in a mouse heart and brain were visible in the two in vivo simultaneous PET/MRI scans without applying image corrections. In conclusion, the insert demonstrated a good overall performance and can be used for small animal multi-modal research applications.

Sinogram Blurring Matrix Estimation From Point Sources Measurements With Rank-One Approximation for Fully 3-D PET

An accurate system matrix is essential in positron emission tomography (PET) for reconstructing high quality images. To reduce storage size and image reconstruction time, we factor the system matrix into a product of a geometry projection matrix and a sinogram blurring matrix. The geometric projection matrix is computed analytically and the sinogram blurring matrix is estimated from point source measurements. Previously, we have estimated a 2-D blurring matrix for a preclinical PET scanner. The 2-D blurring matrix only considers blurring effects within a transaxial sinogram and does not compensate for inter-sinogram blurring effects. For PET scanners with a long axial field of view, inter-sinogram blurring can be a major problem influencing the image quality in the axial direction. Hence, the estimation of a 4-D blurring matrix is desirable to further improve the image quality. The 4-D blurring matrix estimation is an ill-conditioned problem due to the large number of unknowns. Here, we propose a rank-one approximation for each blurring kernel image formed by a row vector of the sinogram blurring matrix to improve the stability of the 4-D blurring matrix estimation. The proposed method is applied to the simulated data as well as the real data obtained from an Inveon microPET scanner. The results show that the newly estimated 4-D blurring matrix can improve the image quality over those obtained with a 2-D blurring matrix and requires less point source scans to achieve similar image quality compared with an unconstrained 4-D blurring matrix estimation.

Iterative reconstruction using a Monte Carlo based system transfer matrix for dedicated breast positron emission tomography

To maximize sensitivity, it is desirable that ring Positron Emission Tomography (PET) systems dedicated for imaging the breast have a small bore. Unfortunately, due to parallax error this causes substantial degradation in spatial resolution for objects near the periphery of the breast. In this work, a framework for computing and incorporating an accurate system matrix into iterative reconstruction is presented in an effort to reduce spatial resolution degradation towards the periphery of the breast. The GATE Monte Carlo Simulation software was utilized to accurately model the system matrix for a breast PET system. A strategy for increasing the count statistics in the system matrix computation and for reducing the system element storage space was used by calculating only a subset of matrix elements and then estimating the rest of the elements by using the geometric symmetry of the cylindrical scanner. To implement this strategy, polar voxel basis functions were used to represent the object, resulting in a block-circulant system matrix. Simulation studies using a breast PET scanner model with ring geometry demonstrated improved contrast at 45% reduced noise level and 1.5 to 3 times resolution performance improvement when compared to MLEM reconstruction using a simple line-integral model. The GATE based system matrix reconstruction technique promises to improve resolution and noise performance and reduce image distortion at FOV periphery compared to line-integral based system matrix reconstruction.

Accurate and efficient modeling of the detector response in small animal multi-head PET systems

In fully three-dimensional PET imaging, iterative image reconstruction techniques usually outperform analytical algorithms in terms of image quality provided that an appropriate system model is used. In this study we concentrate on the calculation of an accurate system model for the YAP-(S)PET II small animal scanner, with the aim to obtain fully resolution- and contrast-recovered images at low levels of image roughness. For this purpose we calculate the system model by decomposing it into a product of five matrices: (1) a detector response component obtained via Monte Carlo simulations, (2) a geometric component which describes the scanner geometry and which is calculated via a multi-ray method, (3) a detector normalization component derived from the acquisition of a planar source, (4) a photon attenuation component calculated from x-ray computed tomography data, and finally, (5) a positron range component is formally included. This system model factorization allows the optimization of each component in terms of computation time, storage requirements and accuracy. The main contribution of this work is a new, efficient way to calculate the detector response component for rotating, planar detectors, that consists of a GEANT4 based simulation of a subset of lines of flight (LOFs) for a single detector head whereas the missing LOFs are obtained by using intrinsic detector symmetries. Additionally, we introduce and analyze a probability threshold for matrix elements of the detector component to optimize the trade-off between the matrix size in terms of non-zero elements and the resulting quality of the reconstructed images. In order to evaluate our proposed system model we reconstructed various images of objects, acquired according to the NEMA NU 4-2008 standard, and we compared them to the images reconstructed with two other system models: a model that does not include any detector response component and a model that approximates analytically the depth of interaction as detector response component. The comparisons confirm previous research results, showing that the usage of an accurate system model with a realistic detector response leads to reconstructed images with better resolution and contrast recovery at low levels of image roughness.

Patient-adaptive lesion metabolism analysis by dynamic PET images

Dynamic PET imaging provides important spatial-temporal information for metabolism analysis of organs and tissues, and generates a great reference for clinical diagnosis and pharmacokinetic analysis. Due to poor statistical properties of the measurement data in low count dynamic PET acquisition and disturbances from surrounding tissues, identifying small lesions inside the human body is still a challenging issue. The uncertainties in estimating the arterial input function will also limit the accuracy and reliability of the metabolism analysis of lesions. Furthermore, the sizes of the patients and the motions during PET acquisition will yield mismatch against general purpose reconstruction system matrix, this will also affect the quantitative accuracy of metabolism analyses of lesions. In this paper, we present a dynamic PET metabolism analysis framework by defining a patient adaptive system matrix to improve the lesion metabolism analysis. Both patient size information and potential small lesions are incorporated by simulations of phantoms of different sizes and individual point source responses. The new framework improves the quantitative accuracy of lesion metabolism analysis, and makes the lesion identification more precisely. The requirement of accurate input functions is also reduced. Experiments are conducted on Monte Carlo simulated data set for quantitative analysis and validation, and on real patient scans for assessment of clinical potential.

High Performance 3D PET Reconstruction Using Spherical Basis Functions on a Polar Grid

Statistical iterative methods are a widely used method of image reconstruction in emission tomography. Traditionally, the image space is modelled as a combination of cubic voxels as a matter of simplicity. After reconstruction, images are routinely filtered to reduce statistical noise at the cost of spatial resolution degradation. An alternative to produce lower noise during reconstruction is to model the image space with spherical basis functions. These basis functions overlap in space producing a significantly large number of non-zero elements in the system response matrix (SRM) to store, which additionally leads to long reconstruction times. These two problems are partly overcome by exploiting spherical symmetries, although computation time is still slower compared to non-overlapping basis functions. In this work, we have implemented the reconstruction algorithm using Graphical Processing Unit (GPU) technology for speed and a precomputed Monte-Carlo-calculated SRM for accuracy. The reconstruction time achieved using spherical basis functions on a GPU was 4.3 times faster than the Central Processing Unit (CPU) and 2.5 times faster than a CPU-multi-core parallel implementation using eight cores. Overwriting hazards are minimized by combining a random line of response ordering and constrained atomic writing. Small differences in image quality were observed between implementations.

Geometrical and Monte Carlo projectors in 3D PET reconstruction

PURPOSE

In the present work, the authors compare geometrical and Monte Carlo projectors in detail. The geometrical projectors considered were the conventional geometrical Siddon ray-tracer (S-RT) and the orthogonal distance-based ray-tracer (OD-RT), based on computing the orthogonal distance from the center of image voxel to the line-of-response. A comparison of these geometrical projectors was performed using different point spread function (PSF) models. The Monte Carlo-based method under consideration involves an extensive model of the system response matrix based on Monte Carlo simulations and is computed off-line and stored on disk.

METHODS

Comparisons were performed using simulated and experimental data of the commercial small animal PET scanner rPET.

RESULTS

The results demonstrate that the orthogonal distance-based ray-tracer and Siddon ray-tracer using PSF image-space convolutions yield better images in terms of contrast and spatial resolution than those obtained after using the conventional method and the multiray-based S-RT. Furthermore, the Monte Carlo-based method yields slight improvements in terms of contrast and spatial resolution with respect to these geometrical projectors.

CONCLUSIONS

The orthogonal distance-based ray-tracer and Siddon ray-tracer using PSF image-space convolutions represent satisfactory alternatives to factorizing the system matrix or to the conventional on-the-fly ray-tracing methods for list-mode reconstruction, where an extensive modeling based on Monte Carlo simulations is unfeasible.

Characterization of the ringing artifacts in rotator-based reconstruction with Monte Carlo-based resolution compensation for PET

PURPOSE

Studies have shown that Monte Carlo-based reconstruction could effectively improve the image quality of positron emission tomography. The authors have previously used a Gaussian rotator-based algorithm to efficiently reduce the computational cost for system matrix (SM) calculation and to meet the large memory requirements for SM storage. However, pronounced ringing artifacts were observed in the reconstructed image. In this article, the authors investigated and characterized these artifacts.

METHODS

The authors proposed an "ideal" rotator and used it as a baseline in the artifacts evaluation. This ideal rotator produces perfectly rotated images. The Gaussian rotator method was evaluated by a full system model and a partial system model without positron range and acolinearity, which could be compensated for by the blurring of the Gaussian rotator for 18F studies. Noiseless data, Monte Carlo simulation data, as well as acquired experimental data were used to quantitatively characterize the behavior of the artifacts.

RESULTS

The study of the noiseless data indicated that the artifacts were mainly attributed to the rotator, which further blurred the simulated system responses. The simulation study suggested that the artifacts become less pronounced and not quantitatively significant in practice. This result is consistent with the experimental data study. Better contrast recovery was achieved with an over-compensated system model. Traditionally, an undercompensated system model was preferred to avoid artifacts. The authors' studies suggest that the Gaussian rotator with the full system model yields the best image quality among the evaluated methods with considerably reduced quantitative error and quantitatively insignificant artifacts in practice.

CONCLUSIONS

The authors' investigation indicated that a moderately overcompensated system model (about 2 mm FWHM in this study) yielded better contrast recovery and quantitatively insignificant artifacts in practice.