Implementation and evaluation of a 3D one-step late reconstruction algorithm for 3D positron emission tomography brain studies using median root prior

Recent advances in combined Positron Emission Tomography and Magnetic Resonance Imaging

Hybrid imaging modalities combine two or more medical imaging techniques offering exciting new possibilities to image the structure, function and biochemistry of the human body in far greater detail than has previously been possible to improve patient diagnosis. In this context, simultaneous Positron Emission Tomography and Magnetic Resonance (PET/MR) imaging offers great complementary information, but it also poses challenges from the point of view of hardware and software compatibility. The PET signal may interfere with the MR magnetic field and vice-versa, posing several challenges and constrains in the PET instrumentation for PET/MR systems. Additionally, anatomical maps are needed to properly apply attenuation and scatter corrections to the resulting reconstructed PET images, as well motion estimates to minimize the effects of movement throughout the acquisition. In this review, we summarize the instrumentation implemented in modern PET scanners to overcome these limitations, describing the historical development of hybrid PET/MR scanners. We pay special attention to the methods used in PET to achieve attenuation, scatter and motion correction when it is combined with MR, and how both imaging modalities may be combined in PET image reconstruction algorithms.

Dictionary-based software for proton dose reconstruction and submilimetric range verification

Objective. This paper presents a new method for fast reconstruction (compatible with in-beam use) of deposited dose during proton therapy using data acquired from a PET scanner. The most innovative feature of this novel method is the production of noiseless reconstructed dose distributions from which proton range can be derived with high precision. Approach. A new MLEM & simulated annealing (MSA) algorithm, developed especially in this work, reconstructs the deposited dose distribution from a realistic pre-calculated activity-dose dictionary. This dictionary contains the contribution of each beam in the plan to the 3D activity and dose maps, as calculated by a Monte Carlo simulation. The MSA algorithm, using a priori information of the treatment plan, seeks for the linear combination of activities of the precomputed beams that best fits the observed PET data, obtaining at the same time the deposited dose. Main results. the method has been tested using simulated data to determine its performance under 4 different test cases: (1) dependency of range detection accuracy with delivered dose, (2) in-beam versus offline verification, (3) ability to detect anatomical changes and (4) reconstruction of a realistic spread-out Bragg peak. The results show the ability of the method to accurately reconstruct doses from PET data corresponding to 1 Gy irradiations, both in intra-fraction and inter-fraction verification scenarios. For this dose level (1 Gy) the method was able to spot range variations as small as 0.6 mm. Significance. out method is able to reconstruct dose maps with remarkable accuracy from clinically relevant dose levels down to 1 Gy. Furthermore, due to the noiseless nature of reconstructed dose maps, an accuracy better than one millimeter was obtained in proton range estimates. These features make of this method a realistic option for range verification in proton therapy.

PET image reconstruction using physical and mathematical modelling for time of flight PET-MR scanners in the STIR library

This work demonstrates how computational and physical modelling of the positron emission tomography (PET) image acquisition process for a state-of-the-art integrated PET and magnetic resonance imaging (PET-MR) system can produce images comparable to the manufacturer. The GE SIGNA PET/MR scanner is manufactured by General Electric and has time-of-flight (TOF) capabilities of about 390 ps. All software development took place in the Software for Tomographic Image Reconstruction (STIR: http://stir.sf.net) library, which is a widely used open source software to reconstruct data as exported from emission tomography scanners. The new software developments will be integrated into STIR, providing the opportunity for researchers worldwide to establish and expand their image reconstruction methods. Furthermore, this work is of particular significance as it provides the first validation of TOF PET image reconstruction for real scanner datasets using the STIR library. This paper presents the methodology, analysis, and critical issues encountered in implementing an independent reconstruction software package. Acquired PET data were processed via several appropriate algorithms which are necessary to produce an accurate and precise quantitative image. This included mathematical, physical and anatomical modelling of the patient and simulation of various aspects of the acquisition. These included modelling of random coincidences using 'singles' rates per crystals, detector efficiencies and geometric effects. Attenuation effects were calculated by using the STIR's attenuation correction model. Modelling all these effects within the system matrix allowed the reconstruction of PET images which demonstrates the metabolic uptake of the administered radiopharmaceutical. These implementations were validated using measured phantom and clinical datasets. The developments are tested using the ordered subset expectation maximisation (OSEM) and the more recently proposed kernelised expectation maximisation (KEM) algorithm which incorporates anatomical information from MR images into PET reconstruction.

Transmission-reflection optoacoustic ultrasound (TROPUS) computed tomography of small animals

Rapid progress in the development of multispectral optoacoustic tomography techniques has enabled unprecedented insights into biological dynamics and molecular processes in vivo and noninvasively at penetration and spatiotemporal scales not covered by modern optical microscopy methods. Ultrasound imaging provides highly complementary information on elastic and functional tissue properties and further aids in enhancing optoacoustic image quality. We devised the first hybrid transmission-reflection optoacoustic ultrasound (TROPUS) small animal imaging platform that combines optoacoustic tomography with both reflection- and transmission-mode ultrasound computed tomography. The system features full-view cross-sectional tomographic imaging geometry for concomitant noninvasive mapping of the absorbed optical energy, acoustic reflectivity, speed of sound, and acoustic attenuation in whole live mice with submillimeter resolution and unrivaled image quality. Graphics-processing unit (GPU)-based algorithms employing spatial compounding and bent-ray-tracing iterative reconstruction were further developed to attain real-time rendering of ultrasound tomography images in the full-ring acquisition geometry. In vivo mouse imaging experiments revealed fine details on the organ parenchyma, vascularization, tissue reflectivity, density, and stiffness. We further used the speed of sound maps retrieved by the transmission ultrasound tomography to improve optoacoustic reconstructions via two-compartment modeling. The newly developed synergistic multimodal combination offers unmatched capabilities for imaging multiple tissue properties and biomarkers with high resolution, penetration, and contrast.

Direct parametric reconstruction in dynamic PET myocardial perfusion imaging: in vivo studies

Dynamic PET myocardial perfusion imaging (MPI) used in conjunction with tracer kinetic modeling enables the quantification of absolute myocardial blood flow (MBF). However, MBF maps computed using the traditional indirect method (i.e. post-reconstruction voxel-wise fitting of kinetic model to PET time-activity-curves-TACs) suffer from poor signal-to-noise ratio (SNR). Direct reconstruction of kinetic parameters from raw PET projection data has been shown to offer parametric images with higher SNR compared to the indirect method. The aim of this study was to extend and evaluate the performance of a direct parametric reconstruction method using in vivo dynamic PET MPI data for the purpose of quantifying MBF. Dynamic PET MPI studies were performed on two healthy pigs using a Siemens Biograph mMR scanner. List-mode PET data for each animal were acquired following a bolus injection of ~7-8 mCi of 18F-flurpiridaz, a myocardial perfusion agent. Fully-3D dynamic PET sinograms were obtained by sorting the coincidence events into 16 temporal frames covering ~5 min after radiotracer administration. Additionally, eight independent noise realizations of both scans-each containing 1/8th of the total number of events-were generated from the original list-mode data. Dynamic sinograms were then used to compute parametric maps using the conventional indirect method and the proposed direct method. For both methods, a one-tissue compartment model accounting for spillover from the left and right ventricle blood-pools was used to describe the kinetics of 18F-flurpiridaz. An image-derived arterial input function obtained from a TAC taken in the left ventricle cavity was used for tracer kinetic analysis. For the indirect method, frame-by-frame images were estimated using two fully-3D reconstruction techniques: the standard ordered subset expectation maximization (OSEM) reconstruction algorithm on one side, and the one-step late maximum a posteriori (OSL-MAP) algorithm on the other side, which incorporates a quadratic penalty function. The parametric images were then calculated using voxel-wise weighted least-square fitting of the reconstructed myocardial PET TACs. For the direct method, parametric images were estimated directly from the dynamic PET sinograms using a maximum a posteriori (MAP) parametric reconstruction algorithm which optimizes an objective function comprised of the Poisson log-likelihood term, the kinetic model and a quadratic penalty function. Maximization of the objective function with respect to each set of parameters was achieved using a preconditioned conjugate gradient algorithm with a specifically developed pre-conditioner. The performance of the direct method was evaluated by comparing voxel- and segment-wise estimates of [Formula: see text], the tracer transport rate (ml · min-1 · ml-1), to those obtained using the indirect method applied to both OSEM and OSL-MAP dynamic reconstructions. The proposed direct reconstruction method produced [Formula: see text] maps with visibly lower noise than the indirect method based on OSEM and OSL-MAP reconstructions. At normal count levels, the direct method was shown to outperform the indirect method based on OSL-MAP in the sense that at matched level of bias, reduced regional noise levels were obtained. At lower count levels, the direct method produced [Formula: see text] estimates with significantly lower standard deviation across noise realizations than the indirect method based on OSL-MAP at matched bias level. In all cases, the direct method yielded lower noise and standard deviation than the indirect method based on OSEM. Overall, the proposed direct reconstruction offered a better bias-variance tradeoff than the indirect method applied to either OSEM and OSL-MAP. Direct parametric reconstruction as applied to in vivo dynamic PET MPI data is therefore a promising method for producing MBF maps with lower variance.

Resolution Improvement in Positron Emission Tomography Using Anatomical Magnetic Resonance Imaging

An ideal imaging system should provide information with high-sensitivity, high spatial, and temporal resolution. Unfortunately, it is not possible to satisfy all of these desired features in a single modality. In this paper, we discuss methods to improve the spatial resolution in positron emission imaging (PET) using a priori information from Magnetic Resonance Imaging (MRI). Our approach uses an image restoration algorithm based on the maximization of mutual information (MMI), which has found significant success for optimizing multimodal image registration. The MMI criterion is used to estimate the parameters in the Sharpness-Constrained Wiener filter. The generated filter is then applied to restore PET images of a realistic digital brain phantom. The resulting restored images show improved resolution and better signal-to-noise ratio compared to the interpolated PET images. We conclude that a Sharpness-Constrained Wiener filter having parameters optimized from a MMI criterion may be useful for restoring spatial resolution in PET based on a priori information from correlated MRI.

Advances in pinhole and multi-pinhole collimators for single photon emission computed tomography imaging

The collimator in single photon emission computed tomography (SPECT), is an important part of the imaging chain. One of the most important collimators that used in research, preclinical study, small animal, and organ imaging is the pinhole collimator. Pinhole collimator can improve the tradeoff between sensitivity and resolution in comparison with conventional parallel-hole collimator and facilities diagnosis. However, a major problem with pinhole collimator is a small field of view (FOV). Multi-pinhole collimator has been investigated in order to increase the sensitivity and FOV with a preserved spatial resolution. The geometry of pinhole and multi-pinhole collimators is a critical factor in the image quality and plays a key role in SPECT imaging. The issue of the material and geometry for pinhole and multi-pinhole collimators have been a controversial and much disputed subject within the field of SPECT imaging. On the other hand, recent developments in collimator optimization have heightened the need for appropriate reconstruction algorithms for pinhole SPECT imaging. Therefore, iterative reconstruction algorithms were introduced to minimize the undesirable effect on image quality. Current researches have focused on geometry and configuration of pinhole and multi-pinhole collimation rather than reconstruction algorithm. The lofthole and multi-lofthole collimator are samples of novel designs. The purpose of this paper is to provide a review on recent researches in the pinhole and multi-pinhole collimators for SPECT imaging.

Integration of advanced 3D SPECT modeling into the open-source STIR framework

PURPOSE

The Software for Tomographic Image Reconstruction (STIR, http://stir.sourceforge.net) package is an open source object-oriented library implemented in C++. Although its modular design is suitable for reconstructing data from several modalities, it currently only supports Positron Emission Tomography (PET) data. In this work, the authors present results for Single Photon Emission Computed Tomography (SPECT) imaging.

METHODS

This was achieved by the complete integration of a 3D SPECT system matrix modeling library into STIR.

RESULTS

The authors demonstrate the flexibility of the combined software by reconstructing simulated and acquired projections from three different scanners with different iterative algorithms of STIR.

CONCLUSIONS

The extension of the open source STIR project with advanced SPECT modeling will enable the research community to study the performance of several algorithms on SPECT data, and potentially implement new algorithms by expanding the existing framework.

A Virtual Clinical Trial of FDG-PET Imaging of Breast Cancer: Effect of Variability on Response Assessment

INTRODUCTION

There is growing interest in using positron emission tomography (PET) standardized uptake values (SUVs) to assess tumor response to therapy. However, many error sources compromise the ability to detect SUV changes. We explore relationships between these errors and overall SUV variability.

METHODS

We used simulations in a virtual clinical trial framework to study impacts of error sources from scanning and analysis effects on assessment of SUV changes. We varied tumor diameter, scan duration, pretherapy SUV, magnitude of change in SUV, image reconstruction filter, and SUV metric. Poisson noise was added to the raw data before image reconstruction. Variance from global sources of error, e.g., scanner calibration, was incorporated. Two thousand independent noisy sinograms per scenario were generated and reconstructed. We used SUVs to create receiver operating characteristic (ROC) curves to quantify ability to assess response. Integrating area under the ROC curve summarized ability to detect SUV changes.

RESULTS

Scan duration and image reconstruction method had relatively little impact on ability to measure response. SUVMAX is nearly as effective as SUVMEAN, especially with increased image smoothing and despite size-matched region of interest placement. For an effective variability of 15%, we found the Positron Emission Tomography Response Criteria in Solid Tumors criteria for measuring response (±30%) similar to the European Organization for Research and Treatment of Cancer criteria (±25%).

CONCLUSIONS

For typical PET variance levels, tumor response must be 30% to 40% to be reliably determined using SUVs. PET scan duration and image reconstruction method had relatively little effect.

The effect of regularization in motion compensated PET image reconstruction: a realistic numerical 4D simulation study

Following continuous improvement in PET spatial resolution, respiratory motion correction has become an important task. Two of the most common approaches that utilize all detected PET events to motion-correct PET data are the reconstruct-transform-average method (RTA) and motion-compensated image reconstruction (MCIR). In RTA, separate images are reconstructed for each respiratory frame, subsequently transformed to one reference frame and finally averaged to produce a motion-corrected image. In MCIR, the projection data from all frames are reconstructed by including motion information in the system matrix so that a motion-corrected image is reconstructed directly. Previous theoretical analyses have explained why MCIR is expected to outperform RTA. It has been suggested that MCIR creates less noise than RTA because the images for each separate respiratory frame will be severely affected by noise. However, recent investigations have shown that in the unregularized case RTA images can have fewer noise artefacts, while MCIR images are more quantitatively accurate but have the common salt-and-pepper noise. In this paper, we perform a realistic numerical 4D simulation study to compare the advantages gained by including regularization within reconstruction for RTA and MCIR, in particular using the median-root-prior incorporated in the ordered subsets maximum a posteriori one-step-late algorithm. In this investigation we have demonstrated that MCIR with proper regularization parameters reconstructs lesions with less bias and root mean square error and similar CNR and standard deviation to regularized RTA. This finding is reproducible for a variety of noise levels (25, 50, 100 million counts), lesion sizes (8 mm, 14 mm diameter) and iterations. Nevertheless, regularized RTA can also be a practical solution for motion compensation as a proper level of regularization reduces both bias and mean square error.

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.

Effect of anatomical variability, reconstruction algorithms and scattered photons on the SPM output of brain PET studies

Statistical parametric mapping (SPM) has become the standard technique to statistically evaluate differences between functional images. The aim of this paper was to assess the effect of anatomical variability of skull, the reconstruction algorithm and the scattering of photons in the brain on the output of an SPM analysis of brain PET studies. To this end, Monte Carlo simulation was used to generate suitable PET sinograms and bootstrap techniques were employed to increase the reliability of the conclusions. Activity distribution maps were obtained by segmenting thirty nine T1-weighted magnetic resonance images. Foci were placed on the posterior cingulate cortex (PCC) and the superior temporal cortex (STC) and activation factors ranging between -25% and +25% were simulated. Preprocessing of the reconstructed images and statistical analysis were performed using SPM2. Our findings show that intersubject anatomical differences can cause the minimum sample size to increase between 10 and 42% for posterior cingulate Cortex and between 40 and 80% for superior temporal cortex. Ideal scatter correction (ISC) allowed us to diminish the sample size up to 18% and fully 3D reconstruction reduced the minimum sample size between 8 and 33%. Detection sensitivity was higher for hypo-activation than for hyper-activation situations and higher for superior temporal cortex than for posterior cingulate cortex.

FIRST: Fast Iterative Reconstruction Software for (PET) tomography

Small animal PET scanners require high spatial resolution and good sensitivity. To reconstruct high-resolution images in 3D-PET, iterative methods, such as OSEM, are superior to analytical reconstruction algorithms, although their high computational cost is still a serious drawback. The higher performance of modern computers could make iterative image reconstruction fast enough to be viable, provided we are able to deal with the large number of probability coefficients for the system response matrix in high-resolution PET scanners, which is a difficult task that prevents the algorithms from reaching peak computing performance. Considering all possible axial and in-plane symmetries, as well as certain quasi-symmetries, we have been able to reduce the memory requirements to store the system response matrix (SRM) well below 1 GB, which allows us to keep the whole response matrix of the system inside RAM of ordinary industry-standard computers, so that the reconstruction algorithm can achieve near peak performance. The elements of the SRM are stored as cubic spline profiles and matched to voxel size during reconstruction. In this way, the advantages of 'on-the-fly' calculation and of fully stored SRM are combined. The on-the-fly part of the calculation (matching the profile functions to voxel size) of the SRM accounts for 10-30% of the reconstruction time, depending on the number of voxels chosen. We tested our approach with real data from a commercial small animal PET scanner. The results (image quality and reconstruction time) show that the proposed technique is a feasible solution.

Generalization of median root prior reconstruction

Penalized iterative algorithms for image reconstruction in emission tomography contain conditions on which kind of images are accepted as solutions. The penalty term has commonly been a function of pairwise pixel differences in the activity in a local neighborhood, such that smooth images are favored. Attempts to ensure better edge and detail preservation involve difficult tailoring of parameter values or the penalty function itself. The previously introduced median root prior (MRP) favors locally monotonic images. MRP preserves sharp edges while reducing locally nonmonotonic noise at the same time. Quantitative properties of MRP are good, because differences in the neighboring pixel values are not penalized as such. The median is used as an estimate for a penalty reference, against which the pixel value is compared when setting the penalty. In order to generalize the class of MRP-type of priors, the standard median was replaced by other order statistic operations, the L and finite-impluse-response median hybrid (FMH) filters. They allow for smoother appearance as they apply linear weighting together with robust nonlinear operations. The images reconstructed using the new MRP-L and MRP-FMH priors are visually more conventional. Good quantitative properties of MRP are not significantly altered by the new priors.