Direct 4D PET MLEM reconstruction of parametric images using the simplified reference tissue model with the basis function method for [11C]raclopride

Molecular imaging using dynamic positron emission tomography (PET) can provide in vivo images of physiologically or biochemically important parameters. Direct reconstruction of parametric images from dynamic PET sinograms is statistically more efficient than the conventional indirect methods, which perform image reconstruction and kinetic modeling in two separate steps. Most existing direct reconstruction methods are derived based on a known blood input function. This paper presents a direct reconstruction algorithm using a simplified reference tissue model, which does not require a blood input function. We have derived a minorization-maximization algorithm to find the penalized maximum likelihood solution. Computer simulations show that the proposed method has better bias-variance tradeoff than the conventional indirect method for estimating parametric images of receptor binding potential using dynamic PET.

The aim of this study is to develop and evaluate a novel direct reconstruction method to improve the signal-to-noise ratio (SNR) of parametric images in dynamic positron-emission tomography (PET), especially for applications in myocardial perfusion studies. Simulation studies were used to test the performance in SNR and computational efficiency for different methods. The NCAT phantom was used to generate simulated dynamic data. Noise realization was performed in the sinogram domain and repeated for 30 times with four different noise levels by varying the injection dose (ID) from standard ID to 1/8 of it. The parametric images were calculated by (1) three direct methods that compute the kinetic parameters from the sinogram and (2) an indirect method, which computes the kinetic parameter with pixel-by-pixel curve fitting in image space using weighted least-squares. The first direct reconstruction maximizes the likelihood function using trust-region-reflective (TRR) algorithm. The second approach uses tabulated parameter sets to generate precomputed time-activity curves for maximizing the likelihood functions. The third approach, as a newly proposed method, assumes separable complete data to derive the M-step for maximizing the likelihood. The proposed method with the separable complete data performs similarly to the other two direct reconstruction methods in terms of the SNR, providing a 5%-10% improvement as compared to the indirect parametric reconstruction under the standard ID. The improvement of SNR becomes more obvious as the noise level increases, reaching more than 30% improvement under 1/8 ID. Advantage of the proposed method lies in the computation efficiency by shortening the time requirement to 25% of the indirect approach and 3%-6% of other direct reconstruction methods. With results provided from this simulation study, direct reconstruction of myocardial blood flow shows a high potential for improving the parametric image quality for clinical use.

The role of the norepinephrine transporter (NET) in cocaine dependence has never been demonstrated via in vivo imaging due to the lack of suitable NET radioligands. Here we report our preliminary studies evaluting the NET in individuals with cocaine dependence (COC) in comparison to healthy controls (HC) using (S,S)-[(11)C]methylreboxetine ([(11)C]MRB), the most promising C-11 labeled positron-emission tomography (PET) radioligand for NET developed to date. Twenty two human volunteers (10 COC and 12 HC) underwent dynamic (11)C-MRB-PET acquisition using a High Resolution Research Tomograph (HRRT). Binding potential (BP(ND)) parametric images were computed using the simplified reference tissue model (SRTM2) with occipital cortex as reference region. BP(ND) values were compared between the two groups. Locus coeruleus (LC), hypothalamus, and pulvinar showed a significant inverse correlation with age among HC (age range = 25-54 years; P = 0.04, 0.009, 0.03 respectively). The BP(ND) was significantly increased in thalamus (27%; P < 0.02) and dorsomedial thalamic nuclei (30%; P < 0.03) in COC as compared to HC. Upon age normalization, the upregulation of NET in COC also reached significance in LC (63%, P < 0.01) and pulvinar (55%, P < 0.02) regions. Our results suggest that (a) brain NET concentration declines with age in HC, and (b) there is a significant upregulation of NET in thalamus and dorsomedial thalamic nucleus in COC as compared to HC. Our results also suggest that the use of [(11)C]MRB and HRRT provides an effective strategy for studying alterations of the NET system in humans.

This [11C]flumazenil (FMZ) study evaluates the performance of various parametric analysis methods and their ability to detect statistically significant group differences. Dynamic 60-min FMZ scans were performed in eight healthy and nine individuals with major depressive disorder. Parametric volume of distribution (VT) images were generated using a basis function method (BFM) implementation of the single tissue compartment model (1T) and Logan plot analysis, both with a metabolite-corrected arterial plasma input function. Parametric binding potential (BP ND) images were generated using multilinear reference tissue methods (MRTM0-4), reference Logan and receptor parametric mapping (RPM1-2), with pons as a reference region. Standardized uptake value (SUV) and SUV ratio-to-pons (SUVr) images were calculated over the time interval 30-40 and 20-60 min postinjection. The resulting VT, BP ND, SUV and SUVr values were compared with nonlinear regression values, using both the 1T model and the simplified reference tissue model. Statistical parametric mapping (SPM5) was used to detect group differences, with an emphasis on the bilateral parahippocampal gyri. BFM was more accurate than Logan, but showed more variability. Both RPM methods and MRTM2 showed the best average correlation with the simplified reference tissue model. In using SPM, SUV and SUVr images provided the best contrast between groups in the parahippocampal gyri, but provided large underestimation and overestimation in quantitative comparisons. BFM and RPM methods allowed for the determination of perfusion effects. Parametric Logan VT, MRTM2 and RPM1-2 BP ND methods allow the best quantitative comparison of FMZ binding between groups and show good discriminating performance in SPM analysis.

The discontinuous Galerkin (DG) method is based on the idea of projection using integration. The recent direct flux reconstruction (DFR) method by Romero et al. (J Sci Comput 67(1):351–374, 2016) is derived via interpolation and results in a scheme identical to DG (on hexahedral meshes). The DFR method is further studied and developed here. Two proofs for its equivalence with the DG scheme considerably simpler than the original proof are presented. The first proof employs the $$ 2K - 1 $$ degree of precision by a $$ K $$-point Gauss quadrature. The second shows the equivalence of DG, FR, and DFR by using the property that the derivative of the degree $$ K + 1 $$ Lobatto polynomial vanishes at the $$ K $$ Gauss points. Fourier analysis for these schemes are presented using an approach more geometric compared with existing analytic approaches. The effects of nonuniform mesh and those of high-order mesh transformation (a precursor for curved meshes in two and three spatial dimensions) on stability and accuracy are examined. These nonstandard analyses are obtained via an in-depth study of the behavior of eigenvalues and eigenvectors.

The LFER 150 PET/CT device (large-field-of-view extreme-resolution portable research imager) is a system for nonhuman primate (NHP) imaging. The objective of this study was to evaluate the performance of the system using the National Electrical Manufacturers Association NU 4-2008 standard protocol. As a preliminary in vivo evaluation of the system, a PET measurement in an NHP was also performed. Methods: Resolution, sensitivity, image quality, and noise-equivalent count rate (NECR) were measured. NECR measurement was performed with a ratlike phantom and a monkeylike phantom. A Derenzo phantom experiment was performed to test the resolution using 3-dimensional ordered-subset expectation maximization reconstruction. One cynomolgus monkey (4.5 kg, intravenous ketamine/xylazine anesthesia) was examined with the dopamine transporter radioligand 18F-FE-PE2I (94 MBq) to evaluate the in vivo performance of the system. List-mode PET data acquired for 93 min were reconstructed into 38 frames with the Tera-Tomo 3-dimensional engine. Binding potential for caudate nucleus, putamen, and substantia nigra was evaluated using the simplified reference tissue model. Results: Radial full-width half-maximum resolution using Fourier rebinning and a 2-dimensional filtered backprojection algorithm was less than 2.2 mm and less than 3.2 mm in the central 60-mm-diameter and 140-mm-diameter regions, respectively. Maximum sensitivity in the 400- to 600-keV and 250- to 750-keV energy windows was 30.03 cps/kBq (3.3%) and 49.11 cps/kBq (5.4%), respectively. The uniformity in the image-quality phantom was 3.3%, and the spillover ratio for air and water was 0.1. The peak of the NECR curve was 430 kcps (at 115 MBq) with the ratlike phantom and 78 kcps (at 139 MBq) with the monkeylike phantom. Rods of the Derenzo phantom with 1-mm diameter could be distinguished by eye. In the NHP experiment, binding potentials in the caudate, putamen, and substantia nigra (4.9, 4.9, and 1, respectively) were similar to those previously reported using the same radioligand and a high-resolution research tomograph. Conclusion: The results obtained from phantom experiments and 1 representative PET measurement in an NHP confirm that the LFER 150 is a high-resolution PET/CT system with suitable performance for brain imaging in NHPs.

Metabotropic glutamate receptor type 5 (mGluR5) is a G protein-coupled receptor that has been implicated in several psychiatric and neurological diseases. The radiopharmaceutical [(11)C]ABP688 allows for in vivo quantification of mGluR5 availability using positron emission tomography (PET). In this study, we aimed to detail the regional distribution of [(11)C]ABP688 binding potential (BPND) and the existence of age/sex effects in healthy individuals. Thirty-one healthy individuals aged 20 to 77 years (men, n = 18, 45.3 ± 18.2 years; females, n = 13, 41.5 ± 19.6 years) underwent imaging with [(11)C]ABP688 using the high-resolution research tomograph (HRRT). We developed an advanced partial volume correction (PVC) method using surface-based analysis in order to accurately estimate the regional variation of radioactivity. BPND was calculated using the simplified reference tissue model, with the cerebellum as the reference region. Surface-based and volume-based analyses were performed for 39 cortical and subcortical regions of interest per hemisphere. We found the highest [(11)C]ABP688 BPND in the lateral prefrontal and anterior cingulate cortices. The lowest [(11)C]ABP688 BPND was observed in the pre- and post-central gyri as well as the occipital lobes and the thalami. No sex effect was observed. Associations between age and [(11)C]ABP688 BPND without PVC were observed in the right amygdala and left putamen, but were not significant after multiple comparisons correction. The present results highlight complexities underlying brain adaptations during the aging process, and support the notion that certain aspects of neurotransmission remain stable during the adult life span.

Computational methods, such as the linear parametric neurotransmitter PET (lp-ntPET) method, have been developed to characterize the transient changes in radiotracer kinetics in the target tissue during endogenous neurotransmitter release. In this paper, we describe and evaluate a parametric reconstruction algorithm that uses an expectation maximization framework, along with the lp-ntPET model, to estimate the endogenous neurotransmitter response to stimuli directly from the measured PET data. Computer simulations showed that the proposed direct reconstruction method offers improved accuracy and precision for the estimated timing parameters of the neurotransmitter response at the voxel level ( td=1±2 min, for activation onset bias and standard deviation) compared with conventional post reconstruction modeling ( td=4±7 min). In addition, we applied the proposed direct parameter estimation methodology to a [11C]raclopride displacement study of an awake rat and generated parametric maps illustrating the magnitude of ligand displacement from striatum. Although the estimated parametric maps of activation magnitude obtained from both direct and post reconstruction methodologies suffered from false positive activations, the proposed direct reconstruction framework offered more reliable parametric maps when the activation onset parameter was constrained.

We investigate the robustness of Compressive Sensing (CS) as a direct signal acquisition and reconstruction method at the wireless receiver in fading channels. The wireless channel introduces additive as well as multiplicative random perturbations to the received signal. The original CS theory considers only additive and bounded perturbations for signal reconstruction with an a priori known basis. However, the impact of multiplicative perturbations, which manifests itself as basis mismatch, on the CS reconstruction performance is largely unknown. In this paper we first formulate such multiplicative perturbations due to wireless fading channel in the CS acquisition and reconstruction problem. We then show that these perturbations can result in significant errors in signal reconstruction if the basis is not properly adjusted. Furthermore, we will propose a method for adjusting the elements of basis to the fading channel coefficients and discuss possible improvements in the signal reconstruction.

Direct parametric reconstruction algorithms have been developed to improve the statistical reliability of parametric images estimated from dynamic PET imaging data. However, these estimates are degraded by noise due to measurement error and noise propagation during reconstruction. In this study, we develop a deep image prior (DIP) regularized direct reconstruction method, where the DIP network is used to represent the estimated parametric image. By initializing the DIP with pre-trained weights and updating its network to learn the intermediate information during reconstruction, the DIP regularization leverages the available population and subject-specific features. The proposed method is applied to reconstruct K1 from both simulated and patient data acquired by 82Rb dynamic PET myocardial perfusion imaging. Benefiting from the nonlinear representation capability of the DIP network, the proposed method achieves superior noise versus bias/mean performance compared with the indirect and direct reconstruction methods with various regularizations formed by quadratic smoothness, dictionary learning, or fully-connected neural network. To summarize, the proposed method demonstrates its potential in improving the precision of dynamic PET imaging measurements, which will contribute to diagnostic accuracy and disease monitoring.

Accurate 3D reconstruction by a new PDS-OSEM algorithm for HRRT

Dopamine D 2 receptor binding in drug-naïve patients with schizophrenia examined with raclopride-C11 and positron emission tomography

Kinetic parametric PET imaging provides valuable information about physiological and biochemical processes. Direct reconstruction of parametric images combines kinetic modelling and image reconstruction to estimate parametric images from raw dynamic PET projection data. Compared to indirect methods, direct methods lead to improved parametric images, often with lower bias and variance. However, raw dynamic PET data may not always be available, and even when it is, there are complex scanner-specific data corrections (e.g. scatter, attenuation and normalisation) as well as the need for a fully 3D forward and back projector. In this proof-ofconcept work we apply our synthesized PET image reconstruction methodology to exploit the benefits of direct parametric reconstruction methodology when only previously reconstructed dynamic PET images are available. The synthesised reconstruction framework creates a new reconstruction problem from standard reconstructed images (which have already used scannerspecific software with all data corrections accounted for). Our synthesised approach has already shown benefits for spatial resolution recovery [1] and post-reconstruction image enhancement with anatomical guidance via the kernel method and the deep image prior [2]. This present work now proposes the synthesised reconstruction framework (which generates synthetic dynamic PET sinograms from dynamic PET images) to perform direct estimation of kinetic parameters from the synthetic data. This allows the direct parametric reconstruction methodology to be applied even when there is no access to the original raw PET data nor the forward-or-back projectors.

This work explores the feasibility and impact of including both the motion correction and the image registration transformation parameters from positron emission tomography (PET) image space to magnetic resonance (MR), or stereotaxic, image space within the system matrix of PET image reconstruction. This approach is motivated by the fields of neuroscience and psychiatry, where PET is used to investigate differences in activation patterns between different groups of participants, requiring all images to be registered to a common spatial atlas. Currently, image registration is performed after image reconstruction which introduces interpolation effects into the final image. Furthermore, motion correction (also requiring registration) introduces a further level of interpolation, and the overall result of these operations can lead to resolution degradation and possibly artifacts. It is important to note that performing such operations on a post-reconstruction basis means, strictly speaking, that the final images are not ones which maximize the desired objective function (e.g. maximum likelihood (ML), or maximum a posteriori reconstruction (MAP)). To correctly seek parameter estimates in the desired spatial atlas which are in accordance with the chosen reconstruction objective function, it is necessary to include the transformation parameters for both motion correction and registration within the system modeling stage of image reconstruction. Such an approach not only respects the statistically chosen objective function (e.g. ML or MAP), but furthermore should serve to reduce the interpolation effects. To evaluate the proposed method, this work investigates registration (including motion correction) using 2D and 3D simulations based on the high resolution research tomograph (HRRT) PET scanner geometry, with and without resolution modeling, using the ML expectation maximization (MLEM) reconstruction algorithm. The quality of reconstruction was assessed using bias-variance and root mean squared error analyses, comparing the proposed method to conventional post-reconstruction registration methods. An overall reduction in bias (for a cold region: from 41% down to 31% (2D) and 97% down to 65% (3D), and for a hot region: from 11% down to 8% (2D) and from 16% down to 14% (3D)) and in root mean squared error analyses (for a cold region: from 43% to 37% (2D) and from 97% to 65% (3D), and for a hot region: from 11% to 9% (2D) and from 16% down to 14% (3D)) in reconstructed regional mean activities (full regions of interest; all with statistical significance: p < 5 × 10−10) is found when including the motion correction and registration in the system matrix of the MLEM reconstruction, with resolution modeling. However, this improvement in performance comes with an extra computational cost of about 40 min. In this context, this work constitutes an important step toward the goal of estimating parameters of interest directly from the raw Poisson-distributed PET data, and hence toward the complete elimination of post-processing steps.

The current study aimed to derive accurate esti­mates of regional cerebral blood flow (rCBF) from noisy dynamic [ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">15</sup> O]H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> O PET images acquired on the High Resolution Research Tomograph (HRRT), whilst retaining the high spatial resolution of this scanner (2–3 mm) in parametric images. We compared the PET autoradiographic and the generalised linear least squares (GLLS) methods to the non-linear least squares (NLLS) method for rCBF estimation. Six healthy volunteers underwent two [ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">15</sup> O]H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> O PET scans which included continuous arterial blood sampling. rCBF estimates were obtained from different methods of image reconstruction: 3DRP, OP-OSEM, and RM-OP-OSEM which includes a resolution model. A range of filters (3D Gaussian, 0–6 mm FWHM) were considered, as were a range of accumulation times (40–120 s) in the case of the autoradiogrpahic method. Whole-brain rCBF values were found to be relatively insensitive to the method of reconstruction and rCBF quantification. The average whole-brain gray matter (GM) rCBF for 3DRP reconstruction and NLLS was 0.44±0.03 mL min cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> , in agreement with literature values. Similar values were obtained from other methods. For generation of parametric images using GLLS or the autoradiographic method, a filter of ≥4 mm was required in order to suppress noise in the PET images which can otherwise produce large biases in the rCBF estimates.