MRI Application and Challenges of Hyperpolarized Carbon-13 Pyruvate in Translational and Clinical Cardiovascular Studies: A Literature Review.

Cardiovascular disease shows, or may even be caused by, changes in metabolism. Hyperpolarized magnetic resonance spectroscopy and imaging is a technique that could assess the role of different aspects of metabolism in heart disease, allowing real-time metabolic flux assessment in vivo. In this review, we introduce the main hyperpolarization techniques. Then, we summarize the use of dedicated radiofrequency 13C coils, and report a state of the art of 13C data acquisition. Finally, this review provides an overview of the pre-clinical and clinical studies on cardiac metabolism in the healthy and diseased heart. We furthermore show what advances have been made to translate this technique into the clinic in the near future and what technical challenges still remain, such as exploring other metabolic substrates.

Machine Learning for the Design and the Simulation of Radiofrequency Magnetic Resonance Coils: Literature Review, Challenges, and Perspectives.

Radiofrequency (RF) coils for magnetic resonance imaging (MRI) applications serve to generate RF fields to excite the nuclei in the sample (transmit coil) and to pick up the RF signals emitted by the nuclei (receive coil). For the purpose of optimizing the image quality, the performance of RF coils has to be maximized. In particular, the transmit coil has to provide a homogeneous RF magnetic field, while the receive coil has to provide the highest signal-to-noise ratio (SNR). Thus, particular attention must be paid to the coil simulation and design phases, which can be performed with different computer simulation techniques. Being largely used in many sectors of engineering and sciences, machine learning (ML) is a promising method among the different emerging strategies for coil simulation and design. Starting from the applications of ML algorithms in MRI and a short description of the RF coil's performance parameters, this narrative review describes the applications of such techniques for the simulation and design of RF coils for MRI, by including deep learning (DL) and ML-based algorithms for solving electromagnetic problems.

Bayesian Convolutional Neural Networks in Medical Imaging Classification: A Promising Solution for Deep Learning Limits in Data Scarcity Scenarios.

Deep neural networks (DNNs) have already impacted the field of medicine in data analysis, classification, and image processing. Unfortunately, their performance is drastically reduced when datasets are scarce in nature (e.g., rare diseases or early-research data). In such scenarios, DNNs display poor capacity for generalization and often lead to highly biased estimates and silent failures. Moreover, deterministic systems cannot provide epistemic uncertainty, a key component to asserting the model's reliability. In this work, we developed a probabilistic system for classification as a framework for addressing the aforementioned criticalities. Specifically, we implemented a Bayesian convolutional neural network (BCNN) for the classification of cardiac amyloidosis (CA) subtypes. We prepared four different CNNs: base-deterministic, dropout-deterministic, dropout-Bayesian, and Bayesian. We then trained them on a dataset of 1107 PET images from 47 CA and control patients (data scarcity scenario). The Bayesian model achieved performances (78.28 (1.99) % test accuracy) comparable to the base-deterministic, dropout-deterministic, and dropout-Bayesian ones, while showing strongly increased "Out of Distribution" input detection (validation-test accuracy mismatch reduction). Additionally, both the dropout-Bayesian and the Bayesian models enriched the classification through confidence estimates, while reducing the criticalities of the dropout-deterministic and base-deterministic approaches. This in turn increased the model's reliability, also providing much needed insights into the network's estimates. The obtained results suggest that a Bayesian CNN can be a promising solution for addressing the challenges posed by data scarcity in medical imaging classification tasks.

Pancreatic fatty replacement as risk marker for altered glucose metabolism and cardiac iron and complications in thalassemia major.

OBJECTIVES: This multicenter study assessed the extent of pancreatic fatty replacement and its correlation with demographics, iron overload, glucose metabolism, and cardiac complications in a cohort of well-treated patients with thalassemia major (TM). METHODS: We considered 308 TM patients (median age: 39.79 years; 182 females) consecutively enrolled in the Extension-Myocardial Iron Overload in Thalassemia Network. Magnetic resonance imaging was used to quantify iron overload (IO) and pancreatic fat fraction (FF) by T2* technique, cardiac function by cine images, and to detect replacement myocardial fibrosis by late gadolinium enhancement technique. The glucose metabolism was assessed by the oral glucose tolerance test. RESULTS: Pancreatic FF was associated with age, body mass index, and history of hepatitis C virus infection. Patients with normal glucose metabolism showed a significantly lower pancreatic FF than patients with impaired fasting glucose (p = 0.030), impaired glucose tolerance (p < 0.0001), and diabetes (p < 0.0001). A normal pancreatic FF (< 6.6%) showed a negative predictive value of 100% for abnormal glucose metabolism. A pancreatic FF > 15.33% predicted the presence of abnormal glucose metabolism. Pancreas FF was inversely correlated with global pancreas and heart T2* values. A normal pancreatic FF showed a negative predictive value of 100% for cardiac iron. Pancreatic FF was significantly higher in patients with myocardial fibrosis (p = 0.002). All patients with cardiac complications had fatty replacement, and they showed a significantly higher pancreatic FF than complications-free patients (p = 0.002). CONCLUSION: Pancreatic FF is a risk marker not only for alterations of glucose metabolism, but also for cardiac iron and complications, further supporting the close link between pancreatic and cardiac disease. KEY POINTS: • In thalassemia major, pancreatic fatty replacement by MRI is a frequent clinical entity, predicted by a pancreas T2* < 20.81 ms and associated with a higher risk of alterations in glucose metabolism. • In thalassemia major, pancreatic fatty replacement is a strong risk marker for cardiac iron, replacement fibrosis, and complications, highlighting a deep connection between pancreatic and cardiac impairment.

Left Ventricle Detection from Cardiac Magnetic Resonance Relaxometry Images Using Visual Transformer.

Left Ventricle (LV) detection from Cardiac Magnetic Resonance (CMR) imaging is a fundamental step, preliminary to myocardium segmentation and characterization. This paper focuses on the application of a Visual Transformer (ViT), a novel neural network architecture, to automatically detect LV from CMR relaxometry sequences. We implemented an object detector based on the ViT model to identify LV from CMR multi-echo T2* sequences. We evaluated performances differentiated by slice location according to the American Heart Association model using 5-fold cross-validation and on an independent dataset of CMR T2*, T2, and T1 acquisitions. To the best of our knowledge, this is the first attempt to localize LV from relaxometry sequences and the first application of ViT for LV detection. We collected an Intersection over Union (IoU) index of 0.68 and a Correct Identification Rate (CIR) of blood pool centroid of 0.99, comparable with other state-of-the-art methods. IoU and CIR values were significantly lower in apical slices. No significant differences in performances were assessed on independent T2* dataset (IoU = 0.68, p = 0.405; CIR = 0.94, p = 0.066). Performances were significantly worse on the T2 and T1 independent datasets (T2: IoU = 0.62, CIR = 0.95; T1: IoU = 0.67, CIR = 0.98), but still encouraging considering the different types of acquisition. This study confirms the feasibility of the application of ViT architectures in LV detection and defines a benchmark for relaxometry imaging.

Deep Learning Staging of Liver Iron Content From Multiecho MR Images.

BACKGROUND: MRI represents the most established liver iron content (LIC) evaluation approach by estimation of liver T2* value, but it is dependent on the choice of the measurement region and the software used for image analysis. PURPOSE: To develop a deep-learning method for unsupervised classification of LIC from magnitude T2* multiecho MR images. STUDY TYPE: Retrospective. POPULATION/SUBJECTS: A total of 1069 thalassemia major patients enrolled in the core laboratory of the Myocardial Iron Overload in Thalassemia (MIOT) network, which were included in the training (80%) and test (20%) sets. Twenty patients from different MRI vendors included in the external test set. FIELD STRENGTH/SEQUENCE: A5 T, T2* multiecho magnitude images. ASSESSMENT: Four deep-learning convolutional neural networks (HippoNet-2D, HippoNet-3D, HippoNet-LSTM, and an ensemble network HippoNet-Ensemble) were used to achieve unsupervised staging of LIC using five classes (normal, borderline, middle, moderate, severe). The training set was employed to construct the deep-learning model. The performance of the LIC staging model was evaluated in the test set and in the external test set. The model's performances were assessed by evaluating the accuracy, sensitivity, and specificity with respect to the ground truth labels obtained by T2* measurements and by comparison with operator-induced variability originating from different region of interest (ROI) placements. STATISTICAL TESTS: The network's performances were evaluated by single-class accuracy, specificity, and sensitivity and compared by one-way repeated measures analysis of variance (ANOVA) and one-way ANOVA. RESULTS: HippoNet-Ensemble reached an accuracy significantly higher than the other networks, and a sensitivity and specificity higher than HippoNet-LSTM. Accuracy, sensitivity, and specificity values for the LIC stages were: normal: 0.96/0.93/0.97, borderline: 0.95/0.85/0.98, mild: 0.96/0.88/0.98, moderate: 0.95/0.89/0.97, severe: 0.97/0.95/0.98. Correctly staging of cases was in the range of 85%-95%, depending on the LIC class. Multiclass accuracy was 0.90 against 0.92 for the interobserver variability. DATA CONCLUSION: The proposed HippoNet-Ensemble network can perform unsupervised LIC staging and achieves good prognostic performance. EVIDENCE LEVEL: 4 TECHNICAL EFFICACY: Stage 2.

An Explainable Convolutional Neural Network for the Early Diagnosis of Alzheimer's Disease from 18F-FDG PET.

Convolutional Neural Networks (CNN) which support the diagnosis of Alzheimer's Disease using 18F-FDG PET images are obtaining promising results; however, one of the main challenges in this domain is the fact that these models work as black-box systems. We developed a CNN that performs a multiclass classification task of volumetric 18F-FDG PET images, and we experimented two different post hoc explanation techniques developed in the field of Explainable Artificial Intelligence: Saliency Map (SM) and Layerwise Relevance Propagation (LRP). Finally, we quantitatively analyze the explanations returned and inspect their relationship with the PET signal. We collected 2552 scans from the Alzheimer's Disease Neuroimaging Initiative labeled as Cognitively Normal (CN), Mild Cognitive Impairment (MCI), and Alzheimer's Disease (AD) and we developed and tested a 3D CNN that classifies the 3D PET scans into its final clinical diagnosis. The model developed achieves, to the best of our knowledge, performances comparable with the relevant literature on the test set, with an average Area Under the Curve (AUC) for prediction of CN, MCI, and AD 0.81, 0.63, and 0.77 respectively. We registered the heatmaps with the Talairach Atlas to perform a regional quantitative analysis of the relationship between heatmaps and PET signals. With the quantitative analysis of the post hoc explanation techniques, we observed that LRP maps were more effective in mapping the importance metrics in the anatomic atlas. No clear relationship was found between the heatmap and the PET signal.

Deep-learning-based cardiac amyloidosis classification from early acquired pet images.

The objective of the present work was to evaluate the potential of deep learning tools for characterizing the presence of cardiac amyloidosis from early acquired PET images, i.e. 15 min after [18F]-Florbetaben tracer injection. 47 subjects were included in the study: 13 patients with transthyretin-related amyloidosis cardiac amyloidosis (ATTR-CA), 15 patients with immunoglobulin light-chain amyloidosis (AL-CA), and 19 control-patients (CTRL). [18F]-Florbetaben PET/CT images were acquired in list mode and data was sorted into a sinogram, covering a time interval of 5 min starting 15 min after the injection. The resulting sinogram was reconstructed using OSEM iterative algorithm. A deep convolutional neural network (CAclassNet) was designed and implemented, consisting of five 2D convolutional layers, three fully connected layers and a final classifier returning AL, ATTR and CTRL scores. A total of 1107 2D images (375 from AL-subtype patients, 312 from ATTR-subtype, and 420 from Controls) have been considered in the study and used to train, validate and test the proposed network. CAclassNet cross-validation resulted with train error mean ± sd of 2.001% ± 0.96%, validation error of 4.5% ± 2.26%, and net accuracy of 95.49% ± 2.26%. Network test error resulted in a mean ± sd values of 10.73% ± 0.76%. Sensitivity, specificity, and accuracy evaluated on the test dataset were respectively for AL-CA sub-type: 1, 0.912, 0.936; for ATTR-CA: 0.935, 0.897, 0.972; for control subjects: 0.809, 0.971, 0.909. In conclusion, the proposed CAclassNet model seems very promising as an aid for the clinician in the diagnosis of CA from cardiac [18F]-Florbetaben PET images acquired a few minutes after the injection.

[18F]-Florbetaben PET/CT for Differential Diagnosis Among Cardiac Immunoglobulin Light Chain, Transthyretin Amyloidosis, and Mimicking Conditions.

OBJECTIVES: This study aimed to test the diagnostic value of [18F]-florbetaben positron emission tomography (PET) in patients with suspicion of CA. BACKGROUND: Diagnosis of cardiac involvement in immunoglobulin light-chain-derived amyloidosis (AL) and transthyretin-related amyloidosis (ATTR), which holds major importance in risk stratification and decision making, is frequently delayed. Furthermore, although diphosphonate radiotracers allow a noninvasive diagnosis of ATTR, demonstration of cardiac amyloidosis (CA) in AL may require endomyocardial biopsy. METHODS: Forty patients with biopsy-proven diagnoses of CA (20 ALs, 20 ATTRs) and 20 patients referred with the initial clinical suspicion and later diagnosed with non-CA pathology underwent a cardiac PET/computed tomography scan with a 60-min dynamic [18F]-florbetaben PET acquisition, and 4 10-min static scans at 5, 30, 50, and 110 min after radiotracer injection. RESULTS: Visual qualitative assessment showed intense early cardiac uptake in all subsets. Patients with AL displayed a high, persistent cardiac uptake in all the static scans, whereas patients with ATTR and those with non-CA showed an uptake decrease soon after the early scan. Semiquantitative assessment demonstrated higher mean standardized uptake value (SUVmean) in patients with AL, sustained over the whole acquisition period (early SUVmean: 5.55; interquartile range [IQR]: 4.00 to 7.43; vs. delayed SUVmean: 3.50; IQR: 2.32 to 6.10; p = NS) compared with in patients with ATTR (early SUVmean: 2.55; IQR: 1.80 to 2.97; vs. delayed SUVmean: 1.25; IQR: 0.90 to 1.60; p < 0.001) and in patients with non-CA (early SUVmean: 3.50; IQR: 1.60 to 3.37; vs. delayed SUVmean: 1.40; IQR: 1.20 to 1.60; p < 0.001). Similar results were found comparing heart-to-background ratio and molecular volume. CONCLUSIONS: Delayed [18F]-florbetaben cardiac uptake may discriminate CA due to AL from either ATTR or other mimicking conditions. [18F]-florbetaben PET/computed tomography may represent a promising noninvasive tool for the diagnosis of AL amyloidosis, which is still often challenging and delayed. (A Prospective Triple-Arm, Monocentric, Phase-II Explorative Study on Evaluation of Diagnostic Efficacy of the PET Tracer [18F]-Florbetaben [Neuraceq] in Patients With Cardiac Amyloidosis [FLORAMICAR2]; EudraCT number: 2017-001660-38).

Probabilistic Graphical Models for Dynamic PET: A Novel Approach to Direct Parametric Map Estimation and Image Reconstruction.

In the context of dynamic emission tomography, the conventional processing pipeline consists of independent image reconstruction of single-time frames, followed by the application of a suitable kinetic model to time-activity curves (TACs) at the voxel or region-of-interest level. Direct 4D positron emission tomography (PET) reconstruction, by contrast, seeks to move beyond this scheme and incorporate information from multiple time frames within the reconstruction task. Established direct methods are based on a deterministic description of voxelwise TACs, captured by the chosen kinetic model, considering the photon counting process the only source of uncertainty. In this paper, we introduce a new probabilistic modeling strategy based on the key assumption that activity time course would be subject to uncertainty even if the parameters of the underlying dynamic process are known. This leads to a hierarchical model that we formulate using the formalism of probabilistic graphical modeling. The inference is addressed using a new iterative algorithm, in which kinetic modeling results are treated as prior expectation of activity time course, rather than as a deterministic match, making it possible to control the trade-off between a data-driven and a model-driven reconstruction. The proposed method is flexible to an arbitrary choice of (linear and nonlinear) kinetic models, it enables the inclusion of arbitrary (sub)differentiable priors for parametric maps, and it is simple to implement. Computer simulations and an application to a real-patient scan show how the proposed method is able to generalize over conventional indirect and direct approaches, providing a bridge between them by properly tuning the impact of the kinetic modeling step on image reconstruction.

Negative binomial maximum likelihood expectation maximization (NB-MLEM) algorithm for reconstruction of pre-corrected PET data.

PURPOSE: Positron emission tomography (PET) image reconstruction is usually performed using maximum likelihood (ML) iterative reconstruction methods, under the assumption of Poisson distributed data. Pre-correcting raw measured counts, this assumption is no longer realistic. The goal of this work is to develop a reconstruction algorithm based on the Negative Binomial (NB) distribution, which can generalize over the Poisson distribution in case of over-dispersion of raw data, that may occur if sinogram pre-correction is used. METHODS: The mathematical derivation of a Negative Binomial Maximum Likelihood Expectation-Maximization (NB-MLEM) algorithm is presented. A simulation study to compare the performance of the proposed NB-MLEM algorithm with respect to a Poisson-based MLEM (P-MLEM) method was performed, in reconstructing PET data. The proposed NB-MLEM reconstruction was tested on a real phantom and human brain data. RESULTS: For the property of NB distribution, it is a generalization of the conventional P-MLEM: for not over dispersed data, the proposed NB-MLEM algorithm behaves like the conventional P-MLEM; for over-dispersed PET data, the additional evaluation of the dispersion parameter after each reconstruction iteration leads to a more accurate final image with respect to P-MLEM. CONCLUSIONS: A novel approach for PET image reconstruction from pre-corrected data has been developed, which exhibits a statistical behavior that deviates from the Poisson distribution. Simulation study and preliminary tests on real data showed how the NB-MLEM algorithm, being able to explain the over-dispersion of pre-corrected data, can outperform other algorithms that assume no over-dispersion of pre-corrected data, while still not accounting for the presence of negative data, such as P-MLEM.

Direct Parametric Maps Estimation from Dynamic PET Data: An Iterated Conditional Modes Approach.

We propose and test a novel approach for direct parametric image reconstruction of dynamic PET data. We present a theoretical description of the problem of PET direct parametric maps estimation as an inference problem, from a probabilistic point of view, and we derive a simple iterative algorithm, based on the Iterated Conditional Mode (ICM) framework, which exploits the simplicity of a two-step optimization and the efficiency of an analytic method for estimating kinetic parameters from a nonlinear compartmental model. The resulting method is general enough to be flexible to an arbitrary choice of the kinetic model, and unlike many other solutions, it is capable to deal with nonlinear compartmental models without the need for linearization. We tested its performance on a two-tissue compartment model, including an analytical solution to the kinetic parameters evaluation, based on an auxiliary parameter set, with the aim of reducing computation errors and approximations. The new method is tested on simulated and clinical data. Simulation analysis led to the conclusion that the proposed algorithm gives a good estimation of the kinetic parameters in any noise condition. Furthermore, the application of the proposed method to clinical data gave promising results for further studies.

Accelerated PET kinetic maps estimation by analytic fitting method.

In this work, we propose and test a new approach for non-linear kinetic parameters' estimation from dynamic PET data. A technique is discussed, to derive an analytical closed-form expression of the compartmental model used for kinetic parameters' evaluation, using an auxiliary parameter set, with the aim of reducing the computational burden and speeding up the fitting of these complex mathematical expressions to noisy TACs. Two alternative algorithms based on numeric calculations are considered and compared to the new proposal. We perform a simulation study aimed at (i) assessing agreement between the proposed method and other conventional ways of implementing compartmental model fitting, and (ii) quantifying the reduction in computational time required for convergence. It results in a speed-up factor of ∼120 when compared to a fully numeric version, or ∼38, with respect to a more conventional implementation, while converging to very similar values for the estimated model parameters. The proposed method is also tested on dynamic 3D PET clinical data of four control subjects. The results obtained supported those of the simulation study, and provided input and promising perspectives for the application of the proposed technique in clinical practice.

Estimation of pancreatic R2* for iron overload assessment in the presence of fat: a comparison of different approaches.

OBJECTIVES: To propose a method for estimating pancreatic relaxation rate, R2*, from conventional multi-echo MRI, based on the nonlinear fitting of the acquired magnitude signal decay to MR signal models that take into account both the signal oscillations induced by fat and the different R2* values of pancreatic parenchyma and fat. MATERIALS AND METHODS: Single-peak fat (SPF) and multi-peak fat (MPF) models were introduced. Single-R2* and dual-R2* assumptions were considered as well. Analyses were conducted on simulated data and 20 thalassemia major patients. RESULTS: Simulations revealed the ability of the MPF model to correctly estimate the R2* value in a large range of fat fractions and R2* values. From the comparison between the results obtained with a single R2* value for water and fat and the dual-R2* approach, the latter is more accurate in both water R2* and fat fraction estimation. In patient's data analysis, a strong concordance was found between SPF and MPF estimated data with measurements done with manual signal correction and from fat-saturated images. The MPF method showed better reproducibility. CONCLUSION: The MPF dual-R2* approach improves reproducibility and reduces image analysis time in the assessment of pancreatic R2* value in patients with iron overload.

Non-compact myocardium assessment by cardiac magnetic resonance: dependence on image analysis method.

To compare image analysis methods for the assessment of left ventricle non-compaction from cardiac magnetic resonance (CMR) imaging. CMR images were analyzed in 20 patients and 10 normal subjects. A reference model of the MR signal was introduced and validated based on image data. Non-compact (NC) myocardium size and distribution were assessed by tracing a single, continuous contour delimiting trabeculated region (Jacquier) or by one-by-one selection of trabeculae (Grothoff). The global non-compact/compact (NC/C) ratio, the NC mass, and the segmental NC/C ratio were assessed. Results were compared with the reference model. A significant difference between Grothoff and Jacquier approaches in the estimation of NC/C ratio (32.08 ± 6.63 vs. 19.81 ± 5.72, p < 0.0001) and NC mass (26.59 ± 8.36 vs. 14.15 ± 5.73 g/m2, p < 0.0001) was found. The Grothoff approach better matches the expected signal distribution. Inter-observer reproducibility of both Grothoff and Jacquier methods was adequate (9.71 and 8.22%, respectively) with no significant difference between observers. Jacquier and Grothoff approaches are not interchangeable so that specific diagnostic thresholds should be used for different image analysis methods. Grothoff method seems to better capture the true extension of trabeculated tissue.

Biomolecular imaging of 13C-butyrate with dissolution-DNP: Polarization enhancement and formulation for in vivo studies.

Magnetic Resonance Spectroscopy of hyperpolarized isotopically enriched molecules facilitates the non-invasive real-time investigation of in vivo tissue metabolism in the time-frame of a few minutes; this opens up a new avenue in the development of biomolecular probes. Dissolution Dynamic Nuclear Polarization is a hyperpolarization technique yielding a more than four orders of magnitude increase in the 13C polarization for in vivo Magnetic Resonance Spectroscopy studies. As reported in several studies, the dissolution Dynamic Nuclear Polarization polarization performance relies on the chemico-physical properties of the sample. In this study, we describe and quantify the effects of the different sample components on the dissolution Dynamic Nuclear Polarization performance of [1-13C]butyrate. In particular, we focus on the polarization enhancement provided by the incremental addition of the glassy agent dimethyl sulfoxide and gadolinium chelate to the formulation. Finally, preliminary results obtained after injection in healthy rats are also reported, showing the feasibility of an in vivo Magnetic Resonance Spectroscopy study with hyperpolarized [1-13C]butyrate using a 3T clinical set-up.

New Imaging Frontiers in Cardiology: Fast and Quantitative Maps from Raw Data.

BACKGROUND: Among the novelties in the field of cardiovascular imaging, the construction of quantitative maps in a fast and efficient way is one of the most interesting aspects of the clinical research. Quantitative parametric maps are typically obtained by post processing dynamic images, that is, sets of images usually acquired in different temporal intervals, where several images with different contrasts are obtained. Magnetic resonance imaging, and emission tomography (positron emission and single photon emission) are the imaging techniques best suited for the formation of quantitative maps. METHODS: In this review article we present several methods that can be used for obtaining parametric maps, in a fast way, starting from the acquired raw data. We describe both methods commonly used in clinical research, and more innovative methods that build maps directly from the raw data, without going through the image reconstruction. RESULTS: We briefly described recently developed methods in magnetic resonance imaging that accelerate further the MR raw data generation, based on appropriate sub-sampling of k-space; then, we described recently developed methods for generating MR parametric maps. With regard to the emission tomography techniques, we gave an overview of both conventional methods, and more recently developed direct estimation algorithms for parametric image reconstruction from dynamic positron emission tomography data. CONCLUSION: We have provided an overview of the possible approaches that can be followed to realize useful parametric maps from imaging raw data. We moved from the conventional approaches to more recent and efficient methods for accelerating the raw data generation and the of parametric maps formation.

Measured PET Data Characterization with the Negative Binomial Distribution Model.

Accurate statistical model of PET measurements is a prerequisite for a correct image reconstruction when using statistical image reconstruction algorithms, or when pre-filtering operations must be performed. Although radioactive decay follows a Poisson distribution, deviation from Poisson statistics occurs on projection data prior to reconstruction due to physical effects, measurement errors, correction of scatter and random coincidences. Modelling projection data can aid in understanding the statistical nature of the data in order to develop efficient processing methods and to reduce noise. This paper outlines the statistical behaviour of measured emission data evaluating the goodness of fit of the negative binomial (NB) distribution model to PET data for a wide range of emission activity values. An NB distribution model is characterized by the mean of the data and the dispersion parameter α that describes the deviation from Poisson statistics. Monte Carlo simulations were performed to evaluate: (a) the performances of the dispersion parameter α estimator, (b) the goodness of fit of the NB model for a wide range of activity values. We focused on the effect produced by correction for random and scatter events in the projection (sinogram) domain, due to their importance in quantitative analysis of PET data. The analysis developed herein allowed us to assess the accuracy of the NB distribution model to fit corrected sinogram data, and to evaluate the sensitivity of the dispersion parameter α to quantify deviation from Poisson statistics. By the sinogram ROI-based analysis, it was demonstrated that deviation on the measured data from Poisson statistics can be quantitatively characterized by the dispersion parameter α, in any noise conditions and corrections.

A Conway-Maxwell-Poisson (CMP) model to address data dispersion on positron emission tomography.

Positron emission tomography (PET) in medicine exploits the properties of positron-emitting unstable nuclei. The pairs of γ- rays emitted after annihilation are revealed by coincidence detectors and stored as projections in a sinogram. It is well known that radioactive decay follows a Poisson distribution; however, deviation from Poisson statistics occurs on PET projection data prior to reconstruction due to physical effects, measurement errors, correction of deadtime, scatter, and random coincidences. A model that describes the statistical behavior of measured and corrected PET data can aid in understanding the statistical nature of the data: it is a prerequisite to develop efficient reconstruction and processing methods and to reduce noise. The deviation from Poisson statistics in PET data could be described by the Conway-Maxwell-Poisson (CMP) distribution model, which is characterized by the centring parameter λ and the dispersion parameter ν, the latter quantifying the deviation from a Poisson distribution model. In particular, the parameter ν allows quantifying over-dispersion (ν<1) or under-dispersion (ν>1) of data. A simple and efficient method for λ and ν parameters estimation is introduced and assessed using Monte Carlo simulation for a wide range of activity values. The application of the method to simulated and experimental PET phantom data demonstrated that the CMP distribution parameters could detect deviation from the Poisson distribution both in raw and corrected PET data. It may be usefully implemented in image reconstruction algorithms and quantitative PET data analysis, especially in low counting emission data, as in dynamic PET data, where the method demonstrated the best accuracy.

Variable density randomized stack of spirals (VDR-SoS) for compressive sensing MRI.

PURPOSE: To develop a 3D sampling strategy based on a stack of variable density spirals for compressive sensing MRI. METHODS: A random sampling pattern was obtained by rotating each spiral by a random angle and by delaying for few time steps the gradient waveforms of the different interleaves. A three-dimensional (3D) variable sampling density was obtained by designing different variable density spirals for each slice encoding. The proposed approach was tested with phantom simulations up to a five-fold undersampling factor. Fully sampled 3D dataset of a human knee, and of a human brain, were obtained from a healthy volunteer. The proposed approach was tested with off-line reconstructions of the knee dataset up to a four-fold acceleration and compared with other noncoherent trajectories. RESULTS: The proposed approach outperformed the standard stack of spirals for various undersampling factors. The level of coherence and the reconstruction quality of the proposed approach were similar to those of other trajectories that, however, require 3D gridding for the reconstruction. CONCLUSION: The variable density randomized stack of spirals (VDR-SoS) is an easily implementable trajectory that could represent a valid sampling strategy for 3D compressive sensing MRI. It guarantees low levels of coherence without requiring 3D gridding. Magn Reson Med 76:59-69, 2016. © 2015 Wiley Periodicals, Inc.