DIFFUSION MODEL-BASED POSTERIOR DISTRIBUTION PREDICTION FOR KINETIC PARAMETER ESTIMATION IN DYNAMIC PET.

Pharmacokinetic analysis of Positron Emission Tomography (PET) data typically requires at least one hour of image acquisition, which poses a great disadvantage in clinical practice. In this work, we propose a novel approach for pharmacokinetic modelling with significantly reduced PET acquisition time, by incorporating the blood flow information from simultaneously acquired arterial spin labelling (ASL) magnetic resonance imaging (MRI). A relationship is established between blood flow, measured by ASL, and the transfer rate constant from plasma to tissue of the PET tracer, leading to modified PET kinetic models with ASL-derived flow information. Evaluation on clinical amyloid imaging data from an Alzheimer’s disease (AD) study shows that the proposed approach with the simplified reference tissue model can achieve amyloid burden estimation from 30 min [\(^{18}\)F]florbetapir PET data and 5 min simultaneous ASL MR data, which is comparable with the estimation from 60 min PET data (mean error\(\,=-0.03\)). Conversely, standardised uptake value ratio (SUVR), the alternative measure from the data showed a positive bias in areas of higher amyloid burden (mean error\(\,=0.07\)).

The correct interpretation of clinical positron emission tomography (PET) data depends largely on the physical limits of the PET scanner. The partial volume effect (PVE) is related to the size of the studied object compared to the spatial resolution. It represents one of the most important limiting factors in quantitative data analysis. This effect is increased in the case of atrophy, as in patients with Alzheimer disease (AD), and it influences measurement of the metabolic reduction generally seen in cerebral degeneration. In this case, interpretation can be biased, because cortical activity will be underestimated due to the atrophy. In general, anatomical images of AD patients have shown diffuse atrophy, while PET studies have found widespread hypometabolism affecting the parietal and temporal lobes. Although hypometabolic areas usually correspond to atrophic regions, they also occur without such changes. Thus, the aim is to differentiate authentic hypometabolism (decrease of glucose consumption per unit volume of gray matter) from that due to PVE from atrophy (cell loss). Consequently, we are using a method for three-dimensional (3D) correction of human PET data with 3D magnetic resonance imaging (MRI). We measured atrophy and metabolism by using both T1-weighted MR images and high and medium resolution PET scans. We injected 12 patients and controls with [18F]fluorodeoxyglucose for glucose consumption measurements. Atrophy was estimated in the following way. We isolated the cerebral structures, using a segmentation technique on the MRI scans, into gray matter (GM), white matter, and cerebrospinal fluid. We superimposed the PET images onto the MR images to obtain anatomo-functional correlations. We degraded the segmented MR images to the resolution of the PET images by a convolution process to create a PET image correction map. We corrected the metabolic PET data for the PVE. We studied the cerebral metabolic rate of glucose in the GM where metabolic variation is the most relevant to AD. By dealing with problems relating to the sensitivity to the segmentation and to the PET-MRI coregistration, computation of MRI convolution processes provided the degree of PVE on a pixel-by-pixel basis, allowing correction of hypometabolisms contained in GM PET values. Global cortical metabolism increased after correction for PVE by, on average, 29 and 24% for tomographs acquired with medium (TTV03 LETI) and high (ECAT 953B CTI/Siemens) resolution, respectively, whereas the cortical metabolism increased by 75 and 65% for the respective tomographs in AD patients. The difference of metabolism between scans after correction for PVE was less than before correction, decreasing from 31 to 17%. This difference was most marked in the frontal and temporal lobes. Fusion imaging allowed correction for PVE in metabolic data using 3D MRI and determination of whether a change in the apparent radiotracer concentration in PET data reflected an alteration in GM volume, a change in radiotracer concentration per unit volume of GM, or both.

On May 1-2, 1989, a PET Data Analysis Working Group convened to consider positron emission tomography (PET) methodology and data analysis. The papers presented and the recommendations of the Group are reviewed. The Group recommended that a standard phantom of the human brain be used by different institutions to examine machine and data reconstruction PET variables. Interinstitutional comparisons could be aided by using a standard three-dimensional coordinate system. Deformations within individual diseased or atypical brains would require nonlinear as well as linear transformations to the standard space, using magnetic resonance images in register with the PET images. Methods for intersubject averaging of pixel-by-pixel or region-of-interest data, as well as appropriate statistical methods, need to be developed. PET data may first be exploratory and hypothesis-generating (with less stringent statistical theory), then later used to test hypotheses (with more stringent statistical criteria). Common databases, obtained by computer simulation models with known inherent structure, or directly by PET measurements on different groups, could be used to compare analytical and statistical methods among institutions.

The purpose of this study was to do a feasibility study on a microstrip transmission line (MS) RF coil for a positron emission tomography (PET) insert in a 7 Tesla human MRI system. The proposed MS coil integrated the RF shield of the PET detector as the ground conductor of the coil. We called the integrated module "MS PET coil." A single-channel MS PET coil was developed with an integrated RF-shielded PET detector module. For comparison, we also studied a conventional MS coil with a single-layer ground conductor. A lutetium fine silicate (LFS) scintillation crystal block (14 × 14 × 4-layer) with a silicon photomultiplier (Hamamatsu Photonics K.K., Shizuoka, Japan) and a front-end readout circuit board were mounted inside the shield cage of the MS PET coil. The MS PET coil was studied with and without PET detectors. All three coil configurations were studied with a homogeneous phantom in a 7T MRI system (Siemens Healthineers, Erlangen, Germany). PET data measurements were conducted using a Cesium-137 radiation point source. The MR images were similar for the MS coil and the empty MS PET coil, as well as for the cases of MS PET coil with and without PET measurements. Compared to the empty MS PET coil (without PET detector and cable RF shield), decreases in SNR, increases in image noise and RF power, and a slight decrease in resonance frequency were seen for the case of the MS PET coil with the detector and cable shield. Differences in the PET energy histograms or in the crystal identification maps with and without MRI measurements were negligible. Both the MRI and PET performances of the MS PET coil showed responses that matched the MS coil responses. The performance variations of MRI data with and without PET measurement and PET data with and without MR imaging were negligible.

Brain imaging measurements of fibrillar amyloid-β burden, paired helical filament tau burden, and atrophy in cognitively unimpaired persons with two, one, and no copies of the APOE ε4 allele

BackgroundCardiac positron emission tomography (PET) offers non-invasive assessment of perfusion and left ventricular (LV) function from a single dynamic scan. However, no prior assessment of mitral regurgitation severity by PET has been presented. Application of indicator dilution techniques and gated image analyses to PET data enables calculation of forward stroke volume and total LV stroke volume. We aimed to evaluate a combination of these methods for measurement of regurgitant volume (RegVol) and fraction (RegF) using dynamic 15O-water and 11C-acetate PET in comparison to cardiovascular magnetic resonance (CMR).ResultsTwenty-one patients with severe primary mitral valve regurgitation underwent same-day dynamic PET examinations (15O-water and 11C-acetate) and CMR. PET data were reconstructed into dynamic series with short time frames during the first pass, gated 15O-water blood pool images, and gated 11C-acetate myocardial uptake images. PET-based RegVol and RegF correlated strongly with CMR (RegVol: 15O-water r = 0.94, 11C-acetate r = 0.91 and RegF: 15O-water r = 0.88, 11C-acetate r = 0.84, p < 0.001). A systematic underestimation (bias) was found for PET (RegVol: 15O-water − 11 ± 13 mL, p = 0.002, 11C-acetate − 28 ± 16 mL, p < 0.001 and RegF: 15O-water − 4 ± 6%, p = 0.01, 11C-acetate − 10 ± 7%, p < 0.001). PET measurements in patients were compared to healthy volunteers (n = 18). Mean RegVol and RegF was significantly lower in healthy volunteers compared to patients for both tracers. The accuracy of diagnosing moderately elevated regurgitant volume (> 30mL) was 95% for 15O-water and 92% for 11C-acetate.ConclusionsLV regurgitation severity quantified using cardiac PET correlated with CMR and showed high accuracy for discriminating patients from healthy volunteers.

Thermodynamic and kinetic origins of Alzheimer's and related diseases: A chemical engineer's perspective

Identification of contaminant sources in rivers is crucial for river protection and emergency response. This study presents an innovative approach for identifying river pollution sources by using Bayesian inference and cellular automata (CA) modeling. A general Bayesian framework is proposed that combines the CA model with observed data to identify unknown sources of river pollution. To reduce the computational burden of the Bayesian inference, a CA contaminant transport model is developed to efficiently simulate pollutant concentration values in the river. These simulated concentration values are then used to calculate the likelihood function of available measurements. The Markov chain Monte Carlo (MCMC) method is used to produce the posterior distribution of contaminant source parameters, which is a sampling-based method that enables the estimation of complex posterior distributions. The suggested methodology is applied to a real case study of the Fen River in Yuncheng City, Shanxi Province, Northern China, and it estimates the release time, release mass, and source location with relative errors below 19%. The research indicates that the proposed methodology is an effective and flexible way to identify the location and concentrations of river contaminant sources.

Bayesian model updating has received considerable attention and has been extensively used in structural damage detection. It provides a rigorous statistical framework for realizing structural system identification and characterizing uncertainties associated with modeling and measurements. The Markov Chain Monte Carlo (MCMC) is a promising tool for inferring the posterior distribution of model parameters to avoid the intractable evaluation of multi-dimensional integration. However, the efficacy of most MCMC techniques suffers from the curse of parameter dimension, which restricts the application of Bayesian model updating to the damage detection of large-scale systems. In addition, there are several MCMC techniques that require users to properly choose application-specific models, based on the understanding of algorithm mechanisms and limitations. As seen in the literature, there is a lack of comprehensive work that investigates the performances of various MCMC algorithms in their application of structural damage detection. In this study, the Differential Evolutionary Adaptive Metropolis (DREAM), a multi-chain MCMC, is explored and adapted to Bayesian model updating. This paper illustrates how DREAM is used for model updating with many uncertainty parameters (i.e., 40 parameters). Furthermore, the study provides a tutorial to users who may be less experienced with Bayesian model updating and MCMC. Two advanced single-chain MCMC algorithms, namely, the Delayed Rejection Adaptive Metropolis (DRAM) and Transitional Markov Chain Monte Carlo (TMCMC), and DREAM are elaborately introduced to allow practitioners to understand better the concepts and practical implementations. Their performances in model updating and damage detection are compared through three different engineering applications with increased complexity, e.g., a forty-story shear building, a two-span continuous steel beam, and a large-scale steel pedestrian bridge.

Traditional full-waveform inversion (FWI) methods only render a “best-fit” model that cannot account for uncertainties of the ill-posed inverse problem. Additionally, local optimization-based FWI methods cannot always converge to a geologically meaningful solution unless the inversion starts with an accurate background model. We seek the solution for FWI in the Bayesian inference framework to address those two issues. In Bayesian inference, the model space is directly probed by sampling methods such that we obtain a reliable uncertainty appraisal, determine optimal models, and avoid entrapment in a small local region of the model space. The solution of such a statistical inverse method is completely described by the posterior distribution, which quantifies the distributions for parameters and inversion uncertainties. To efficiently sample the posterior distribution, we introduce a sampling algorithm in which the proposal distribution is constructed by the local gradient and the diagonal approximate Hessian of the local log posterior. Our algorithm is called the gradient-based Markov chain Monte Carlo (GMCMC) method. The GMCMC FWI method can quantify inversion uncertainties with estimated posterior distribution given sufficiently long Markov chains. By directly sampling the posterior distribution, we obtain a global view of the model space. Theoretically speaking, statistical assessments do not depend on starting models. Our method is applied to the 2D Marmousi model with the frequency-domain FWI setting. Numerical results suggest that our method can be readily applied to 2D cases with affordable computational efforts.

Markov Chain Monte Carlo (MCMC) methods have become increasingly popular for estimating the posterior probability distribution of parameters in hydrologic models. However, MCMC methods require the a priori definition of a proposal or sampling distribution, which determines the explorative capabilities and efficiency of the sampler and therefore the statistical properties of the Markov Chain and its rate of convergence. In this paper we present an MCMC sampler entitled the Shuffled Complex Evolution Metropolis algorithm (SCEM‐UA), which is well suited to infer the posterior distribution of hydrologic model parameters. The SCEM‐UA algorithm is a modified version of the original SCE‐UA global optimization algorithm developed by Duan et al. [1992]. The SCEM‐UA algorithm operates by merging the strengths of the Metropolis algorithm, controlled random search, competitive evolution, and complex shuffling in order to continuously update the proposal distribution and evolve the sampler to the posterior target distribution. Three case studies demonstrate that the adaptive capability of the SCEM‐UA algorithm significantly reduces the number of model simulations needed to infer the posterior distribution of the parameters when compared with the traditional Metropolis‐Hastings samplers.

Bayesian model updating provides a rigorous framework to account for uncertainty induced by lack of knowledge about engineering systems in their respective mathematical models through updates of the joint probability density function (PDF), the so-called posterior PDF, of the unknown model parameters. The Markov chain Monte Carlo (MCMC) methods are currently the most popular approaches for generating samples from the posterior PDF. However, these methods often found wanting when sampling from difficult distributions (e.g., high-dimensional PDFs, PDFs with flat manifolds, multimodal PDFs, and very peaked PDFs). This paper introduces a new multi-level sampling approach for Bayesian model updating, called Sequential Gauss-Newton algorithm, which is inspired by the Transitional Markov chain Monte Carlo (TMCMC) algorithm. The Sequential Gauss-Newton algorithm improves two aspects of TMCMC to make an efficient and effective MCMC algorithm for drawing samples from difficult posterior PDFs. First, the statistical efficiency of the algorithm is enhanced by use of the systematic resampling scheme. Second, a new MCMC algorithm, called Gauss-Newton MCMC algorithm, is proposed which is essentially an M-H algorithm with a Gaussian proposal PDF tailored to the posterior PDF using the gradient and Hessian information of the negative log posterior. The effectiveness of the proposed algorithm for solving the Bayesian model updating problem is illustrated using three examples with irregularly shaped posterior PDFs.

A Markov Chain Monte Carlo technique for parameter estimation and inference in pesticide fate and transport modeling

Small-animal positron emission tomography as a tool for neuropharmacology

The Bayesian approach to inverse problems, in which the posterior probability distribution on an unknown field is sampled for the purposes of computing posterior expectations of quantities of interest, is starting to become computationally feasible for partial differential equation (PDE) inverse problems. Balancing the sources of error arising from finite-dimensional approximation of the unknown field, the PDE forward solution map and the sampling of the probability space under the posterior distribution are essential for the design of efficient computational Bayesian methods for PDE inverse problems. We study Bayesian inversion for a model elliptic PDE with an unknown diffusion coefficient. We provide complexity analyses of several Markov chain Monte Carlo (MCMC) methods for the efficient numerical evaluation of expectations under the Bayesian posterior distribution, given data δ. Particular attention is given to bounds on the overall work required to achieve a prescribed error level ε. Specifically, we first bound the computational complexity of ‘plain’ MCMC, based on combining MCMC sampling with linear complexity multi-level solvers for elliptic PDE. Our (new) work versus accuracy bounds show that the complexity of this approach can be quite prohibitive. Two strategies for reducing the computational complexity are then proposed and analyzed: first, a sparse, parametric and deterministic generalized polynomial chaos (gpc) ‘surrogate’ representation of the forward response map of the PDE over the entire parameter space, and, second, a novel multi-level Markov chain Monte Carlo strategy which utilizes sampling from a multi-level discretization of the posterior and the forward PDE. For both of these strategies, we derive asymptotic bounds on work versus accuracy, and hence asymptotic bounds on the computational complexity of the algorithms. In particular, we provide sufficient conditions on the regularity of the unknown coefficients of the PDE and on the approximation methods used, in order for the accelerations of MCMC resulting from these strategies to lead to complexity reductions over ‘plain’ MCMC algorithms for the Bayesian inversion of PDEs.