Angel R. Pineda

Iterative Decomposition of Water and Fat With Echo Asymmetry and Least-Squares Estimation (IDEAL): Application With Fast Spin-Echo Imaging

Chemical shift based methods are often used to achieve uniform water–fat separation that is insensitive to Bo inhomogeneities. Many spin‐echo (SE) or fast SE (FSE) approaches acquire three echoes shifted symmetrically about the SE, creating time‐dependent phase shifts caused by water–fat chemical shift. This work demonstrates that symmetrically acquired echoes cause artifacts that degrade image quality. According to theory, the noise performance of any water–fat separation method is dependent on the proportion of water and fat within a voxel, and the position of echoes relative to the SE. To address this problem, we propose a method termed “iterative decomposition of water and fat with echo asymmetric and least‐squares estimation” (IDEAL). This technique combines asymmetrically acquired echoes with an iterative least‐squares decomposition algorithm to maximize noise performance. Theoretical calculations predict that the optimal echo combination occurs when the relative phase of the echoes is separated by 2π/3, with the middle echo centered at π/2+πk (k = any integer), i.e., (–π/6+πk, π/2+πk, 7π/6+πk). Only with these echo combinations can noise performance reach the maximum possible and be independent of the proportion of water and fat. Close agreement between theoretical and experimental results obtained from an oil–water phantom was observed, demonstrating that the iterative least‐squares decomposition method is an efficient estimator. Magn Reson Med, 2005.

Multicoil Dixon Chemical Species Separation with an Iterative Least-Squares Estimation Method

This work describes a new approach to multipoint Dixon fat–water separation that is amenable to pulse sequences that require short echo time (TE) increments, such as steady‐state free precession (SSFP) and fast spin‐echo (FSE) imaging. Using an iterative linear least‐squares method that decomposes water and fat images from source images acquired at short TE increments, images with a high signal‐to‐noise ratio (SNR) and uniform separation of water and fat are obtained. This algorithm extends to multicoil reconstruction with minimal additional complexity. Examples of single‐ and multicoil fat–water decompositions are shown from source images acquired at both 1.5T and 3.0T. Examples in the knee, ankle, pelvis, abdomen, and heart are shown, using FSE, SSFP, and spoiled gradient‐echo (SPGR) pulse sequences. The algorithm was applied to systems with multiple chemical species, and an example of water–fat–silicone separation is shown. An analysis of the noise performance of this method is described, and methods to improve noise performance through multicoil acquisition and field map smoothing are discussed. Magn Reson Med 51:35–45, 2004.

Multiecho reconstruction for simultaneous water‐fat decomposition and T2* estimation

To describe and demonstrate the feasibility of a novel multiecho reconstruction technique that achieves simultaneous water‐fat decomposition and T2* estimation. The method removes interference of water‐fat separation with iron‐induced T2* effects and therefore has potential for the simultaneous characterization of hepatic steatosis (fatty infiltration) and iron overload.

Water–fat separation with IDEAL gradient‐echo imaging

To combine gradient‐echo (GRE) imaging with a multipoint water–fat separation method known as “iterative decomposition of water and fat with echo asymmetry and least squares estimation” (IDEAL) for uniform water–fat separation. Robust fat suppression is necessary for many GRE imaging applications; unfortunately, uniform fat suppression is challenging in the presence of B0 inhomogeneities. These challenges are addressed with the IDEAL technique.

Cramér-rao bounds for three-point decomposition of water and fat

The noise analysis for three‐point decomposition of water and fat was extended to account for the uncertainty in the field map. This generalization leads to a nonlinear estimation problem. The Crámer–Rao bound (CRB) was used to study the variance of the estimates of the magnitude, phase, and field map by computing the maximum effective number of signals averaged (NSA) for any choice of echo time shifts. The analysis shows that the noise properties of the reconstructed magnitude, phase, and field map depend not only on the choice of echo time shifts but also on the amount of fat and water in each voxel and their alignment at the echo. The choice of echo time shifts for spin‐echo, spoiled gradient echo, and steady‐state free precession imaging techniques were optimized using the CRB. The noise analysis for the magnitude explains rough interfaces seen clinically in the boundary of fat and water with source images obtained symmetrically about the spin‐echo. It also provides a solution by choosing appropriate echo time shifts (−π/6 + πk, π/2 + πk, 7π/6 + πk), with k an integer. With this choice of echo time shifts it is possible to achieve the maximum NSA uniformly across all fat:water ratios. The optimization is also carried out for the estimation of phase and field map. These theoretical results were verified using Monte Carlo simulations with a newly developed nonlinear least‐squares reconstruction algorithm that achieves the CRB. Magn Reson Med, 2005.

The influence of transport on the kinetics of binding to surface receptors: application to cells and BIAcore

Accurate estimation of biomolecular reaction rates from binding data, when ligands in solution bind to receptors on the surfaces of cells or biosensors, requires an understanding of the contributions of both molecular transport and reaction. Efficient estimation of parameters requires relatively simple models. In this review, we give conditions under which various transport effects are negligible and identify simple binding models that incorporate the effects of transport, when transport cannot be neglected. We consider effects of diffusion of ligands to cell or biosensor surfaces, flow in a BIAcore biosensor, and distribution of receptors in a dextran layer above the sensor surface. We also give conditions under which soluble receptors can be expected to compete effectively with surface‐bound receptors. Copyright

Independent estimation of T*2 for water and fat for improved accuracy of fat quantification

Noninvasive biomarkers of intracellular accumulation of fat within the liver (hepatic steatosis) are urgently needed for detection and quantitative grading of nonalcoholic fatty liver disease, the most common cause of chronic liver disease in the United States. Accurate quantification of fat with MRI is challenging due the presence of several confounding factors, including T*2 decay. The specific purpose of this work is to quantify the impact of T*2 decay and develop a multiexponential T*2 correction method for improved accuracy of fat quantification, relaxing assumptions made by previous T*2 correction methods. A modified Gauss‐Newton algorithm is used to estimate the T*2 for water and fat independently. Improved quantification of fat is demonstrated, with independent estimation of T*2 for water and fat using phantom experiments. The tradeoffs in algorithm stability and accuracy between multiexponential and single exponential techniques are discussed. Magn Reson Med 63:849–857, 2010.

On the performance of T2* correction methods for quantification of hepatic fat content.

Nonalcoholic fatty liver disease is the most prevalent chronic liver disease in Western societies. MRI can quantify liver fat, the hallmark feature of nonalcoholic fatty liver disease, so long as multiple confounding factors including T2* decay are addressed. Recently developed MRI methods that correct for T2* to improve the accuracy of fat quantification either assume a common T2* (single‐T2*) for better stability and noise performance or independently estimate the T2* for water and fat (dual‐T2*) for reduced bias, but with noise performance penalty. In this study, the tradeoff between bias and variance for different T2* correction methods is analyzed using the Cramér‐Rao bound analysis for biased estimators and is validated using Monte Carlo experiments. A noise performance metric for estimation of fat fraction is proposed. Cramér‐Rao bound analysis for biased estimators was used to compute the metric at different echo combinations. Optimization was performed for six echoes and typical T2* values. This analysis showed that all methods have better noise performance with very short first echo times and echo spacing of ∼π/2 for single‐T2* correction, and ∼2π/3 for dual‐T2* correction. Interestingly, when an echo spacing and first echo shift of ∼π/2 are used, methods without T2* correction have less than 5% bias in the estimates of fat fraction. Magn Reson Med, 2012.

Beyond noise power in 3D computed tomography: the local NPS and off-diagonal elements of the Fourier domain covariance matrix.

PURPOSE To investigate the correlation and stationarity of noise in volumetric computed tomography (CT) using the local discrete noise-power spectrum (NPS) and off-diagonal elements of the covariance matrix of the discrete Fourier transform of noise-only images (denoted Σ(DFT)). Experimental conditions were varied to affect noise correlation and stationarity, the effects were quantified in terms of the NPS and Σ(DFT), and practical considerations in CT performance characterization were identified. METHODS Cone-beam CT (CBCT) images were acquired using a benchtop system comprising an x-ray tube and flat-panel detector for a range of acquisition techniques (e.g., dose and x-ray scatter) and three phantom configurations hypothesized to impart distinct effects on the NPS and Σ(DFT): (A) air, (B) a 20-cm-diameter water cylinder with a bowtie filter, and (C) the cylinder without a bowtie filter. The NPS and off-diagonal elements of the Σ(DFT) were analyzed as a function of position within the reconstructions. RESULTS The local NPS varied systematically throughout the axial plane in a manner consistent with changes in fluence transmitted to the detector and view sampling effects. Variability in fluence was manifest in the NPS magnitude-e.g., a factor of ~2 variation in NPS magnitude within the axial plane for case C (cylinder without bowtie), compared to nearly constant NPS magnitude for case B (bowtie filter matched to the cylinder). View sampling effects were most prominent in case A (air) where the variance increased at greater distance from the center of reconstruction and in case C (cylinder) where the NPS exhibited correlations in the radial direction. The effects of detector lag were observed as azimuthal correlation. The cylinder (without bowtie) had the strongest nonstationarity because of the larger variability in fluence transmitted to the detector. The diagonal elements of the Σ(DFT) were equivalent to the NPS estimated from the periodogram, and the average off-diagonal elements of the Σ(DFT) exhibited amplitude of ~1% of the NPS for the experimental conditions investigated. Furthermore, the off-diagonal elements demonstrated fairly long tails of nearly constant amplitude, with magnitude somewhat reduced for experimental conditions associated with greater stationarity (viz., lower Σ(DFT) tails for cases A and B in comparison to case C). CONCLUSIONS Volumetric CT exhibits nonstationarity in the NPS as hypothesized in relation to fluence uniformity and view sampling. Measurement of the NPS should seek to minimize such changes in noise correlations and include careful reporting of experimental conditions (e.g., phantom design and use of a bowtie filter) and spatial dependence (e.g., analysis at fixed radius within a phantom). Off-diagonal elements of the Σ(DFT) similarly depend on experimental conditions and can be readily computed from the same data as the NPS. This work begins to check assumptions in NPS analysis examine the extent to which NPS is an appropriate descriptor of noise correlations, and investigate the magnitude of off-diagonal elements of the Σ(DFT). While the magnitude of such off-diagonal elements appears to be low, their cumulative effect on space-variant detectability remains to be investigated-e.g., using task-specific figures of merit.

Figures of merit for detectors in digital radiography. I. Flat background and deterministic blurring

Digital radiography systems can be thought of as continuous linear shift-invariant systems followed by sampling. This view, along with the large number of pixels used for flat-panel systems, has motivated much of the work which attempts to extend figures of merit developed for analog systems, in particular noise equivalent quanta (NEQ) and detective quantum efficiency (DQE). A more general approach looks at the system as a continuous-to-discrete mapping and evaluates the signal-to-noise ratio (SNR) completely from the discrete data. In this paper, we study the effect of presampling blur on these figures of merit for a simple model that assumes that the background fluence is constant and that the blurring of the signal is deterministic. We find that for small signals, even in this idealized model, commonly used DQE/NEQ formulations do not accurately track the behavior of the fully digital SNR. Using these NEQ-based figures of merit would lead to different design decisions than using the ideal SNR. This study is meant to bring attention to the assumptions implicitly made when using Fourier methods.