Lin-Ching Chang

RESTORE: robust estimation of tensors by outlier rejection.

Signal variability in diffusion weighted imaging (DWI) is influenced by both thermal noise and spatially and temporally varying artifacts such as subject motion and cardiac pulsation. In this paper, the effects of DWI artifacts on estimated tensor values, such as trace and fractional anisotropy, are analyzed using Monte Carlo simulations. A novel approach for robust diffusion tensor estimation, called RESTORE (for robust estimation of tensors by outlier rejection), is proposed. This method uses iteratively reweighted least‐squares regression to identify potential outliers and subsequently exclude them. Results from both simulated and clinical diffusion data sets indicate that the RESTORE method improves tensor estimation compared to the commonly used linear and nonlinear least‐squares tensor fitting methods and a recently proposed method based on the Geman–McClure M‐estimator. The RESTORE method could potentially remove the need for cardiac gating in DWI acquisitions and should be applicable to other MR imaging techniques that use univariate or multivariate regression to fit MRI data to a model. Magn Reson Med 53:1088–1095, 2005. Published 2005 Wiley‐Liss, Inc.

Comparison of EPI Distortion Correction Methods in Diffusion Tensor MRI Using a Novel Framework

Diffusion weighted images (DWIs) are commonly acquired with Echo-planar imaging (EPI). B0 inhomogeneities affect EPI by producing spatially nonlinear image distortions. Several strategies have been proposed to correct EPI distortions including B0 field mapping (B0M) and image registration. In this study, an experimental framework is proposed to evaluation the performance of different EPI distortion correction methods in improving DT-derived quantities. A deformable registration based method with mutual information metric and cubic B-spline modeled constrained deformation field (BSP) is proposed as an alternative when B0 mapping data are not available. BSP method is qualitatively and quantitatively compared to B0M method using the framework. Both methods can successful reduce EPI distortions and significantly improve the quality of DT-derived quantities. Overall, B0M was clearly superior in infratentorial regions including brainstem and cerebellum, as well as in the ventral areas of the temporal lobes while BSP was better in all rostral brain regions.

Informed RESTORE: A method for robust estimation of diffusion tensor from low redundancy datasets in the presence of physiological noise artifacts

Physiological noise artifacts, especially those originating from cardiac pulsation and subject motion, are common in clinical Diffusion tensor‐MRI acquisitions. Previous works show that signal perturbations produced by artifacts can be severe and neglecting to account for their contribution can result in erroneous diffusion tensor values. The Robust Estimation of Tensors by Outlier Rejection (RESTORE) method has been shown to be an effective strategy for improving tensor estimation on a voxel‐by‐voxel basis in the presence of artifactual data points in diffusion‐weighted images. In this article, we address potential instabilities that may arise when using RESTORE and propose practical constraints to improve its usability. Moreover, we introduce a method, called informed RESTORE designed to remove physiological noise artifacts in datasets acquired with low redundancy (less than 30–40 diffusion‐weighted image volumes)—a condition in which the original RESTORE algorithm may converge to an incorrect solution. This new method is based on the notion that physiological noise is more likely to result in signal dropouts than signal increases. Results from both Monte Carlo simulation and clinical diffusion data indicate that informed RESTORE performs very well in removing physiological noise artifacts for low redundancy diffusion‐weighted image datasets. Magn Reson Med, 2012.

Effects of physiological noise in population analysis of diffusion tensor MRI data.

The goal of this study is to characterize the potential effect of artifacts originating from physiological noise on statistical analysis of diffusion tensor MRI (DTI) data in a population. DTI derived quantities including mean diffusivity (Trace(D)), fractional anisotropy (FA), and principal eigenvector (ε(1)) are computed in the brain of 40 healthy subjects from tensors estimated using two different methods: conventional nonlinear least-squares, and robust fitting (RESTORE). RESTORE identifies artifactual data points as outliers and excludes them on a voxel-by-voxel basis. We found that outlier data points are localized in specific spatial clusters in the population, indicating a consistency in brain regions affected across subjects. In brain parenchyma RESTORE slightly reduces inter-subject variance of FA and Trace(D). The dominant effect of artifacts, however, is bias. Voxel-wise analysis indicates that inclusion of outlier data points results in clusters of under- and over-estimation of FA, while Trace(D) is always over-estimated. Removing outliers affects ε(1) mostly in low anisotropy regions. It was found that brain regions known to be affected by cardiac pulsation - cerebellum and genu of the corpus callosum, as well as regions not previously reported, splenium of the corpus callosum-show significant effects in the population analysis. It is generally assumed that statistical properties of DTI data are homogenous across the brain. This assumption does not appear to be valid based on these results. The use of RESTORE can lead to a more accurate evaluation of a population, and help reduce spurious findings that may occur due to artifacts in DTI data.

Variance of Estimated DTI-Derived Parameters via First- Order Perturbation Methods

In typical applications of diffusion tensor imaging (DTI), DT‐derived quantities are used to make a diagnostic, therapeutic, or scientific determination. In such cases it is essential to characterize the variability of these tensor‐derived quantities. Parametric and empirical methods have been proposed to estimate the variance of the estimated DT, and quantities derived from it. However, the former method cannot be generalized since a parametric distribution cannot be found for all DT‐derived quantities. Although powerful empirical methods, such as the bootstrap, are available, they require oversampling of the diffusion‐weighted imaging (DWI) data. Statistical perturbation methods represent a hybrid between parametric and empirical approaches, and can overcome the primary limitations of both methods. In this study we used a first‐order perturbation method to obtain analytic expressions for the variance of DT‐derived quantities, such as the trace, fractional anisotropy (FA), eigenvalues, and eigenvectors, for a given experimental design. We performed Monte Carlo (MC) simulations of DTI experiments to test and validate these formulae, and to determine their range of applicability for different experimental design parameters, including the signal‐to‐noise ratio (SNR), diffusion gradient sampling scheme, and number of DWI acquisitions. This information should be useful for designing DTI studies and assessing the quality of inferences drawn from them. Magn Reson Med 57:141–149, 2007. Published 2006 Wiley‐Liss, Inc.

Linear least‐squares method for unbiased estimation of T1 from SPGR signals

The longitudinal relaxation time, T1, can be estimated from two or more spoiled gradient recalled echo images (SPGR) acquired with different flip angles and/or repetition times (TRs). The function relating signal intensity to flip angle and TR is nonlinear; however, a linear form proposed 30 years ago is currently widely used. Here we show that this linear method provides T1 estimates that have similar precision but lower accuracy than those obtained with a nonlinear method. We also show that T1 estimated by the linear method is biased due to improper accounting for noise in the fitting. This bias can be significant for clinical SPGR images; for example, T1 estimated in brain tissue (800 ms < T1 < 1600 ms) can be overestimated by 10% to 20%. We propose a weighting scheme that correctly accounts for the noise contribution in the fitting procedure. Monte Carlo simulations of SPGR experiments are used to evaluate the accuracy of the estimated T1 from the widely‐used linear, the proposed weighted‐uncertainty linear, and the nonlinear methods. We show that the linear method with weighted uncertainties reduces the bias of the linear method, providing T1 estimates comparable in precision and accuracy to those of the nonlinear method while reducing computation time significantly. Magn Reson Med 60:496–501, 2008.

Error Propagation Framework for Diffusion Tensor Imaging via Diffusion Tensor Representations

An analytical framework of error propagation for diffusion tensor imaging (DTI) is presented. Using this framework, any uncertainty of interest related to the diffusion tensor elements or to the tensor-derived quantities such as eigenvalues, eigenvectors, trace, fractional anisotropy (FA), and relative anisotropy (RA) can be analytically expressed and derived from the noisy diffusion-weighted signals. The proposed framework elucidates the underlying geometric relationship between the variability of a tensor-derived quantity and the variability of the diffusion weighted signals through the nonlinear least squares objective function of DTI. Monte Carlo simulations are carried out to validate and investigate the basic statistical properties of the proposed framework.

The Elliptical Cone of Uncertainty and Its Normalized Measures in Diffusion Tensor Imaging

Diffusion tensor magnetic resonance imaging (DT-MRI) is capable of providing quantitative insights into tissue microstructure in the brain. An important piece of information offered by DT-MRI is the directional preference of diffusing water molecules within a voxel. Building upon this local directional information, DT-MRI tractography attempts to construct global connectivity of white matter tracts. The interplay between local directional information and global structural information is crucial in understanding changes in tissue microstructure as well as in white matter tracts. To this end, the right circular cone of uncertainty was proposed by Basser as a local measure of tract dispersion. Recent experimental observations by Jeong et al. and Lazar et al. that the cones of uncertainty in the brain are mostly elliptical motivate the present study to investigate analytical approaches to quantify their findings. Two analytical approaches for constructing the elliptical cone of uncertainty, based on the first-order matrix perturbation and the error propagation method via diffusion tensor representations, are presented and their theoretical equivalence is established. We propose two normalized measures, circumferential and areal, to quantify the uncertainty of the major eigenvector of the diffusion tensor. We also describe a new technique of visualizing the cone of uncertainty in 3-D.

Parsimonious Model Selection for Tissue Segmentation and Classification Applications: A Study Using Simulated and Experimental DTI Data

One aim of this work is to investigate the feasibility of using a hierarchy of models to describe diffusion tensor magnetic resonance (MR) data in fixed tissue. Parsimonious model selection criteria are used to choose among different models of diffusion within tissue. Using this information, we assess whether we can perform simultaneous tissue segmentation and classification. Both numerical phantoms and diffusion weighted imaging (DWI) data obtained from excised pig spinal cord are used to test and validate this model selection framework. Three hierarchical approaches are used for parsimonious model selection: the Schwarz criterion (SC), the F-test t-test (F-t), proposed by Hext, and the F-test F-test (F-F), adapted from Snedecor. The F-t approach is more robust than the others for selecting between isotropic and general anisotropic (full tensor) models. However, due to its high sensitivity to the variance estimate and bias in sorting eigenvalues, the F-F and SC are preferred for segmenting models with transverse isotropy (cylindrical symmetry). Additionally, the SC method is easier to implement than the F-t and F-F methods and has better performance. As such, this approach can be efficiently used for evaluating large MRI data sets. In addition, the proposed voxel-by-voxel segmentation framework is not susceptible to artifacts caused by the inhomogeneity of the variance in neighboring voxels with different degrees of anisotropy, which might contaminate segmentation results obtained with the techniques based on voxel averaging.

An automatic method for estimating noise-induced signal variance in magnitude-reconstructed magnetic resonance images

Signal intensity in magnetic resonance images (MRIs) is affected by random noise. Assessing noise-induced signal variance is important for controlling image quality. Knowledge of signal variance is required for correctly computing the chi-square value, a measure of goodness of fit, when fitting signal data to estimate quantitative parameters such as T1 and T2 relaxation times or diffusion tensor elements. Signal variance can be estimated from measurements of the noise variance in an object- and ghost-free region of the image background. However, identifying a large homogeneous region automatically is problematic. In this paper, a novel, fully automated approach for estimating the noise-induced signal variance in magnitude-reconstructed MRIs is proposed. This approach is based on the histogram analysis of the image signal intensity, explicitly by extracting the peak of the underlining Rayleigh distribution that would characterize the distribution of the background noise. The peak is extracted using a nonparametric univariate density estimation like the Parzen window density estimation; the corresponding peak position is shown here to be the expected signal variance in the object. The proposed method does not depend on prior foreground segmentation, and only one image with a small amount of background is required when the signal-to-noise ratio (SNR) is greater than three. This method is applicable to magnitude-reconstructed MRIs, though diffusion tensor (DT)-MRI is used here to demonstrate the approach.