Error propagation framework for diffusion tensor imaging via diffusion tensor representations

Brain Age Difference at Baseline Predicts Clinical Dementia Rating Change in Approximately Two Years

BACKGROUND

The Clinical Dementia Rating (CDR) has been widely used to assess dementia severity, but it is limited in predicting dementia progression, thus unable to advise preventive measures to those who are at high risk.

OBJECTIVE

Predicted age difference (PAD) was proposed to predict CDR change.

METHODS

All diffusion magnetic resonance imaging and CDR scores were obtained from the OASIS-3 databank. A brain age model was trained by a machine learning algorithm using the imaging data of 258 cognitively healthy adults. Two diffusion indices, i.e., mean diffusivity and fractional anisotropy, over the whole brain white matter were extracted to serve as the features for model training. The validated brain age model was applied to a longitudinal cohort of 217 participants who had CDR = 0 (CDR0), 0.5 (CDR0.5), and 1 (CDR1) at baseline. Participants were grouped according to different baseline CDR and their subsequent CDR in approximately 2 years of follow-up. PAD was compared between different groups with multiple comparison correction.

RESULTS

PADs were significantly different among participants with different baseline CDRs. PAD in participants with relatively stable CDR0.5 was significantly smaller than PAD in participants who had CDR0.5 at baseline but converted to CDR1 in the follow-up. Similarly, participants with relatively stable CDR0 had significantly smaller PAD than those who were CDR0 at baseline but converted to CDR0.5 in the follow-up.

CONCLUSION

Our results imply that PAD might be a potential imaging biomarker for predicting CDR outcomes in patients with CDR0 or CDR0.5.

Assessment of the systematic errors caused by diffusion gradient inhomogeneity in DTI-computer simulations

Diffusion tensor imaging (DTI) is a powerful MRI modality that allows the investigation of the microstructure of tissues both in vivo and noninvasively. Its reliability is strictly dependent on the performance of diffusion-sensitizing gradients, of which spatial nonuniformity is a known issue in the case of virtually all clinical MRI scanners. The influence of diffusion gradient inhomogeneity on the accuracy of the diffusion tensor imaging was investigated by means of computer simulations supported by an MRI experiment performed at the isocenter and 15 cm away. The DTI measurements of two diffusion phantoms were simulated assuming a nonuniform diffusion-sensitizing gradient and various levels of noise. Thereafter, the tensors were calculated by two methods: (i) assuming a spatially constant b-matrix (standard DTI) and (ii) applying the b-matrix spatial distribution in the DTI (BSD-DTI) technique, a method of indicating the b-matrix for each voxel separately using an anisotropic phantom as a standard of diffusion. The average eigenvalues and fractional anisotropy across the homogeneous region of interest were calculated and compared with the expected values. Diffusion gradient inhomogeneity leads to overestimation of the largest eigenvalue, underestimation of the smallest one and thus overestimation of fractional anisotropy. The effect is similar to that caused by noise; however, it could not be corrected by increasing SNR. The MRI measurements, performed using a 3 T clinical scanner, revealed that the split of the eigenvalues measured 15 cm away from the isocenter is significant (up to 25%). The BSD-DTI calibration allowed the reduction of the measured fractional anisotropy of the isotropic medium from 0.174 to 0.031, suggesting that gradient inhomogeneity was the main cause of this error. For the phantom measured at the isocenter, however, the split was almost not observed; the average eigenvalues were shifted from the expected value by ~ 5%.

Simultaneous magnetic resonance diffusion and pseudo-diffusion tensor imaging

PURPOSE

An emerging topic in diffusion magnetic resonance is imaging blood microcirculation alongside water diffusion using the intravoxel incoherent motion (IVIM) model. Recently, a combined IVIM diffusion tensor imaging (IVIM-DTI) model was proposed, which accounts for both anisotropic pseudo-diffusion due to blood microcirculation and anisotropic diffusion due to tissue microstructures. In this article, we propose a robust IVIM-DTI approach for simultaneous diffusion and pseudo-diffusion tensor imaging.

METHODS

Conventional IVIM estimation methods can be broadly divided into two-step (diffusion and pseudo-diffusion estimated separately) and one-step (diffusion and pseudo-diffusion estimated simultaneously) methods. Here, both methods were applied on the IVIM-DTI model. An improved one-step method based on damped Gauss-Newton algorithm and a Gaussian prior for the model parameters was also introduced. The sensitivities of these methods to different parameter initializations were tested with realistic in silico simulations and experimental in vivo data.

RESULTS

The one-step damped Gauss-Newton method with a Gaussian prior was less sensitive to noise and the choice of initial parameters and delivered more accurate estimates of IVIM-DTI parameters compared to the other methods.

CONCLUSION

One-step estimation using damped Gauss-Newton and a Gaussian prior is a robust method for simultaneous diffusion and pseudo-diffusion tensor imaging using IVIM-DTI model. Magn Reson Med 79:2367-2378, 2018. © 2017 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Bayesian uncertainty quantification in linear models for diffusion MRI

Diffusion MRI (dMRI) is a valuable tool in the assessment of tissue microstructure. By fitting a model to the dMRI signal it is possible to derive various quantitative features. Several of the most popular dMRI signal models are expansions in an appropriately chosen basis, where the coefficients are determined using some variation of least-squares. However, such approaches lack any notion of uncertainty, which could be valuable in e.g. group analyses. In this work, we use a probabilistic interpretation of linear least-squares methods to recast popular dMRI models as Bayesian ones. This makes it possible to quantify the uncertainty of any derived quantity. In particular, for quantities that are affine functions of the coefficients, the posterior distribution can be expressed in closed-form. We simulated measurements from single- and double-tensor models where the correct values of several quantities are known, to validate that the theoretically derived quantiles agree with those observed empirically. We included results from residual bootstrap for comparison and found good agreement. The validation employed several different models: Diffusion Tensor Imaging (DTI), Mean Apparent Propagator MRI (MAP-MRI) and Constrained Spherical Deconvolution (CSD). We also used in vivo data to visualize maps of quantitative features and corresponding uncertainties, and to show how our approach can be used in a group analysis to downweight subjects with high uncertainty. In summary, we convert successful linear models for dMRI signal estimation to probabilistic models, capable of accurate uncertainty quantification.

On the averaging of cardiac diffusion tensor MRI data: the effect of distance function selection

Diffusion tensor magnetic resonance imaging (DT-MRI) allows a unique insight into the microstructure of highly-directional tissues. The selection of the most proper distance function for the space of diffusion tensors is crucial in enhancing the clinical application of this imaging modality. Both linear and nonlinear metrics have been proposed in the literature over the years. The debate on the most appropriate DT-MRI distance function is still ongoing. In this paper, we presented a framework to compare the Euclidean, affine-invariant Riemannian and log-Euclidean metrics using actual high-resolution DT-MRI rat heart data. We employed temporal averaging at the diffusion tensor level of three consecutive and identically-acquired DT-MRI datasets from each of five rat hearts as a means to rectify the background noise-induced loss of myocyte directional regularity. This procedure is applied here for the first time in the context of tensor distance function selection. When compared with previous studies that used a different concrete application to juxtapose the various DT-MRI distance functions, this work is unique in that it combined the following: (i) metrics were judged by quantitative-rather than qualitative-criteria, (ii) the comparison tools were non-biased, (iii) a longitudinal comparison operation was used on a same-voxel basis. The statistical analyses of the comparison showed that the three DT-MRI distance functions tend to provide equivalent results. Hence, we came to the conclusion that the tensor manifold for cardiac DT-MRI studies is a curved space of almost zero curvature. The signal to noise ratio dependence of the operations was investigated through simulations. Finally, the 'swelling effect' occurrence following Euclidean averaging was found to be too unimportant to be worth consideration.

Choosing the polarity of the phase-encoding direction in diffusion MRI: Does it matter for group analysis?

Notorious for degrading diffusion MRI data quality are so-called susceptibility-induced off-resonance fields, which cause non-linear geometric image deformations. While acquiring additional data to correct for these distortions alleviates the adverse effects of this artifact drastically - e.g., by reversing the polarity of the phase-encoding (PE) direction - this strategy is often not an option due to scan time constraints. Especially in a clinical context, where patient comfort and safety are of paramount importance, acquisition specifications are preferred that minimize scan time, typically resulting in data obtained with only one PE direction. In this work, we investigated whether choosing a different polarity of the PE direction would affect the outcome of a specific clinical research study. To address this methodological question, fractional anisotropy (FA) estimates of FreeSurfer brain regions were obtained in civilian and combat controls, remitted posttraumatic stress disorder (PTSD) patients, and persistent PTSD patients before and after trauma-focused therapy and were compared between diffusion MRI data sets acquired with different polarities of the PE direction (posterior-to-anterior, PA and anterior-to-posterior, AP). Our results demonstrate that regional FA estimates differ on average in the order of 5% between AP and PA PE data. In addition, when comparing FA estimates between different subject groups for specific cingulum subdivisions, the conclusions for AP and PA PE data were not in agreement. These findings increase our understanding of how one of the most pronounced data artifacts in diffusion MRI can impact group analyses and should encourage users to be more cautious when interpreting and reporting study outcomes derived from data acquired along a single PE direction.

Tract Orientation and Angular Dispersion Deviation Indicator (TOADDI): A framework for single-subject analysis in diffusion tensor imaging

The purpose of this work is to develop a framework for single-subject analysis of diffusion tensor imaging (DTI) data. This framework is termed Tract Orientation and Angular Dispersion Deviation Indicator (TOADDI) because it is capable of testing whether an individual tract as represented by the major eigenvector of the diffusion tensor and its corresponding angular dispersion are significantly different from a group of tracts on a voxel-by-voxel basis. This work develops two complementary statistical tests based on the elliptical cone of uncertainty, which is a model of uncertainty or dispersion of the major eigenvector of the diffusion tensor. The orientation deviation test examines whether the major eigenvector from a single subject is within the average elliptical cone of uncertainty formed by a collection of elliptical cones of uncertainty. The shape deviation test is based on the two-tailed Wilcoxon-Mann-Whitney two-sample test between the normalized shape measures (area and circumference) of the elliptical cones of uncertainty of the single subject against a group of controls. The False Discovery Rate (FDR) and False Non-discovery Rate (FNR) were incorporated in the orientation deviation test. The shape deviation test uses FDR only. TOADDI was found to be numerically accurate and statistically effective. Clinical data from two Traumatic Brain Injury (TBI) patients and one non-TBI subject were tested against the data obtained from a group of 45 non-TBI controls to illustrate the application of the proposed framework in single-subject analysis. The frontal portion of the superior longitudinal fasciculus seemed to be implicated in both tests (orientation and shape) as significantly different from that of the control group. The TBI patients and the single non-TBI subject were well separated under the shape deviation test at the chosen FDR level of 0.0005. TOADDI is a simple but novel geometrically based statistical framework for analyzing DTI data. TOADDI may be found useful in single-subject, graph-theoretic and group analyses of DTI data or DTI-based tractography techniques.

Data-driven optimized flip angle selection for T1 estimation from spoiled gradient echo acquisitions

PURPOSE

Define criteria for selection of optimal flip angle sets for T1 estimation and evaluate effects on T1 mapping.

THEORY AND METHODS

Flip angle sets for spoiled gradient echo-based T1 mapping were selected by minimizing T1 estimate variance weighted by the joint density of M0 and T1 in an initial acquisition. The effect of optimized flip angle selection on T1 estimate error was measured using simulations and experimental data in the human and rat brain.

RESULTS

For two-point acquisitions, optimized angle sets were similar to those proposed by other groups and, therefore, performed similarly. For multipoint acquisitions, optimal angle sets for T1 mapping in the brain consisted of a repetition of two angles. Implementation of optimal angles reduced T1 estimate variance by 30-40% compared with a multipoint acquisition using a range of angles. Performance of the optimal angle set was equivalent to that of a repetition of the two-angle set selected using criteria proposed by other researchers.

CONCLUSION

Repetition of two carefully selected flip angles notably improves the precision of resulting T1 estimates compared with acquisitions using a range of flip angles. This work provides a flexible and widely applicable optimization method of particular use for those who repeatedly perform T1 estimation. Magn Reson Med 76:792-802, 2016. © 2015 Wiley Periodicals, Inc.

Conceptual Foundations of Diffusion in Magnetic Resonance

A thorough review of the q-space technique is presented starting from a discussion of Fick's laws. The work presented here is primarily conceptual, theoretical and hopefully pedagogical. We offered the notion of molecular concentration to unify Fick's laws and diffusion MRI within a coherent conceptual framework. The fundamental relationship between diffusion MRI and the Fick's laws are carefully established. The conceptual and theoretical basis of the q-space technique is investigated from first principles.

Sparse and optimal acquisition design for diffusion MRI and beyond

PURPOSE

Diffusion magnetic resonance imaging (MRI) in combination with functional MRI promises a whole new vista for scientists to investigate noninvasively the structural and functional connectivity of the human brain-the human connectome, which had heretofore been out of reach. As with other imaging modalities, diffusion MRI data are inherently noisy and its acquisition time-consuming. Further, a faithful representation of the human connectome that can serve as a predictive model requires a robust and accurate data-analytic pipeline. The focus of this paper is on one of the key segments of this pipeline-in particular, the development of a sparse and optimal acquisition (SOA) design for diffusion MRI multiple-shell acquisition and beyond.

METHODS

The authors propose a novel optimality criterion for sparse multiple-shell acquisition and quasimultiple-shell designs in diffusion MRI and a novel and effective semistochastic and moderately greedy combinatorial search strategy with simulated annealing to locate the optimum design or configuration. The goal of the optimality criteria is threefold: first, to maximize uniformity of the diffusion measurements in each shell, which is equivalent to maximal incoherence in angular measurements; second, to maximize coverage of the diffusion measurements around each radial line to achieve maximal incoherence in radial measurements for multiple-shell acquisition; and finally, to ensure maximum uniformity of diffusion measurement directions in the limiting case when all the shells are coincidental as in the case of a single-shell acquisition. The approach taken in evaluating the stability of various acquisition designs is based on the condition number and the A-optimal measure of the design matrix.

RESULTS

Even though the number of distinct configurations for a given set of diffusion gradient directions is very large in general-e.g., in the order of 10(232) for a set of 144 diffusion gradient directions, the proposed search strategy was found to be effective in finding the optimum configuration. It was found that the square design is the most robust (i.e., with stable condition numbers and A-optimal measures under varying experimental conditions) among many other possible designs of the same sample size. Under the same performance evaluation, the square design was found to be more robust than the widely used sampling schemes similar to that of 3D radial MRI and of diffusion spectrum imaging (DSI).

CONCLUSIONS

A novel optimality criterion for sparse multiple-shell acquisition and quasimultiple-shell designs in diffusion MRI and an effective search strategy for finding the best configuration have been developed. The results are very promising, interesting, and practical for diffusion MRI acquisitions.

Considerations in high-resolution skeletal muscle diffusion tensor imaging using single-shot echo planar imaging with stimulated-echo preparation and sensitivity encoding

Previous studies have shown that skeletal muscle diffusion tensor imaging (DTI) can noninvasively probe changes in the muscle fiber architecture and microstructure in diseased and damaged muscles. However, DTI fiber reconstruction in small muscles and in muscle regions close to aponeuroses and tendons remains challenging because of partial volume effects. Increasing the spatial resolution of skeletal muscle single-shot diffusion-weighted echo planar imaging (DW-EPI) can be hindered by the inherently low signal-to-noise ratio (SNR) of muscle DW-EPI because of the short muscle T(2) and the high sensitivity of single-shot EPI to off-resonance effects and T(2)* blurring. In this article, eddy current-compensated diffusion-weighted stimulated-echo preparation is combined with sensitivity encoding (SENSE) to maintain good SNR properties and to reduce the sensitivity to distortions and T(2)* blurring in high-resolution skeletal muscle single-shot DW-EPI. An analytical framework is developed to optimize the reduction factor and diffusion weighting time to achieve maximum SNR. Arguments for the selection of the experimental parameters are then presented considering the compromise between SNR, B(0)-induced distortions, T(2)* blurring effects and tissue incoherent motion effects. On the basis of the selected parameters in a high-resolution skeletal muscle single-shot DW-EPI protocol, imaging protocols at lower acquisition matrix sizes are defined with matched bandwidth in the phase-encoding direction and SNR. In  vivo results show that high-resolution skeletal muscle DTI with minimized sensitivity to geometric distortions and T(2)* blurring is feasible using the proposed methodology. In particular, a significant benefit is demonstrated from a reduction in partial volume effects for resolving multi-pennate muscles and muscles with small cross-sections in calf muscle DTI.

Robust tensor estimation in diffusion tensor imaging

The signal response measured in diffusion tensor imaging is subject to detrimental influences caused by noise. Noise fields arise due to various contributions such as thermal and physiological noise and sources related to the hardware imperfection. As a result, diffusion tensors estimated by different linear and non-linear least squares methods in absence of a proper noise correction tend to be substantially corrupted. In this work, we propose an advanced tensor estimation approach based on the least median squares method of the robust statistics. Both constrained and non-constrained versions of the method are considered. The performance of the developed algorithm is compared to that of the conventional least squares method and of the alternative robust methods proposed in the literature. Two examples of simulated diffusion attenuations and experimental in vivo diffusion data sets were used as a basis for comparison. The robust algorithms were shown to be advantageous compared to the least squares method in the cases where elimination of the outliers is desirable. Additionally, the constraints were applied in order to prevent generation of the non-positive definite tensors and reduce related artefacts in the maps of fractional anisotropy. The developed method can potentially be exploited also by other MR techniques where a robust regression or outlier localisation is required.

Extremely efficient and deterministic approach to generating optimal ordering of diffusion MRI measurements

PURPOSE

Diffusion MRI measurements are typically acquired sequentially with unit gradient directions that are distributed uniformly on the unit sphere. The ordering of the gradient directions has significant effect on the quality of dMRI-derived quantities. Even though several methods have been proposed to generate optimal orderings of gradient directions, these methods are not widely used in clinical studies because of the two major problems. The first problem is that the existing methods for generating highly uniform and antipodally symmetric gradient directions are inefficient. The second problem is that the existing methods for generating optimal orderings of gradient directions are also highly inefficient. In this work, the authors propose two extremely efficient and deterministic methods to solve these two problems.

METHODS

The method for generating nearly uniform point set on the unit sphere (with antipodal symmetry) is based upon the notion that the spacing between two consecutive points on the same latitude should be equal to the spacing between two consecutive latitudes. The method for generating optimal ordering of diffusion gradient directions is based on the idea that each subset of incremental sample size, which is derived from the prescribed and full set of gradient directions, must be as uniform as possible in terms of the modified electrostatic energy designed for antipodally symmetric point set.

RESULTS

The proposed method outperformed the state-of-the-art method in terms of computational efficiency by about six orders of magnitude.

CONCLUSIONS

Two extremely efficient and deterministic methods have been developed for solving the problem of optimal ordering of diffusion gradient directions. The proposed strategy is also applicable to optimal view-ordering in three-dimensional radial MRI.

Technical note: DTI measurements of fractional anisotropy and mean diffusivity at 1.5 T: comparison of two radiofrequency head coils with different functional designs and sensitivities

PURPOSE

Diffusion tensor imaging (DTI) is highly sensitive to noise and improvement of radiofrequency coil technology represents a straightforward way for augmenting signal-to-noise ratio (SNR) performance in magnetic resonance imaging (MRI) scanners. The aim of this study was to characterize the dependence of DTI measurements of fractional anisotropy (FA) and mean diffusivity (MD) on the choice of head coil, comparing two head coils with different functional designs and sensitivities.

METHODS

Fourteen healthy subjects underwent DTI acquisitions at 1.5 T. Every subject was scanned twice, using a standard quadrature birdcage head coil (coil-A) and an eight-channel array head coil (coil-B). FA and MD maps, estimated using both the linear least squares (LLS) and nonlinear least squares (NLLS) methods, were nonlinearly normalized into a standard space. Then, volumetric regions of interest encompassing typical white and gray matter structures [splenium of the corpus callosum (SCC), internal capsule (IC), cerebral peduncles (CP), middle cerebellar peduncles (MCP), globus pallidus (GP), thalamus (TH), caudate (CA), and putamen (PU)] were analyzed. Significant differences and trends of variation in DTI measurements were assessed by the Wilcoxon test for paired samples with and without Bonferroni correction for multiple comparisons, respectively.

RESULTS

The overall SNR of coil-B was 30% higher than that of coil-A. When comparing DTI measurements (coil-B versus coil-A), mean FA values (SCC, IC, and TH), mean MD values (IC, CP, GP, and TH), FA standard deviation (CP, MCP, GP, and CA), and MD standard deviation (IC, CP, TH, and PU) resulted decreased (significant difference, p(cor) < 0.05, or trend of variation, P(uncor) < 0.05) in several gray and white matter regions of the human brain. With the exception of CP, the results in terms of revealed significant difference or trend of variation were independent of the method (LLS and NLLS) used for estimating the diffusion tensor.

CONCLUSIONS

In various gray and white matter structures, the eight-channel array head coil yielded more precise and accurate measurements of DTI derived indices compared to the standard quadrature birdcage head coil.

Quantification of accuracy and precision of multi-center DTI measurements: a diffusion phantom and human brain study

The inter-site and intra-site variability of system performance of MRI scanners (due to site-dependent and time-variant variations) can have significant adverse effects on the integration of multi-center DTI data. Measurement errors in accuracy and precision of each acquisition determine both the inter-site and intra-site variability. In this study, multiple scans of an identical isotropic diffusion phantom and of the brain of a traveling human volunteer were acquired at MRI scanners from the same vendor and with similar configurations at three sites. We assessed the feasibility of multi-center DTI studies by direct quantification of accuracy and precision of each dataset. Accuracy was quantified via comparison to carefully constructed gold standard datasets while precision (the within-scan variability) was estimated by wild bootstrap analysis. The results from both the phantom and human data suggest that the inter-site variation in system performance, although relatively small among scanners of the same vendor, significantly affects DTI measurement accuracy and precision and therefore the effectiveness for the integration of multi-center DTI measurements. Our results also highlight the value of a DTI-specific phantom in identifying and quantifying measurement errors due to site-dependent variations in the system performance, and its usefulness for quality assurance/quality control in multi-center DTI studies. In addition, we observed that the within-scan variability of each data acquisition, as assessed by wild bootstrap analysis, is of the same magnitude as the inter-site and intra-site variability. We propose that by weighing datasets based on their variability, as evaluated by wild bootstrap analysis, one can improve the quality of the dataset. This approach will provide a more effective integration of datasets from multi-center DTI studies.

A full bi-tensor neural tractography algorithm using the unscented Kalman filter

We describe a technique that uses tractography to visualize neural pathways in human brains by extending an existing framework that uses overlapping Gaussian tensors to model the signal. At each point on the fiber, an unscented Kalman filter is used to find the most consistent direction as a mixture of previous estimates and of the local model. In our previous framework, the diffusion ellipsoid had a cylindrical shape, i.e., the diffusion tensor's second and third eigenvalues were identical. In this paper, we extend the tensor representation so that the diffusion tensor is represented by an arbitrary ellipsoid. Experiments on synthetic data show a reduction in the angular error at fiber crossings and branchings. Tests on in vivo data demonstrate the ability to trace fibers in areas containing crossings or branchings, and the tests also confirm the superiority of using a full tensor representation over the simplified model.

Segmentation of fiber tracts based on an accuracy analysis on diffusion tensor software phantoms

Due to its unique sensitivity to tissue microstructure, one of the primary applications of diffusion-weighted magnetic resonance imaging is the reconstruction of neural fiber pathways by means of fiber-tracking algorithms. In this work, we make use of realistic diffusion-tensor software phantoms in order to carry out an analysis of the precision of streamline tractography by systematically varying certain properties of the simulated image data (noise, tensor anisotropy, and image resolution) as well as certain fiber-tracking parameters (number of seed points and step length). Building upon the gained knowledge about the precision of the analyzed fiber-tracking algorithm, we proceed by suggesting a fuzzy segmentation algorithm for diffusion tensor images which better estimates the precise spatial extent of a tracked fiber bundle. The presented segmentation algorithm utilizes information given by the estimated main diffusion direction in a voxel and the respective uncertainty, and its validity is confirmed by both qualitative and quantitative analyses.

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.

Estimation of diffusion properties in crossing fiber bundles

There is an ongoing debate on how to model diffusivity in fiber crossings. We propose an optimization framework for the selection of a dual tensor model and the set of diffusion weighting parameters b, such that both the diffusion shape and orientation parameters can be precisely as well as accurately estimated. For that, we have adopted the Cramér-Rao lower bound (CRLB) on the variance of the model parameters, and performed Monte Carlo simulations. We have found that the axial diffusion lambda(parallel) needs to be constrained, while an isotropic fraction can be modeled by a single parameter f(iso). Under these circumstances, the Fractional Anisotropy (FA) of both tensors can theoretically be independently estimated with a precision of 9% (at SNR = 25). Levenberg-Marquardt optimization of the Maximum Likelihood function with a Rician noise model approached this precision while the bias was insignificant. A two-element b-vector b = [1.0 3.5] x 10(3) mm(-2)s was found to be sufficient for estimating parameters of heterogeneous tissue with low error. This has allowed us to estimate consistent FA-profiles along crossing tracts. This work defines fundamental limits for comparative studies to correctly analyze crossing white matter structures.

Diffusion tensor field registration in the presence of uncertainty

We propose a novel method for deformable tensor-to-tensor registration of Diffusion Tensor Imaging (DTI) data. Our registration method considers estimated diffusion tensors as normally distributed random variables whose covariance matrices describe uncertainties in the mean estimated tensor due to factors such as noise in diffusion weighted images (DWIs), tissue diffusion properties, and experimental design. The dissimilarity between distributions of tensors in two different voxels is computed using the Kullback-Leibler divergence to drive a deformable registration process, which is not only affected by principal diffusivities and principal directions, but also the underlying DWI properties. We in general do not assume the positive definite nature of the tensor space given the pervasive influence of noise and other factors. Results indicate that the proposed metric weights voxels more heavily whose diffusion tensors are estimated with greater certainty and exhibit anisotropic diffusion behavior thus, intrinsically favoring coherent white matter regions whose tensors are estimated with high confidence.

How does angular resolution affect diffusion imaging measures?

A key question in diffusion imaging is how many diffusion-weighted images suffice to provide adequate signal-to-noise ratio (SNR) for studies of fiber integrity. Motion, physiological effects, and scan duration all affect the achievable SNR in real brain images, making theoretical studies and simulations only partially useful. We therefore scanned 50 healthy adults with 105-gradient high-angular resolution diffusion imaging (HARDI) at 4T. From gradient image subsets of varying size (6 Collapse

Key Words

• high-angular resolution diffusion imaging
• anisotropic scalar
• generalized fractional anisotropy
• tensor
• signal-to-noise ratio
• kullback-leibler divergence

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MESH Headings

• Algorithms
• Anisotropy
• Computer Simulation
• Corpus Callosum/physiology
• Diffusion
• Diffusion Magnetic Resonance Imaging/methods
• Female
• Humans
• Imaging, Three-Dimensional/methods
• Male
• Models, Neurological
• Young Adult

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Grants

• EB007813 NIBIB NIH HHS
• R01 EB007813 NIBIB NIH HHS
• AG020098 NIA NIH HHS
• R56 AG020098 NIA NIH HHS
• HD050735 NICHD NIH HHS
• EB008432 NIBIB NIH HHS
• R01 EB008281-14 NIBIB NIH HHS
• R01 AG020098-09 NIA NIH HHS
• R01 EB008281 NIBIB NIH HHS
• R01 EB007813-04 NIBIB NIH HHS
• R01 HD050735 NICHD NIH HHS
• R01 EB008432 NIBIB NIH HHS
• EB008281 NIBIB NIH HHS
• R01 AG020098 NIA NIH HHS
• R01 EB008432-03 NIBIB NIH HHS

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Affiliation(s)

Liang Zhan Laboratory of Neuro Imaging, Department of Neurology, UCLA School of Medicine, 635 Charles E. Young Drive South, Suite 225E, Los Angeles, CA 90095-7332, USA
Alex D Leow
Neda Jahanshad
Ming-Chang Chiang
Marina Barysheva
Agatha D Lee
Arthur W Toga
Katie L McMahon
Greig I de Zubicaray
Margaret J Wright
Paul M Thompson

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On the six-dimensional orthogonal tensor representation of the rotation in three dimensions: A simplified approach

The six-dimensional orthogonal tensor representation of the rotation about an axis in three dimensions was first proposed by (Mehrabadi et al. 1995). In this brief note, a simple and coherent approach is presented to construct the six-dimensional orthogonal tensor representation of the rotation of any parametrization in three dimensions and to prove its orthogonality.

Probabilistic Identification and Estimation of Noise (PIESNO): a self-consistent approach and its applications in MRI

Data analysis in MRI usually entails a series of processing procedures. One of these procedures is noise assessment, which in the context of this work, includes both the identification of noise-only pixels and the estimation of noise variance (standard deviation). Although noise assessment is critical to many MRI processing techniques, the identification of noise-only pixels has received less attention than has the estimation of noise variance. The main objectives of this paper are, therefore, to demonstrate (a) that the identification of noise-only pixels has an important role to play in the analysis of MRI data, (b) that the identification of noise-only pixels and the estimation of noise variance can be combined into a coherent framework, and (c) that this framework can be made self-consistent. To this end, we propose a novel iterative approach to simultaneously identify noise-only pixels and estimate the noise standard deviation from these identified pixels in a commonly used data structure in MRI. Experimental and simulated data were used to investigate the feasibility, the accuracy and the stability of the proposed technique.

In vivo diffusion tensor imaging of the human optic chiasm at sub-millimeter resolution

In this work we report findings from an in vivo diffusion tensor imaging (DTI) study of the human optic chiasm at sub-millimeter voxel resolution. Data were collected at 3 T using a diffusion-weighted radial-FSE sequence, which provides images free from typical magnetic susceptibility artifacts. The general DTI features observed in the optic chiasm region were consistent across subjects. They included a central area with high anisotropy and highest diffusivity in a predominately right/left direction corresponding to the decussation of nasal hemiretinae fibers, surrounded by a band of low anisotropy reflecting heterogeneous orientation of fibers within the voxel, and a lateral area with high anisotropy and highest diffusivity in a predominately anterior/posterior direction corresponding to temporal hemiretinae fibers that do not cross. Animal studies indicate that there is a significant dorsal-ventral reorganization of the retinotopic distribution of fibers along the optic pathways. We found that diffusion ellipsoids in the central portion of the optic chiasm show considerable planar anisotropy in the coronal plane indicating fiber crossings in the superior/inferior direction, rather than strictly right/left. This architectural feature of the chiasm suggests that dorso-ventral reorganization of fibers in the optic pathways also occurs in humans. We have shown that by collecting sub-millimeter resolution data, DTI can be used to investigate fine details of small and complex white matter structures, in vivo, with a clinical scanner. High spatial resolution, however, is necessary in the slice direction as well as in-plane to reduce the CSF contribution to the signal and to increase fiber coherence within voxels.

A signal transformational framework for breaking the noise floor and its applications in MRI

A long-standing problem in magnetic resonance imaging (MRI) is the noise-induced bias in the magnitude signals. This problem is particularly pressing in diffusion MRI at high diffusion-weighting. In this paper, we present a three-stage scheme to solve this problem by transforming noisy nonCentral Chi signals to noisy Gaussian signals. A special case of nonCentral Chi distribution is the Rician distribution. In general, the Gaussian-distributed signals are of interest rather than the Gaussian-derived (e.g., Rayleigh, Rician, and nonCentral Chi) signals because the Gaussian-distributed signals are generally more amenable to statistical treatment through the principle of least squares. Monte Carlo simulations were used to validate the statistical properties of the proposed framework. This scheme opens up the possibility of investigating the low signal regime (or high diffusion-weighting regime in the case of diffusion MRI) that contains potentially important information about biophysical processes and structures of the brain.

How background noise shifts eigenvectors and increases eigenvalues in DTI

INTRODUCTION

The signal-to-noise ratio of in vivo diffusion tensor imaging (DTI) is usually very limited, especially if high resolution data is acquired. In a variety of settings, the signal of diffusion weighted images can drop below the background noise level yielding an underestimated diffusion constant. In this work, we report two new artefacts in DTI that are important in this regime.

METHODS

Both artifacts are described analytically and numerically and are demonstrated in DTI phantoms and in subjects in vivo.

RESULTS

First, eigenvectors are systematically shifted towards distinct 'attractive' orientations of the gradient scheme. Second, certain eigenvalues can be overestimated due to the underestimation of the measured diffusion, which can result in the misordering of eigenvalues.

DISCUSSION

We show that these effects are relevant for current clinical settings of DTI.

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.