Noise considerations in the determination of diffusion tensor anisotropy

Widespread effects of dMRI data quality on diffusion measures in children

Diffusion magnetic resonance imaging (dMRI) datasets are susceptible to several confounding factors related to data quality, which is especially true in studies involving young children. With the recent trend of large‐scale multicenter studies, it is more critical to be aware of the varied impacts of data quality on measures of interest. Here, we investigated data quality and its effect on different diffusion measures using a multicenter dataset. dMRI data were obtained from 691 participants (5–17 years of age) from six different centers. Six data quality metrics—contrast to noise ratio, outlier slices, and motion (absolute, relative, translation, and rotational)—and four diffusion measures—fractional anisotropy, mean diffusivity, tract density, and length—were computed for each of 36 major fiber tracts for all participants. The results indicated that four out of six data quality metrics (all except absolute and translation motion) differed significantly between centers. Associations between these data quality metrics and the diffusion measures differed significantly across the tracts and centers. Moreover, these effects remained significant after applying recently proposed harmonization algorithms that purport to remove unwanted between‐site variation in diffusion data. These results demonstrate the widespread impact of dMRI data quality on diffusion measures. These tracts and measures have been routinely associated with individual differences as well as group‐wide differences between neurotypical populations and individuals with neurological or developmental disorders. Accordingly, for analyses of individual differences or group effects (particularly in multisite dataset), we encourage the inclusion of data quality metrics in dMRI analysis.

Non-local means based Rician noise filtering for diffusion tensor and kurtosis imaging in human brain and spinal cord

BACKGROUND

To investigate the effect of using a Rician nonlocal means (NLM) filter on quantification of diffusion tensor (DT)- and diffusion kurtosis (DK)-derived metrics in various anatomical regions of the human brain and the spinal cord, when combined with a constrained linear least squares (CLLS) approach.

METHODS

Prospective brain data from 9 healthy subjects and retrospective spinal cord data from 5 healthy subjects from a 3 T MRI scanner were included in the study. Prior to tensor estimation, registered diffusion weighted images were denoised by an optimized blockwise NLM filter with CLLS. Mean kurtosis (MK), radial kurtosis (RK), axial kurtosis (AK), mean diffusivity (MD), radial diffusivity (RD), axial diffusivity (AD) and fractional anisotropy (FA), were determined in anatomical structures of the brain and the spinal cord. DTI and DKI metrics, signal-to-noise ratio (SNR) and Chi-square values were quantified in distinct anatomical regions for all subjects, with and without Rician denoising.

RESULTS

The averaged SNR significantly increased with Rician denoising by a factor of 2 while the averaged Chi-square values significantly decreased up to 61% in the brain and up to 43% in the spinal cord after Rician NLM filtering. In the brain, the mean MK varied from 0.70 (putamen) to 1.27 (internal capsule) while AK and RK varied from 0.58 (corpus callosum) to 0.92 (cingulum) and from 0.70 (putamen) to 1.98 (corpus callosum), respectively. In the spinal cord, FA varied from 0.78 in lateral column to 0.81 in dorsal column while MD varied from 0.91 × 10^-3 mm²/s (lateral) to 0.93 × 10^-3 mm²/s (dorsal). RD varied from 0.34 × 10^-3 mm²/s (dorsal) to 0.38 × 10^-3 mm²/s (lateral) and AD varied from 1.96 × 10^-3 mm²/s (lateral) to 2.11 × 10^-3 mm²/s (dorsal).

CONCLUSIONS

Our results show a Rician denoising NLM filter incorporated with CLLS significantly increases SNR and reduces estimation errors of DT- and KT-derived metrics, providing the reliable metrics estimation with adequate SNR levels.

A deep learning approach to estimation of subject-level bias and variance in high angular resolution diffusion imaging

The ability to evaluate empirical diffusion MRI acquisitions for quality and to correct the resulting imaging metrics allows for improved inference and increased replicability. Previous work has shown promise for estimation of bias and variance of generalized fractional anisotropy (GFA) but comes at the price of computational complexity. This paper aims to provide methods for estimating GFA, bias of GFA and standard deviation of GFA quickly and accurately. In order to provide a method for bias and variance estimation that can return results faster than the previously studied statistical techniques, three deep, fully-connected neural networks are developed for GFA, bias of GFA, and standard deviation of GFA. The results of these networks are compared to the observed values of the metrics as well as those fit from the statistical techniques (i.e. Simulation Extrapolation (SIMEX) for bias estimation and wild bootstrap for variance estimation). Our GFA network provides predictions that are closer to the true GFA values than a Q-ball fit of the observed data (root-mean-square error (RMSE) 0.0077 vs 0.0082, p < .001). The bias network also shows statistically significant improvement in comparison to the SIMEX-estimated error of GFA (RMSE 0.0071 vs. 0.01, p < .001).

Empirical single sample quantification of bias and variance in Q-ball imaging

PURPOSE

The bias and variance of high angular resolution diffusion imaging methods have not been thoroughly explored in the literature and may benefit from the simulation extrapolation (SIMEX) and bootstrap techniques to estimate bias and variance of high angular resolution diffusion imaging metrics.

METHODS

The SIMEX approach is well established in the statistics literature and uses simulation of increasingly noisy data to extrapolate back to a hypothetical case with no noise. The bias of calculated metrics can then be computed by subtracting the SIMEX estimate from the original pointwise measurement. The SIMEX technique has been studied in the context of diffusion imaging to accurately capture the bias in fractional anisotropy measurements in DTI. Herein, we extend the application of SIMEX and bootstrap approaches to characterize bias and variance in metrics obtained from a Q-ball imaging reconstruction of high angular resolution diffusion imaging data.

RESULTS

The results demonstrate that SIMEX and bootstrap approaches provide consistent estimates of the bias and variance of generalized fractional anisotropy, respectively. The RMSE for the generalized fractional anisotropy estimates shows a 7% decrease in white matter and an 8% decrease in gray matter when compared with the observed generalized fractional anisotropy estimates. On average, the bootstrap technique results in SD estimates that are approximately 97% of the true variation in white matter, and 86% in gray matter.

CONCLUSION

Both SIMEX and bootstrap methods are flexible, estimate population characteristics based on single scans, and may be extended for bias and variance estimation on a variety of high angular resolution diffusion imaging metrics.

Diffusion MRI of white matter microstructure development in childhood and adolescence: Methods, challenges and progress

Diffusion magnetic resonance imaging (dMRI) continues to grow in popularity as a useful neuroimaging method to study brain development, and longitudinal studies that track the same individuals over time are emerging. Over the last decade, seminal work using dMRI has provided new insights into the development of brain white matter (WM) microstructure, connections and networks throughout childhood and adolescence. This review provides an introduction to dMRI, both diffusion tensor imaging (DTI) and other dMRI models, as well as common acquisition and analysis approaches. We highlight the difficulties associated with ascribing these imaging measurements and their changes over time to specific underlying cellular and molecular events. We also discuss selected methodological challenges that are of particular relevance for studies of development, including critical choices related to image acquisition, image analysis, quality control assessment, and the within-subject and longitudinal reliability of dMRI measurements. Next, we review the exciting progress in the characterization and understanding of brain development that has resulted from dMRI studies in childhood and adolescence, including brief overviews and discussions of studies focusing on sex and individual differences. Finally, we outline future directions that will be beneficial to the field.

Load-induced changes in the diffusion tensor of ovine anulus fibrosus: A pilot MRI study

PURPOSE

To assess the feasibility of diffusion tensor imaging (DTI) for evaluating changes in anulus fibrosus (AF) microstructure following uniaxial compression.

MATERIALS AND METHODS

Six axially aligned samples of AF were obtained from a merino sheep disc; two each from the anterior, lateral, and posterior regions. The samples were mechanically loaded in axial compression during five cycles at a rate and maximum compressive strain that reflected physiological conditions. DTI was conducted at 7T for each sample before and after mechanical testing.

RESULTS

The mechanical response of all samples in unconfined compression was nonlinear. A stiffer response during the first loading cycle, compared to the remaining cycles, was observed. Change in diffusion parameters appeared to be region-dependent. The mean fractional anisotropy increased following mechanical testing. This was smallest in the lateral (2% and 9%) and largest in the anterior and posterior samples (17-25%). The mean average diffusivity remained relatively constant (<2%) after mechanical testing in the lateral and posterior samples, but increased (by 5%) in the anterior samples. The mean angle made by the principal eigenvector with the spine axis in the lateral samples was 73° and remained relatively constant (<2%) following mechanical testing. This angle was smaller in the anterior (55°) and posterior (47°) regions and increased by 6-16° following mechanical testing.

CONCLUSION

These preliminary results suggest that axial compression reorients the collagen fibers, such that they become more consistently aligned parallel to the plane of the endplates.

LEVEL OF EVIDENCE

1 Technical Efficacy: Stage 1 J. MAGN. RESON. IMAGING 2017;45:1723-1735.

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.

The influence of molecular order and microstructure on the R2* and the magnetic susceptibility tensor

In this work, we demonstrate that in the presence of ordered sub-voxel structure such as tubular organization, biomaterials with molecular isotropy exhibits only apparent R2* anisotropy, while biomaterials with molecular anisotropy exhibit both apparent R2* and susceptibility anisotropy by means of susceptibility tensor imaging (STI). To this end, R2* and STI from gradient echo magnitude and phase data were examined in phantoms made from carbon fiber and Gadolinium (Gd) solutions with and without intrinsic molecular order and sub-voxel structure as well as in the in vivo brain. Confidence in the tensor reconstructions was evaluated with a wild bootstrap analysis. Carbon fiber showed both apparent anisotropy in R2* and anisotropy in STI, while the Gd filled capillary tubes only showed apparent anisotropy on R2*. Similarly, white matter showed anisotropic R2* and magnetic susceptibility with higher confidence, while the cerebral veins displayed only strong apparent R2* tensor anisotropy. Ordered sub-voxel tissue microstructure leads to apparent R2* anisotropy, which can be found in both white matter tracts and cerebral veins. However, additional molecular anisotropy is required for magnetic susceptibility anisotropy, which can be found in white matter tracts but not in cerebral veins.

A simple noise correction scheme for diffusional kurtosis imaging

PURPOSE

Diffusional kurtosis imaging (DKI) is sensitive to the effects of signal noise due to strong diffusion weightings and higher order modeling of the diffusion weighted signal. A simple noise correction scheme is proposed to remove the majority of the noise bias in the estimated diffusional kurtosis.

METHODS

Weighted linear least squares (WLLS) fitting together with a voxel-wise, subtraction-based noise correction from multiple, independent acquisitions are employed to reduce noise bias in DKI data. The method is validated in phantom experiments and demonstrated for in vivo human brain for DKI-derived parameter estimates.

RESULTS

As long as the signal-to-noise ratio (SNR) for the most heavily diffusion weighted images is greater than 2.1, errors in phantom diffusional kurtosis estimates are found to be less than 5 percent with noise correction, but as high as 44 percent for uncorrected estimates. In human brain, noise correction is also shown to improve diffusional kurtosis estimates derived from measurements made with low SNR.

CONCLUSION

The proposed correction technique removes the majority of noise bias from diffusional kurtosis estimates in noisy phantom data and is applicable to DKI of human brain. Features of the method include computational simplicity and ease of integration into standard WLLS DKI post-processing algorithms.

Improving the accuracy of PGSE DTI experiments using the spatial distribution of b matrix

A novel method for improving the accuracy of diffusion tensor imaging (DTI) is proposed. It takes into account the b matrix spatial variations, which can be easily determined using a simple anisotropic diffusion phantom. In opposite to standard numerical procedure of the b matrix calculation that requires the exact knowledge of amplitudes, shapes and time dependencies of diffusion gradients, the new method, which we call BSD-DTI (B-matrix spatial distribution in DTI), relies on direct measurements of its space-dependent components. The proposed technique was demonstrated on the Bruker Biospec 94/20USR system, using the spin echo diffusion sequence to image an isotropic water phantom and an anisotropic capillary phantom. The accuracy of the diffusion tensor determination was improved by an overall factor of about 8 for the isotropic water phantom.

Comparison of parameter threshold combinations for diffusion tensor tractography in chronic stroke patients and healthy subjects

BACKGROUND

Although quantitative evaluation of diffusion tensor imaging (DTI) data seemed to be extremely important for clinical research its application is under debate. Besides fractional anisotropy (FA) the quantitative comparison between hemispheres of the number of fibers reconstructed by means of diffusion tensor tractography (DTT) is commonly used. However, the tractography-related parameters FA, minimum tract length (LENGTH) and the angle between two contiguous tracking steps (ANGLE) are inconsistently applied. Using 18 combinations we tested for the influence of parameter thresholds on the amount of reconstructed fibers for the posterior pyramidal tract in both hemispheres in order to obtain meaningful thresholds for DTT.

RESULTS

In 14 chronic stroke patients with unilateral lesions of the pyramidal tract around the height of the internal capsule and considerable motor deficits a 3-way repeated-measures ANOVA showed a significant interaction between the effects of FA and ANGLE level on reconstructed fiber lateralization, F (2.9, 37.67) = 3.01, p = 0.044, and a significant main effect FA, F (1.4, 18.1) = 11.58, p = 0.001. Post-hoc pairwise comparisons showed that this interaction was completely driven by FA. In 22 right-handed healthy subjects no significant interactions or main effects could be found.

CONCLUSION

The parameter threshold combinations with highest FA showed highest effect. ANGLE and LENGTH insofar influenced the lateralization effect when selected as liberal as possible, short LENGTH and large ANGLE thresholds. The DTT approach should be used with great care since results are highly dependent on the thresholds applied.

Assessment of cardiac motion effects on the fiber architecture of the human heart in vivo

The use of diffusion tensor imaging (DTI) for studying the human heart in vivo is very challenging due to cardiac motion. This paper assesses the effects of cardiac motion on the human myocardial fiber architecture. To this end, a model for analyzing the effects of cardiac motion on signal intensity is presented. A Monte-Carlo simulation based on polarized light imaging data is then performed to calculate the diffusion signals obtained by the displacement of water molecules, which generate diffusion weighted (DW) images. Rician noise and in vivo motion data obtained from DENSE acquisition are added to the simulated cardiac DW images to produce motion-induced datasets. An algorithm based on principal components analysis filtering and temporal maximum intensity projection (PCATMIP) is used to compensate for motion-induced signal loss. Diffusion tensor parameters derived from motion-reduced DW images are compared to those derived from the original simulated DW images. Finally, to assess cardiac motion effects on in vivo fiber architecture, in vivo cardiac DTI data processed by PCATMIP are compared to those obtained from one trigger delay (TD) or one single phase acquisition. The results showed that cardiac motion produced overestimated fractional anisotropy and mean diffusivity as well as a narrower range of fiber angles. The combined use of shifted TD acquisitions and postprocessing based on image registration and PCATMIP effectively improved the quality of in vivo DW images and subsequently, the measurement accuracy of fiber architecture properties. This suggests new solutions to the problems associated with obtaining in vivo human myocardial fiber architecture properties in clinical conditions.

A better characterization of spinal cord damage in multiple sclerosis: a diffusional kurtosis imaging study

BACKGROUND AND PURPOSE

The spinal cord is a site of predilection for MS lesions. While diffusion tensor imaging is useful for the study of anisotropic systems such as WM tracts, it is of more limited utility in tissues with more isotropic microstructures (on the length scales studied with diffusion MR imaging) such as gray matter. In contrast, diffusional kurtosis imaging, which measures both Gaussian and non-Gaussian properties of water diffusion, provides more biomarkers of both anisotropic and isotropic structural changes. The aim of this study was to investigate the cervical spinal cord of patients with MS and to characterize lesional and normal-appearing gray matter and WM damage by using diffusional kurtosis imaging.

MATERIALS AND METHODS

Nineteen patients (13 women, mean age = 41.1 ± 10.7 years) and 16 controls (7 women, mean age = 35.6 ± 11.2-years) underwent MR imaging of the cervical spinal cord on a 3T scanner (T2 TSE, T1 magnetization-prepared rapid acquisition of gradient echo, diffusional kurtosis imaging, T2 fast low-angle shot). Fractional anisotropy, mean diffusivity, and mean kurtosis were measured on the whole cord and in normal-appearing gray matter and WM.

RESULTS

Spinal cord T2-hyperintense lesions were identified in 18 patients. Whole spinal cord fractional anisotropy and mean kurtosis (P = .0009, P = .003), WM fractional anisotropy (P = .01), and gray matter mean kurtosis (P = .006) were significantly decreased, and whole spinal cord mean diffusivity (P = .009) was increased in patients compared with controls. Mean spinal cord area was significantly lower in patients (P = .04).

CONCLUSIONS

Diffusional kurtosis imaging of the spinal cord can provide a more comprehensive characterization of lesions and normal-appearing WM and gray matter damage in patients with MS. Diffusional kurtosis imaging can provide additional and complementary information to DTI on spinal cord pathology.

Geometrical constraints for robust tractography selection

Tract-based analysis from DTI has become a widely employed procedure to study the white matter of the brain and its alterations in neurological and neurosurgical pathologies. Automatic tractography selection methods, where a subset of detected tracts corresponding to a specific white matter structure are selected, are a key component of the DTI processing pipeline. Using automatic tractography selection, repeatable results free of intra and inter-expert variability can be obtained rapidly, without the need for cumbersome manual segmentation. Many of the current approaches for automatic tractography selection rely on a previous registration procedure using an atlas; hence, these methods are likely very sensitive to the accuracy of the registration. In this paper we show that the performance of the registration step is critical to the overall result. This effect can in turn affect the calculation of scalar parameters derived subsequently from the selected tracts and often used in clinical practice; we show that such errors may be comparable in magnitude to the subtle differences found in clinical studies to differentiate between healthy and pathological. As an alternative, we propose a tractography selection method based on the use of geometrical constraints specific for each fiber bundle. Our experimental results show that the approach proposed performs with increased robustness and accuracy with respect to other approaches in the literature, particularly in the presence of imperfect registration.

Optimal diffusion tensor imaging with repeated measurements

Several data acquisition schemes for diffusion MRI have been proposed and explored to date for the reconstruction of the 2nd order tensor. Our main contributions in this paper are: (i) the definition of a new class of sampling schemes based on repeated measurements in every sampling point; (ii) two novel schemes belonging to this class; and (iii) a new reconstruction framework for the second scheme. We also present an evaluation, based on Monte Carlo computer simulations, of the performances of these schemes relative to known optimal sampling schemes for both 2nd and 4th order tensors. The results demonstrate that tensor estimation by the proposed sampling schemes and estimation framework is more accurate and robust.

The influence of spatial registration on detection of cerebral asymmetries using voxel-based statistics of fractional anisotropy images and TBSS

The sensitivity of diffusion tensor imaging (DTI) for detecting microstructural white matter alterations has motivated the application of voxel-based statistics (VBS) to fractional anisotropy (FA) images (FA-VBS). However, detected group differences may depend on the spatial registration method used. The objective of this study was to investigate the influence of spatial registration on detecting cerebral asymmetries in FA-VBS analyses with reference to data obtained using Tract-Based Spatial Statistics (TBSS). In the first part of this study we performed FA-VBS analyses using three single-contrast and one multi-contrast registration: (i) whole-brain registration based on T2 contrast, (ii) whole-brain registration based on FA contrast, (iii) individual-hemisphere registration based on FA contrast, and (iv) a combination of (i) and (iii). We then compared the FA-VBS results with those obtained from TBSS. We found that the FA-VBS results depended strongly on the employed registration approach, with the best correspondence between FA-VBS and TBSS results when approach (iv), the “multi-contrast individual-hemisphere” method was employed. In the second part of the study, we investigated the spatial distribution of residual misregistration for each registration approach and the effect on FA-VBS results. For the FA-VBS analyses using the three single-contrast registration methods, we identified FA asymmetries that were (a) located in regions prone to misregistrations, (b) not detected by TBSS, and (c) specific to the applied registration approach. These asymmetries were considered candidates for apparent FA asymmetries due to systematic misregistrations associated with the FA-VBS approach. Finally, we demonstrated that the “multi-contrast individual-hemisphere” approach showed the least residual spatial misregistrations and thus might be most appropriate for cerebral FA-VBS analyses.

Estrogen treatment prevents gray matter atrophy in experimental autoimmune encephalomyelitis

Gray matter atrophy is an important correlate to clinical disability in multiple sclerosis (MS), and many treatment trials include atrophy as an outcome measure. Atrophy has been shown to occur in experimental autoimmune encephalomyelitis (EAE), the most commonly used animal model of MS. The clinical severity of EAE is reduced in estrogen-reated mice, but it remains unknown whether estrogen treatment can reduce gray matter atrophy in EAE. In this study, mice with EAE were treated with either estrogen receptor (ER)-α ligand or ER-β ligand, and diffusion tensor images (DTI) were collected and neuropathology was performed. DTI showed atrophy in the cerebellar gray matter of vehicle-treated EAE mice compared with healthy controls but not in ER-α or ER-β ligand-treated EAE mice. Neuropathology demonstrated that Purkinje cell numbers were decreased in vehicle-treated EAE mice, whereas neither ER ligand-treated EAE groups showed a decrease. This is the first report of a neuroprotective therapy in EAE that unambiguously prevents gray matter atrophy while sparing a major neuronal cell type. Fractional anisotropy (FA) in the cerebellar white matter was decreased in vehicle- and ER-β ligand-treated but not in ER-α ligand-treated EAE mice. Inflammatory cell infiltration was increased in vehicle- and ER-β ligand-treated but not in ER-α ligand-treated EAE mice. Myelin staining was decreased in vehicle-treated EAE mice and was spared in both ER ligand-treated groups. This is consistent with decreased FA as a potential biomarker for inflammation rather than myelination or axonal damage in the cerebellum in EAE.

A VARIATIONAL MODEL FOR DENOISING HIGH ANGULAR RESOLUTION DIFFUSION IMAGING

The presence of noise in High Angular Resolution Diffusion Imaging (HARDI) data of the brain can limit the accuracy with which fiber pathways of the brain can be extracted. In this work, we present a variational model to denoise HARDI data corrupted by Rician noise. Numerical experiments are performed on three types of data: 2D synthetic data, 3D diffusion-weighted Magnetic Resonance Imaging (DW-MRI) data of a hardware phantom containing synthetic fibers, and 3D real HARDI brain data. Experiments show that our model is effective for denoising HARDI-type data while preserving important aspects of the fiber pathways such as fractional anisotropy and the orientation distribution functions.

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.

Geometric analysis of the b-dependent effects of Rician signal noise on diffusion tensor imaging estimates and determining an optimal b value

The optimal diffusion weighting (DW) factor, b, for use in diffusion tensor imaging (DTI) studies remains uncertain. In this study, the geometric relations of DW quantities are examined, in particular, the effects of Rician noise in the measured magnetic resonance signal. This geometric analysis is used to make theoretical predictions for selecting a b value to reduce the influence of noise. It is shown that the optimal b value for DTI studies in healthy human parenchyma is approximately b=1200 s mm(-2), with a simple relation given as well for a given expected apparent diffusion coefficient. Monte-Carlo simulations on sets of realistic DTI measures are then performed, verifying the optimal DW for minimizing estimate errors. The effects of noise on various DTI parameters such as anisotropy indices (fractional anisotropy and scaled relative anisotropy), mean diffusivity, radial diffusivity, eigenvalues and the direction of the first eigenvector are investigated as well.

Evaluation of corticospinal tract impairment in the brain of patients with amyotrophic lateral sclerosis by using diffusion tensor imaging acquisition schemes with different numbers of diffusion-weighting directions

Amyotrophic lateral sclerosis is characterized by degeneration of upper and lower motor neurons. Diffusion tensor imaging (DTI) indexes obtained along the corticospinal tracts distinguish ALS patients and control subjects. Diffusion tensor imaging can be estimated from at least 6 diffusion-weighted images; however an acquisition scheme with a higher number of diffusion directions allows a more robust estimation of DTI indexes. The aim of the study was to establish if a higher number of diffusion encoding gradients increases the diagnostic accuracy of DTI in ALS. We studied 18 patients and 16 control subjects acquiring 2 DTI data sets with 6 and 31 gradient orientations. The mean diffusivity and fractional anisotropy values were measured along the corticospinal tract. Mean diffusivity in ALS was significantly increased (P = 0.026) with respect to control subjects in acquisition scheme with 31 but not (P = 0.214) with 6 diffusion-weighting directions. Fractional anisotropy was significantly lower in patients both with 6 (P = 0.0036) and with 31 (P = 0.0004) diffusion-weighting directions (0.538 vs 0.588 and 0.530 vs 0.594). Fractional anisotropy receiver operating characteristic curve analysis showed a higher diagnostic accuracy by using 31 diffusion-weighting direction (85.76%) with respect to 6 directions (79.86%). Diffusion tensor imaging confirms its potentials in diagnosing ALS with a good accuracy; the acquisition scheme with a higher diffusion-weighting directions seems to better discriminate between ALS patients and control subjects.

Integrity of the hippocampus and surrounding white matter is correlated with language training success in aphasia

Aphasia after middle cerebral artery (MCA) stroke shows highly variable degrees of recovery. One possible explanation may be offered by the variability of the occlusion location. Branches from the proximal portion of the MCA often supply the mesial temporal lobe including parts of the hippocampus, a structure known to be involved in language learning. Therefore, we assessed whether language recovery in chronic aphasia is dependent on the proximity of the MCA infarct and correlated with the integrity of the hippocampus and its surrounding white matter. Language reacquisition capability was determined after 2weeks of intensive language therapy and 8months after treatment in ten chronic aphasia patients. Proximity of MCA occlusion relative to the internal carotid artery was determined by magnetic resonance imaging (MRI) based on the most proximal anatomical region infarcted. Structural damage to the hippocampus was assessed by MRI-based volumetry, regional microstructural integrity of hippocampus adjacent white matter by fractional anisotropy. Language learning success for trained materials was correlated with the proximity of MCA occlusion, microstructural integrity of the left hippocampus and its surrounding white matter, but not with lesion size, overall microstructural brain integrity and a control region outside of the MCA territory. No correlations were found for untrained language materials, underlining the specificity of our results for training-induced recovery. Our results suggest that intensive language therapy success in chronic aphasia after MCA stroke is critically dependent on damage to the hippocampus and its surrounding structures.

White matter abnormalities in bipolar disorder: insights from diffusion tensor imaging studies

Diffusion tensor imaging (DTI) is a neuroimaging technique with the potential to elucidate white matter abnormalities. Recently, it has been applied to help in better understanding of the pathophysiology of bipolar disorder (BD). This review sought to synthesise existing literature on DTI studies in BD, summarise current findings and highlight brain regions that have consistently been implicated in BD, as well as posit possible future directions for DTI research in BD. The extant findings from this review suggest loss of white matter network connectivity as a possible phenomenon associated with bipolar disorder, involving prefrontal and frontal regions, projection, associative and commissural fibres, with sparse and less consistent evidence implicating the subcortical and non-frontal lobes of the brain. There are some differences in the direction of changes observed in white matter indices, and these may be attributed to factors including sample heterogeneity and limitations of DTI techniques. The possible roles of the parietal, temporal and occipital lobes and subcortical regions in BD await further investigation. Studies of bipolar disorder using DTI lag behind other neuropsychiatric diseases such as schizophrenia, but DTI research in BD is fast gaining pace. The emerging trends from these DTI findings underscore the importance of further research to unravel the underlying neural mechanisms and clinico-anatomical correlations involving white matter in BD.

Dependence of brain DTI maps of fractional anisotropy and mean diffusivity on the number of diffusion weighting directions

The rotational variance dependence of diffusion tensor imaging (DTI) derived parameters on the number of diffusion weighting directions (N) has been investigated by several Monte Carlo simulation studies. However, the dependence of fractional anisotropy (FA) and mean diffusivity (MD) maps on N, in terms of accuracy and contrast between different anatomical structures, has not been assessed in detail. This experimental study further investigated in vivo the effect of the number of diffusion weighting directions on DTI maps of FA and MD. Human brain FA and MD maps of six healthy subjects were acquired at 1.5T with varying N (6, 11, 19, 27, 55). Then, FA and MD mean values in high (FAH,MDH) and low (FAL,MDL) anisotropy segmented brain regions were measured. Moreover, the contrast‐to‐signal variance ratio (CVRFA,CVRMD) between the main white matter and the surrounding regions was calculated. Analysis of variance showed that FAL,FAH and CVRFA significantly (p<0.05) depend on N. In particular, FAL decreased (6%–11%) with N, whereas FAH (1.6%–2.5%) and CVRFA (4%–6.5%) increased with N.MDL,MDH and CVRMD did not significantly (p>0.05) depend on N. Unlike MD values, FA values significantly vary with N. It is noteworthy that the observed variation is opposite in low and high anisotropic regions. In clinical studies, the effect of N may represent a confounding variable for anisotropy measurements and the employment of DTI acquisition schemes with high N(>20) allows an increased CVR and a better visualization of white matter structures in FA maps.

PACS number: 87.61.Tg, 82.56.Lz

Robust correction of spike noise: application to diffusion tensor imaging

Echo-planar imaging (EPI) -based diffusion tensor imaging (DTI) is particularly prone to spike noise. However, existing spike noise correction methods are impractical for corrupted DTI data because the methods correct the complex MRI signal, which is not usually stored on clinical MRI systems. The present work describes a novel Outlier Detection De-spiking technique (ODD) that consists of three steps: detection, localization, and correction. Using automated outlier detection schemes, ODD exploits the data redundancy available in DTI data sets that are acquired with a minimum of six different diffusion-weighted images (DWIs) with similar signal and noise properties. A mathematical formulation, describing the effects of spike noise on magnitude images, yields appropriate measures for an outlier detection scheme used for spike detection while a normalization-dependent outlier detection scheme is used for spike localization. ODD performs accurately on diverse DTI data sets corrupted by spike noise and can be used for automated control of DTI data quality. ODD can also be extended to other MRI applications with data redundancy, such as dynamic imaging and functional MRI.

Meta-analysis of apparent diffusion coefficients in the newborn brain

Diffusion-weighted imaging and its quantitative apparent diffusion coefficient can assess severity in newborn hypoxic-ischemic injuries. A meta-analysis established normative values in term newborns, in comparison to those values in hypoxic-ischemic newborns with good versus poor outcomes. Measurements from 14 reports were stratified into three levels of increasing specificity: tissue type (gray matter, white matter, or cerebellum), tissue distribution (e.g., cortex or white-matter tracts), and anatomic structures (e.g., frontal white matter or posterior limb of the internal capsule). Normative apparent diffusion coefficients constituted white matter > gray matter = cerebellum, with lowest values in the posterior limb of the internal capsule and thalamus, and the highest in frontal and occipital white matter. Differences between normative and hypoxic-ischemic injury good-outcome groups were not evident. Values in the poor outcome group were significantly lower than normative data in white matter, gray matter, cortical gray matter, white matter tracts, posterior limb of the internal capsule, and cortical, frontal, and occipital white matter. Comparisons between injury groups found that coefficients were only significantly lower in the occipital cortex among poor outcomes. Coefficient values were lower in deep brain compared with cortical structures, reflecting tissue maturation and myelination. Differences between normative and hypoxic-ischemic injury poor-outcome groups suggest pathologies associated with neurologic sequelae. This meta-analysis provides the basis for normative apparent diffusion coefficient values in the newborn brain.

Altered white matter microstructure in adolescent substance users

Chronic marijuana use during adolescence is frequently comorbid with heavy alcohol consumption and associated with CNS alterations, yet the influence of early cannabis and alcohol use on microstructural white matter integrity is unclear. Building on evidence that cannabinoid receptors are present in myelin precursors and affect glial cell processing, and that excessive ethanol exposure is associated with persistently impaired myelination, we used diffusion tensor imaging (DTI) to characterize white matter integrity in heavy substance using and non-using adolescents. We evaluated 36 marijuana and alcohol-using (MJ+ALC) adolescents (ages 16-19) and 36 demographically similar non-using controls with DTI. The diffusion parameters fractional anisotropy (FA) and mean diffusivity (MD) were subjected to whole-brain voxelwise group comparisons using tract-based spatial statistics (Smith, S.M., Jenkinson, M., Johansen-Berg, H., Rueckert, D., Nichols, T.E., Mackay, C.E., Watkins, K.E., Ciccarelli, O., Cader, M.Z., Matthews, P.M., Behrens, T.E., 2006. Tract-based spatial statistics: voxelwise analysis of multi-subject diffusion data. Neuroimage 31, 1487-1505). MJ+ALC teens had significantly lower FA than controls in 10 regions, including left superior longitudinal fasciculus (SLF), left postcentral gyrus, bilateral crus cerebri, and inferior frontal and temporal white matter tracts. These diminutions occurred in the context of increased FA in right occipital, internal capsule, and SLF regions. Changes in MD were less distributed, but increased MD was evident in the right occipital lobe, whereas the left inferior longitudinal fasciculus showed lower MD in MJ+ALC users. Findings suggest that fronto-parietal circuitry may be particularly impacted in adolescent users of the most prevalent intoxicants: marijuana and alcohol. Disruptions to white matter in this young group could indicate aberrant axonal and myelin maturation with resultant compromise of fiber integrity. Findings of increased anisotropic diffusion in alternate brain regions suggest possible neuroadaptive processes and can be examined in future studies of connectivity to determine how aberrancies in specific tracts might influence efficient cognitive processing.

Assessing and minimizing the effects of noise and motion in clinical DTI at 3 T

Compared with conventional MRI, diffusion tensor imaging (DTI) is more prone to thermal noise and motion. Optimized sampling schemes have been proposed that reduce the propagation of noise. At 3 T, however, motion may play a more dominant role than noise. Although the effects of noise at 3 T are less compared with 1.5 T because of the higher signal-to-noise ratio, motion is independent of field strength and will persist. To improve the reliability of clinical DTI at 3 T, it is important to know to what extent noise and motion contribute to the uncertainties of the DTI indices. In this study, the effects of noise- and motion-related signal uncertainties are disentangled using in vivo measurements and computer simulations. For six clinically standard available sampling schemes, the reproducibility was assessed in vivo, with and without motion correction applied. Additionally, motion and noise simulations were performed to determine the relative contributions of motion and noise to the uncertainties of the mean diffusivity (MD) and fractional anisotropy (FA). It is shown that the contributions of noise and motion are of the same order of magnitude at 3 T. Similar to the propagation of noise, the propagation of motion-related signal perturbations is also influenced by the choice of sampling scheme. Sampling schemes with only six diffusion directions demonstrated a lower reproducibility compared with schemes with 15 and 32 directions and feature a positive bias for the FA in relatively isotropic tissue. Motion correction helps improving the precision and accuracy of DTI indices.

Regression Models for Identifying Noise Sources in Magnetic Resonance Images

Stochastic noise, susceptibility artifacts, magnetic field and radiofrequency inhomogeneities, and other noise components in magnetic resonance images (MRIs) can introduce serious bias into any measurements made with those images. We formally introduce three regression models including a Rician regression model and two associated normal models to characterize stochastic noise in various magnetic resonance imaging modalities, including diffusion-weighted imaging (DWI) and functional MRI (fMRI). Estimation algorithms are introduced to maximize the likelihood function of the three regression models. We also develop a diagnostic procedure for systematically exploring MR images to identify noise components other than simple stochastic noise, and to detect discrepancies between the fitted regression models and MRI data. The diagnostic procedure includes goodness-of-fit statistics, measures of influence, and tools for graphical display. The goodness-of-fit statistics can assess the key assumptions of the three regression models, whereas measures of influence can isolate outliers caused by certain noise components, including motion artifacts. The tools for graphical display permit graphical visualization of the values for the goodness-of-fit statistic and influence measures. Finally, we conduct simulation studies to evaluate performance of these methods, and we analyze a real dataset to illustrate how our diagnostic procedure localizes subtle image artifacts by detecting intravoxel variability that is not captured by the regression models.

Rey Visual Design Learning Test performance correlates with white matter structure

OBJECTIVE

Studies exploring relation of visual memory to white matter are extensively lacking. The Rey Visual Design Learning Test (RVDLT) is an elementary motion, colour and word independent visual memory test. It avoids a significant contribution from as many additional higher order visual brain functions as possible to visual performance, such as three-dimensional, colour, motion or word-dependent brain operations. Based on previous results, we hypothesised that test performance would be related with white matter of dorsal hippocampal commissure, corpus callosum, posterior cingulate, superior longitudinal fascicle and internal capsule.

METHODS

In 14 healthy subjects, we measured intervoxel coherence (IC) by diffusion tensor imaging as an indication of connectivity and visual memory performance measured by the RVDLT. IC considers the orientation of the adjacent voxels and has a better signal-to-noise ratio than the commonly used fractional anisotropy index.

RESULTS

Using voxelwise linear regression analyses of the IC values, we found a significant and direct relationship between 11 clusters and visual memory test performance. The fact that memory performance correlated with white matter structure in left and right dorsal hippocampal commissure, left and right posterior cingulate, right callosal splenium, left and right superior longitudinal fascicle, right medial orbitofrontal region, left anterior cingulate, and left and right anterior limb of internal capsule emphasises our hypothesis.

CONCLUSION

Our observations in healthy subjects suggest that individual differences in brain function related to the performance of a task of higher cognitive demands might partially be associated with structural variation of white matter regions.

The ellipsoidal area ratio: an alternative anisotropy index for diffusion tensor imaging

In the processing and analysis of diffusion tensor imaging (DTI) data, certain predefined morphological features of diffusion tensors are often represented as simplified scalar indices, termed diffusion anisotropy indices (DAIs). When comparing tensor morphologies across differing voxels of an image, or across corresponding voxels in different images, DAIs are mathematically and statistically more tractable than are the full tensors, which are probabilistic ellipsoids consisting of three orthogonal vectors that each has a direction and an associated scalar magnitude. We have developed a new DAI, the "ellipsoidal area ratio" (EAR), to represent the degree of anisotropy in the morphological features of a diffusion tensor. The EAR is a normalized geometrical measure of surface curvature in the 3D diffusion ellipsoid. Monte Carlo simulations and applications to the study of in vivo human data demonstrate that, at low noise levels, EAR provides a similar contrast-to-noise ratio (CNR) but a higher signal-to-noise ratio (SNR) than does fractional anisotropy (FA), which is currently the most popular anisotropy index in active use. Moreover, at the high noise levels encountered most commonly in real-world DTI datasets, EAR compared with FA is consistently much more robust to perturbations from noise and it provides a higher CNR, features useful for the analysis of DTI data that are inherently noise sensitive.

Characterizing fiber directional uncertainty in diffusion tensor MRI

Image noise in diffusion tensor MRI (DT-MRI) causes errors in the measured tensor and hence variance in the estimated fiber orientation. Uncertainty in fiber orientation has been described using a circular "cone of uncertainty" (CU) around the principal eigenvector of the DT. The CU has proved to be a useful construct for quantifying and visualizing the variability of DT-MRI parameters and fiber tractography. The assumption of circularity of the CU has not been tested directly, however. In this work, bootstrap analysis and simple theoretical arguments were used to show that the CU is elliptical and multivariate normal in the vast majority of white matter (WM) voxels for typical measurement conditions. The dependence of the cone angle on the signal-to-noise ratio (SNR) and eigenvalue contrast was established. The major and minor cone axes are shown to be coincident with the second and third eigenvectors of the tensor, respectively, in the limit of many uniformly spaced diffusion-encoding directions. The deviation between the major cone axis and the second eigenvector was quantified for typical sets of diffusion-weighting (DW) directions. The elliptical CU provides more realistic error information for fiber-tracking algorithms and a quantitative basis for selecting DT imaging acquisition protocols.

Diffusion-tensor neuronal fiber tractography and manganese-enhanced MR imaging of primate visual pathway in the common marmoset: preliminary results

PURPOSE

To investigate whether diffusion-tensor tractography (DTT) of neuronal fibers is useful for delineating the configuration of the neuronal fiber trajectories in the primate visual pathway, including the well-developed optic chiasm, in comparison with tract tracing at manganese-enhanced magnetic resonance (MR) imaging.

MATERIALS AND METHODS

The handling methods used for all the animals in this study were approved by the institutional committee for animal experiments. Diffusion-tensor MR imaging was performed in four healthy common marmosets, and in two of these animals, manganese-enhanced MR imaging tract tracing was performed by using a 7.0-T MR imaging unit. The visual pathways were quantitatively investigated in terms of the manganese distribution observed on the manganese-enhanced MR images. The images obtained with DTT and manganese-enhanced MR imaging tract tracing were qualitatively compared, and the features of the visual pathway were verified through fusion of the reconstructed images obtained by using these two modalities.

RESULTS

DTT provided information regarding the neuroanatomic features of the marmoset visual pathway and revealed the bilateral branching patterns of the typical primate retinogeniculate pathways, although several incorrectly tracked fibers were noted. The distribution of manganese on the manganese-enhanced MR images revealed bilateral innervation of the retinal projections and depicted the layered internal structure of the lateral geniculate nuclei bilaterally, depending on the ocularity of each layer. These morphologic findings were consistent with those of previous histopathologic studies.

CONCLUSION

The findings of this preliminary study raise the possibility that DTT is useful for visualizing the neuronal fiber trajectories in primate visual pathways.

SUPPLEMENTAL MATERIAL

http://radiology.rsnajnls.org/cgi/content/full/249/3/855/DC1.

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.

Functional diffusion tensor imaging: measuring task-related fractional anisotropy changes in the human brain along white matter tracts

Background

Functional neural networks in the human brain can be studied from correlations between activated gray matter regions measured with fMRI. However, while providing important information on gray matter activation, no information is gathered on the co-activity along white matter tracts in neural networks.

Methodology/Principal Findings

We report on a functional diffusion tensor imaging (fDTI) method that measures task-related changes in fractional anisotropy (FA) along white matter tracts. We hypothesize that these fractional anisotropy changes relate to morphological changes of glial cells induced by axonal activity although the exact physiological underpinnings of the measured FA changes remain to be elucidated. As expected, these changes are very small as compared to the physiological noise and a reliable detection of the signal change would require a large number of measurements. However, a substantial increase in signal-to-noise ratio was achieved by pooling the signal over the complete fiber tract. Adopting such a tract-based statistics enabled us to measure the signal within a practically feasible time period. Activation in the sensory thalamocortical tract and optic radiation in eight healthy human subjects was found during tactile and visual stimulation, respectively.

Conclusions/Significance

The results of our experiments indicate that these FA changes may serve as a functional contrast mechanism for white matter. This noninvasive fDTI method may provide a new approach to study functional neural networks in the human brain.

On the effects of dephasing due to local gradients in diffusion tensor imaging experiments: relevance for diffusion tensor imaging fiber phantoms

The effect of susceptibility differences between fluid and fibers on the properties of DTI fiber phantoms was investigated. Thereto, machine-made, easily producible and inexpensive DTI fiber phantoms were constructed by winding polyamide fibers of 15 microm diameter around a circular acrylic glass spindle. The achieved fractional anisotropy was 0.78+/-0.02. It is shown by phantom measurements and Monte Carlo simulations that the transversal relaxation time T(2) strongly depends on the angle between the fibers and the B(0) field if the susceptibilities of the fibers and fluid are not identical. In the phantoms, the measured T(2) time at 3 T decreased by 60% for fibers running perpendicular to B(0). Monte Carlo simulations confirmed this result and revealed that the exact relaxation time depends strongly on the exact packing of the fibers. In the phantoms, the measured diffusion was independent of fiber orientation. Monte Carlo simulations revealed that the measured diffusion strongly depends on the exact fiber packing and that field strength and -orientation dependencies of measured diffusion may be minimal for hexagonal packing while the diffusion can be underestimated by more than 50% for cubic packing at 3 T. To overcome these effects, the susceptibilities of fibers and fluid were matched using an aqueous sodium chloride solution (83 g NaCl per kilogram of water). This enables an orientation independent and reliable use of DTI phantoms for evaluation purposes.

Using the wild bootstrap to quantify uncertainty in diffusion tensor imaging

Estimation of noise-induced variability in diffusion tensor imaging (DTI) is needed to objectively follow disease progression in therapeutic monitoring and to provide consistent readouts of pathophysiology. The noise variability of nonlinear quantities of the diffusion tensor (e.g., fractional anisotropy, fiber orientation, etc.) have been quantified using the bootstrap, in which the data are resampled from the experimental averages, yet this approach is only applicable to DTI scans that contain multiple averages from the same sampling direction. It has been shown that DTI acquisitions with a modest to large number of directions, in which each direction is only sampled once, outperform the multiple averages approach. These acquisitions resist the traditional (regular) bootstrap analysis though. In contrast to the regular bootstrap, the wild bootstrap method can be applied to such protocols in which there is only one observation per direction. Here, we compare and contrast the wild bootstrap with the regular bootstrap using Monte Carlo numerical simulations for a number of diffusion scenarios. The regular and wild bootstrap methods are applied to human DTI data and empirical distributions are obtained for fractional anisotropy and the diffusion tensor eigensystem. Spatial maps of the estimated variability in the diffusion tensor principal eigenvector are provided. The wild bootstrap method can provide empirical distributions for tensor-derived quantities, such as fractional anisotropy and principal eigenvector direction, even when the exact distributions are not easily derived.

Maximum a posteriori estimation of diffusion tensor parameters using a Rician noise model: why, how and but

The diffusion tensor is a commonly used model for diffusion-weighted MR image data. The parameters are typically estimated by ordinary or weighted least squares on log-transformed data, assuming normal or log-normal distribution of measurement errors respectively. This may not be adequate when using high b-values and or performing high-resolution scans, resulting in poor SNR, in which case the difference between the assumed and the true (Rician) noise model becomes important. As a consequence the estimated diffusion parameters will be biased, underestimating the true diffusion. In this paper a computational framework is presented where parameters pertaining to a spectral decomposition of the diffusion tensor are estimated using a Rician noise model. The parameters are estimated using a Fisher-scoring scheme which gives robust and rapid convergence. It is demonstrated how the Fisher-information matrix can be used as a generic tool for designing optimal experiments. It is shown that the Rician noise model leads to significantly less biased estimates for a large range of b-values and SNR, but that the Rician estimates have a poorer precision compared to the Gaussian model for very low SNR. By pooling the Rician estimates of uncertainty over neighbouring voxel estimates with higher precision, but still not as high as with a Gaussian model, can be obtained. We suggest the use of a Rician estimator when it is important with truly quantitative values and when comparing different predictive models. The higher precision of the Gaussian estimates may be more important when the objective is to compare diffusion related parameters over time or across groups.

Towards in vivo diffusion tensor MRI on human heart using edge-preserving regularization

We investigate the noise sensitivity in various Diffusion Tensor MRI acquisition protocols in sixteen human ex vivo hearts. In particular, we compare the accuracy of protocols with various numbers of excitations and diffusion sensitizing directions for estimating the principal diffusion directions in the myocardium. It is observed that noise sensitivity decreases as the number of excitations and the number of sensitizing directions increase (and hence as the acquisition time increases). To reduce the effects of noise and to improve the results obtained with a smaller number of excitations and/or a smaller number of sensitizing directions, we introduce a 3-D edge-preserving regularization method operating on diffusion weighted images. It allows to maintain the quality of the principal diffusion direction field while minimizing the acquisition time, which is a necessary step for in vivo diffusion tensor MR imaging of the human heart.

On diffusion tensor estimation

In this paper we propose a formal formulation for the estimation of Diffusion Tensors in the space of symmetric positive semidefinite (PSD) tensors. Traditionally, diffusion tensor model estimation has been carried out imposing tensor symmetry without constraints for negative eigenvalues. When diffusion weighted data does not follow the diffusion model, due to noise or signal drop, negative eigenvalues may arise. An estimation method that accounts for the positive definiteness is desirable to respect the underlying principle of diffusion. This paper proposes such an estimation method and provides a theoretical interpretation of the result. A closed-form solution is derived that is the optimal data-fit in the matrix 2-norm sense, removing the need for optimization-based tensor estimation.

Whole brain voxel-wise analysis of single-subject serial DTI by permutation testing

Diffusion tensor MRI (DTI) has been widely used to investigate brain microstructural changes in pathological conditions as well as for normal development and aging. In particular, longitudinal changes are vital to the understanding of progression but these studies are typically designed for specific regions of interest. To analyze changes in these regions traditional statistical methods are often employed to elucidate group differences which are measured against the variability found in a control cohort. However, in some cases, rather than collecting multiple subjects into two groups, it is necessary and more informative to analyze the data for individual subjects. There is also a need for understanding changes in a single subject without prior information regarding the spatial distribution of the pathology, but no formal statistical framework exists for these voxel-wise analyses of DTI. In this study, we present PERVADE (permutation voxel-wise analysis of diffusion estimates), a whole brain analysis method for detecting localized FA changes between two separate points in time of any given subject, without any prior hypothesis about where changes might occur. Exploiting the nature of DTI that it is calculated from multiple diffusion-weighted images of each region, permutation testing, a non-parametric hypothesis testing technique, was modified for the analysis of serial DTI data and implemented for voxel-wise hypothesis tests of diffusion metric changes, as well as for suprathreshold cluster analysis to correct for multiple comparisons. We describe PERVADE in detail and present results from Monte Carlo simulation supporting the validity of the technique as well as illustrative examples from a healthy subject and patients in the early stages of multiple sclerosis.

Clinical DT-MRI estimation, smoothing, and fiber tracking with log-Euclidean metrics

Diffusion tensor magnetic resonance imaging (DT-MRI or DTI) is an imaging modality that is gaining importance in clinical applications. However, in a clinical environment, data have to be acquired rapidly, often at the expense of the image quality. This often results in DTI datasets that are not suitable for complex postprocessing like fiber tracking. We propose a new variational framework to improve the estimation of DT-MRI in this clinical context. Most of the existing estimation methods rely on a log-Gaussian noise (Gaussian noise on the image logarithms), or a Gaussian noise, that do not reflect the Rician nature of the noise in MR images with a low signal-to-noise ratio (SNR). With these methods, the Rician noise induces a shrinking effect: the tensor volume is underestimated when other noise models are used for the estimation. In this paper, we propose a maximum likelihood strategy that fully exploits the assumption of a Rician noise. To further reduce the influence of the noise, we optimally exploit the spatial correlation by coupling the estimation with an anisotropic prior previously proposed on the spatial regularity of the tensor field itself, which results in a maximum a posteriori estimation. Optimizing such a nonlinear criterion requires adapted tools for tensor computing. We show that Riemannian metrics for tensors, and more specifically the log-Euclidean metrics, are a good candidate and that this criterion can be efficiently optimized. Experiments on synthetic data show that our method correctly handles the shrinking effect even with very low SNR, and that the positive definiteness of tensors is always ensured. Results on real clinical data demonstrate the truthfulness of the proposed approach and show promising improvements of fiber tracking in the brain and the spinal cord.

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.