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

Log-Cholesky filtering of diffusion tensor fields: Impact on noise reduction

Diffusion tensor imaging (DTI) is a powerful neuroimaging technique that provides valuable insights into the microstructure and connectivity of the brain. By measuring the diffusion of water molecules along neuronal fibers, DTI allows the visualization and study of intricate networks of neural pathways. DTI is a noise-sensitive method, where a low signal-to-noise ratio (SNR) results in significant errors in the estimated tensor field. Tensor field regularization is an effective solution for noise reduction. Diffusion tensors are represented by symmetric positive-definite (SPD) matrices. The space of SPD matrices may be viewed as a Riemannian manifold after defining a suitable metric on its tangent bundle. The Log-Cholesky metric is a recently developed concept with advantages over previously defined Riemannian metrics, such as the affine-invariant and Log-Euclidean metrics. The utility of the Log-Cholesky metric for tensor field regularization and noise reduction has not been investigated in detail. This manuscript provides a quantitative investigation of the impact of Log-Cholesky filtering on noise reduction in DTI. It also provides sufficient details of the linear algebra and abstract differential geometry concepts necessary to implement this technique as a simple and effective solution to filtering diffusion tensor fields.

Structural Brain Connectivity and Treatment Improvement in Mood Disorder

Background: The treatment of depressive episodes is well established, with clearly demonstrated effectiveness of antidepressants and psychotherapies. However, more than one-third of depressed patients do not respond to treatment. Identifying the brain structural basis of treatment-resistant depression could prevent useless pharmacological prescriptions, adverse events, and lost therapeutic opportunities. Methods: Using diffusion magnetic resonance imaging, we performed structural connectivity analyses on a cohort of 154 patients with mood disorder (MD) and 77 sex- and age-matched healthy control (HC) participants. To assess illness improvement, the patients with MD went through two clinical interviews at baseline and at 6-month follow-up and were classified based on the Clinical Global Impression-Improvement score into improved or not-improved (NI). First, the threshold-free network-based statistics (NBS) was conducted to measure the differences in regional network architecture. Second, nonparametric permutations tests were performed on topological metrics based on graph theory to examine differences in connectome organization. Results: The threshold-free NBS revealed impaired connections involving regions of the basal ganglia in patients with MD compared with HC. Significant increase of local efficiency and clustering coefficient was found in the lingual gyrus, insula, and amygdala in the MD group. Compared with the NI, the improved displayed significantly reduced network integration and segregation, predominately in the default-mode regions, including the precuneus, middle temporal lobe, and rostral anterior cingulate. Conclusions: This study highlights the involvement of regions belonging to the basal ganglia, the fronto-limbic network, and the default mode network, leading to a better understanding of MD disease and its unfavorable outcome.

Regularization of dielectric tensor tomography

Dielectric tensor tomography reconstructs the three-dimensional dielectric tensors of microscopic objects and provides information about the crystalline structure orientations and principal refractive indices. Because dielectric tensor tomography is based on transmission measurement, it suffers from the missing cone problem, which causes poor axial resolution, underestimation of the refractive index, and halo artifacts. In this study, we study the application of total variation and positive semi-definiteness regularization to three-dimensional tensor distributions. In particular, we demonstrate the reduction of artifacts when applied to dielectric tensor tomography.

What's new and what's next in diffusion MRI preprocessing

Diffusion MRI (dMRI) provides invaluable information for the study of tissue microstructure and brain connectivity, but suffers from a range of imaging artifacts that greatly challenge the analysis of results and their interpretability if not appropriately accounted for. This review will cover dMRI artifacts and preprocessing steps, some of which have not typically been considered in existing pipelines or reviews, or have only gained attention in recent years: brain/skull extraction, B-matrix incompatibilities w.r.t the imaging data, signal drift, Gibbs ringing, noise distribution bias, denoising, between- and within-volumes motion, eddy currents, outliers, susceptibility distortions, EPI Nyquist ghosts, gradient deviations, B1 bias fields, and spatial normalization. The focus will be on "what's new" since the notable advances prior to and brought by the Human Connectome Project (HCP), as presented in the predecessing issue on "Mapping the Connectome" in 2013. In addition to the development of novel strategies for dMRI preprocessing, exciting progress has been made in the availability of open source tools and reproducible pipelines, databases and simulation tools for the evaluation of preprocessing steps, and automated quality control frameworks, amongst others. Finally, this review will consider practical considerations and our view on "what's next" in dMRI preprocessing.

Categorical Smoothness of 4-Manifolds from Quantum Symmetries and the Information Loss Paradox

In this paper, we focus on some aspects of the relation of spacetime and quantum mechanics and the study counterparts (in Set) of the categorical local symmetries of smooth 4-manifolds. In the set-theoretic limit, there emerge some exotic smoothness structures on R4 (hence the Riemannian nonvanishing curvature), which fit well with the quantum mechanical lattice of projections on infinite-dimensional Hilbert spaces. The method we follow is formalization localized on the open covers of the spacetime manifold. We discuss our findings in the context of the information paradox assigned to evaporating black holes. A black hole can evaporate entirely, but the smoothness structure of spacetime will be altered and, in this way, the missing information about the initial states of matter forming the black hole will be encoded. Thus, the possible global geometric remnant of black holes in spacetime is recognized as exotic 4-smoothness. The full-fledged verification of this proposal will presumably be possible within the scope of future quantum gravity theory research.

Geodesic Uncertainty in Diffusion MRI

We study theoretical and operational issues of geodesic tractography, a geometric methodology for retrieving biologically plausible neural fibers in the brain from diffusion weighted magnetic resonance imaging. The premise is that true positives are geodesics in a suitably constructed metric space, but unlike traditional first order methods these are not a priori constrained to connect nongeneric points on subdimensional manifolds, such as the characteristics in traditional streamline methods. By virtue of the Hopf-Rinow theorem geodesic tractography furnishes a huge amount of redundancy, ensuring the a priori existence of at least one tentative fiber between any two points and permitting additional tractometric and data-extrinsic constraints for (fuzzy or crisp) classification of true and false positives. In our feasibility study we consider a hybrid paradigm that unifies existing ideas on tractography, combining deterministic and probabilistic elements in a way naturally supported by metric geometry. Particular attention is paid to an analytical prediction of geodesic deviation on numerically computed geodesics, a ‘tidal’ effect induced by small perturbations resulting from data noise. Taking these effects into account clarifies the inherent uncertainty of geodesics, while simultaneosuly offering a dimensionality reduction of the tractography problem.

WIKIBrainStem: An online atlas to manually segment the human brainstem at the mesoscopic scale from ultrahigh field MRI

The brainstem is one of the most densely packed areas of the central nervous system in terms of gray, but also white, matter structures and, therefore, is a highly functional hub. It has mainly been studied by the means of histological techniques, which requires several hundreds of slices with a loss of the 3D coherence of the whole specimen. Access to the inner structure of the brainstem is possible using Magnetic Resonance Imaging (MRI), but this method has a limited spatial resolution and contrast in vivo. Here, we scanned an ex vivo specimen using an ultra-high field (11.7T) preclinical MRI scanner providing data at a mesoscopic scale for anatomical T2-weighted (100 µm and 185 µm isotropic) and diffusion-weighted imaging (300 µm isotropic). We then proposed a hierarchical segmentation of the inner gray matter of the brainstem and defined a set of rules for each segmented anatomical class. These rules were gathered in a freely accessible web-based application, WIKIBrainStem (https://fibratlas.univ-tours.fr/brainstems/index.html), for 99 structures, from which 13 were subdivided into 29 substructures. This segmentation is, to date, the most detailed one developed from ex vivo MRI of the brainstem. This should be regarded as a tool that will be complemented by future results of alternative methods, such as Optical Coherence Tomography, Polarized Light Imaging or histology… This is a mandatory step prior to segmenting multiple specimens, which will be used to create a probabilistic automated segmentation method of ex vivo, but also in vivo, brainstem and may be used for targeting anatomical structures of interest in managing some degenerative or psychiatric disorders.

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.

The ventral attention network: the mirror of the language network in the right brain hemisphere

Resting-state functional MRI (RfMRI) analyses have identified two anatomically separable fronto-parietal attention networks in the human brain: a bilateral dorsal attention network and a right-lateralised ventral attention network (VAN). The VAN has been implicated in visuospatial cognition and, thus, potentially in the unilateral spatial neglect associated with right hemisphere lesions. Its parietal, frontal and temporal endpoints are thought to be structurally supported by undefined white matter tracts. We investigated the white matter tract connecting the VAN. We used three approaches to study the structural anatomy of the VAN: (a) independent component analysis on RfMRI (50 subjects), defining the endpoints of the VAN, (b) tractography in the same 50 healthy volunteers, with regions of interest defined by the MNI coordinates of cortical areas involved in the VAN used in a seed-based approach and (c) dissection, by Klingler's method, of 20 right hemispheres, for ex vivo studies of the fibre tracts connecting VAN endpoints. The VAN includes the temporoparietal junction and the ventral frontal cortex. The endpoints of the superior longitudinal fasciculus in its third portion (SLF III) and the arcuate fasciculus (AF) overlap with the VAN endpoints. The SLF III connects the supramarginal gyrus to the ventral portion of the precentral gyrus and the pars opercularis. The AF connects the middle and inferior temporal gyrus and the middle and inferior frontal gyrus. We reconstructed the structural connectivity of the VAN and considered it in the context if the pathophysiology of unilateral neglect and right hemisphere awake brain surgery.

Denoise magnitude diffusion magnetic resonance images via variance-stabilizing transformation and optimal singular-value manipulation

Although shown to have a great utility for a wide range of neuroscientific and clinical applications, diffusion-weighted magnetic resonance imaging (dMRI) faces a major challenge of low signal-to-noise ratio (SNR), especially when pushing the spatial resolution for improved delineation of brain's fine structure or increasing the diffusion weighting for increased angular contrast or both. Here, we introduce a comprehensive denoising framework for denoising magnitude dMRI. The framework synergistically combines the variance stabilizing transform (VST) with optimal singular value manipulation. The purpose of VST is to transform the Rician data to Gaussian-like data so that an asymptotically optimal singular value manipulation strategy tailored for Gaussian data can be used. The output of the framework is the estimated underlying diffusion signal for each voxel in the image domain. The usefulness of the proposed framework for denoising magnitude dMRI is demonstrated using both simulation and real-data experiments. Our results show that the proposed denoising framework can significantly improve SNR across the entire brain, leading to substantially enhanced performances for estimating diffusion tensor related indices and for resolving crossing fibers when compared to another competing method. More encouragingly, the proposed method when used to denoise a single average of 7 ​Tesla Human Connectome Project-style diffusion acquisition provided comparable performances relative to those achievable with ten averages for resolving multiple fiber populations across the brain. As such, the proposed denoising method is expected to have a great utility for high-quality, high-resolution whole-brain dMRI, desirable for many neuroscientific and clinical applications.

Statistical model for dynamically-changing correlation matrices with application to brain connectivity

BACKGROUND

Recent studies have indicated that functional connectivity is dynamic even during rest. A common approach to modeling the dynamic functional connectivity in whole-brain resting-state fMRI is to compute the correlation between anatomical regions via sliding time windows. However, the direct use of the sample correlation matrices is not reliable due to the image acquisition and processing noises in resting-sate fMRI.

NEW METHOD

To overcome these limitations, we propose a new statistical model that smooths out the noise by exploiting the geometric structure of correlation matrices. The dynamic correlation matrix is modeled as a linear combination of symmetric positive-definite matrices combined with cosine series representation. The resulting smoothed dynamic correlation matrices are clustered into disjoint brain connectivity states using the k-means clustering algorithm.

RESULTS

The proposed model preserves the geometric structure of underlying physiological dynamic correlation, eliminates unwanted noise in connectivity and obtains more accurate state spaces. The difference in the estimated dynamic connectivity states between males and females is identified.

COMPARISON WITH EXISTING METHODS

We demonstrate that the proposed statistical model has less rapid state changes caused by noise and improves the accuracy in identifying and discriminating different states.

CONCLUSIONS

We propose a new regression model on dynamically changing correlation matrices that provides better performance over existing windowed correlation and is more reliable for the modeling of dynamic connectivity.

Advances in computational and statistical diffusion MRI

Computational methods are crucial for the analysis of diffusion magnetic resonance imaging (MRI) of the brain. Computational diffusion MRI can provide rich information at many size scales, including local microstructure measures such as diffusion anisotropies or apparent axon diameters, whole-brain connectivity information that describes the brain's wiring diagram and population-based studies in health and disease. Many of the diffusion MRI analyses performed today were not possible five, ten or twenty years ago, due to the requirements for large amounts of computer memory or processor time. In addition, mathematical frameworks had to be developed or adapted from other fields to create new ways to analyze diffusion MRI data. The purpose of this review is to highlight recent computational and statistical advances in diffusion MRI and to put these advances into context by comparison with the more traditional computational methods that are in popular clinical and scientific use. We aim to provide a high-level overview of interest to diffusion MRI researchers, with a more in-depth treatment to illustrate selected computational advances.

Diffusion MRI fiber tractography of the brain

The ability of fiber tractography to delineate non-invasively the white matter fiber pathways of the brain raises possibilities for clinical applications and offers enormous potential for neuroscience. In the last decade, fiber tracking has become the method of choice to investigate quantitative MRI parameters in specific bundles of white matter. For neurosurgeons, it is quickly becoming an invaluable tool for the planning of surgery, allowing for visualization and localization of important white matter pathways before and even during surgery. Fiber tracking has also claimed a central role in the field of "connectomics," a technique that builds and studies comprehensive maps of the complex network of connections within the brain, and to which significant resources have been allocated worldwide. Despite its unique abilities and exciting applications, fiber tracking is not without controversy, in particular when it comes to its interpretation. As neuroscientists are eager to study the brain's connectivity, the quantification of tractography-derived "connection strengths" between distant brain regions is becoming increasingly popular. However, this practice is often frowned upon by fiber-tracking experts. In light of this controversy, this paper provides an overview of the key concepts of tractography, the technical considerations at play, and the different types of tractography algorithm, as well as the common misconceptions and mistakes that surround them. We also highlight the ongoing challenges related to fiber tracking. While recent methodological developments have vastly increased the biological accuracy of fiber tractograms, one should be aware that, even with state-of-the-art techniques, many issues that severely bias the resulting structural "connectomes" remain unresolved.

Structure Prior Constrained Estimation of Human Cardiac Diffusion Tensors

OBJECTIVE

The purpose of this paper is to increase the accuracy of human cardiac diffusion tensor (DT) estimation in diffusion magnetic resonance imaging (dMRI) with a few diffusion gradient directions.

METHODS

A structure prior constrained (SPC) method is proposed. The method consists in introducing two regularizers in the conventional nonlinear least squares estimator. The two regularizers penalize the dissimilarity between neighboring DTs and the difference between estimated and prior fiber orientations, respectively. A novel numerical solution is presented to ensure the positive definite estimation.

RESULTS

Experiments on ex vivo human cardiac data show that the SPC method is able to well estimate DTs at most voxels, and is superior to state-of-the-art methods in terms of the mean errors of principal eigenvector, second eigenvector, helix angle, transverse angle, fractional anisotropy, and mean diffusivity.

CONCLUSION

The SPC method is a practical and reliable alternative to current denoising- or regularization-based methods for the estimation of human cardiac DT.

SIGNIFICANCE

The SPC method is able to accurately estimate human cardiac DTs in dMRI with a few diffusion gradient directions.

White matter abnormalities in depression: A categorical and phenotypic diffusion MRI study

Mood depressive disorder is one of the most disabling chronic diseases with a high rate of everyday life disability that affects 350 million people around the world. Recent advances in neuroimaging have reported widespread structural abnormalities, suggesting a dysfunctional frontal-limbic circuit involved in the pathophysiological mechanisms of depression. However, a variety of different white matter regions has been implicated and is sought to suffer from lack of reproducibility of such categorical-based biomarkers. These inconsistent results might be attributed to various factors: actual categorical definition of depression as well as clinical phenotype variability. In this study, we 1/ examined WM changes in a large cohort (114 patients) compared to a healthy control group and 2/ sought to identify specific WM alterations in relation to specific depressive phenotypes such as anhedonia (i.e. lack of pleasure), anxiety and psychomotor retardation –three core symptoms involved in depression. Consistent with previous studies, reduced white matter was observed in the genu of the corpus callosum extending to the inferior fasciculus and posterior thalamic radiation, confirming a frontal-limbic circuit abnormality. Our analysis also reported other patterns of increased fractional anisotropy and axial diffusivity as well as decreased apparent diffusion coefficient and radial diffusivity in the splenium of the corpus callosum and posterior limb of the internal capsule. Moreover, a positive correlation between FA and anhedonia was found in the superior longitudinal fasciculus as well as a negative correlation in the cingulum. Then, the analysis of the anxiety and diffusion metric revealed that increased anxiety was associated with greater FA values in genu and splenium of corpus callosum, anterior corona radiata and posterior thalamic radiation. Finally, the motor retardation analysis showed a correlation between increased Widlöcher depressive retardation scale scores and reduced FA in the body and genu of the corpus callosum, fornix, and superior striatum. Through this twofold approach (categorical and phenotypic), this study has underlined the need to move forward to a symptom-based research area of biomarkers, which help to understand the pathophysiology of mood depressive disorders and to stratify precise phenotypes of depression with targeted therapeutic strategies.

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Mood depressive disorder is one of the most disabling chronic disease.

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Past studies of diffusion analysis had found inconsistent results.

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We analyzed white matter integrity in a large cohort of depressed patients.

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We conducted both categorical and dimensional approaches.

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In the future, these biomarkers could help to develop new therapeutic strategies.

Diffusion tensor imaging (DTI) and Tractography of the spinal cord in pediatric population with spinal lipomas: preliminary study

PURPOSE

Diffusion tensor imaging (DTI) allows studying the micro and macro architecture. One of the major challenges in dysraphism is to know the morphologic organization of the spinal cord. In a preliminary work, spinal lipoma was chosen for analyzing the micro-architecture parameters and fiber morphology of the spinal cord by DTI with tractography.

METHODS

Twelve patients (0-8 years) related to spinal lipomas treated between May 2017 and March 2018 were included. Tractography reconstruction of the conus medullaris of 12 patients were obtained using the MedINRIA software. The diffusion parameters have been calculated by Osirix DTImap plugin.

RESULTS

We found a significant difference in the FA (p = 0.024) between two age groups (< 24 months old and > 24 months old). However, no significant differences in the mean values of FA, RD, and MD between the level of the lipoma and the level above were noted. The tractography obtained in each case was coherent with morphologic sequences and reproducible. The conus medullaris was deformed and shifted. Destruction or disorganization of fibers and any passing inside the lipomas was not observed.

CONCLUSIONS

Tractography of the conus medullaris in a very young pediatric population (0-8 years old) with a spinal lipoma is possible, reproductive, and allows visualization of the spinal cord within the dysraphism. Analysis of the FA shows that the presence of a lipoma seems to have an effect on the myelination of the conus medullaris. It is during the probable myelination phase that the majority of symptoms appear. Is the myelination per se the cause?

Microstructural imaging of the human brain with a 'super-scanner': 10 key advantages of ultra-strong gradients for diffusion MRI

The key component of a microstructural diffusion MRI 'super-scanner' is a dedicated high-strength gradient system that enables stronger diffusion weightings per unit time compared to conventional gradient designs. This can, in turn, drastically shorten the time needed for diffusion encoding, increase the signal-to-noise ratio, and facilitate measurements at shorter diffusion times. This review, written from the perspective of the UK National Facility for In Vivo MR Imaging of Human Tissue Microstructure, an initiative to establish a shared 300 mT/m-gradient facility amongst the microstructural imaging community, describes ten advantages of ultra-strong gradients for microstructural imaging. Specifically, we will discuss how the increase of the accessible measurement space compared to a lower-gradient systems (in terms of Δ, b-value, and TE) can accelerate developments in the areas of 1) axon diameter distribution mapping; 2) microstructural parameter estimation; 3) mapping micro-vs macroscopic anisotropy features with gradient waveforms beyond a single pair of pulsed-gradients; 4) multi-contrast experiments, e.g. diffusion-relaxometry; 5) tractography and high-resolution imaging in vivo and 6) post mortem; 7) diffusion-weighted spectroscopy of metabolites other than water; 8) tumour characterisation; 9) functional diffusion MRI; and 10) quality enhancement of images acquired on lower-gradient systems. We finally discuss practical barriers in the use of ultra-strong gradients, and provide an outlook on the next generation of 'super-scanners'.

Exploration of male urethral sphincter complex using diffusion tensor imaging (DTI)-based fiber-tracking

BACKGROUND

Urinary incontinence is a major clinical problem arising primarily from age-related degenerative changes to the sphincter muscles. However, the precise anatomy of the normal male sphincter muscles has yet to be established. Diffusion tensor imaging (DTI) may offer a unique insight into muscle microstructure and fiber architecture.

PURPOSE

To explore the anatomy of the urethral sphincter muscles pertinent to urinary continence function using DT-MRI.

STUDY TYPE

Prospective cohort study.

SUBJECTS

Eleven normal male subjects (mean age: 25.4 years); two subjects were scanned in three separate sessions to assess reproducibility.

FIELD STRENGTH/SEQUENCE

3T; using a diffusion-weighted spin echo planar sequence.

ASSESSMENT

DT parameters including fractional anisotropy (FA), primary (λ1 ), secondary (λ2 ), and tertiary (λ3 ) eigenvalues, Apparent diffusion coefficient and radial diffusivity were analyzed statistically, while tracked muscle fibers were assessed visually.

STATISTICAL TESTS

Regional differences (sphincters and longitudinal muscle of the urethra) in the DTI indices were assessed by one-way analysis of variance. A Tukey post-hoc test was used to identify significant differences between muscle regions.

RESULTS

Two sphincter muscles, one proximal near the base of the bladder, corresponding to the lisso-sphincter, and the other distal to the end of the prostate corresponding to the rhabdo-sphincter, surrounding a central urethral muscle fiber bundle, were clearly identified. FA was higher and λ3 lower in the proximal sphincter muscle compared to the central urethral muscle and the distal sphincter (P < 0.05). The average coefficient of variation ranged from 5-12% for the DTI indices.

DATA CONCLUSION

Since DTI values are known to reflect underlying tissue microarchitecture, significant differences in DTI indices identified here between the muscles of the urethral complex may potentially arise from differences in tissue microarchitecture that may in turn be related to the specific function of the sphincter and other muscles.

LEVEL OF EVIDENCE

1 Technical Efficacy: Stage 2 J. Magn. Reson. Imaging 2018;48:1002-1011.

Non-local diffusion-weighted image super-resolution using collaborative joint information

Due to the clinical durable scanning time and other physical constraints, the spatial resolution of diffusion-weighted magnetic resonance imaging (DWI) is highly limited. Using a post-processing method to improve the resolution of DWI holds the potential to improve the investigation of smaller white-matter structures and to reduce partial volume effects. In the present study, a novel non-local mean super-resolution method was proposed to increase the spatial resolution of DWI datasets. Based on a non-local strategy, joint information from the adjacent scanning directions was taken advantage of through the implementation of a novel weighting scheme. Besides this, an efficient rotationally invariant similarity measure was introduced for further improvement of high-resolution image reconstruction and computational efficiency. Quantitative and qualitative comparisons in synthetic and real DWI datasets demonstrated that the proposed method significantly enhanced the resolution of DWI, and is thus beneficial in improving the estimation accuracy for diffusion tensor imaging as well as high-angular resolution diffusion imaging.

Multivariate Heteroscedasticity Models for Functional Brain Connectivity

Functional brain connectivity is the co-occurrence of brain activity in different areas during resting and while doing tasks. The data of interest are multivariate timeseries measured simultaneously across brain parcels using resting-state fMRI (rfMRI). We analyze functional connectivity using two heteroscedasticity models. Our first model is low-dimensional and scales linearly in the number of brain parcels. Our second model scales quadratically. We apply both models to data from the Human Connectome Project (HCP) comparing connectivity between short and conventional sleepers. We find stronger functional connectivity in short than conventional sleepers in brain areas consistent with previous findings. This might be due to subjects falling asleep in the scanner. Consequently, we recommend the inclusion of average sleep duration as a covariate to remove unwanted variation in rfMRI studies. A power analysis using the HCP data shows that a sample size of 40 detects 50% of the connectivity at a false discovery rate of 20%. We provide implementations using R and the probabilistic programming language Stan.

Diffusion tensor imaging of spinal cord parenchyma lesion in rat with chronic spinal cord injury

PURPOSE

Adequate evaluation of spinal cord parenchyma and accurate identification of injury range are considered two premises for the research and treatment of chronic spinal cord injury (SCI). Diffusion tensor imaging (DTI) provides information about water diffusion in spinal cord, and thus makes it possible to realize these premises.

METHOD

In this study, we conducted magnetic resonance imaging (MRI) for Wistar rats 84days after spinal cord contusion. DTI metrics including fractional anisotropy (FA), mean diffusivity (MD), axial diffusivity (AD), and radial diffusivity (RD) from different positions of the injured cord were collected, analyzed, and compared with the histological results and locomotor outcomes. Moreover, we performed fiber tractography, and examined the difference in cavity percentage obtained respectively via conventional MRI, DTI and histology.

RESULTS

Results showed that the chronic SCI rats had the largest changes of all DTI metrics at the epicenter; the farther away from the epicenter, the smaller the variation. FA, AD and RD were all influenced by SCI in a greater space range than MD. The good consistency of FA values and histological results in specific regions evidenced FA's capability of reflecting Wallerian degeneration after SCI. DTI metrics at the epicenter in ventral funiculus also showed a close correlation with the BBB scores. Additionally, supported by the histological results, DTI enables a more accurate measurement of cavity percentage compared to the conventional MRI.

CONCLUSION

DTI parameters might comprehensively reflect the post-SCI pathological status of spinal cord parenchyma at the epicenter and distal parts during the chronic stage, while showing good consistency with locomotor performance. DTI combined with tractography could intuitively display the distribution of spared fibers after SCI and accurately provide information such as cavity area. This may shed light on the research and treatment of chronic SCI.

The brain anatomy of attention-deficit/hyperactivity disorder in young adults - a magnetic resonance imaging study

Background

This is one of the first studies to examine the structural brain anatomy and connectivity associated with an ADHD diagnosis and child as well as adult ADHD symptoms in young adults. It was hypothesized that an adult ADHD diagnosis and in particular childhood symptoms, are associated with widespread changes in the brain macro- and microstructure, which can be used to develop a morphometric biomarker for ADHD.

Methods

Voxel-wise linear regression models were used to examine structural and diffusion-weighted MRI data in 72 participants (31 young adults with ADHD and 41 controls without ADHD) in relation to diagnosis and the number of self-reported child and adult symptoms.

Results

Findings revealed significant associations between ADHD diagnosis and widespread changes to the maturation of white matter fiber bundles and gray matter density in the brain, such as structural shape changes (incomplete maturation) of the middle and superior temporal gyrus, and fronto-basal portions of both frontal lobes. ADHD symptoms in childhood showed the strongest association with brain macro- and microstructural abnormalities. At the brain circuitry level, the superior longitudinal fasciculus (SLF) and cortico-limbic areas are dysfunctional in individuals with ADHD. The morphometric findings predicted an ADHD diagnosis correctly up to 83% of all cases.

Conclusion

An adult ADHD diagnosis and in particular childhood symptoms are associated with widespread micro- and macrostructural changes. The SLF and cortico-limbic findings suggest complex audio-visual, motivational, and emotional dysfunctions associated with ADHD in young adults. The sensitivity of the morphometric findings in predicting an ADHD diagnosis was sufficient, which indicates that MRI-based assessments are a promising strategy for the development of a biomarker.

Tractography in the clinics: Implementing a pipeline to characterize early brain development

In imaging studies of neonates, particularly in the clinical setting, diffusion tensor imaging-based tractography is typically unreliable due to the use of fast acquisition protocols that yield low resolution and signal-to-noise ratio (SNR). These image acquisition protocols are implemented with the aim of reducing motion artifacts that may be produced by the movement of the neonate's head during the scanning session. Furthermore, axons are not yet fully myelinated in these subjects. As a result, the water molecules' movements are not as constrained as in older brains, making it even harder to define structure using diffusion profiles. Here, we introduce a post-processing method that overcomes the difficulties described above, allowing the determination of reliable tracts in newborns. We tested our method using neonatal data and successfully extracted some of the limbic, association and commissural fibers, all of which are typically difficult to obtain by direct tractography. Geometrical and diffusion based features of the tracts are then utilized to compare premature babies to term babies. Our results quantify the maturation of white matter fiber tracts in neonates.

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The proposed method enables consistent tractography in clinical datasets.

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The tractography is used to structural positioning purposes

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Geometrical features and diffusion variables in the tracts' paths are analyzed.

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The gestational age was predicted with regressions in term and preterm babies.

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The extracted features can be used as indexes of early neurodevelopment.

Lognormal Distributions and Geometric Averages of Symmetric Positive Definite Matrices

This article gives a formal definition of a lognormal family of probability distributions on the set of symmetric positive definite (SPD) matrices, seen as a matrix-variate extension of the univariate lognormal family of distributions. Two forms of this distribution are obtained as the large sample limiting distribution via the central limit theorem of two types of geometric averages of i.i.d. SPD matrices: the log-Euclidean average and the canonical geometric average. These averages correspond to two different geometries imposed on the set of SPD matrices. The limiting distributions of these averages are used to provide large-sample confidence regions and two-sample tests for the corresponding population means. The methods are illustrated on a voxelwise analysis of diffusion tensor imaging data, permitting a comparison between the various average types from the point of view of their sampling variability.

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.

Neurophysiological evidence of preserved connectivity in tuber tissue

We present a case of preserved corticospinal connectivity in a cortical tuber, in a 10 year-old boy with intractable epilepsy and tuberous sclerosis complex (TSC). The patient had multiple subcortical tubers, one of which was located in the right central sulcus. In preparation for epilepsy surgery, motor mapping, by neuronavigated transcranial magnetic stimulation (nTMS) coupled with surface electromyography (EMG) was performed to locate the primary motor cortical areas. The resulting functional motor map revealed expected corticospinal connectivity in the left precentral gyrus. Surprisingly, robust contralateral deltoid and tibialis anterior motor evoked potentials (MEPs) were also elicited with direct stimulation of the cortical tuber in the right central sulcus. MRI with diffusion tensor imaging (DTI) tractography confirmed corticospinal fibers originating in the tuber. As there are no current reports of preserved connectivity between a cortical tuber and the corticospinal tract, this case serves to highlight the functional interdigitation of tuber and eloquent cortex. Our case also illustrates the widening spectrum of neuropathological abnormality in TSC that is becoming apparent with modern MRI methodology. Finally, our finding underscores the need for further study of preserved function in tuber tissue during presurgical workup in patients with TSC.

FIBER DIRECTION ESTIMATION, SMOOTHING AND TRACKING IN DIFFUSION MRI

Diffusion magnetic resonance imaging is an imaging technology designed to probe anatomical architectures of biological samples in an in vivo and noninvasive manner through measuring water diffusion. The contribution of this paper is threefold. First, it proposes a new method to identify and estimate multiple diffusion directions within a voxel through a new and identifiable parametrization of the widely used multi-tensor model. Unlike many existing methods, this method focuses on the estimation of diffusion directions rather than the diffusion tensors. Second, this paper proposes a novel direction smoothing method which greatly improves direction estimation in regions with crossing fibers. This smoothing method is shown to have excellent theoretical and empirical properties. Last, this paper develops a fiber tracking algorithm that can handle multiple directions within a voxel. The overall methodology is illustrated with simulated data and a data set collected for the study of Alzheimer's disease by the Alzheimer's Disease Neuroimaging Initiative (ADNI).

Combined Tensor Fitting and TV Regularization in Diffusion Tensor Imaging Based on a Riemannian Manifold Approach

In this paper, we consider combined TV denoising and diffusion tensor fitting in DTI using the affine-invariant Riemannian metric on the space of diffusion tensors. Instead of first fitting the diffusion tensors, and then denoising them, we define a suitable TV type energy functional which incorporates the measured DWIs (using an inverse problem setup) and which measures the nearness of neighboring tensors in the manifold. To approach this functional, we propose generalized forward- backward splitting algorithms which combine an explicit and several implicit steps performed on a decomposition of the functional. We validate the performance of the derived algorithms on synthetic and real DTI data. In particular, we work on real 3D data. To our knowledge, the present paper describes the first approach to TV regularization in a combined manifold and inverse problem setup.

Motor and cortico-striatal-thalamic connectivity alterations in intrauterine growth restriction

BACKGROUND

Intrauterine growth restriction is associated with short- and long-term neurodevelopmental problems. Structural brain changes underlying these alterations have been described with the use of different magnetic resonance-based methods that include changes in whole structural brain networks. However, evaluation of specific brain circuits and its correlation with related functions has not been investigated in intrauterine growth restriction.

OBJECTIVES

In this study, we aimed to investigate differences in tractography-related metrics in cortico-striatal-thalamic and motor networks in intrauterine growth restricted children and whether these parameters were related with their specific function in order to explore its potential use as an imaging biomarker of altered neurodevelopment.

METHODS

We included a group of 24 intrauterine growth restriction subjects and 27 control subjects that were scanned at 1 year old; we acquired T1-weighted and 30 directions diffusion magnetic resonance images. Each subject brain was segmented in 93 regions with the use of anatomical automatic labeling atlas, and deterministic tractography was performed. Brain regions included in motor and cortico-striatal-thalamic networks were defined based in functional and anatomic criteria. Within the streamlines that resulted from the whole brain tractography, those belonging to each specific circuit were selected and tractography-related metrics that included number of streamlines, fractional anisotropy, and integrity were calculated for each network. We evaluated differences between both groups and further explored the correlation of these parameters with the results of socioemotional, cognitive, and motor scales from Bayley Scale at 2 years of age.

RESULTS

Reduced fractional anisotropy (cortico-striatal-thalamic, 0.319 ± 0.018 vs 0.315 ± 0.015; P = .010; motor, 0.322 ± 0.019 vs 0.319 ± 0.020; P = .019) and integrity cortico-striatal-thalamic (0.407 ± 0.040 vs 0.399 ± 0.034; P = .018; motor, 0.417 ± 0.044 vs 0.409 ± 0.046; P = .016) in both networks were observed in the intrauterine growth restriction group, with no differences in number of streamlines. More importantly, strong specific correlation was found between tractography-related metrics and its relative function in both networks in intrauterine growth restricted children. Motor network metrics were correlated specifically with motor scale results (fractional anisotropy: rho = 0.857; integrity: rho = 0.740); cortico-striatal-thalamic network metrics were correlated with cognitive (fractional anisotropy: rho = 0.793; integrity, rho = 0.762) and socioemotional scale (fractional anisotropy: rho = 0.850; integrity: rho = 0.877).

CONCLUSIONS

These results support the existence of altered brain connectivity in intrauterine growth restriction demonstrated by altered connectivity in motor and cortico-striatal-thalamic networks, with reduced fractional anisotropy and integrity. The specific correlation between tractography-related metrics and neurodevelopmental outcomes in intrauterine growth restriction shows the potential to use this approach to develop imaging biomarkers to predict specific neurodevelopmental outcome in infants who are at risk because of intrauterine growth restriction and other prenatal diseases.

Adaptive anisotropic gaussian filtering to reduce acquisition time in cardiac diffusion tensor imaging

Diffusion tensor imaging (DTI) is used to quantify myocardial fiber orientation based on helical angles (HA). Accurate HA measurements require multiple excitations (NEX) and/or several diffusion encoding directions (DED). However, increasing NEX and/or DED increases acquisition time (TA). Therefore, in this study, we propose to reduce TA by implementing a 3D adaptive anisotropic Gaussian filter (AAGF) on the DTI data acquired from ex-vivo healthy and infarcted porcine hearts. DTI was performed on ex-vivo hearts [9-healthy, 3-myocardial infarction (MI)] with several combinations of DED and NEX. AAGF, mean (AVF) and median filters (MF) were applied on the primary eigenvectors of the diffusion tensor prior to HA estimation. The performance of AAGF was compared against AVF and MF. Root mean square error (RMSE), concordance correlation-coefficients and Bland-Altman's technique was used to determine optimal combination of DED and NEX that generated the best HA maps in the least possible TA. Lastly, the effect of implementing AAGF on the infarcted porcine hearts was also investigated. RMSE in HA estimation for AAGF was lower compared to AVF or MF. Post-filtering (AAGF) fewer DED and NEX were required to achieve HA maps with similar integrity as those obtained from higher NEX and/or DED. Pathological alterations caused in HA orientation in the MI model were preserved post-filtering (AAGF). Our results demonstrate that AAGF reduces TA without affecting the integrity of the myocardial microstructure.

Noise reduction of diffusion tensor images by sparse representation and dictionary learning

Background

The low quality of diffusion tensor image (DTI) could affect the accuracy of oncology diagnosis.

Methods

We present a novel sparse representation based denoising method for three dimensional DTI by learning adaptive dictionary with the context redundancy between neighbor slices. In this study, the context redundancy among the adjacent slices of the diffusion weighted imaging volumes is utilized to train sparsifying dictionaries. Therefore, higher redundancy could be achieved for better description of image with lower computation complexity. The optimization problem is solved efficiently using an iterative block-coordinate relaxation method.

Results

The effectiveness of our proposed method has been assessed on both simulated and real experimental DTI datasets. Qualitative and quantitative evaluations demonstrate the performance of the proposed method on the simulated data. The experiments on real datasets with different b-values also show the effectiveness of the proposed method for noise reduction of DTI.

Conclusions

The proposed approach well removes the noise in the DTI, which has high potential to be applied for clinical oncology applications.

Automated retinofugal visual pathway reconstruction with multi-shell HARDI and FOD-based analysis

Diffusion MRI tractography provides a non-invasive modality to examine the human retinofugal projection, which consists of the optic nerves, optic chiasm, optic tracts, the lateral geniculate nuclei (LGN) and the optic radiations. However, the pathway has several anatomic features that make it particularly challenging to study with tractography, including its location near blood vessels and bone-air interface at the base of the cerebrum, crossing fibers at the chiasm, somewhat-tortuous course around the temporal horn via Meyer's Loop, and multiple closely neighboring fiber bundles. To date, these unique complexities of the visual pathway have impeded the development of a robust and automated reconstruction method using tractography. To overcome these challenges, we develop a novel, fully automated system to reconstruct the retinofugal visual pathway from high-resolution diffusion imaging data. Using multi-shell, high angular resolution diffusion imaging (HARDI) data, we reconstruct precise fiber orientation distributions (FODs) with high order spherical harmonics (SPHARM) to resolve fiber crossings, which allows the tractography algorithm to successfully navigate the complicated anatomy surrounding the retinofugal pathway. We also develop automated algorithms for the identification of ROIs used for fiber bundle reconstruction. In particular, we develop a novel approach to extract the LGN region of interest (ROI) based on intrinsic shape analysis of a fiber bundle computed from a seed region at the optic chiasm to a target at the primary visual cortex. By combining automatically identified ROIs and FOD-based tractography, we obtain a fully automated system to compute the main components of the retinofugal pathway, including the optic tract and the optic radiation. We apply our method to the multi-shell HARDI data of 215 subjects from the Human Connectome Project (HCP). Through comparisons with post-mortem dissection measurements, we demonstrate the retinotopic organization of the optic radiation including a successful reconstruction of Meyer's loop. Then, using the reconstructed optic radiation bundle from the HCP cohort, we construct a probabilistic atlas and demonstrate its consistency with a post-mortem atlas. Finally, we generate a shape-based representation of the optic radiation for morphometry analysis.

Tubers are neither static nor discrete: Evidence from serial diffusion tensor imaging

OBJECTIVE

To assess the extent and evolution of tissue abnormality of tubers, perituber tissue, and normal-appearing white matter (NAWM) in patients with tuberous sclerosis complex using serial diffusion tensor imaging.

METHODS

We applied automatic segmentation based on a combined global-local intensity mixture model of 3T structural and 35 direction diffusion tensor MRIs (diffusion tensor imaging) to define 3 regions: tuber tissue, an equal volume perituber rim, and the remaining NAWM. For each patient, scan, lobe, and tissue type, we analyzed the averages of mean diffusivity (MD) and fractional anisotropy (FA) in a generalized additive mixed model.

RESULTS

Twenty-five patients (mean age 5.9 years; range 0.5-24.5 years) underwent 2 to 6 scans each, totaling 70 scans. Average time between scans was 1.2 years (range 0.4-2.9). Patient scans were compared with those of 73 healthy controls. FA values were lowest, and MD values were highest in tubers, next in perituber tissue, then in NAWM. Longitudinal analysis showed a positive (FA) and negative (MD) correlation with age in tubers, perituber tissue, and NAWM. All 3 tissue types followed a biexponential developmental trajectory, similar to the white matter of controls. An additional qualitative analysis showed a gradual transition of diffusion values across the tissue type boundaries.

CONCLUSIONS

Similar to NAWM, tuber and perituber tissues in tuberous sclerosis complex undergo microstructural evolution with age. The extent of diffusion abnormality decreases with distance to the tuber, in line with known extension of histologic, immunohistochemical, and molecular abnormalities beyond tuber pathology.

Characterizing brain tissue by assessment of the distribution of anisotropic microstructural environments in diffusion-compartment imaging (DIAMOND)

PURPOSE

To develop a statistical model for the tridimensional diffusion MRI signal at each voxel that describes the signal arising from each tissue compartment in each voxel.

THEORY AND METHODS

In prior work, a statistical model of the apparent diffusion coefficient was shown to well-characterize the diffusivity and heterogeneity of the mono-directional diffusion MRI signal. However, this model was unable to characterize the three-dimensional anisotropic diffusion observed in the brain. We introduce a new model that extends the statistical distribution representation to be fully tridimensional, in which apparent diffusion coefficients are extended to be diffusion tensors. The set of compartments present at a voxel is modeled by a finite sum of unimodal continuous distributions of diffusion tensors. Each distribution provides measures of each compartment microstructural diffusivity and heterogeneity.

RESULTS

The ability to estimate the tridimensional diffusivity and heterogeneity of multiple fascicles and of free diffusion is demonstrated.

CONCLUSION

Our novel tissue model allows for the characterization of the intra-voxel orientational heterogeneity, a prerequisite for accurate tractography while also characterizing the overall tridimensional diffusivity and heterogeneity of each tissue compartment. The model parameters can be estimated from short duration acquisitions. The diffusivity and heterogeneity microstructural parameters may provide novel indicator of the presence of disease or injury. Magn Reson Med 76:963-977, 2016. © 2015 Wiley Periodicals, Inc.

Cross-hemispheric collaboration and segregation associated with task difficulty as revealed by structural and functional connectivity

Although it is known that brain regions in one hemisphere may interact very closely with their corresponding contralateral regions (collaboration) or operate relatively independent of them (segregation), the specific brain regions (where) and conditions (how) associated with collaboration or segregation are largely unknown. We investigated these issues using a split field-matching task in which participants matched the meaning of words or the visual features of faces presented to the same (unilateral) or to different (bilateral) visual fields. Matching difficulty was manipulated by varying the semantic similarity of words or the visual similarity of faces. We assessed the white matter using the fractional anisotropy (FA) measure provided by diffusion tensor imaging (DTI) and cross-hemispheric communication in terms of fMRI-based connectivity between homotopic pairs of cortical regions. For both perceptual and semantic matching, bilateral trials became faster than unilateral trials as difficulty increased (bilateral processing advantage, BPA). The study yielded three novel findings. First, whereas FA in anterior corpus callosum (genu) correlated with word-matching BPA, FA in posterior corpus callosum (splenium-occipital) correlated with face-matching BPA. Second, as matching difficulty intensified, cross-hemispheric functional connectivity (CFC) increased in domain-general frontopolar cortex (for both word and face matching) but decreased in domain-specific ventral temporal lobe regions (temporal pole for word matching and fusiform gyrus for face matching). Last, a mediation analysis linking DTI and fMRI data showed that CFC mediated the effect of callosal FA on BPA. These findings clarify the mechanisms by which the hemispheres interact to perform complex cognitive tasks.

Anisotropic Smoothing Improves DT-MRI-Based Muscle Fiber Tractography

Purpose

To assess the effect of anisotropic smoothing on fiber tracking measures, including pennation angle, fiber tract length, and fiber tract number in the medial gastrocnemius (MG) muscle in healthy subjects using diffusion-weighted magnetic resonance imaging (DW-MRI).

Materials and Methods

3T DW-MRI data were used for muscle fiber tractography in the MG of healthy subjects. Anisotropic smoothing was applied at three levels (5%, 10%, 15%), and pennation angle, tract length, fiber tract number, fractional anisotropy, and principal eigenvector orientation were quantified for each smoothing level.

Results

Fiber tract length increased with pre-fiber tracking smoothing, and local heterogeneities in fiber direction were reduced. However, pennation angle was not affected by smoothing.

Conclusion

Modest anisotropic smoothing (10%) improved fiber-tracking results, while preserving structural features.

Approximate joint diagonalization and geometric mean of symmetric positive definite matrices

We explore the connection between two problems that have arisen independently in the signal processing and related fields: the estimation of the geometric mean of a set of symmetric positive definite (SPD) matrices and their approximate joint diagonalization (AJD). Today there is a considerable interest in estimating the geometric mean of a SPD matrix set in the manifold of SPD matrices endowed with the Fisher information metric. The resulting mean has several important invariance properties and has proven very useful in diverse engineering applications such as biomedical and image data processing. While for two SPD matrices the mean has an algebraic closed form solution, for a set of more than two SPD matrices it can only be estimated by iterative algorithms. However, none of the existing iterative algorithms feature at the same time fast convergence, low computational complexity per iteration and guarantee of convergence. For this reason, recently other definitions of geometric mean based on symmetric divergence measures, such as the Bhattacharyya divergence, have been considered. The resulting means, although possibly useful in practice, do not satisfy all desirable invariance properties. In this paper we consider geometric means of covariance matrices estimated on high-dimensional time-series, assuming that the data is generated according to an instantaneous mixing model, which is very common in signal processing. We show that in these circumstances we can approximate the Fisher information geometric mean by employing an efficient AJD algorithm. Our approximation is in general much closer to the Fisher information geometric mean as compared to its competitors and verifies many invariance properties. Furthermore, convergence is guaranteed, the computational complexity is low and the convergence rate is quadratic. The accuracy of this new geometric mean approximation is demonstrated by means of simulations.

Effect of increasing diffusion gradient direction number on diffusion tensor imaging fiber tracking in the human brain

Objective

To assess the effects of varying the number of diffusion gradient directions (NDGDs) on diffusion tensor fiber tracking (FT) in human brain white matter using tract characteristics.

Materials and Methods

Twelve normal volunteers underwent diffusion tensor imaging (DTI) scanning with NDGDs of 6, 11, 15, 21, and 31 orientations. Three fiber tract groups, including the splenium of the corpus callosum (CC), the entire CC, and the full brain tract, were reconstructed by deterministic DTI-FT. Tract architecture was first qualitatively evaluated by visual observation. Six quantitative tract characteristics, including the number of fibers (NF), average length (AL), fractional anisotropy (FA), relative anisotropy (RA), mean diffusivity (MD), and volume ratio (VR) were measured for the splenium of the CC at the tract branch level, for the entire CC at tract level, and for the full brain tract at the whole brain level. Visual results and those of NF, AL, FA, RA, MD, and VR were compared among the five different NDGDs.

Results

The DTI-FT with NDGD of 11, 15, 21, and 31 orientations gave better tracking results compared with NDGD of 6 after the visual evaluation. NF, FA, RA, MD, and VR values with NDGD of six were significantly greater (smallest p = 0.001 to largest p = 0.042) than those with four other NDGDs (11, 15, 21, or 31 orientations), whereas AL measured with NDGD of six was significantly smaller (smallest p = 0.001 to largest p = 0.041) than with four other NDGDs (11, 15, 21, or 31 orientations). No significant differences were observed in the results among the four NDGD groups of 11, 15, 21, and 31 directions (smallest p = 0.059 to largest p = 1.000).

Conclusion

The main fiber tracts were detected with NDGD of six orientations; however, the use of larger NDGD (≥ 11 orientations) could provide improved tract characteristics at the expense of longer scanning time.

Patient-specific modeling of ventricular activation pattern using surface ECG-derived vectorcardiogram in bundle branch block

Patient-specific computational models have promise to improve cardiac disease diagnosis and therapy planning. Here a new method is described to simulate left-bundle branch block (LBBB) and RV-paced ventricular activation patterns in three dimensions from non-invasive, routine clinical measurements. Activation patterns were estimated in three patients using vectorcardiograms (VCG) derived from standard 12-lead electrocardiograms (ECG). Parameters of a monodomain model of biventricular electrophysiology were optimized to minimize differences between the measured and computed VCG. Electroanatomic maps of local activation times measured on the LV and RV endocardial surfaces of the same patients were used to validate the simulated activation patterns. For all patients, the optimal estimated model parameters predicted a time-averaged mean activation dipole orientation within 6.7 ± 0.6° of the derived VCG. The predicted local activation times agreed within 11.5 ± 0.8 ms of the measured electroanatomic maps, on the order of the measurement accuracy.

Characterization of U-shape streamline fibers: Methods and applications

Diffusion tensor imaging (DTI), high angular resolution diffusion imaging (HARDI), and diffusion spectrum imaging (DSI) have been widely used in the neuroimaging field to examine the macro-scale fiber connection patterns in the cerebral cortex. However, the topographic and geometric relationships between diffusion imaging derived streamline fiber connection patterns and cortical folding patterns remain largely unknown. This paper specifically identifies and characterizes the U-shapes of diffusion imaging derived streamline fibers via a novel fiber clustering framework and examines their co-localization patterns with cortical sulci based on DTI, HARDI, and DSI datasets of human, chimpanzee and macaque brains. We verified the presence of these U-shaped streamline fibers that connect neighboring gyri by coursing around cortical sulci such as the central sulcus, pre-central sulcus, post-central sulcus, superior temporal sulcus, inferior frontal sulcus, and intra-parietal sulcus. This study also verified the existence of U-shape fibers across data modalities (DTI/HARDI/DSI) and primate species (macaque, chimpanzee and human), and suggests that the common pattern of U-shape fibers coursing around sulci is evolutionarily-preserved in cortical architectures.