The tensor distribution function

Diffusion weighted magnetic resonance imaging is a powerful tool that can be employed to study white matter microstructure by examining the 3D displacement profile of water molecules in brain tissue. By applying diffusion-sensitized gradients along a minimum of six directions, second-order tensors (represented by three-by-three positive definite matrices) can be computed to model dominant diffusion processes. However, conventional DTI is not sufficient to resolve more complicated white matter configurations, e.g., crossing fiber tracts. Recently, a number of high-angular resolution schemes with more than six gradient directions have been employed to address this issue. In this article, we introduce the tensor distribution function (TDF), a probability function defined on the space of symmetric positive definite matrices. Using the calculus of variations, we solve the TDF that optimally describes the observed data. Here, fiber crossing is modeled as an ensemble of Gaussian diffusion processes with weights specified by the TDF. Once this optimal TDF is determined, the orientation distribution function (ODF) can easily be computed by analytic integration of the resulting displacement probability function. Moreover, a tensor orientation distribution function (TOD) may also be derived from the TDF, allowing for the estimation of principal fiber directions and their corresponding eigenvalues.

Improved delineation of short cortical association fibers and gray/white matter boundary using whole-brain three-dimensional diffusion tensor imaging at submillimeter spatial resolution.

Recent emergence of human connectome imaging has led to a high demand on angular and spatial resolutions for diffusion magnetic resonance imaging (MRI). While there have been significant growths in high angular resolution diffusion imaging, the improvement in spatial resolution is still limited due to a number of technical challenges, such as the low signal-to-noise ratio and high motion artifacts. As a result, the benefit of a high spatial resolution in the whole-brain connectome imaging has not been fully evaluated in vivo. In this brief report, the impact of spatial resolution was assessed in a newly acquired whole-brain three-dimensional diffusion tensor imaging data set with an isotropic spatial resolution of 0.85 mm. It was found that the delineation of short cortical association fibers is drastically improved as well as the definition of fiber pathway endings into the gray/white matter boundary-both of which will help construct a more accurate structural map of the human brain connectome.

MRI diffusion tractography study in individuals with schizotypal features: A pilot study

Diffusion tensor imaging (DTI) studies have identified changes in white matter tracts in schizophrenia patients and those at high risk of transition. Schizotypal samples represent a group on the schizophrenia continuum that share some aetiological risk factors but without the confounds of illness. The aim of the current study was to compare tract microstructural coherence as measured by
fractional anisotropy (FA) between 12 psychometrically defined schizotypes and controls. We investigated bilaterally the uncinate and arcuate fasciculi (UF and AF) via a probabilistic tractography algorithm (PICo), with FA values compared between groups. Partial correlations were also examined between measures of subclinical hallucinatory/delusional experiences and FA values. High schizotypes
were found to have significantly higher FA values in bilateral UF only, but failed to reach significance in each hemisphere. In the whole sample there was a positive correlation between increasing FA values and measures of hallucinatory experience in the right AF. These findings suggest subtle changes in microstructural coherence are present in schizotypes. Correlations between mild hallucinatory experience and increasing FA values could indicate increasing coherence could be associated with symptom formation.

Targetting of the ventro-intermediate nucleus using ultra-high field (7T) MRI for gamma knife surgery purposes: A pilot in vivo study on healthy subjects.

INTRODUCTION: Gamma Knife surgery (GKS) is a non-invasive neurosurgical stereotactic procedure, increasingly used as an alternative to open functional procedures. This includes targeting of the ventro-intermediate nucleus of the thalamus (e.g. Vim) for tremor. We currently perform an indirect targeting, as the Vim is not visible on current 3Tesla MRI acquisitions. Our objective was to enhance anatomic imaging (aiming at refining the precision of anatomic target selection by direct visualisation) in patients treated for tremor with Vim GKS, by using high field 7T MRI. MATERIALS AND METHODSH: Five young healthy subjects were scanned on 3 (T1-w and diffusion tensor imaging) and 7T (high-resolution susceptibility weighted images (SWI)) MRI in Lausanne. All images were further integrated for the first time into the Gamma Plan Software(®) (Elekta Instruments, AB, Sweden) and co-registered (with T1 was a reference). A simulation of targeting of the Vim was done using various methods on the 3T images. Furthermore, a correlation with the position of the found target with the 7T SWI was performed. The atlas of Morel et al. (Zurich, CH) was used to confirm the findings on a detailed analysis inside/outside the Gamma Plan. RESULTS: The use of SWI provided us with a superior resolution and an improved image contrast within the basal ganglia. This allowed visualization and direct delineation of some subgroups of thalamic nuclei in vivo, including the Vim. The position of the target, as assessed on 3T, perfectly matched with the supposed one of the Vim on the SWI. Furthermore, a 3-dimensional model of the Vim-target area was created on the basis of the obtained images. CONCLUSION: This is the first report of the integration of SWI high field MRI into the LGP, aiming at the improvement of targeting validation of the Vim in tremor. The anatomical correlation between the direct visualization on 7T and the current targeting methods on 3T (e.g. quadrilatere of Guyot, histological atlases) seems to show a very good anatomical matching. Further studies are needed to validate this technique, both by improving the accuracy of the targeting of the Vim (potentially also other thalamic nuclei) and to perform clinical assessment.

Analyzing diffusion tensor images with ghosting artifacts: the effects of direct and indirect normalization

The current study aims to assess the applicability of direct or indirect normalization for the analysis of fractional anisotropy (FA) maps in the context of diffusion-weighted images (DWIs) contaminated by ghosting artifacts. We found that FA maps acquired by direct normalization showed generally higher anisotropy than indirect normalization, and the disparities were aggravated by the presence of ghosting artifacts in DWIs. The voxel-wise statistical comparisons demonstrated that indirect normalization reduced the influence of artifacts and enhanced the sensitivity of detecting anisotropy differences between groups. This suggested that images contaminated with ghosting artifacts can be sensibly analyzed using indirect normalization.

K-Surfer: a KNIME extension for the management and analysis of Human brain MRI FreeSurfer/FSL data

Human brain imaging techniques, such as Magnetic Resonance Imaging (MRI) or Diffusion Tensor Imaging (DTI), have been established as scientific and diagnostic tools and their adoption is growing in popularity. Statistical methods, machine learning and data mining algorithms have successfully been adopted to extract predictive and descriptive models from neuroimage data. However, the knowledge discovery process typically requires also the adoption of pre-processing, post-processing and visualisation techniques in complex data workflows. Currently, a main problem for the integrated preprocessing and mining of MRI data is the lack of comprehensive platforms able to avoid the manual invocation of preprocessing and mining tools, that yields to an error-prone and inefficient process. In this work we present K-Surfer, a novel plug-in of the Konstanz Information Miner (KNIME) workbench, that automatizes the preprocessing of brain images and leverages the mining capabilities of KNIME in an integrated way. K-Surfer supports the importing, filtering, merging and pre-processing of neuroimage data from FreeSurfer, a tool for human brain MRI feature extraction and interpretation. K-Surfer automatizes the steps for importing FreeSurfer data, reducing time costs, eliminating human errors and enabling the design of complex analytics workflow for neuroimage data by leveraging the rich functionalities available in the KNIME workbench.

Corpus callosum in maltreated children with posttraumatic stress disorder: A diffusion tensor imaging study

Contrary to expectations derived from preclinical studies of the effects of stress, and imaging studies of adults with posttraumatic stress disorder (PTSD), there is no evidence of hippocampus atrophy in children with PTSD. Multiple pediatric studies have reported reductions in the corpus callosum - the primary white matter tract in the brain. Consequently, in the present study, diffusion tensor imaging was used to assess white matter integrity in the corpus callosum in 17 maltreated children with PTSD and 15 demographically matched normal controls. Children with PTSD had reduced fractional anisotropy in the medial and posterior corpus, a region which contains interhemispheric projections from brain structures involved in circuits that mediate the processing of emotional stimuli and various memory functions - core disturbances associated with a history of trauma. Further exploration of the effects of stress on the corpus callosum and white matter development appears a promising strategy to better understand the pathophysiology of PTSD in children. (C) 2007 Elsevier Ireland Ltd. All rights reserved.

White matter abnormalities associated with Alzheimer's disease and mild cognitive impairment: A critical review of MRI studies

In this article, the authors aim to present a critical review of recent MRI studies addressing white matter (WM) abnormalities in Alzheimer's disease (AD) and mild cognitive impairment (MCI), by searching PubMed and reviewing MRI studies evaluating subjects with AD or MCI using WM volumetric methods, diffusion tensor imaging and assessment of WM hyperintensities. Studies have found that, compared with healthy controls, AD and MCI samples display WM volumetric reductions and diffusion tensor imaging findings suggestive of reduced WM integrity. These changes affect complex networks relevant to episodic memory and other cognitive processes, including fiber connections that directly link medial temporal structures and the corpus callosum. Abnormalities in cortico-cortical and cortico-subcortical WM interconnections are associated with an increased risk of progression from MCI to dementia. It can be concluded that WM abnormalities are detectable in early stages of AD and MCI. Degeneration of WM networks causes disconnection among neural cells and the degree of such changes is related to cognitive decline. © 2013 2013 Expert Reviews Ltd.

Examining the gateway to the limbic system with diffusion tensor imaging: the perforant pathway in dementia

Current treatments for Alzheimer's disease (AD) are only able to slow the progression of mental deterioration, making early and reliable diagnosis an essential part of any promising therapeutic strategy. In the initial stages of AD, the first neuropathological alterations occur in the perforant pathway (PP), a large neuronal fiber tract located at the entrance to the limbic system. However, to date, there is no sensitive diagnostic tool for performing in vivo assessments of this structure. In the present bimodal magnetic resonance imaging (MRI) study, we examined 10 elderly controls, 10 subjects suffering from mild cognitive impairment (MCI), and 10 AD patients in order to evaluate the sensitivity of diffusion tensor imaging (DTI), a new MRI technique, for detecting changes in the PP. Furthermore, the diagnostic explanatory power of DTI data of the PP should be compared to high-resolution MRI volumetry and intervoxel coherences (COH) of the hippocampus and the entorhinal cortex, two limbic regions also involved in the pathophysiology of early AD. DTI revealed a marked decrease in COH values in the PP region of MCI (right side: 26%, left side: 29%, as compared to controls) and AD patients (right side: 37%, left side: 43%, as compared to controls). Reductions in COH values of the PP region were significantly correlated with cognitive impairment. DTI data of the PP zone were the only parameter differing significantly between control subjects and MCI patients, while the volumetric measures and the COH values of the hippocampus and the entorhinal cortex did not. DTI of medial temporal brain regions is a promising non-invasive tool for the in vivo diagnosis of the early/preclinical stages of AD.

New evidence for involvement of the entorhinal region in schizophrenia: a combined MRI volumetric and DTI study

Postmortem examinations and magnetic resonance imaging (MRI) studies suggest involvement of the entorhinal cortex (EC) in schizophrenic psychoses. However, the extent and nature of the possible pathogenetical process underlying the observed alterations of this limbic key region for processing of multimodal sensory information remains unclear. Three-dimensional high-resolution MRI volumetry and evaluation of the regional diffusional anisotropy based on diffusion tensor imaging (DTI) were performed on the EC of 15 paranoid schizophrenic patients and 15 closely matched control subjects. In schizophrenic patients, EC volumes showed a slight, but not significant, decrease. However, the anisotropy values, expressed as inter-voxel coherences (COH), were found to be significantly decreased by 17.9% (right side) and 12.5% (left side), respectively, in schizophrenics. Reduction of entorhinal diffusional anisotropy can be hypothesized to be functionally related to disturbances in the perforant path, the principal efferent EC fiber tract supplying the limbic system with neuronal input from multimodal association centers. Combinations of different MRI modalities are a promising approach for the detection and characterization of subtle brain tissue alterations.

Diffusion tensor imaging of two unrelated Chinese men with hereditary spastic paraplegia associated with thin corpus callosum

Hereditary spastic paraplegia (HSP) associated with thin corpus callosum is a rare autosomal recessive neurodegenerative disorder characterized by an abnormally thin corpus callosum, normal motor development, slowly progressive spastic paraparesis and cognitive deterioration. To investigate and localize abnormalities in the brains of two Chinese patients with HSP-TCC, with mutations in the spatacsin gene. Diffusion tensor imaging (DTI) was used to determine the mean diffusion (MD) and fractional anisotropy (FA) in the brains of the patients in comparison to 20 healthy subjects. Voxel-based analysis (VBA) of both the diffusion and anisotropy values were performed using statistical parametric mapping (SPM). Significant changes with MD increase and FA reduction were found in the already known lesions including the corpus callosum, cerebellum and thalamus. In addition, changes were also found in regions that appear to be normal in conventional MRI, such as the brain stem, internal capsule, cingulum and subcortical white matter including superior longitudinal fascicle and inferior longitudinal fascicle. Neither increase in FA nor reduction in MD was detected in the brain. Our study provides clear in vivo MR imaging evidence of a more widespread brain involvement of HSP-TCC. MD is more sensitive than FA in detecting lesions in thalamus and subcortical white matter, suggesting that MD may be a better marker of the disease progression.

Volumetry and diffusion tensor imaging of hippocampal subregions in schizophrenia

Previous MRI-volumetric studies in schizophrenic psychoses have demonstrated more or less pronounced volume reductions of the hippocampus in patients. Correspondingly, neuropathological examinations on the brains of schizophrenics showed diverse structural changes of the hippocampus. Employing a high-resolution 3D-MPRAGE sequence, we found volume reductions in most hippocampal subregions of schizophrenic patients, which, however, did not reach significant levels. An analysis of co-registered diffusion tensor imaging (DTI) data revealed significant alterations of the inter-voxel coherences in single hippocampal subdivisions of these patients, supporting the assumption of characteristic microstructural tissue changes relevant for the pathogenesis of schizophrenic psychoses. Our results argue for the usage of additional MRI modalities like DTI in order to detect subtle regional alterations of hippocampal structure in schizophrenics.

Diffusion tensor imaging of rat spinal cord in vivo

Magnetic resonance imaging, with its exquisite soft tissue contrast, is an ideal modality for investigating spinal cord pathology. While conventional MRI techniques are very sensitive for spinal cord pathology, their specificity is somewhat limited. Diffusion MRI is an advanced technique which is a very sensitive and specific indicator of the integrity of white matter tracts. Diffusion imaging has been shown to detect early ischemic changes in white matter, while conventional imaging demonstrates no change. By acquiring the complete apparent diffusion tensor (ADT), tissue diffusion properties can be expressed in terms of quantitative and rotationally invariant parameters. ^ Systematic study of SCI in vivo requires controlled animal models such as the popular rat model. To date, studies of spinal cord using ADT imaging have been performed exclusively in fixed, excised spinal cords, introducing inevitable artifacts and losing the benefits of MRI's noninvasive nature. In vivo imaging reflects the actual in vivo tissue properties, and allows each animal to be imaged at multiple time points, greatly reducing the number of animals required to achieve statistical significance. Because the spinal cord is very small, the available signal-to-noise ratio (SNR) is very low. Prior spin-echo based ADT studies of rat spinal cord have relied on high magnetic field strengths and long imaging times—on the order of 10 hours—for adequate SNR. Such long imaging times are incompatible with in vivo imaging, and are not relevant for imaging the early phases following SCI. Echo planar imaging (EPI) is one of the fastest imaging methods, and is popular for diffusion imaging. However, EPI further lowers the image SNR, and is very sensitive to small imperfections in the magnetic field, such as those introduced by the bony spine. Additionally, The small field-of-view (FOV) needed for spinal cord imaging requires large imaging gradients which generate EPI artifacts. The addition of diffusion gradients introduces yet further artifacts. ^ This work develops a method for rapid EPI-based in vivo diffusion imaging of rat spinal cord. The method involves improving the SNR using an implantable coil; reducing magnetic field inhomogeneities by means of an autoshim, and correcting EPI artifacts by post-processing. New EPI artifacts due to diffusion gradients described, and post-processing correction techniques are developed. ^ These techniques were used to obtain rotationally invariant diffusion parameters from 9 animals in vivo, and were validated using the gold-standard, but slow, spinecho based diffusion sequence. These are the first reported measurements of the ADT in spinal cord in vivo . ^ Many of the techniques described are equally applicable toward imaging of human spinal cord. We anticipate that these techniques will aid in evaluating and optimizing potential therapies, and will lead to improved patient care. ^

In-vivo diffusion tensor imaging of rat spinal cord with a phased array coil at 7T

Magnetic resonance imaging (MRI) is a non-invasive technique that offers excellent soft tissue contrast for characterizing soft tissue pathologies. Diffusion tensor imaging (DTI) is an MRI technique that has shown to have the sensitivity to detect subtle pathology that is not evident on conventional MRI. ^ Rats are commonly used as animal models in characterizing the spinal cord pathologies including spinal cord injury (SCI), cancer, multiple sclerosis, etc. These pathologies could affect both thoracic and cervical regions and complete characterization of these pathologies using MRI requires DTI characterization in both the thoracic and cervical regions. Prior to the application of DTI for investigating the pathologic changes in the spinal cord, it is essential to establish DTI metrics in normal animals. ^ To date, in-vivo DTI studies of rat spinal cord have used implantable coils for high signal-to-noise ratio (SNR) and spin-echo pulse sequences for reduced geometric distortions. Implantable coils have several disadvantages including: (1) the invasive nature of implantation, (2) loss of SNR due to frequency shift with time in the longitudinal studies, and (3) difficulty in imaging the cervical region. While echo planar imaging (EPI) offers much shorter acquisition times compared to spin-echo imaging, EPI is very sensitive to static magnetic field inhomogeneities and the existing shimming techniques implemented on the MRI scanner do not perform well on spinal cord because of its geometry. ^ In this work, an integrated approach has been implemented for in-vivo DTI characterization of rat spinal cord in the thoracic and cervical regions. A three element phased array coil was developed for improved SNR and extended spatial coverage. A field-map shimming technique was developed for minimizing the geometric distortions in EPI images. Using these techniques, EPI based DWI images were acquired with optimized diffusion encoding scheme from 6 normal rats and the DTI-derived metrics were quantified. ^ The phantom studies indicated higher SNR and smaller bias in the estimated DTI metrics than the previous studies in the cervical region. In-vivo results indicated no statistical difference in the DTI characteristics of either gray matter or white matter between the thoracic and cervical regions. ^

Evidence of altered prefrontal-thalamic circuitry in schizophrenia: An optimised diffusion MRI study

MRI diffusion tensor imaging (DTI), optimized for measuring the trace of the diffusion tensor, was used to investigate microstructural changes in the brains of 12 individuals with schizophrenia compared with 12 matched control subjects. To control for the effects of anatomic variation between subject groups, all participants' diffusion images were non-linearly registered to standard anatomical space. Significant statistical differences in mean diffusivity (MD) measures between the two groups were determined on a pixel-by-pixel basis, using Gaussian random field theory. We found significantly elevated MD measures within temporal, parietal and prefrontal cortical regions in the schizophrenia group (P > 0.001), especially within the medial frontal gyrus and anterior cingulate. The dorsal medial and anterior nucleus of the thalamus, including the caudate, also exhibited significantly increased MD in the schizophrenia group (P > 0.001). This study has shown for the first time that MD measures offer an alternative strategy for investigating altered prefrontal-thalamic circuitry in schizophrenia. (c) 2006 Elsevier Inc. All rights reserved.