Concepts from tensor analysis and differential geometry.

Mode of access: Internet.

Robust tensor analysis with L1-norm

Tensor analysis plays an important role in modern image and vision computing problems. Most of the existing tensor analysis approaches are based on the Frobenius norm, which makes them sensitive to outliers. In this paper, we propose L1-norm-based tensor analysis (TPCA-L1), which is robust to outliers. Experimental results upon face and other datasets demonstrate the advantages of the proposed approach. © 2006 IEEE.

Individual prediction of cognitive decline in mild cognitive impairment using support vector machine-based analysis of diffusion tensor imaging data.

Although cross-sectional diffusion tensor imaging (DTI) studies revealed significant white matter changes in mild cognitive impairment (MCI), the utility of this technique in predicting further cognitive decline is debated. Thirty-five healthy controls (HC) and 67 MCI subjects with DTI baseline data were neuropsychologically assessed at one year. Among them, there were 40 stable (sMCI; 9 single domain amnestic, 7 single domain frontal, 24 multiple domain) and 27 were progressive (pMCI; 7 single domain amnestic, 4 single domain frontal, 16 multiple domain). Fractional anisotropy (FA) and longitudinal, radial, and mean diffusivity were measured using Tract-Based Spatial Statistics. Statistics included group comparisons and individual classification of MCI cases using support vector machines (SVM). FA was significantly higher in HC compared to MCI in a distributed network including the ventral part of the corpus callosum, right temporal and frontal pathways. There were no significant group-level differences between sMCI versus pMCI or between MCI subtypes after correction for multiple comparisons. However, SVM analysis allowed for an individual classification with accuracies up to 91.4% (HC versus MCI) and 98.4% (sMCI versus pMCI). When considering the MCI subgroups separately, the minimum SVM classification accuracy for stable versus progressive cognitive decline was 97.5% in the multiple domain MCI group. SVM analysis of DTI data provided highly accurate individual classification of stable versus progressive MCI regardless of MCI subtype, indicating that this method may become an easily applicable tool for early individual detection of MCI subjects evolving to dementia.

Assessment of the diagnostic value of diffusion tensor imaging in patients with spinal cord compression: a meta-analysis

We investigated the diagnostic value of the apparent diffusion coefficient (ADC) and fractional anisotropy (FA) of magnetic resonance diffusion tensor imaging (DTI) in patients with spinal cord compression (SCC) using a meta-analysis framework. Multiple scientific literature databases were exhaustively searched to identify articles relevant to this study. Mean values and standardized mean differences (SMDs) were calculated for the ADC and FA in normal and diseased tissues. The STATA version 12.0 software was used for statistical analysis. Of the 41 articles initially retrieved through database searches, 11 case-control studies were eligible for the meta-analysis and contained a combined total of 645 human subjects (394 patients with SCC and 251 healthy controls). All 11 studies reported data on FA, and 9 contained data related to the ADC. The combined SMDs of the ADC and FA showed that the ADC was significantly higher and the FA was lower in patients with SCC than in healthy controls. Subgroup analysis based on the b value showed higher ADCs in patients with SCC than in healthy controls at b values of both ≤500 and >500 s/mm2. In summary, the main findings of this meta-analysis revealed an increased ADC and decreased FA in patients with SCC, indicating that DTI is an important diagnostic imaging tool to assess patients suspected to have SCC.

Analysis of diffusion tensor magnetic resonance imaging data using principal component analysis

An analysis method for diffusion tensor (DT) magnetic resonance imaging data is described, which, contrary to the standard method (multivariate fitting), does not require a specific functional model for diffusion-weighted (DW) signals. The method uses principal component analysis (PCA) under the assumption of a single fibre per pixel. PCA and the standard method were compared using simulations and human brain data. The two methods were equivalent in determining fibre orientation. PCA-derived fractional anisotropy and DT relative anisotropy had similar signal-to-noise ratio (SNR) and dependence on fibre shape. PCA-derived mean diffusivity had similar SNR to the respective DT scalar, and it depended on fibre anisotropy. Appropriate scaling of the PCA measures resulted in very good agreement between PCA and DT maps. In conclusion, the assumption of a specific functional model for DW signals is not necessary for characterization of anisotropic diffusion in a single fibre.

Tensor regression based on linked multiway parameter analysis

Classical regression methods take vectors as covariates and estimate the corresponding vectors of regression parameters. When addressing regression problems on covariates of more complex form such as multi-dimensional arrays (i.e. tensors), traditional computational models can be severely compromised by ultrahigh dimensionality as well as complex structure. By exploiting the special structure of tensor covariates, the tensor regression model provides a promising solution to reduce the model’s dimensionality to a manageable level, thus leading to efficient estimation. Most of the existing tensor-based methods independently estimate each individual regression problem based on tensor decomposition which allows the simultaneous projections of an input tensor to more than one direction along each mode. As a matter of fact, multi-dimensional data are collected under the same or very similar conditions, so that data share some common latent components but can also have their own independent parameters for each regression task. Therefore, it is beneficial to analyse regression parameters among all the regressions in a linked way. In this paper, we propose a tensor regression model based on Tucker Decomposition, which identifies not only the common components of parameters across all the regression tasks, but also independent factors contributing to each particular regression task simultaneously. Under this paradigm, the number of independent parameters along each mode is constrained by a sparsity-preserving regulariser. Linked multiway parameter analysis and sparsity modeling further reduce the total number of parameters, with lower memory cost than their tensor-based counterparts. The effectiveness of the new method is demonstrated on real data sets.

Eye movement and diffusion tensor imaging analysis of treatment effects in a Niemann-Pick Type C patient

New treatment options for Niemann-Pick Type C (NPC) have recently become available. To assess the efficiency and efficacy of these new treatment markers for disease status and progression are needed. Both the diagnosis and the monitoring of disease progression are challenging and mostly rely on clinical impression and functional testing of horizontal eye movements. Diffusion tensor imaging (DTI) provides information about the microintegrity especially of white matter. We show here in a case report how DTI and measures derived from this imaging method can serve as adjunct quantitative markers for disease management in Niemann-Pick Type C. Two approaches are taken--first, we compare the fractional anisotropy (FA) in the white matter globally between a 29-year-old NPC patient and 18 healthy age-matched controls and show the remarkable difference in FA relatively early in the course of the disease. Second, a voxelwise comparison of FA values reveals where white matter integrity is compromised locally and demonstrate an individualized analysis of FA changes before and after 1year of treatment with Miglustat. This method might be useful in future treatment trials for NPC to assess treatment effects.

Incremental tensor biased discriminant analysis:a new color-based visual tracking method

Most existing color-based tracking algorithms utilize the statistical color information of the object as the tracking clues, without maintaining the spatial structure within a single chromatic image. Recently, the researches on the multilinear algebra provide the possibility to hold the spatial structural relationship in a representation of the image ensembles. In this paper, a third-order color tensor is constructed to represent the object to be tracked. Considering the influence of the environment changing on the tracking, the biased discriminant analysis (BDA) is extended to the tensor biased discriminant analysis (TBDA) for distinguishing the object from the background. At the same time, an incremental scheme for the TBDA is developed for the tensor biased discriminant subspace online learning, which can be used to adapt to the appearance variant of both the object and background. The experimental results show that the proposed method can track objects precisely undergoing large pose, scale and lighting changes, as well as partial occlusion. © 2009 Elsevier B.V.

A positional FEM Formulation for geometrical non-linear analysis of shells

This work presents a fully non-linear finite element formulation for shell analysis comprising linear strain variation along the thickness of the shell and geometrically exact description for curved triangular elements. The developed formulation assumes positions and generalized unconstrained vectors as the variables of the problem, not displacements and finite rotations. The full 3D Saint-Venant-Kirchhoff constitutive relation is adopted and, to avoid locking, the rate of thickness variation enhancement is introduced. As a consequence, the second Piola-Kirchhoff stress tensor and the Green strain measure are employed to derive the specific strain energy potential. Curved triangular elements with cubic approximation are adopted using simple notation. Selected numerical simulations illustrate and confirm the objectivity, accuracy, path independence and applicability of the proposed technique.

An evaluation of the time dependence of the anisotropy of the water diffusion tensor in acute human ischemia

We have performed MRI examinations to determine the water diffusion tensor in the brain of six patients who were admitted to the hospital within 12 h after the onset of cerebral ischemic symptoms. The examinations have been carried out immediately after admission, and thereafter at varying intervals up to 90 days post admission. Maps of the trace of the diffusion tensor, the fractional anisotropy and the lattice index, as well as maps of cerebral blood perfusion parameters, were generated to quantitatively assess the character of the water diffusion tensor in the infarcted area. In patients with significant perfusion deficits and substantial lesion volume changes, four of six cases, our measurements show a monotonic and significant decrease in the diffusion anisotropy within the ischemic lesion as a function of time. We propose that retrospective analysis of this quantity, in combination with brain tissue segmentation and cerebral perfusion maps, may be used in future studies to assess the severity of the ischemic event. (C) 1999 Elsevier Science Inc.

Caracterização de regiões encefálicas no cérebro normal por tensor de difusão e aplicação à epilepsia pós-traumática

Mestrado em Radiações Aplicadas às Tecnologias da Saúde.

Characterizing aging in the human brainstem using quantitative multimodal MRI analysis.

Aging is ubiquitous to the human condition. The MRI correlates of healthy aging have been extensively investigated using a range of modalities, including volumetric MRI, quantitative MRI (qMRI), and diffusion tensor imaging. Despite this, the reported brainstem related changes remain sparse. This is, in part, due to the technical and methodological limitations in quantitatively assessing and statistically analyzing this region. By utilizing a new method of brainstem segmentation, a large cohort of 100 healthy adults were assessed in this study for the effects of aging within the human brainstem in vivo. Using qMRI, tensor-based morphometry (TBM), and voxel-based quantification (VBQ), the volumetric and quantitative changes across healthy adults between 19 and 75 years were characterized. In addition to the increased R2* in substantia nigra corresponding to increasing iron deposition with age, several novel findings were reported in the current study. These include selective volumetric loss of the brachium conjunctivum, with a corresponding decrease in magnetization transfer and increase in proton density (PD), accounting for the previously described "midbrain shrinkage." Additionally, we found increases in R1 and PD in several pontine and medullary structures. We consider these changes in the context of well-characterized, functional age-related changes, and propose potential biophysical mechanisms. This study provides detailed quantitative analysis of the internal architecture of the brainstem and provides a baseline for further studies of neurodegenerative diseases that are characterized by early, pre-clinical involvement of the brainstem, such as Parkinson's and Alzheimer's diseases.

Magnetic resonance imaging determinants of intraindividual variability in the elderly: combined analysis of grey and white matter.

Elderly individuals display a rapid age-related increase in intraindividual variability (IIV) of their performances. This phenomenon could reflect subtle changes in frontal lobe integrity. However, structural studies in this field are still missing. To address this issue, we computed an IIV index for a simple reaction time (RT) task and performed magnetic resonance imaging (MRI) including voxel based morphometry (VBM) and the tract based spatial statistics (TBSS) analysis of diffusion tensor imaging (DTI) in 61 adults aged from 22 to 88 years. The age-related IIV increase was associated with decreased fractional anisotropy (FA) as well as increased radial (RD) and mean (MD) diffusion in the main white matter (WM) fiber tracts. In contrast, axial diffusion (AD) and grey matter (GM) densities did not show any significant correlation with IIV. In multivariate models, only FA has an age-independent effect on IIV. These results revealed that WM but not GM changes partly mediated the age-related increase of IIV. They also revealed that the association between WM and IIV could not be only attributed to the damage of frontal lobe circuits but concerned the majority of interhemispheric and intrahemispheric corticocortical connections.

Anti-basal ganglia antibodies and Tourette's syndrome: a voxel-based morphometry and diffusion tensor imaging study in an adult population.

Anti-basal ganglia antibodies (ABGAs) have been suggested to be a hallmark of autoimmunity in Gilles de la Tourette's syndrome (GTS), possibly related to prior exposure to streptococcal infection. In order to detect whether the presence of ABGAs was associated with subtle structural changes in GTS, whole-brain analysis using independent sets of T(1) and diffusion tensor imaging MRI-based methods were performed on 22 adults with GTS with (n = 9) and without (n = 13) detectable ABGAs in the serum. Voxel-based morphometry analysis failed to detect any significant difference in grey matter density between ABGA-positive and ABGA-negative groups in caudate nuclei, putamina, thalami and frontal lobes. These results suggest that ABGA synthesis is not related to structural changes in grey and white matter (detectable with these methods) within frontostriatal circuits.

Brain network analysis of patients with Temporal Lobe Epilepsy

Patients with Temporal Lobe Epilepsy (TLE) suffer from widespread subtle white matter abnormalities and abnormal functional connectivity extending beyond the affected lobe, as revealed by Diffusion Tensor MR Imaging, volumetric and functional MRI studies. Diffusion Spectrum Imaging (DSI) is a diffusion imaging technique with high angular resolution for improving the mapping of white matter pathways. In this study, we used DSI, connectivity matrices and topological measures to investigate how the alteration in structural connectivity influences whole brain structural networks. Eleven patients with right-sided TLE and hippocampal sclerosis and 18 controls underwent our DSI protocol at 3T. The cortical and subcortical grey matters were parcellated into 86 regions of interest and the connectivity between every region pair was estimated using global tractography and a connectivity matrix (the adjacency matrix of the structural network). We then compared the networks of patients and controls using topological measures. In patients, we found a higher characteristic path length and a lower clustering coefficient compared to controls. Local measures at node level of the clustering and efficiency showed a significant difference after a multiple comparison correction (Bonferroni). These significant nodes were located within as well outside the temporal lobe, and the localisation of most of them was consistent with regions known to be part of epileptic networks in TLE. Our results show altered connectivity patterns that are concordant with the mapping of functional epileptic networks in patients with TLE. Further studies are needed to establish the relevance of these findings for the propagation of epileptic activity, cognitive deficits in medial TLE and outcome of epilepsy surgery in individual patients.