scholarly journals On What Manifold do Diffusion Tensors Live?

2008 ◽  
Author(s):  
Ofer Pasternak ◽  
Ragini Verma ◽  
Nir Sochen ◽  
Peter J. Basser
Keyword(s):  
Diffusion Tensor ◽  
Affine Invariant ◽  
Clinical Tool ◽  
Basic Notion ◽  
Euclidean Metric ◽  
Statistical Framework ◽  
Euclidean Metrics ◽  
Diffusion Tensors ◽  
Tensor Data ◽  
Confidence Estimates

Diffusion tensor imaging has become an important research and clinical tool, owing to its unique ability to infer microstructural properties of living tissue. Increased use has led to a demand for statistical tools to analyze diffusion tensor data and perform, for example, confidence estimates, ROI analysis, and group comparisons. A first step towards developing a statistical framework is establishing the basic notion of distance between tensors. We investigate the properties of two previously proposed metrics that define a Riemannian manifold: the affine-invariant and Euclidean metrics. We find that the Euclidean metric is more appropriate for intra-voxel comparisons, and suggest that a context-dependent metric may be required for inter-voxel comparisons.

scholarly journals Exploiting Spatial Information to Enhance DTI Segmentations via Spatial Fuzzy c-Means with Covariance Matrix Data and Non-Euclidean Metrics

2021 ◽  
Vol 11 (15) ◽  
pp. 7003
Author(s):  
Safa Elsheikh ◽  
Andrew Fish ◽  
Diwei Zhou
Keyword(s):  
Spatial Information ◽  
Diffusion Tensor ◽  
Contextual Information ◽  
Fuzzy C Means ◽  
Tensor Models ◽  
Diffusion Tensor Images ◽  
Fuzzy C Means Clustering ◽  
Euclidean Metrics ◽  
Diffusion Tensors ◽  
Tensor Data

A diffusion tensor models the covariance of the Brownian motion of water at a voxel and is required to be symmetric and positive semi-definite. Therefore, image processing approaches, designed for linear entities, are not effective for diffusion tensor data manipulation, and the existence of artefacts in diffusion tensor imaging acquisition makes diffusion tensor data segmentation even more challenging. In this study, we develop a spatial fuzzy c-means clustering method for diffusion tensor data that effectively segments diffusion tensor images by accounting for the noise, partial voluming, magnetic field inhomogeneity, and other imaging artefacts. To retain the symmetry and positive semi-definiteness of diffusion tensors, the log and root Euclidean metrics are used to estimate the mean diffusion tensor for each cluster. The method exploits spatial contextual information and provides uncertainty information in segmentation decisions by calculating the membership values for assigning a diffusion tensor at one voxel to different clusters. A regularisation model that allows the user to integrate their prior knowledge into the segmentation scheme or to highlight and segment local structures is also proposed. Experiments on simulated images and real brain datasets from healthy and Spinocerebellar ataxia 2 subjects showed that the new method was more effective than conventional segmentation methods.

Human Brain Diffusion Tensor Imaging Visualization With Virtual Reality

2010 ◽  
Author(s):  
Bin Chen ◽  
John Moreland
Keyword(s):  
Virtual Reality ◽  
Diffusion Tensor Imaging ◽  
White Matter ◽  
Diffusion Tensor ◽  
Biological Tissues ◽  
Head Tracking ◽  
Fiber Tractography ◽  
Brain White Matter ◽  
Diffusion Tensors ◽  
Visualization Techniques

Magnetic resonance diffusion tensor imaging (DTI) is sensitive to the anisotropic diffusion of water exerted by its macromolecular environment and has been shown useful in characterizing structures of ordered tissues such as the brain white matter, myocardium, and cartilage. The water diffusivity inside of biological tissues is characterized by the diffusion tensor, a rank-2 symmetrical 3×3 matrix, which consists of six independent variables. The diffusion tensor contains much information of diffusion anisotropy. However, it is difficult to perceive the characteristics of diffusion tensors by looking at the tensor elements even with the aid of traditional three dimensional visualization techniques. There is a need to fully explore the important characteristics of diffusion tensors in a straightforward and quantitative way. In this study, a virtual reality (VR) based MR DTI visualization with high resolution anatomical image segmentation and registration, ROI definition and neuronal white matter fiber tractography visualization and fMRI activation map integration is proposed. The VR application will utilize brain image visualization techniques including surface, volume, streamline and streamtube rendering, and use head tracking and wand for navigation and interaction, the application will allow the user to switch between different modalities and visualization techniques, as well making point and choose queries. The main purpose of the application is for basic research and clinical applications with quantitative and accurate measurements to depict the diffusivity or the degree of anisotropy derived from the diffusion tensor.

scholarly journals Directional volume growing for the extraction of white matter tracts from diffusion tensor data

2005 ◽  
Author(s):  
D. Merhof ◽  
P. Hastreiter ◽  
C. Nimsky ◽  
R. Fahlbusch ◽  
G. Greiner
Keyword(s):  
White Matter ◽  
Diffusion Tensor ◽  
White Matter Tracts ◽  
Tensor Data

scholarly journals Combined diffusion and strain tensor MRI reveals a heterogeneous, planar pattern of strain development during isometric muscle contraction

2011 ◽  
Vol 300 (5) ◽  
pp. R1079-R1090 ◽  
Author(s):  
Erin K. Englund ◽  
Christopher P. Elder ◽  
Qing Xu ◽  
Zhaohua Ding ◽  
Bruce M. Damon
Keyword(s):  
Muscle Contraction ◽  
Muscle Fiber ◽  
Diffusion Tensor ◽  
Strain Tensor ◽  
Three Dimensional ◽  
Fiber Direction ◽  
Strain Pattern ◽  
Isometric Muscle Contraction ◽  
Diffusion Tensors

The purposes of this study were to create a three-dimensional representation of strain during isometric contraction in vivo and to interpret it with respect to the muscle fiber direction. Diffusion tensor MRI was used to measure the muscle fiber direction of the tibialis anterior (TA) muscle of seven healthy volunteers. Spatial-tagging MRI was used to measure linear strains in six directions during separate 50% maximal isometric contractions of the TA. The strain tensor (E) was computed in the TA's deep and superficial compartments and compared with the respective diffusion tensors. Diagonalization of E revealed a planar strain pattern, with one nonzero negative strain (εN) and one nonzero positive strain (εP); both strains were larger in magnitude ( P < 0.05) in the deep compartment [εN = −40.4 ± 4.3%, εP = 35.1 ± 3.5% (means ± SE)] than in the superficial compartment (εN = −24.3 ± 3.9%, εP = 6.3 ± 4.9%). The principal shortening direction deviated from the fiber direction by 24.0 ± 1.3° and 39.8 ± 6.1° in the deep and superficial compartments, respectively ( P < 0.05, deep vs. superficial). The deviation of the shortening direction from the fiber direction was due primarily to the lower angle of elevation of the shortening direction over the axial plane than that of the fiber direction. It is concluded that three-dimensional analyses of strain interpreted with respect to the fiber architecture are necessary to characterize skeletal muscle contraction in vivo. The deviation of the principal shortening direction from the fiber direction may relate to intramuscle variations in fiber length and pennation angle.

Potential of a statistical approach for the standardization of multicenter diffusion tensor data: A phantom study

2019 ◽  
Vol 49 (4) ◽  
pp. 955-965 ◽  
Author(s):  
Charlotte Timmermans ◽  
Dirk Smeets ◽  
Jan Verheyden ◽  
Vasilis Terzopoulos ◽  
Vincenzo Anania ◽  
...  
Keyword(s):  
Statistical Approach ◽  
Diffusion Tensor ◽  
Phantom Study ◽  
Tensor Data

Some Comments on Non-Euclidean Mental Maps

1982 ◽  
Vol 14 (1) ◽  
pp. 107-118 ◽  
Author(s):  
R G Golledge ◽  
L J Hubert
Keyword(s):  
Spatial Representation ◽  
Mental Maps ◽  
Curved Spaces ◽  
Euclidean Metric ◽  
General Properties ◽  
Cognitive Information ◽  
Euclidean Metrics

The Euclidean metric is perhaps the most commonly used and most convenient one for representing mapped phenomena. In this paper we examine the suitability of representing cognitive phenomena via the Euclidean metric. Some general properties of spaces are examined with particular emphasis on the properties of isotropy, incompleteness, and curvature, and a more detailed discussion is undertaken of the suitability of using curved spaces (particularly Reimannian spaces) for the representation of cognitive information. A final discussion is presented on the problems of handling manifolds with folds, warps, and tears; and speculations are made concerning the appropriateness of non-Euclidean metrics for the spatial representation of mental maps.

Morphometry on diffusion tensor data

NeuroImage ◽  
2001 ◽  
Vol 13 (6) ◽  
pp. 128 ◽  
Author(s):  
V. Glauche ◽  
M. Sach ◽  
M. Koch ◽  
G. Winkler ◽  
U. Nolte ◽  
...  
Keyword(s):  
Diffusion Tensor ◽  
Tensor Data

scholarly journals Streamline Visualization of Diffusion Tensor Data Based on Triangle Strips

2006 ◽  
pp. 271-275 ◽  
Author(s):  
Dorit Merhof ◽  
Markus Sonntag ◽  
Frank Enders ◽  
Christopher Nimsky ◽  
Peter Hastreiter ◽  
...  
Keyword(s):  
Diffusion Tensor ◽  
Triangle Strips ◽  
Tensor Data

scholarly journals Clinical Translation of Three-Dimensional Scar, Diffusion Tensor Imaging, Four-Dimensional Flow, and Quantitative Perfusion in Cardiac MRI: A Comprehensive Review

2021 ◽  
Vol 8 ◽  
Author(s):  
Sophie Paddock ◽  
Vasiliki Tsampasian ◽  
Hosamadin Assadi ◽  
Bruno Calife Mota ◽  
Andrew J. Swift ◽  
...  
Keyword(s):  
Diffusion Tensor Imaging ◽  
Diffusion Tensor ◽  
Personalised Medicine ◽  
Three Dimensional ◽  
Reference Method ◽  
Tissue Characterisation ◽  
Clinical Tool ◽  
4D Flow ◽  
Ablation Therapy ◽  
Dimensional Flow

Cardiovascular magnetic resonance (CMR) imaging is a versatile tool that has established itself as the reference method for functional assessment and tissue characterisation. CMR helps to diagnose, monitor disease course and sub-phenotype disease states. Several emerging CMR methods have the potential to offer a personalised medicine approach to treatment. CMR tissue characterisation is used to assess myocardial oedema, inflammation or thrombus in various disease conditions. CMR derived scar maps have the potential to inform ablation therapy—both in atrial and ventricular arrhythmias. Quantitative CMR is pushing boundaries with motion corrections in tissue characterisation and first-pass perfusion. Advanced tissue characterisation by imaging the myocardial fibre orientation using diffusion tensor imaging (DTI), has also demonstrated novel insights in patients with cardiomyopathies. Enhanced flow assessment using four-dimensional flow (4D flow) CMR, where time is the fourth dimension, allows quantification of transvalvular flow to a high degree of accuracy for all four-valves within the same cardiac cycle. This review discusses these emerging methods and others in detail and gives the reader a foresight of how CMR will evolve into a powerful clinical tool in offering a precision medicine approach to treatment, diagnosis, and detection of disease.

Sign in / Sign up

Export Citation Format

Share Document