scholarly journals Fast and Analytical EAP Approximation from a 4th-Order Tensor

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Aurobrata Ghosh ◽  
Rachid Deriche
Keyword(s):  
Diffusion Tensor ◽  
Hermite Polynomials ◽  
Synthetic Data ◽  
Orientation Distribution ◽  
Underlying Structure ◽  
Diffusivity Coefficient ◽  
Model Complex ◽  
Higher Order Tensors ◽  
Diffusion Tensors

Generalized diffusion tensor imaging (GDTI) was developed to model complex apparent diffusivity coefficient (ADC) using higher-order tensors (HOTs) and to overcome the inherent single-peak shortcoming of DTI. However, the geometry of a complex ADC profile does not correspond to the underlying structure of fibers. This tissue geometry can be inferred from the shape of the ensemble average propagator (EAP). Though interesting methods for estimating a positive ADC using 4th-order diffusion tensors were developed, GDTI in general was overtaken by other approaches, for example, the orientation distribution function (ODF), since it is considerably difficult to recuperate the EAP from a HOT model of the ADC in GDTI. In this paper, we present a novel closed-form approximation of the EAP using Hermite polynomials from a modified HOT model of the original GDTI-ADC. Since the solution is analytical, it is fast, differentiable, and the approximation converges well to the true EAP. This method also makes the effort of computing a positive ADC worthwhile, since now both the ADC and the EAP can be used and have closed forms. We demonstrate our approach with 4th-order tensors on synthetic data and in vivo human data.

scholarly journals Probing tissue microstructure by diffusion skewness tensor imaging

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Lipeng Ning ◽  
Filip Szczepankiewicz ◽  
Markus Nilsson ◽  
Yogesh Rathi ◽  
Carl-Fredrik Westin
Keyword(s):  
Diffusion Processes ◽  
Diffusion Tensor ◽  
Fundamental Problem ◽  
Medical Science ◽  
Synthetic Data ◽  
Full Rank ◽  
Imaging Data ◽  
Tissue Microstructure ◽  
Diffusion Tensors

AbstractProbing the cellular structure of in vivo biological tissue is a fundamental problem in biomedical imaging and medical science. This work introduces an approach for analyzing diffusion magnetic resonance imaging data acquired by the novel tensor-valued encoding technique for characterizing tissue microstructure. Our approach first uses a signal model to estimate the variance and skewness of the distribution of apparent diffusion tensors modeling the underlying tissue. Then several novel imaging indices, such as weighted microscopic anisotropy and microscopic skewness, are derived to characterize different ensembles of diffusion processes that are indistinguishable by existing techniques. The contributions of this work also include a theoretical proof that shows that, to estimate the skewness of a diffusion tensor distribution, the encoding protocol needs to include full-rank tensor diffusion encoding. This proof provides a guideline for the application of this technique. The properties of the proposed indices are illustrated using both synthetic data and in vivo data acquired from a human brain.

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.

scholarly journals In vivo generalized diffusion tensor imaging (GDTI) using higher-order tensors (HOT)

2009 ◽  
Vol 63 (1) ◽  
pp. 243-252 ◽  
Author(s):  
Chunlei Liu ◽  
Sarah C. Mang ◽  
Michael E. Moseley
Keyword(s):  
Diffusion Tensor Imaging ◽  
Diffusion Tensor ◽  
Higher Order ◽  
Higher Order Tensors

scholarly journals Enabling constrained spherical deconvolution and diffusional variance decomposition with tensor-valued diffusion MRI

2021 ◽  
Author(s):  
Philippe Karan ◽  
Alexis Reymbaut ◽  
Guillaume Gilbert ◽  
Maxime Descoteaux
Keyword(s):  
Diffusion Mri ◽  
Diffusion Tensor ◽  
Simulated Data ◽  
Orientation Distribution ◽  
Variance Decomposition ◽  
Distribution Functions ◽  
Constrained Spherical Deconvolution ◽  
Spherical Deconvolution ◽  
Fiber Orientation Distribution

Diffusion tensor imaging (DTI) is widely used to extract valuable tissue measurements and white matter (WM) fiber orientations, even though its lack of specificity is now well-known, especially for WM fiber crossings. Models such as constrained spherical deconvolution (CSD) take advantage of HARDI data to compute fiber orientation distribution functions (fODF) and tackle the orientational part of the DTI limitations. Furthermore, the recent introduction of tensor-valued diffusion MRI allows for diffusional variance decomposition (DIVIDE), opening the door to the computation of measures more specific to microstructure than DTI measures, such as microscopic fractional anisotropy (μFA). However, tensor-valued diffusion MRI data is not compatible with latest versions of CSD and the impacts of such atypical data on fODF reconstruction with CSD are yet to be studied. In this work, we lay down the mathematical and computational foundations of a tensor-valued CSD and use simulated data to explore the effects of various combinations of diffusion encodings on the angular resolution of extracted fOFDs. We also compare the combinations with regards to their performance at producing accurate and precise μFA with DIVIDE, and present an optimised protocol for both methods. We show that our proposed protocol enables the reconstruction of both fODFs and μFA on in vivo data.

scholarly journals A new framework for MR diffusion tensor distribution

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Kulam Najmudeen Magdoom ◽  
Sinisa Pajevic ◽  
Gasbarra Dario ◽  
Peter J. Basser
Keyword(s):  
Diffusion Processes ◽  
Diffusion Tensor ◽  
Ground Truth ◽  
Structural Heterogeneity ◽  
Wide Range ◽  
Mr Diffusion ◽  
Diffusion Tensors ◽  
Well Posed ◽  
New Framework

AbstractThe ability to characterize heterogeneous and anisotropic water diffusion processes within macroscopic MRI voxels non-invasively and in vivo is a desideratum in biology, neuroscience, and medicine. While an MRI voxel may contain approximately a microliter of tissue, our goal is to examine intravoxel diffusion processes on the order of picoliters. Here we propose a new theoretical framework and efficient experimental design to describe and measure such intravoxel structural heterogeneity and anisotropy. We assume that a constrained normal tensor-variate distribution (CNTVD) describes the variability of positive definite diffusion tensors within a voxel which extends its applicability to a wide range of b-values while preserving the richness of diffusion tensor distribution (DTD) paradigm unlike existing models. We introduce a new Monte Carlo (MC) scheme to synthesize realistic 6D DTD numerical phantoms and invert the MR signal. We show that the signal inversion is well-posed and estimate the CNTVD parameters parsimoniously by exploiting the different symmetries of the mean and covariance tensors of CNTVD. The robustness of the estimation pipeline is assessed by adding noise to calculated MR signals and compared with the ground truth. A family of invariant parameters and glyphs which characterize microscopic shape, size and orientation heterogeneity within a voxel are also presented.

scholarly journals A New Framework for MR Diffusion Tensor Distribution

2020 ◽  
Author(s):  
Kulam Najmudeen Magdoom ◽  
Sinisa Pajevic ◽  
Gasbarra Dario ◽  
Peter J. Basser
Keyword(s):  
Diffusion Processes ◽  
Diffusion Tensor ◽  
Ground Truth ◽  
Structural Heterogeneity ◽  
Wide Range ◽  
Mr Diffusion ◽  
Diffusion Tensors ◽  
Well Posed ◽  
New Framework

AbstractThe ability to characterize heterogeneous and anisotropic water diffusion processes within macro-scopic MRI voxels non-invasively and in vivo is a desideratum in biology, neuroscience, and medicine. While an MRI voxel may contain approximately a microliter of tissue, our goal is to examine intravoxel diffusion processes on the order of picoliters. Here we propose a new theoretical framework and experimental design to describe and measure such intravoxel structural heterogeneity and anisotropy. We assume that a constrained normal tensor-variate distribution (CNTVD) describes the variability of positive definite diffusion tensors within a voxel which extends its applicability to a wide range of b-values unlike existing models. We use a Monte Carlo scheme to synthesize realistic numerical diffusion tensor distribution (DTD) phantoms and invert the MR signal. We show that the signal inversion is well-posed and estimate the CNTVD parameters parsimoniously by exploiting the different symmetries of the mean and covariance tensors of CNTVD. The robustness of the estimation pipeline is assessed by adding noise to calculated MR signals and compared with the ground truth. A family of invariant parameters which characterize microscopic shape, size and orientation heterogeneity within a voxel are also presented.

scholarly journals Crossing Fibers Detection with an Analytical High Order Tensor Decomposition

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
T. Megherbi ◽  
M. Kachouane ◽  
F. Oulebsir-Boumghar ◽  
R. Deriche
Keyword(s):  
Human Brain ◽  
Synthetic Data ◽  
Tensor Decomposition ◽  
Orientation Distribution ◽  
High Order ◽  
Order Tensor ◽  
Brain White Matter ◽  
Fiber Orientation Distribution ◽  
Crossing Fibers

Diffusion magnetic resonance imaging (dMRI) is the only technique to probein vivoand noninvasively the fiber structure of human brain white matter. Detecting the crossing of neuronal fibers remains an exciting challenge with an important impact in tractography. In this work, we tackle this challenging problem and propose an original and efficient technique to extract all crossing fibers from diffusion signals. To this end, we start by estimating, from the dMRI signal, the so-called Cartesian tensor fiber orientation distribution (CT-FOD) function, whose maxima correspond exactly to the orientations of the fibers. The fourth order symmetric positive definite tensor that represents the CT-FOD is then analytically decomposed via the application of a new theoretical approach and this decomposition is used to accurately extract all the fibers orientations. Our proposed high order tensor decomposition based approach is minimal and allows recovering the whole crossing fibers without any a priori information on the total number of fibers. Various experiments performed on noisy synthetic data, on phantom diffusion, data and on human brain data validate our approach and clearly demonstrate that it is efficient, robust to noise and performs favorably in terms of angular resolution and accuracy when compared to some classical and state-of-the-art approaches.

scholarly journals Fiber Visualization with LIC Maps Using Multidirectional Anisotropic Glyph Samples

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Mark Höller ◽  
Kay-M. Otto ◽  
Uwe Klose ◽  
Samuel Groeschel ◽  
Hans-H. Ehricke
Keyword(s):  
Diffusion Tensor ◽  
Diffusion Imaging ◽  
Three Dimensional ◽  
Orientation Distribution ◽  
Brain Regions ◽  
High Angular Resolution ◽  
Tumor Patient ◽  
Integral Convolution ◽  
Fiber Orientation Distribution

Line integral convolution (LIC) is used as a texture-based technique in computer graphics for flow field visualization. In diffusion tensor imaging (DTI), LIC bridges the gap between local approaches, for example directionally encoded fractional anisotropy mapping and techniques analyzing global relationships between brain regions, such as streamline tracking. In this paper an advancement of a previously published multikernel LIC approach for high angular resolution diffusion imaging visualization is proposed: a novel sampling scheme is developed to generate anisotropic glyph samples that can be used as an input pattern to the LIC algorithm. Multicylindrical glyph samples, derived from fiber orientation distribution (FOD) functions, are used, which provide a method for anisotropic packing along integrated fiber lines controlled by a uniform random algorithm. This allows two- and three-dimensional LIC maps to be generated, depicting fiber structures with excellent contrast, even in regions of crossing and branching fibers. Furthermore, a color-coding model for the fused visualization of slices from T1 datasets together with directionally encoded LIC maps is proposed. The methodology is evaluated by a simulation study with a synthetic dataset, representing crossing and bending fibers. In addition, results fromin vivostudies with a healthy volunteer and a brain tumor patient are presented to demonstrate the method's practicality.

In vivo diffusion tensor imaging of the neonatal rat brain development

2013 ◽  
Vol 44 (S 01) ◽  
Author(s):  
M Breu ◽  
D Reisinger ◽  
D Wu ◽  
Y Zhang ◽  
A Fatemi ◽  
...  
Keyword(s):  
Diffusion Tensor Imaging ◽  
Brain Development ◽  
Rat Brain ◽  
Diffusion Tensor ◽  
Neonatal Rat ◽  
Neonatal Rat Brain

scholarly journals Meyer’s Loop Anatomy Demonstrated Using Diffusion Tensor MR Imaging and Fiber Tractography at 3T

2014 ◽  
Vol 60 (5) ◽  
pp. 215-222 ◽  
Author(s):  
Cristina Goga ◽  
Zeynep Firat ◽  
Klara Brinzaniuc ◽  
Is Florian
Keyword(s):  
Diffusion Tensor Imaging ◽  
Diffusion Tensor ◽  
Region Of Interest ◽  
Fiber Tractography ◽  
Brain Images ◽  
3 Dimensional ◽  
Software Release ◽  
Magnetic Resonance Imaging Mri ◽  
Meyer’S Loop

Abstract Objective: The ultimate anatomy of the Meyer’s loop continues to elude us. Diffusion tensor imaging (DTI) and diffusion tensor tractography (DTT) may be able to demonstrate, in vivo, the anatomy of the complex network of white matter fibers surrounding the Meyer’s loop and the optic radiations. This study aims at exploring the anatomy of the Meyer’s loop by using DTI and fiber tractography. Methods: Ten healthy subjects underwent magnetic resonance imaging (MRI) with DTI at 3 T. Using a region-of-interest (ROI) based diffusion tensor imaging and fiber tracking software (Release 2.6, Achieva, Philips), sequential ROI were placed to reconstruct visual fibers and neighboring projection fibers involved in the formation of Meyer’s loop. The 3-dimensional (3D) reconstructed fibers were visualized by superimposition on 3-planar MRI brain images to enhance their precise anatomical localization and relationship with other anatomical structures. Results: Several projection fiber including the optic radiation, occipitopontine/parietopontine fibers and posterior thalamic peduncle participated in the formation of Meyer’s loop. Two patterns of angulation of the Meyer’s loop were found. Conclusions: DTI with DTT provides a complimentary, in vivo, method to study the details of the anatomy of the Meyer’s loop.

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