Tensor calculation, noise, simulations, and optimization peter b. The six offdiagonal terms dxy, dyz, etc reflect reflect the. Anisotropic acquisition and analysis for diffusion tensor. The three diagonal elements d xx, d yy, d zz represent diffusion coefficients measured along each of the principal x, y and z laboratory axes. Diffusion tensor tractography of traumatic diffuse axonal. Scanning methods and decreased fractional anisotropy regions of the studies included in this metaanalysis of diffusion tensor imaging studies of patients with mdd metaanalysis of the reported coordinates identified 4 regions of decreased fractional anisotropy in patients compared with controls fig. Diffusion tensor imaging dti is a promising method for characterizing microstructural changes or differences with neuropathology and treatment. Aug 23, 2016 importantly, the quantitative analysis of the diffusion tensor yields d. Diffusion tensor images were acquired in the axial plane with diffusion sensitization gradients applied in six noncollinear directions with bvalue of smm 2. A superior method to model diffusion in complex materials is to use the diffusion tensor, a 3 x 3 array of numbers corresponding to diffusion rates in each combination of directions. Diffusion tensor imaging dti is one of the most powerful magnetic resonance. Higherorder tensors in diffusion imaging uchicago stat. The same imaging parameters were applied to acquire t2 weighted b. Pdf voxelbased analysis of the diffusion tensor hiroyuki.
Diffusion tensor imaging and fiber tractography of human. Patent 5,539,310 and implemented by all major commercial mri systems provides information primarily about how water diffuses in the extracellular compartment of tissues, where water mobility is hindered i. Diffusion tensor tractography dttbased quantification may have advantages over roibased dti analysis. Diffusion tensor analysis by twodimensional pair correlation. These results confirm that the proposed approach can reveal anisotropic diffusion in. Fractional anisotropy alterations in individuals born. In vivo cardiac diffusion tensor imaging cdti is uniquely capable of interrogating laminar myocardial dynamics noninvasively.
Diffusion tensor imaging has shown promise in clinical studies of brain pathologies, such as multiple sclerosis and stroke, and in the study of brain connectivity 5. Diffusion tensor mri measurements were obtained from tractography for uncinate, arcuate, inferior longitudinal fasciculi and corticospinal tract in children with left temporal lobe epilepsy and normal conventional mri, and the data were compared to measurements in 12 agematched normal volunteers. Diffusion tensor imaging a practical handbook wim van. Diffusion tensor analysis of temporal and extratemporal lobe. An introduction to diffusion tensor image analysis ncbi nih. Here we explore whether dti abnormalities are present at the time of a first attack or cis in children and whether early dti features can predict the development of ms. Method we used the activation likelihood estimate ale method for the metaanalysis to locate anatomical regions with white matter abnormalities in a group of individuals born preterm and in termborn comparison participants. Dtmri, or dti, the measurement of the diffusion tensor by magnetic resonance imaging. T2fse images were used as the structural target for dti data processing.
The relationship between tensor parameters and duration of. Loss of white matter integrity in major depressive disorder. If an index shows up once on the left hand side lhs of sign, it must show up once and only once on the right hand side rhs of sign. Introduction to diffusion tensor imaging mathematics wiley online. Diffusion tensor imaging dti is a magnetic resonance imaging technique that enables the measurement of the restricted diffusion of water in tissue in order to produce neural tract images instead of using this data solely for the purpose of assigning contrast or colors to pixels in a crosssectional image. Diffusion tensor imaging analysis for psychiatric disorders. This book provides an overview of the practical aspects of diffusion tensor imaging dti, from understanding the basis of the technique through selection of the right protocols, troubleshooting data quality, and analyzing dti data optimally. Pdf diffusion tensor magnetic resonance imaging dti is a relatively new technology that is popular for imaging the white matter of the brain. Predicting dementia in cerebral small vessel disease using. Diffusion refers to the random brownian motion of molecules in a. Several previous reports showed atrophy or diffusion abnormalities of anterior corpus callosum in psp patients, but partitioning method used in these studies was based on data obtained in nonhuman primates.
Pdf quantitative diffusion tensor analysis using multiple. The stress at a point of an elastic solid is an example of a tensor which depends on two directions one normal to the area and other that of the force on it. Wholebrain voxelbased analysis of diffusion tensor imaging and its correlation with visual evoked potential in patients with optic neuritis kai wu1,2, xin huang1,3, gang tan 2, lei ye1, anhua wu, yulin zhong1, nan jiang1, yi shao1 1department of ophthalmology, the first affiliated hospital of nanchang university, nanchang 330006, jiangxi. Methods dti studies that compared mtbi patients and controls were searched using medline, web of science, and embase, 1980 through april 2012. Several times during the preparation of this book we taught a one semester course to students with a very limited background in linear algebra and no background in tensor analysis.
Diffusion tensor mri dti or dtmri a technique described in u. Diffusion tensor imaging analysis guide dartmouth college, gazzaniga laboratory adam c. Diffusion tensor analysis of pediatric multiple sclerosis and. Dtmri provides information about the magnitude and anisotropy of water diffusion in biological tissues. It allows the mapping of the diffusion process of molecules, mainly water, in biological tissues, in vivo and noninvasively. Dti analysis diffusionweighted image preprocessing dti preprocessing, including correction for eddy current distortions, and head movement have been described previously. Data acquisition and processing the diffusion tensor with plain diffusion mri, diffusion is fully described using a single scalar parameter, the diffusion coef.
Diffusion tensor analysis of temporal and extratemporal. Pdf an introduction to diffusion tensor image analysis. The tensor contains the following information about the diffusion. Gridifying a diffusion tensor imaging analysis pipeline. Diffusion tensor dt imaging is an mr imaging technique that can be used to characterize the directional properties of the diffusion of water molecules. Many individual steps in the processing and analysis of dti data can be. Table 2 summary of 3d intravoxel dai formulas that range from 0 isotropic to 1 anisotropic, expressed in terms of tensor elements. Tensor analysis is the type of subject that can make even the best of students shudder. The three diagonal elements dxx, dyy, dzz represent diffusion coefficients measured along each of the principal x, y and z laboratory axes. Research open access metaanalysis of diffusion tensor. Diffusion tensor imaging studies of mild traumatic brain. My own postgraduate instructor in the subject took away much of the fear by speaking of an implicit rhythm in the peculiar notation traditionally used, and helped me to see how this rhythm plays its way throughout the various formalisms.
Statistical analysis of diffusion tensors in diffusion. Ennis1 and gordon kindlmann2 this paper outlines the mathematical development and application of two analytically orthogonal tensor invariants sets. Fractional anisotropy alterations in individuals born preterm. Predicting dementia in cerebral small vessel disease using an. Orthogonal tensor invariants and the analysis of diffusion tensor magnetic resonance images daniel b. However, it is likely that teachers will wish to generate additional exercises. Pdf diffusion tensor imaging dti is one of the most powerful magnetic. After analytical diagonalization of diffusion tensor, a 3d shape is formed by calculating three eigenvectors having three eigenvalues l1, l2 and l3.
If an index shows up once on the left hand side lhs of sign, it must show up once and only once on the right hand side rhs of. The most advanced application is certainly that of. In this way, a summary statistic of data quality can be shown for each slice and for all. For algebra on vectors and tensors, an index must show up twice and only twice. Gridifying a diffusion tensor imaging analysis pipeline matthan w. Relationship between cardiac diffusion tensor imaging. Quantitative diffusion tensor analysis using multiple tensor ellipsoids model and tensor field interpolation at fiber crossing. Diffusion tensor mri dtmri is a noninvasive method for mapping the diffusion properties in vivo. The diffusion tensor basically describes the 3d diffusion phenomenon by using a matrix of numbers derived from measurements of at least six or more applied diffusion gradients in different ways. Pdf a basic introduction to diffusion tensor imaging mathematics. Diffusion tensor analysis of pediatric multiple sclerosis. Elementary tensor analysis this appendix is intended to provide the mathematical preliminaries needed for a clear and rigorous presentation of the basic principles in continuum mechanics. The nmr measurement of the effective diffusion tensor.
Tensors have their applications to riemannian geometry, mechanics, elasticity, theory of relativity. We expect that these methods will be useful in the registration of diffusion tensor images, the production of statistical atlases from diffusion tensor data, and the quanti. Riemannian geometry for the statistical analysis of. Diffusion tensor imaging dti is a specialist mri modality that can identify microstructural changes or abnormalities in the brain. The diffusion tensor dt is a modelbased approach of describing the molecular diffusion displacement in a threedimensional biological medium. Diffusionweighted magnetic resonance imaging dwi or dwmri is the use of specific mri sequences as well as software that generates images from the resulting data that uses the diffusion of water molecules to generate contrast in mr images. Diffusion tensor imaging dti for medical applications, diffusion tensors describe the anisotropic diffusion behavior of water molecules in tissue. A comprehensive dataset of quantative parameters and comparison with subject anthropometrics is required. The reader is expected to be familiar with some notions of vector spaces or matrix algebra. Fiber tractoriented statistics for quantitative diffusion. Van hecke presently divides his time between pursuing research in advanced dti analysis at. In this study, we performed a diffusion tensor analysis using a new partitioning method for the human corpus callosum. Method we used the activation likelihood estimate ale method for the meta analysis to locate anatomical regions with white matter abnormalities in a group of individuals born preterm and in termborn comparison participants.
Pdf or orientation density function odf of the underlying. Olabarriaga academic medical center, university of amsterdam, nl email. Diffusion tensor histogram analysis of pediatric diffuse. Diffusion tensor imaging dti tracks the effective diffusion of water. Riemannian geometry for the statistical analysis of diffusion. Diffusion tensor and qspace mri specimen characterization. Using diffusion tensor imaging dti we employed a voxelbased analysis approach to examine fractional anisotropy fa in 86 patients experiencing an acute major depressive episode. Dti analysis diffusion weighted image preprocessing dti preprocessing, including correction for eddy current distortions, and head movement have been described previously. Data was acquired from the mid left ventricle in 43. Diffusion tensor histogram analysis of pediatric diffuse intrinsic pontine glioma clinical study emilie a. Tensor decompositions are an active and challenging topic in applied mathematics, since fundamental concepts from linear algebra, such as the singular value. An ellipsoid diffusion tensor water molecules move in physical brownian motion t time. Wim van hecke, phd, is an international expert in mri analysis and advanced neuroimaging techniques and applications. February diffusion tensor imaging studies of cervical spondylotic myelopathy.
The effect of diffusion on the mri signal most often a spinecho signal is an attenuation, a, which dependsond andontheb factor. Diffusion tensor interpolation, diffusion tensor statistics, dti analysis. An introduction to tensors for students of physics and. For nontensor or multipletensor based analyses, the. We assessed regionofinterest and tractbased mean adc and mean fa values for 3 major.
Diffusion tensor analysis of corpus callosum in progressive. Kingsley department of radiology,north shore university hospital, 300 community drive,manhasset,new york 11030,and. An academic engineer by training with two masters degrees in applied biomedical engineering and neuroimaging, and a phd in diffusion mri analysis, dr. Original article wholebrain voxelbased analysis of. In a homogeneous liquid such as water, the diffusion coef. The diffusion tensor may be used to characterize the magnitude, anisotropy and orientation of the diffusion tensor. Importantly, the quantitative analysis of the diffusion tensor yields d. The six offdiagonal terms dxy, dyz, etc reflect reflect. Diffusion tensor imaging studies of cervical spondylotic.
Korgaonkar ms, grieve sm, koslow sh, gabrieli jd, gordon e, williams lm. Diffusion tensor magnetic resonance imaging dti is a relatively new technology that is popular for imaging the white matter of the brain. Introduction to diffusion tensor imaging mathematics. Scanning methods and decreased fractional anisotropy regions of the studies included in this meta analysis of diffusion tensor imaging studies of patients with mdd meta analysis of the reported coordinates identified 4 regions of decreased fractional anisotropy in patients compared with controls fig. Examples from a clinical neuroimaging study of the early developing brain illustrate the potential of this new method to assess white matter. Diffusion tensor fiber tractography of the optic radiation. Van hecke presently divides his time between pursuing research in advanced dti analysis at antwerp university hospital and. A basic introduction to diffusion tensor imaging mathematics and.
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