Biomedical subjects

Sinisa Pajevic

Publications and source records attributed to Sinisa Pajevic.

4 recordsLinked to original sources

PubMed2003

Parametric and non-parametric statistical analysis of DT-MRI data.

In this work parametric and non-parametric statistical methods are proposed to analyze Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) data. A Multivariate Normal Distribution is proposed as a parametric statistical model of diffusion tensor data when magnitude MR images contain no artifacts other than Johnson noise. We test this model using Monte Carlo (MC) simulations of DT-MRI experiments. The non-parametric approach proposed here is an implementation of bootstrap methodology that we call the DT-MRI bootstrap. It is used to estimate an empirical probability distribution of experimental DT-MRI data, and to perform hypothesis tests on them. The DT-MRI bootstrap is also used to obtain various statistics of DT-MRI parameters within a single voxel, and within a region of interest (ROI); we also use the bootstrap to study the intrinsic variability of these parameters in the ROI, independent of background noise. We evaluate the DT-MRI bootstrap using MC simulations and apply it to DT-MRI data acquired on human brain in vivo, and on a phantom with uniform diffusion properties.

Artifacts↗

PubMed2003

A normal distribution for tensor-valued random variables: applications to diffusion tensor MRI.

Diffusion tensor magnetic resonance imaging (DT-MRI) provides a statistical estimate of a symmetric, second-order diffusion tensor of water, D, in each voxel within an imaging volume. We propose a new normal distribution, p(D) alpha exp(-1/2 D: A: D), which describes the variability of D in an ideal DT-MRI experiment. The scalar invariant, D : A : D, is the contraction of a positive definite symmetric, fourth-order precision tensor, A, and D. A correspondence is established between D: A: D and the elastic strain energy density function in continuum mechanics--specifically between D and the second-order infinitesimal strain tensor, and between A and the fourth-order tensor of elastic coefficients. We show that A can be further classified according to different classical elastic symmetries (i.e., isotropy, transverse isotropy, orthotropy, planar symmetry, and anisotropy). When A is an isotropic fourth-order tensor, we derive an explicit analytic expression for p(D), and for the distribution of the three eigenvalues of D, p(gamma1, gamma2, gamma3), which are confirmed by Monte Carlo simulations. We show how A can be estimated from either real or synthetic DT-MRI data for any given experimental design. Here we propose a new criterion for an optimal experimental design: that A be an isotropic fourth-order tensor. This condition ensures that the statistical properties of D (and quantities derived from it) are rotationally invariant. We also investigate the degree of isotropy of several DT-MRI experimental designs. Finally, we show that the univariate and multivariate distributions are special cases of the more general tensor-variate normal distribution, and suggest how to generalize p(D) to treat normal random tensor variables that are of third- (or higher) order. We expect that this new distribution, p(D), should be useful in feature extraction; in developing a hypothesis testing framework for segmenting and classifying noisy, discrete tensor data; and in designing experiments to measure tensor quantities.

Algorithms↗

PubMed2002

A continuous tensor field approximation of discrete DT-MRI data for extracting microstructural and architectural features of tissue.

The effective diffusion tensor of water, D, measured by diffusion tensor MRI (DT-MRI), is inherently a discrete, noisy, voxel-averaged sample of an underlying macroscopic effective diffusion tensor field, D(x). Within fibrous tissues this field is presumed to be continuous and smooth at a gross anatomical length scale. Here a new, general mathematical framework is proposed that uses measured DT-MRI data to produce a continuous approximation to D(x). One essential finding is that the continuous tensor field representation can be constructed by repeatedly performing one-dimensional B-spline transforms of the DT-MRI data. The fidelity and noise-immunity of this approximation are tested using a set of synthetically generated tensor fields to which background noise is added via Monte Carlo methods. Generally, these tensor field templates are reproduced faithfully except at boundaries where diffusion properties change discontinuously or where the tensor field is not microscopically homogeneous. Away from such regions, the tensor field approximation does not introduce bias in useful DT-MRI parameters, such as Trace(D(x)). It also facilitates the calculation of several new parameters, particularly differential quantities obtained from the tensor of spatial gradients of D(x). As an example, we show that they can identify tissue boundaries across which diffusion properties change rapidly using in vivo human brain data. One important application of this methodology is to improve the reliability and robustness of DT-MRI fiber tractography.

Anisotropy↗

PubMed2002

Virtual in vivo interactive dissection of white matter fasciculi in the human brain.

This work reports the use of diffusion tensor magnetic resonance tractography to visualize the three-dimensional (3D) structure of the major white matter fasciculi within living human brain. Specifically, we applied this technique to visualize in vivo (i) the superior longitudinal (arcuate) fasciculus, (ii) the inferior longitudinal fasciculus, (iii) the superior fronto-occipital (subcallosal) fasciculus, (iv) the inferior frontooccipital fasciculus, (v) the uncinate fasciculus, (vi) the cingulum, (vii) the anterior commissure, (viii) the corpus callosum, (ix) the internal capsule, and (x) the fornix. These fasciculi were first isolated and were then interactively displayed as a 3D-rendered object. The virtual tract maps obtained in vivo using this approach were faithful to the classical descriptions of white matter anatomy that have previously been documented in postmortem studies. Since we have been able to interactively delineate and visualize white matter fasciculi over their entire length in vivo, in a manner that has only previously been possible by histological means, "virtual in vivo interactive dissection" (VIVID) adds a new dimension to anatomical descriptions of the living human brain.

Adult↗