Publications by Year: 2009

The problem of reconstruction of an apparent propagator from a series of diffusion-attenuated magnetic resonance (MR) signals is revisited. In nonimaging acquisitions, the inverse Fourier transform of the MR signal attenuation is consistent with the notion of an ensemble average propagator. However, in image acquisitions where one is interested in quantifying a displacement distribution in every voxel of the image, the propagator derived in the traditional way may lead to a counter-intuitive profile when it is nonsymmetric, which could be a problem in partially restricted environments. By exploiting the reciprocity of the diffusion propagator, an alternative is introduced, which implies a forward Fourier transform of the MR signal attenuations yielding a propagator reflected around the origin. Two simple problems were considered as examples. In the case of diffusion in the proximity of a restricting barrier, the reflected propagator yields a more meaningful result, whereas in the case of curving fibers, the original propagator is more intuitive. In the final section of the article, two more one-dimensional transformations are introduced, which enable the reconstruction of two- and three-dimensional propagators in, respectively, axially symmetric and isotropic environments - in both cases, from one-dimensional q-space MR data.

A long-standing problem in magnetic resonance imaging (MRI) is the noise-induced bias in the magnitude signals. This problem is particularly pressing in diffusion MRI at high diffusion-weighting. In this paper, we present a three-stage scheme to solve this problem by transforming noisy nonCentral Chi signals to noisy Gaussian signals. A special case of nonCentral Chi distribution is the Rician distribution. In general, the Gaussian-distributed signals are of interest rather than the Gaussian-derived (e.g., Rayleigh, Rician, and nonCentral Chi) signals because the Gaussian-distributed signals are generally more amenable to statistical treatment through the principle of least squares. Monte Carlo simulations were used to validate the statistical properties of the proposed framework. This scheme opens up the possibility of investigating the low signal regime (or high diffusion-weighting regime in the case of diffusion MRI) that contains potentially important information about biophysical processes and structures of the brain.

Theoretical and experimental studies of restricted diffusion have been conducted for decades using single pulsed field gradient (s-PFG) diffusion experiments. In homogenous samples, the diffusion-diffraction phenomenon arising from a single population of diffusing species has been observed experimentally and predicted theoretically. In this study, we introduce a composite bi-compartmental model which superposes restricted diffusion in microcapillaries with free diffusion in an unconfined compartment, leading to fast and slow diffusing components in the NMR signal decay. Although simplified (no exchange), the superposed diffusion modes in this model may exhibit features seen in more complex porous materials and biological tissues. We find that at low q-values the freely diffusing component masks the restricted diffusion component, and that prolongation of the diffusion time shifts the transition from free to restricted profiles to lower q-values. The effect of increasing the volume fraction of freely diffusing water was also studied; we find that the transition in the signal decay from the free mode to the restricted mode occurs at higher q-values when the volume fraction of the freely diffusing water is increased. These findings were then applied to a phantom consisting of crossing fibers, which demonstrated the same qualitative trends in the signal decay. The angular d-PGSE experiment, which has been recently shown to be able to measure small compartmental dimensions even at low q-values, revealed that microscopic anisotropy is lost at low q-values where the fast diffusing component is prominent. Our findings may be of importance in studying realistic systems which exhibit compartmentation.

MR diffusion tensor imaging (DTI) can measure and visualize organization of white matter fibre tracts in vivo. DTI is a relatively new imaging technique, and new tools developed for quantifying fibre tracts require evaluation. The purpose of this study was to compare the reliability of a novel clustering approach with a multiple region of interest (MROI) approach in both healthy and disease (schizophrenia) populations. DTI images were acquired in 20 participants (n=10 patients with schizophrenia: 56+/-15 years; n=10 controls: 51+/-20 years) (1.5 T GE system) with diffusion gradients applied in 23 non-collinear directions, repeated three times. Whole brain seeding and creation of fibre tracts were then performed. Interrater reliability of the clustering approach, and the MROI approach, were each evaluated and the methods compared. There was high spatial (voxel-based) agreement within and between the clustering and MROI methods. Fractional anisotropy, trace, and radial and axial diffusivity values showed high intraclass correlation (p

The primary aim of this work is to propose and investigate the effectiveness of a novel unsupervised tissue clustering and classification algorithm for diffusion tensor MRI (DTI) data. The proposed algorithm utilizes information about the degree of homogeneity of the distribution of diffusion tensors within voxels. We adapt frameworks proposed by Hext and Snedecor, where the null hypothesis of diffusion tensors belonging to the same distribution is assessed by an F-test. Tissue type is classified according to one of the four possible diffusion models, the assignment of which is determined by a parsimonious model selection framework based on Schwarz Criterion. Both numerical phantoms and diffusion-weighted imaging (DWI) data obtained from excised rat and pig spinal cords are used to test and validate these tissue clustering and classification approaches. The unsupervised clustering method effectively identifies distinct regions of interest (ROIs) in phantoms and real experimental DTI data.

Data analysis in MRI usually entails a series of processing procedures. One of these procedures is noise assessment, which in the context of this work, includes both the identification of noise-only pixels and the estimation of noise variance (standard deviation). Although noise assessment is critical to many MRI processing techniques, the identification of noise-only pixels has received less attention than has the estimation of noise variance. The main objectives of this paper are, therefore, to demonstrate (a) that the identification of noise-only pixels has an important role to play in the analysis of MRI data, (b) that the identification of noise-only pixels and the estimation of noise variance can be combined into a coherent framework, and (c) that this framework can be made self-consistent. To this end, we propose a novel iterative approach to simultaneously identify noise-only pixels and estimate the noise standard deviation from these identified pixels in a commonly used data structure in MRI. Experimental and simulated data were used to investigate the feasibility, the accuracy and the stability of the proposed technique.

Relating brain tissue properties to diffusion tensor imaging (DTI) is limited when an image voxel contains partial volume of brain tissue with free water, such as cerebrospinal fluid or edema, rendering the DTI indices no longer useful for describing the underlying tissue properties. We propose here a method for separating diffusion properties of brain tissue from surrounding free water while mapping the free water volume. This is achieved by fitting a bi-tensor model for which a mathematical framework is introduced to stabilize the fitting. Applying the method on datasets from a healthy subject and a patient with edema yielded corrected DTI indices and a more complete tract reconstruction that passed next to the ventricles and through the edema. We were able to segment the edema into areas according to the condition of the underlying tissue. In addition, the volume of free water is suggested as a new quantitative contrast of diffusion MRI. The findings suggest that free water is not limited to the borders of the brain parenchyma; it therefore contributes to the architecture surrounding neuronal bundles and may indicate specific anatomical processes. The analysis requires a conventional DTI acquisition and can be easily merged with existing DTI pipelines.

The multiple scattering extensions of the pulsed field gradient (PFG) experiments can be used to characterize restriction-induced anisotropy at different length scales. In double-PFG acquisitions that involve two pairs of diffusion gradient pulses, the dependence of the MR signal attenuation on the angle between the two gradients is a signature of restriction that can be observed even at low gradient strengths. In this article, a comprehensive theoretical treatment of the double-PFG observation of restricted diffusion is presented. In the first part of the article, the problem is treated for arbitrarily shaped pores under idealized experimental conditions, comprising infinitesimally narrow gradient pulses with long separation times and long or vanishing mixing times. New insights are obtained when the treatment is applied to simple pore shapes of spheres, ellipsoids, and capped cylinders. The capped cylinder geometry is considered in the second part of the article where the solution for a double-PFG experiment with arbitrary experimental parameters is introduced. Although compartment shape anisotropy (CSA) is emphasized here, the findings of this article can be used in gleaning the volume, eccentricity, and orientation distribution function associated with ensembles of anisotropic compartments using double-PFG acquisitions with arbitrary experimental parameters.

Based on a description introduced by Robertson, Grebenkov recently introduced a powerful formalism to represent the diffusion-attenuated NMR signal for simple pore geometries such as slabs, cylinders, and spheres analytically. In this work, we extend this multiple correlation function formalism by allowing for possible variations in the direction of the magnetic field gradient waveform. This extension is necessary, for example, to incorporate the effects of imaging gradients in diffusion-weighted NMR imaging scans and in characterizing anisotropy at different length scales via double pulsed field gradient (PFG) experiments. In cylindrical and spherical pores, respectively, two- and three-dimensional vector operators are employed whose form is deduced from Grebenkov’s results via elementary operator algebra for the case of cylinders and the Wigner-Eckart theorem for the case of spheres. The theory was validated by comparison with known findings and with experimental double-PFG data obtained from water-filled microcapillaries.

In confined geometries, the MR signal attenuation obtained from single pulsed gradient spin echo (s-PGSE) experiments reflects the dimension of the compartment, and in some cases, its geometry. However, to measure compartment size, high q-values must be applied, requiring high gradient strengths and/or long pulse durations and diffusion times. The angular double PGSE (d-PGSE) experiment has been proposed as a means to extract dimensions of confined geometries using low q-values. In one realization of the d-PGSE experiment, the first gradient pair is fixed along the x-axis, and the orientation of the second gradient pair is varied in the X-Y plane. Such a measurement is sensitive to microscopic anisotropy induced by the boundaries of the restricting compartment, and allows extraction of the compartment dimension. In this study, we have juxtaposed angular d-PGSE experiments and simulations to extract sizes from well-characterized NMR phantoms consisting of water filled microcapillaries. We are able to accurately extract sizes of small compartments (5mum) using the angular d-PGSE experiment even when the short gradient pulse (SGP) approximation is violated and over a range of mixing and diffusion times. We conclude that the angular d-PGSE experiment may fill an important niche in characterizing compartment sizes in which restricted diffusion occurs.