Faculty Bibliography

In Diffusion Weighted Magnetic Resonance Image (DW-MRI) processing a 2nd order tensor has been commonly used to approximate the diffusivity function at each lattice point of the DW-MRI data. It is now well known that this 2nd-order approximation fails to approximate complex local tissue structures, such as fibers crossings. In this paper we employ a 4th order symmetric positive semi-definite (PSD) tensor approximation to represent the diffusivity function and present a novel technique to estimate these tensors from the DW-MRI data guaranteeing the PSD property. There have been several published articles in literature on higher order tensor approximations of the diffusivity function but none of them guarantee the positive semi-definite constraint, which is a fundamental constraint since negative values of the diffusivity coefficients are not meaningful. In our methods, we parameterize the 4th order tensors as a sum of squares of quadratic forms by using the so called Gram matrix method from linear algebra and its relation to the Hilbert's theorem on ternary quartics. This parametric representation is then used in a nonlinear-least squares formulation to estimate the PSD tensors of order 4 from the data. We define a metric for the higher-order tensors and employ it for regularization across the lattice. Finally, performance of this model is depicted on synthetic data as well as real DW-MRI from an isolated rat hippocampus.

This report introduces a novel method to characterize the diffusion-time dependence of the diffusion-weighted magnetic resonance (MR) signal in biological tissues. The approach utilizes the theory of diffusion in disordered media where two parameters, the random walk dimension and the spectral dimension, describe the evolution of the average propagators obtained from q-space MR experiments. These parameters were estimated, using several schemes, on diffusion MR spectroscopy data obtained from human red blood cell ghosts and nervous tissue autopsy samples. The experiments demonstrated that water diffusion in human tissue is anomalous, where the mean-square displacements vary slower than linearly with diffusion time. These observations are consistent with a fractal microstructure for human tissues. Differences observed between healthy human nervous tissue and glioblastoma samples suggest that the proposed methodology may provide a novel, clinically useful form of diffusion MR contrast.

The hippocampus is a critical structure for learning and memory formation injured by diverse neuropathologies such as epilepsy or Alzheimer's disease. Recently, clinical investigations have attempted to use diffusion tensor MRI as a more specific surrogate marker for hippocampal damage. To first better understand the tissue architecture of healthy hippocampal regions, this study characterized 10 rat hippocampi with diffusion tensor imaging (DTI) at 50-microm in-plane image resolution using a 14.1-T magnet. Chemical fixation of the dissected and straightened rat hippocampus provided a simple, effective way to reduce partial volume effects when segmenting hippocampal regions and improved mean signal-to-noise per unit time (e.g. 50.6+/-4.4 at b=1250 s/mm2 in 27 min). Contrary to previous reports that water diffusion is homogeneous throughout the nervous system, statistically different mean diffusivities were observed (e.g. 0.238+/-0.054 and 0.318+/-0.084 microm2/ms for the molecular and granule cell layers respectively) (ANOVA, P<0.05). Different hippocampal subregions had lower fractional anisotropy than uniformly fibrous structures like corpus callosum because of their complex architecture. DTI-derived color fiber orientation maps and tractography demonstrated most components of the trisynaptic intrahippocampal pathway (e.g. orientations in stratum lacunosum-moleculare were dominated by perforant and Schaffer fibers) and also permitted some assessment of connectivity in the rat hippocampus.

Ex vivo biological sample imaging can complement in vivo MRI studies. Since ex vivo studies are typically performed at room temperature, and samples are frequently preserved by fixation, it is important to understand how environmental and chemical changes dictated by ex vivo studies alter the physical and MR properties of a sample. Diffusion and relaxation time measurements were used to assess the effects of temperature change and aldehyde fixation on the biophysical and MR properties of a model biological tissue comprised of erythrocyte ghosts suspended in buffer or agarose gel. Sample temperature was varied between 10 degrees C and 37 degrees C. Diffusion MRI data were analyzed with a biophysically appropriate two-compartment exchange model. Temperature change resulted in a complex alteration of water diffusion properties due to the compartmental nature of tissues and alteration in membrane permeability. Formaldehyde, Karnovsky's solution, and glutaraldehyde all caused statistically significant changes to the biophysical and MR properties of the samples. Fixation caused large decreases in water proton T2, which was restored to near prefixation values by washing free fixative from the samples. Water membrane permeability was also significantly altered by fixation. This study demonstrates that relating in vivo MR data to chemically fixed ex vivo data requires an understanding of the effects of sample preparation.

This article describes an accurate and fast method for fiber orientation mapping using multidirectional diffusion-weighted magnetic resonance (MR) data. This novel approach utilizes the Fourier transform relationship between the water displacement probabilities and diffusion-attenuated MR signal expressed in spherical coordinates. The radial part of the Fourier integral is evaluated analytically under the assumption that MR signal attenuates exponentially. The values of the resulting functions are evaluated at a fixed distance away from the origin. The spherical harmonic transform of these functions yields the Laplace series coefficients of the probabilities on a sphere of fixed radius. Alternatively, probability values can be computed nonparametrically using Legendre polynomials. Orientation maps calculated from excised rat nervous tissue data demonstrate this technique's ability to accurately resolve crossing fibers in anatomical regions such as the optic chiasm. This proposed methodology has a trivial extension to multiexponential diffusion-weighted signal decay. The developed methods will improve the reliability of tractography schemes and may make it possible to correctly identify the neural connections between functionally connected regions of the nervous system.

Brain slices provide a useful nervous tissue model to investigate the relationships between magnetic resonance imaging (MRI) contrast mechanisms and tissue microstructure; yet, these acutely isolated tissues remain viable for only 10-12 h. To study slower biological processes, this work describes the first MRI microscopy characterization of organotypic rat hippocampal slice cultures that can be maintained for several weeks. Diffusion-weighted images of slice cultures acquired with a 14.1-T magnet demonstrated the laminar anatomy of the hippocampus with relatively high signal-to-noise ratios. Diffusion data analyzed using a two-compartment model with exchange indicated that cultured slices had a comparable microstructure to acute brain slices and to in vivo brain. Immunohistochemistry indicated that slice cultures tolerated the conditions required for MRI study well. MRI of cultured tissue slices is highly amenable to correlative microscopy techniques and offers great promise for future MRI investigations of pathological tissue reorganization, molecular imaging and stem cell therapies.

Observation of translational self-diffusion of water molecules using magnetic resonance (MR) techniques has proven to be a powerful means to probe tissue microstructure. The collected MR signal depends on experimentally controllable parameters as well as the descriptors of tissue geometry. In order to obtain the latter, one needs to employ accurate models to characterize the dependence of the signal on the varied experimental parameters. In this work, a simple model describing diffusion in disordered media and fractal spaces is shown to describe the diffusion-time dependence of the diffusion attenuated MR signal obtained from biological specimens successfully. The model enables one to quantify the evolution of the average water displacement probabilities in terms of two exponents--dw and ds. The experiments performed on excised human neural tissue samples and human red blood cell ghosts indicate that these two parameters are sensitive to tissue microstructure. Therefore, it may be possible to use the proposed scheme to generate novel contrast mechanism for classifying and segmenting tissue.

This paper introduces a new, accurate and fast method for fiber orientation mapping using high angular resolution diffusion imaging (HARDI) data. The approach utilizes the Fourier relationship between the water displacement probabilities and diffusion attenuated magnetic resonance (MR) signal expressed in spherical coordinates. The Laplace series coefficients of the water displacement probabilities are evaluated at a fixed distance away from the origin. The computations take under one minute for most three-dimensional datasets. We present orientation maps computed from excised rat optic chiasm, brain and spinal cord images. The developed method will improve the reliability of tractography schemes and make it possible to correctly identify the neural connections between functionally connected regions of the nervous system.

Diffusion magnetic resonance imaging (MRI) provides a surrogate marker of acute brain pathology, yet few studies have resolved the evolution of water diffusion changes during the first 8 hours after acute injury, a critical period for therapeutic intervention. To characterize this early period, this study used a 17.6-T wide-bore magnet to measure multicomponent water diffusion at high b-values (7 to 8,080 s/mm(2)) for rat hippocampal slices at baseline and serially for 8 hours after treatment with the calcium ionophore A23187. The mean fast diffusing water fraction (Ffast) progressively decreased for slices treated with 10-microM/L A23187 (-20.9 +/- 6.3% at 8 hours). Slices treated with 50-micromol/L A23187 had significantly reduced Ffast 80 minutes earlier than slices treated with 10-microM/L A23187 (P < 0.05), but otherwise, the two doses had equivalent effects on the diffusion properties of tissue water. Correlative histologic analysis showed dose-related selective vulnerability of hippocampal pyramidal neurons (CA1 > CA3) to pathologic swelling induced by A23187, confirming that particular intravoxel cell populations may contribute disproportionately to water diffusion changes observed by MRI after acute brain injury. These data suggest diffusion-weighted images at high b-values and the diffusion parameter Ffast may be highly sensitive correlates of cell swelling in nervous issue after acute injury.

Diffusion MRI has the potential to probe the compartmental origins of MR signals acquired from human nervous tissue. However, current experiments in human subjects require long diffusion times, which may confound data interpretation due to the effects of compartmental exchange. To investigate human nervous tissue at shorter diffusion times, and to determine the relevance of previous diffusion studies in rat hippocampal slices, water diffusion in 20 perfused human hippocampal slices was measured using a wide-bore 17.6-T magnet equipped with 1000-mT/m gradients. These slices were procured from five patients undergoing temporal lobectomy for epilepsy. Tissue viability was confirmed with electrophysiological measurements. Diffusion-weighted water signal attenuation in the slices was well-described by a biexponential function (R(2) > 0.99). The mean diffusion parameters for slices before osmotic perturbation were 0.686 +/- 0.082 for the fraction of fast diffusing water (F(fast)), 1.22 +/- 0.22 x 10(-3) mm(2)/s for the fast apparent diffusion coefficient (ADC), and 0.06 +/- 0.02 x 10(-3) mm(2)/s for the slow ADC. Slice perturbations with 20% hypotonic and 20% hypertonic artificial cerebrospinal fluid led to changes in F(fast) of -8.2% and +10.1%, respectively (ANOVA, P < 0.001). These data agree with previous diffusion studies of rat brain slices and human brain in vivo, and should aid the development of working models of water diffusion in nervous tissue, and thus increase the clinical utility of diffusion MRI.