Individual white matter fibers cannot be resolved by current magnetic resonance (MR) technology. Many fibers of a fiber bundle will pass through an individual volume element (voxel). Individual visualized fiber tracts are thus the result of interpolation on a relatively coarse voxel grid, and an infinite number of them may be generated in a given volume by interpolation. This paper aims at creating a level set representation of a fiber bundle to describe this apparent continuum of fibers. It further introduces a coordinate system warped to the fiber bundle geometry, allowing for the definition of geometrically meaningful fiber bundle measures.
Diffusion tensor magnetic resonance imaging provides structural information about nerve fiber tissue. The first eigenvector of the diffusion tensor is aligned with the nerve fibers, i.e., longitudinally in the spinal cord. The underlying hypothesis of this study is that the presence of collateral nerve fibers running orthogonal to the longitudinal fibers results in an orderly arrangement of the second eigenvectors. Magnetic resonance diffusion tensor scans were performed with line scan diffusion imaging on a clinical MR scanner. Axial sections were scanned in a human cervical spinal cord specimen at 625 microm resolution and the cervical spinal cord of four normal volunteers at 1250 microm resolution. The spinal cord specimen was fixed and stained for later light microscopy of the collateral fiber architecture at 0.53 microm resolution. Diffusion measured by MR was found to be anisotropic for both white and gray matter areas of the spinal cord specimen; the average fractional anisotropy (FA) was 0.63 +/- 0.09 (diffusion eigenvalues lambda1 0.38 +/- 0.05 micros/mm2, lambda2 0.14 +/- 0.03 micros/mm2, lambda3 0.10 +/- 0.03 micros/mm2) in white matter and 0.27 +/- 0.04 (lambda1 0.36 +/- 0.04 micros/mm2, lambda2 0.28 +/- 0.03 micros/mm2, lambda3 0.21 +/- 0.04 micros/mm2 in gray matter. The normal-volunteer FA values were similar, i.e., 0.66 +/- 0.04 (lambda1 1.66 +/- 0.14 micros/mm2, lambda2 0.55 +/- 0.02 micros/mm2, lambda3 0.40 +/- 0.01 micros/mm2) in white matter and 0.35 +/- 0.03 (lambda1 1.14 +/- 0.07 micros/mm2, lambda2 0.70 +/- 0.03 micros/mm2, lambda3 0.58 +/- 0.02 micros/mm2) in gray matter. The first eigenvector pointed, as expected, in the longitudinal direction. The second eigenvector directions exhibited a striking arrangement, consistent with the distribution of interconnecting collateral nerve fibers discerned on the histology section. This finding was confirmed for the specimen by quantitative pixel-wise comparison of second eigenvector directions and collateral fiber directions assessed on light microscopy image data. Diffusion tensor MRI can reveal non-invasively and in great detail the intricate fiber architecture of the human spinal cord.
Two image reconstruction methods currently dominate parallel MR imaging: SENSE and GRAPPA. While both seek to reconstruct images from subsampled multi-channel MRI data, there exist fundamental differences between the two. In particular, SENSE reconstructs an image of the excited spin-density directly whereas GRAPPA reconstructs estimates of the fully sampled raw coil data and then combines them to obtain an image. In this work we show that these differences can be exploited such that each method can compliment the other. In the case of SENSE, which requires an estimate of the coil sensitivity map before reconstruction, one can use GRAPPA to improve the coil sensitivity estimates. Alternatively, using coil sensitivity estimates and the SENSE reconstruction equations, one can improve the GRAPPA reconstruction parameter estimation. Together, these approaches can provide higher image quality than either method alone.
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
We present a two-step process including white matter atlas generation and automatic segmentation. Our atlas generation method is based on population fiber clustering. We produce an atlas which contains high-dimensional descriptors of fiber bundles as well as anatomical label information. We use the atlas to automatically segment tractography in the white matter of novel subjects and we present quantitative results (FA measurements) in segmented white matter regions from a small population. We demonstrate reproducibility of these measurements across scans. In addition, we introduce the idea of using clustering for automatic matching of anatomical structures across hemispheres.
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.
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.
Segmentation involves separating an object from the background. In this work, we propose a novel segmentation method combining image information with prior shape knowledge, within the level-set framework. Following the work of Leventon et al., we revisit the use of principal component analysis (PCA) to introduce prior knowledge about shapes in a more robust manner. To this end, we utilize Kernel PCA and show that this method of learning shapes outperforms linear PCA, by allowing only shapes that are close enough to the training data. In the proposed segmentation algorithm, shape knowledge and image information are encoded into two energy functionals entirely described in terms of shapes. This consistent description allows to fully take advantage of the Kernel PCA methodology and leads to promising segmentation results. In particular, our shape-driven segmentation technique allows for the simultaneous encoding of multiple types of shapes, and offers a convincing level of robustness with respect to noise, clutter, partial occlusions, or smearing.
A classical neural tract tracer, WGA-HRP, was injected at multiple sites within the brain of a macaque monkey. Histological sections of the labeled fiber tracts were reconstructed in 3D, and the fibers were segmented and registered with the anatomical post-mortem MRI from the same animal. Fiber tracing along the same pathways was performed on the DTI data using a classical diffusion tracing technique. The fibers derived from the DTI were compared with those segmented from the histology in order to evaluate the performance of DTI fiber tracing. While there was generally good agreement between the two methods, our results reveal certain limitations of DTI tractography, particularly at regions of fiber tract crossing or bifurcation.
