We introduce a mathematical framework for computing geometrical properties of white matter fibers directly from diffusion tensor fields. The key idea is to isolate the portion of the gradient of the tensor field corresponding to local variation in tensor orientation, and to project it onto a coordinate frame of tensor eigenvectors. The resulting eigenframe-centered representation then makes it possible to define scalar indices (or measures) that describe the local white matter geometry directly from the diffusion tensor field and its gradient, without requiring prior tractography. We derive new scalar indices of (1) fiber dispersion and (2) fiber curving, and we demonstrate them on synthetic and in vivo data. Finally, we illustrate their applicability to a group study on schizophrenia.
This paper proposes a novel framework for joint orientation distribution function estimation and tractography based on a new class of tensor kernels. Existing techniques estimate the local fiber orientation at each voxel independently so there is no running knowledge of confidence in the measured signal or estimated fiber orientation. In this work, fiber tracking is formulated as recursive estimation: at each step of tracing the fiber, the current estimate of the orientation distribution function is guided by the previous. To do this, second-and higher-order tensor-based kernels are employed. A weighted mixture of these tensor kernels is used for representing crossing and branching fiber structures. While tracing a fiber, the parameters of the mixture model are estimated based on the orientation distribution function at that location and a smoothness term that penalizes deviation from the previous estimate along the fiber direction. This ensures smooth estimation along the direction of propagation of the fiber. In synthetic experiments, using a mixture of two and three components it is shown that this approach improves the angular resolution at crossings. In vivo experiments using two and three components examine the corpus callosum and corticospinal tract and confirm the ability to trace through regions known to contain such crossing and branching.
In healthy adult individuals, late life is a dynamic time of change with respect to the microstructural integrity of white matter tracts. Yet, elderly individuals are generally excluded from diffusion tensor imaging studies in schizophrenia. Therefore, we examined microstructural integrity of frontotemporal and interhemispheric white matter tracts in schizophrenia across the adult lifespan. Diffusion tensor imaging data from 25 younger schizophrenic patients ( or = 55 years), 25 younger controls, 25 older schizophrenic patients (> or = 56 years) and 25 older controls were analysed. Patients with schizophrenia in each group were individually matched to controls. Whole-brain tractography and clustering segmentation were employed to isolate white matter tracts. Groups were compared using repeated measures analysis of variance with 12 within-group measures of fractional anisotropy: (left and right) uncinate fasciculus, arcuate fasciculus, inferior longitudinal fasciculus, inferior occipito-frontal fasciculus, cingulum bundle, and genu and splenium of the corpus callosum. For each white matter tract, fractional anisotropy was then regressed against age in patients and controls, and correlation coefficients compared. The main effect of group (F(3,92) = 12.2, P 0.001), and group by tract interactions (F(26,832) = 1.68, P = 0.018) were evident for fractional anisotropy values. Younger patients had significantly lower fractional anisotropy than younger controls (Bonferroni-corrected alpha = 0.0042) in the left uncinate fasciculus (t(48) = 3.7, P = 0.001) and right cingulum bundle (t(48) = 3.6, P = 0.001), with considerable effect size, but the older groups did not differ. Schizophrenic patients did not demonstrate accelerated age-related decline compared with healthy controls in any white matter tract. To our knowledge, this is the first study to examine the microstructural integrity of frontotemporal white matter tracts across the adult lifespan in schizophrenia. The left uncinate fasciculus and right cingulum bundle are disrupted in younger chronic patients with schizophrenia compared with matched controls, suggesting that these white matter tracts are related to frontotemporal disconnectivity. The absence of accelerated age-related decline, or differences between older community-dwelling patients and controls, suggests that these patients may possess resilience to white matter disruption.
We propose a technique to simultaneously estimate the local fiber orientations and perform multi-fiber tractography. Existing techniques estimate the local fiber orientation at each voxel independently so there is no running knowledge of confidence in the measured signal or estimated fiber orientation. Further, to overcome noise, many algorithms use a filter as a post-processing step to obtain a smooth trajectory. We formulate fiber tracking as causal estimation: at each step of tracing the fiber, the current estimate of the signal is guided by the previous. To do this, we model the signal as a discrete mixture of Watson directional functions and perform tractography within a filtering framework. Starting from a seed point, each fiber is traced to its termination using an unscented Kalman filter to simultaneously fit the signal and propagate in the most consistent direction. Despite the presence of noise and uncertainty, this provides an accurate estimate of the local structure at each point along the fiber. We choose the Watson function since it provides a compact representation of the signal parameterized by the principal diffusion direction and a scaling parameter describing anisotropy, and also allows analytic reconstruction of the oriented diffusion function from those parameters. Using a mixture of two and three components (corresponding to two-fiber and three-fiber models) we demonstrate in synthetic experiments that this approach reduces signal reconstruction error and significantly improves the angular resolution at crossings and branchings. In vivo experiments examine the corpus callosum and internal capsule and confirm the ability to trace through regions known to contain such crossing and branching while providing inherent path regularization.
Water diffusion in nerve fibers is strongly influenced by axon architecture. In this study, fractional diffusion anisotropy and transverse and longitudinal diffusion coefficients were measured in excised human cervical spinal cord with MR line-scan diffusion imaging, at 625 microm in-plane resolution and 3 mm slice thickness. A pixel-based comparison of fractional diffusion anisotropy, transverse diffusion coefficient, and longitudinal diffusion coefficient data with axon packing parameters derived from corresponding stained histological sections was performed for four slices. The axon packing parameters, axon density, axon area-fraction, and average axon size for entire specimen cross-sections were calculated by computerized segmentation of optical microscopy data obtained at 0.53 microm resolution. Salient features could be recognized on fractional diffusion anisotropy, transverse diffusion coefficient, axon density, axon area fraction, and average axon size maps. For white matter regions only, the average correlation coefficients for fractional diffusion anisotropy compared to histology-based parameters axon density and axon area fraction were 0.37 and 0.21, respectively. For transverse diffusion coefficient compared to axon density and axon area fraction, they were -0.40 and -0.36, and for longitudinal diffusion coefficient compared to axon density and axon area fraction, -0.14 and -0.30. All average correlation coefficients for average axon size were low. Correlation coefficients for collectively analyzed white and gray matter regions were significantly higher than correlation coefficients derived from analysis of white matter regions only.
Nyquist ghosts are an inherent artifact in echo planar imaging acquisitions. An approach to robustly eliminate Nyquist ghosts is presented that integrates two previous Nyquist ghost correction techniques: temporal domain encoding (phase labeling for additional coordinate encoding: PLACE and spatial domain encoding (phased array ghost elimination: PAGE). Temporal encoding modulates the echo planar imaging acquisition trajectory from frame to frame, enabling one to interleave data to remove inconsistencies that occur between sampling on positive and negative gradient readouts. With PLACE, one can coherently combine the interleaved data to cancel residual Nyquist ghosts. If the level of ghosting varies significantly from image to image, however, the signal cancellation that occurs with PLACE can adversely affect SNR-sensitive applications such as perfusion imaging with arterial spin labeling. This work proposes integrating PLACE into a PAGE-based reconstruction process to yield significantly better Nyquist ghost correction that is more robust than PLACE or PAGE alone. The robustness of this method is demonstrated in the presence of magnetic field drift with an in-vivo arterial spin labeling perfusion experiment.
The quantification of brain asymmetries may provide biomarkers for presurgical localization of language function and can improve our understanding of neural structure-function relationships in health and disease. We propose a new method for studying the asymmetry of the white matter tracts in the entire brain, and we apply it to a preliminary study of normal subjects across the handedness spectrum. Methods for quantifying white matter asymmetry using diffusion MRI tractography have thus far been based on comparing numbers of fibers or volumes of a single fiber tract across hemispheres. We propose a generalization of such methods, where the "number of fibers" laterality measurement is extended to the entire brain using a soft fiber comparison metric. We summarize the distribution of fiber laterality indices over the whole brain in a histogram, and we measure properties of the distribution such as its skewness, median, and inter-quartile range. The whole-brain fiber laterality histogram can be measured in an exploratory fashion without hypothesizing asymmetries only in particular structures. We demonstrate an overall difference in white matter asymmetry in consistent- and inconsistent-handers: the skewness of the fiber laterality histogram is significantly different across handedness groups.
As the number and complexity of partially sampled dynamic imaging methods continue to increase, reliable strategies to evaluate performance may prove most useful. In the present work, an analytical framework to evaluate given reconstruction methods is presented. A perturbation algorithm allows the proposed evaluation scheme to perform robustly without requiring knowledge about the inner workings of the method being evaluated. A main output of the evaluation process consists of a two-dimensional modulation transfer function, an easy-to-interpret visual rendering of a method’s ability to capture all combinations of spatial and temporal frequencies. Approaches to evaluate noise properties and artifact content at all spatial and temporal frequencies are also proposed. One fully sampled phantom and three fully sampled cardiac cine datasets were subsampled (R = 4 and 8) and reconstructed with the different methods tested here. A hybrid method, which combines the main advantageous features observed in our assessments, was proposed and tested in a cardiac cine application, with acceleration factors of 3.5 and 6.3 (skip factors of 4 and 8, respectively). This approach combines features from methods such as k-t sensitivity encoding, unaliasing by Fourier encoding the overlaps in the temporal dimension-sensitivity encoding, generalized autocalibrating partially parallel acquisition, sensitivity profiles from an array of coils for encoding and reconstruction in parallel, self, hybrid referencing with unaliasing by Fourier encoding the overlaps in the temporal dimension and generalized autocalibrating partially parallel acquisition, and generalized autocalibrating partially parallel acquisition-enhanced sensitivity maps for sensitivity encoding reconstructions.
The pulsed-field gradient (PFG) MR experiment enables one to measure particle displacements, velocities, and even higher moments of complex fluid motions. In diffusion-weighted MRI (DWI) in living tissue, where the PFG MRI experiment is used to measure diffusion, Brownian motion is assumed to dominate the displacements causing the observed signal loss. However, motions of water molecules caused by various active biological processes occurring at different length and time scales may also cause additional dephasing of magnetization and signal loss. To help understand their relative effects on the DWI signal attenuation, we used an integrated experimental and theoretical framework: a Rheo-NMR, which served as an experimental model system to precisely prescribe a microscopic velocity distribution; and a mathematical model that relates the DW signal intensity in the Rheo-NMR to experimental parameters that characterize the impressed velocity field. A technical innovation reported here is our use of ’natural’ (in this case, polar) coordinates both to simplify the description the fluid motion within the Couette cell of the Rheo-NMR, as well as to acquire and reconstruct magnitude and phase MR images obtained within it. We use this integrated model system to demonstrate how shear flows appears as pseudo-diffusion in magnitude DW MR signals obtained using PFG spin-echo (PGSE) NMR and MRI sequences. Our results lead us to reinterpret the possible causes of signal loss in DWI in vivo, in particular to revise and generalize the previous notion of intra-voxel incoherent motion (IVIM) in order to describe activity driven flows that appear as pseudo-diffusion over multiple length and time scales in living tissues.
The present study examined the relationship between hand preference degree and direction, functional language lateralization in Broca’s and Wernicke’s areas, and structural measures of the arcuate fasciculus. Results revealed an effect of degree of hand preference on arcuate fasciculus structure, such that consistently-handed individuals, regardless of the direction of hand preference, demonstrated the most asymmetric arcuate fasciculus, with larger left versus right arcuate, as measured by DTI. Functional language lateralization in Wernicke’s area, measured via fMRI, was related to arcuate fasciculus volume in consistent-left-handers only, and only in people who were not right hemisphere lateralized for language; given the small sample size for this finding, future investigation is warranted. Results suggest handedness degree may be an important variable to investigate in the context of neuroanatomical asymmetries.
