Magnetic resonance (MR) diffusion tensor imaging (DTI) can resolve the white matter fiber orientation within a voxel provided that the fibers are strongly aligned. However, a given voxel may contain a distribution of fiber orientations due to, for example, intravoxel fiber crossing. The present study sought to test whether a geodesic, high b-value diffusion gradient sampling scheme could resolve multiple fiber orientations within a single voxel. In regions of fiber crossing the diffusion signal exhibited multiple local maxima/minima as a function of diffusion gradient orientation, indicating the presence of multiple intravoxel fiber orientations. The multimodality of the observed diffusion signal precluded the standard tensor reconstruction, so instead the diffusion signal was modeled as arising from a discrete mixture of Gaussian diffusion processes in slow exchange, and the underlying mixture of tensors was solved for using a gradient descent scheme. The multitensor reconstruction resolved multiple intravoxel fiber populations corresponding to known fiber anatomy.Magn Key words: diffusion; diffusion-weighted MRI (DWI); diffusion tensor imaging (DTI); white matter; tractographyTissues with regularly ordered microstructure, such as skeletal muscle, spine, tongue, heart, and cerebral white matter, exhibit anisotropic water diffusion due to the alignment of the diffusion compartments in the tissue (1-7). The direction of preferred diffusion, and hence the direction of preferred orientation in the tissue, can be resolved with a method called magnetic resonance (MR) diffusion tensor imaging (DTI) (7), which measures the apparent water self-diffusion tensor under the assumption of Gaussian diffusion. Based on the eigenstructure of the measured diffusion tensor, it is possible to infer the orientation of the diffusion compartments within the voxel so that, for example, the major eigenvector of the diffusion tensor parallels the mean fiber orientation (7), and the minor eigenvector parallels the normal to the mean plane of fiber dispersion (8).The tensor model is incapable, however, of resolving multiple fiber orientations within an individual voxel. This shortcoming of the tensor model stems from the fact that the tensor possesses only a single orientational maximum, i.e., the major eigenvalue of the diffusion tensor (9,10). At the millimeter-scale resolution typical of DTI, the volume of cerebral white matter containing such intravoxel orientational heterogeneity (IVOH) may be considerable given the widespread divergence and convergence of fascicles (11-13). The abundance of IVOH at the millimeter scale can be further appreciated by considering the ubiquity of oblate (pancake-shaped) diffusion tensors in DTI, a hypothesized indicator of IVOH (3,4,8).Given the obstacle that IVOH (particularly fiber crossing (14 -16)) poses to white matter tractography algorithms (14 -20), we sought to determine whether high angular resolution, high b-value diffusion gradient sampling could resolve such intravoxel heterogeneity (9). H...

Methods are presented to map complex fiber architectures in tissues by imaging the 3D spectra of tissue water diffusion with MR. First, theoretical considerations show why and under what conditions diffusion contrast is positive. Using this result, spin displacement spectra that are conventionally phase-encoded can be accurately reconstructed by a Fourier transform of the measured signal's modulus. Second, studies of in vitro and in vivo samples demonstrate correspondence between the orientational maxima of the diffusion spectrum and those of the fiber orientation density at each location. In specimens with complex muscular tissue, such as the tongue, diffusion spectrum images show characteristic local heterogeneities of fiber architectures, including angular dispersion and intersection. Cerebral diffusion spectra acquired in normal human subjects resolve known white matter tracts and tract intersections. Over the past decade, MRI methods have been developed that can nondestructively map the structural anisotropy of fibrous tissues in living systems by mapping the diffusion tensor (DT) of tissue water (for review see Ref. 1). Such methods have been used to elucidate the fiber architecture and functional dynamics of the myocardium (2,3) and skeletal muscle (4). They have also been used in the nervous system to identify and map the trajectories of neural white matter tracts and infer neuroanatomic connectivity (for review see Ref. 5).Notwithstanding this progress, the DT paradigm has notable limitations. Because the distances resolved by MRI are far larger than the diffusion scale, each 3D resolution element (voxel) represents many distinct diffusional environments. This provides a complicated diffusion signal that in general is underspecified by the six degrees of freedom of the DT model. An example of particular interest occurs when a tissue has a composite fiber structure, such that each small region may contain fibers of multiple orientations corresponding to distinct diffusion anisotropies (6).The present study describes a model-free MRI methodology called diffusion spectrum imaging (DSI). This method affords the capacity to resolve intravoxel diffusion heterogeneity of compartments with sufficient angular separation and anisotropy by measuring its diffusion density spectra estimator. In describing this method, we will show that DSI generalizes the analysis of diffusion spectra by demonstrating that the Fourier transform of the diffusion spectrum must be positive. We also discuss how the DSI method encompasses existing alternate analyses of MRI diffusion contrast, and present examples of diffusion contrast in biological tissues analyzed with DSI. THEORY Measuring the Diffusion SpectrumWe consider the classical Stejskal-Tanner experiment (7). It allows the phase-encoding of spin displacements by embedding a strong pulse gradient of duration ␦ and intensity ͉g͉ on each side of the RF-pulse of a conventional spin-echo sequence. In such a manner the MR signal is made proportional to the voxel average (͗ ⅐ ͘) deph...

Image distortion due to field gradient eddy currents can create image artifacts in diffusion-weighted MR images. These images, acquired by measuring the attenuation of NMR signal due to directionally dependent diffusion, have recently been shown to be useful in the diagnosis and assessment of acute stroke and in mapping of tissue structure. This work presents an improvement on the spin-echo (SE) diffusion sequence that displays less distortion and consequently improves image quality. Adding a second refocusing pulse provides better image quality with less distortion at no cost in scanning efficiency or effectiveness, and allows more flexible diffusion gradient timing. Multidirectional diffusion sequences (1-3) have recently been shown to be useful in the diagnosis and assessment of acute stroke and in mapping of tissue structure (4 -10). These methods apply gradient pulses at higher intensity and with longer duration than in any other well known MRI sequence, resulting in comparatively large and persistent eddy currents. Use of the spin-echo (SE) diffusion sequence with an echo planar (EP) readout combines atypically large eddy currents with an eddy current-sensitive EP readout, causing spatial distortion dependent on the direction of the applied diffusion gradient. Misregistration artifacts result when directional diffusion is calculated from multiple images with differing gradient directions.Each on and off field gradient transition produces eddy currents to some degree. If the eddy current (and its associated magnetic field) decays to an inconsequential value between the time of the applied field gradient transition and the image readout, a spatially dependent change in image phase will result with no discernible distortion. Since diffusion encoding relies on the attenuation of the image magnitude, a change in image phase does not change the diffusion measurement as long as the phase gradient per pixel is small (11). However, when the eddy current decays slowly, so that a residual field remains during the image readout, the field behaves like an additional spatial encoding gradient field and causes distortion of the image.While the usual SE diffusion sequence, introduced by Stejkal and Tanner (12), uses a single refocusing RF pulse, many SE diffusion sequence variants can be created using multiple refocusing pulses. SEs result from any combination of refocusing pulses that returns the spins' phase evolution to the origin in classical phase space (13). Using more than one refocusing pulse permits variable intervals between the pulses, requiring only that the spins' alternating defocusing and refocusing times sum equally at the time of the intended SE. This flexibility in timing adds utility when used for diffusion imaging.Since the on and off field gradient transitions produce equal and opposite eddy currents, the shorter the time between on and off transitions, the less decay of the residual fields during the gradient pulse and the more complete the fields' cancellation. Toward this end, a reduction of distor...