To characterize anisotropic water diffusion in brain white matter, a theoretical framework is proposed that combines hindered and restricted models of water diffusion (CHARMED) and an experimental methodology that embodies features of diffusion tensor and q-space MRI. This model contains a hindered extra-axonal compartment, whose diffusion properties are characterized by an effective diffusion tensor, and an intraaxonal compartment, whose diffusion properties are character-

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A double-pulsed gradient spin echo (d-PGSE) filtered MRI sequence is proposed to detect microscopic diffusion anisotropy in heterogeneous specimen. The technique was developed, in particular, to characterize local microscopic anisotropy in specimens that are macroscopically isotropic, such as gray matter. In such samples, diffusion tensor MRI (DTI) produces an isotropic or nearly isotropic diffusion tensor despite the fact that the medium may be anisotropic at a microscopic length scale. Key words: MRI; double; pulsed gradient; diffusion; anisotropy; multiple scattering; white matter; gray matter; spinal cord; phantom; filter; DTI Diffusion tensor imaging (DTI) is a powerful tool for characterizing normal and abnormal brain development as well as pathological changes and aging (1). It can readily detect anisotropic diffusion in white matter comprised of long coherent axons (Fig. 1d), whose extent usually exceeds the MRI voxel length scale (Fig. 1e). By acquiring diffusion-weighted imaging (DWI) data (2,3) with a multiplicity of gradient directions, an apparent diffusion tensor can be estimated, from which one can characterize the degree of voxel-averaged diffusion anisotropy (1) (Fig. 1f). However, difficulties in DTI anisotropy measurements arise when the material's local directors show a large spread of orientations on the voxel length scale. Such is the case for gray matter, which consists of multiple cell types and axonal and dendritic fibers (Fig. 1a) that may be individually anisotropic, but are randomly oriented on a voxel length scale (Fig. 1b). As a result, its apparent diffusion tensor appears considerably less anisotropic that than of the white matter (4 -7) (Fig. 1c).Unlike the single-pulsed gradient spin echo (PGSE) experiment (8), multiple PGSE experiments (9 -11) can detect microscopic anisotropy in materials that are macroscopically isotropic. These techniques extend the StejskalTanner PGSE sequence, which uses a single pair of diffusion gradient pulses, to sequences having multiple pairs of gradients pulses. In practice, all current multiple PGSE methods use only two blocks of PGSE gradient pulse pairs, where in most only two sets of experiments are performed. In the first experiment the gradients are applied along the same direction (i.e., are collinear) and in the second gradients are perpendicular to each other (i.e., are orthogonal). For a PGSE experiment on an anisotropic sample, such as an impermeable tube for example, the echo attenuation resulting from diffusion along the tube axis will differ from the diffusion perpendicular to the tube axis. However, when those tubes are randomly oriented, the PGSE echo attenuations will become independent of the gradient pulse direction. The echo attenuation resulting from two sequential PGSE blocks is essentially a multiplication of the mean square displacement signal resulting from each PGSE block, which is then integrated over the entire sample. Thus, for randomly oriented tubes the echo attenuation will depend on whether the two PGSE blocks were c...