The diffusion tensor is currently the accepted model of diffusion in biological tissues. The measured diffusion behavior may be more complex when two or more distinct tissues with different diffusion tensors occupy the same voxel. In this study, a partial volume model of MRI signal behavior for two diffusion-tensor compartments is presented. Simulations using this model demonstrate that the conventional single diffusion tensor model could lead to highly variable and inaccurate measurements of diffusion behavior. The differences between the single and twotensor models depend on the orientations, fractions, and exchange between the two diffusion tensor compartments, as well as the diffusion-tensor encoding technique and diffusionweighting that is used in the measurements. The current single compartment model's inaccuracies could cause diffusionbased characterization of cerebral ischemia and white matter connectivity to be incorrect. A diffusion-tensor MRI imaging experiment on a normal human brain revealed significant partial volume effects between oblique white matter regions when using very large voxels and large diffusion-weighting (b ϳ 2.69 ؋ 10 3 sec/mm 2 ). However, the apparent partial volume effects in white matter decreased significantly when smaller voxel dimensions were used. The diffusion-tensor is a mathematically elegant description of diffusion as a function of direction. Basser and Pierpaoli (1) applied the tensor formalism to diffusion measurements of biological tissues obtained by MRI and NMR spectroscopy. One of the most important observations is that organized fibrous tissues, such as muscle and cerebral white matter, demonstrate anisotropic diffusion. The direction of greatest diffusivity corresponds to the fiber axis direction. The diffusion tensor describes the magnitude of the water diffusion, the degree of diffusion anisotropy, and the orientation of the anisotropy.Measurements of the diffusion tensor and its components (i.e., the trace) have been found to have several applications in the human brain (2,3). The trace of the diffusion tensor has been found to be valuable for detecting and evaluating brain ischemia and stroke (4,5). Measures of diffusion tensor anisotropy have been used to study white matter in terms of morphology (6), disease and trauma (8,9), brain development (10,11), and neurosurgical planning (12). Several investigators have recently proposed using the principal eigenvectors of the diffusion tensor to estimate white matter connectivity (13)(14)(15). Each of these applications will be influenced by the accuracy of the measurements of the diffusion tensor. Recent studies have investigated the effects of measurement noise (16,17) and the tensor encoding strategy (18) on the accuracy of the diffusion tensor and its derived parameters.Partial volume effects can also significantly influence the accuracy of diffusion tensor measurements. This is particularly true for most DT-MRI studies that use EPI techniques with relatively large voxels (ϳ1.5-5.0 mm on a side). Previous stud...

Diffusion tensor MRI provides unique directional diffusion information that can be used to estimate the patterns of white matter connectivity in the human brain. In this study, the behavior of an algorithm for white matter tractography is examined. The algorithm, called TEND, uses the entire diffusion tensor to deflect the estimated fiber trajectory. Simulations and imaging experiments on in vivo human brains were performed to investigate the behavior of the tractography algorithm. The simulations show that the deflection term is less sensitive than the major eigenvector to image noise. In the human brain imaging experiments, estimated tracts were generated in corpus callosum, corticospinal tract, internal capsule, corona radiata, superior longitudinal fasciculus, inferior longitudinal fasciculus, fronto-occipital fasciculus, and uncinate fasciculus. This approach is promising for mapping the organizational patterns of white matter in the human brain as well as mapping the relationship between major fiber trajectories and the location and extent of brain lesions.

Whole-brain diffusion tensor tractography (DTT) at high signal-to-noise ratio and angular and spatial resolutions were utilized to study the effects of age, sex differences, and lateral asymmetries of 6 white matter pathways (arcuate fasciculus [AF], inferior longitudinal fasciculus, inferior fronto-occipital fasciculus [IFOF], uncinate fasciculus [UF], corticospinal tract [CST], and somatosensory pathway [SS]) in 31 right-handed children (6-17 years). Fractional anisotropy (FA), a measure of the orientational variance in water molecular diffusivity, and the magnitude of water diffusivity (parallel, perpendicular, and mean diffusivity) along the pathways were quantified. Three major patterns of maturation were observed: 1) significant increase in FA with age, accompanied by significant decreases in all 3 diffusivities (e.g., left IFOF); 2) significant decreases in all three diffusivities with age without significant changes in FA (e.g., left CST); and 3) no significant age-related changes in FA or diffusivity (e.g., SS). Sex differences were minimal. Many pathways showed lateral asymmetries. In the right hemisphere, the frontotemporal (FT) segment of AF was not visualized in a substantial (29%) number of participants. FA was higher in the left hemisphere in the FT segment of AF, UF, and CST, whereas it was lower in the frontoparietal segment of AF. This study provides normative data essential for the interpretation of pediatric brain DTT measurements in both health and disease.

The accuracy of single diffusion tensor MRI (DT-MRI) measurements depends upon the encoding scheme used. In this study, the diffusion tensor accuracy of several strategies for DT-MRI encoding are compared. The encoding strategies are based upon heuristic, numerically optimized, and regular polyhedra schemes. The criteria for numerical optimization include the minimum tensor variance (MV), minimum force (MF), minimum potential energy (ME), and minimum condition number. The regular polyhedra scheme includes variations of the icosahedron. Analytical comparisons and Monte Carlo simulations show that the icosahedron scheme is optimum for six encoding directions. The MV, MF, and ME solutions for six directions are functionally equivalent to the icosahedron scheme. Two commonly used heuristic DT-MRI encoding schemes with six directions, which are based upon the geometric landmarks of a cube (vertices, edge centers, and face centers), are found to be suboptimal. For more than six encoding directions, many methods are able to generate a set of equivalent optimum encoding directions including the regular polyhedra, and the ME, MF and MV numerical optimization solutions. For seven directions, a previously described heuristic encoding scheme (tetrahedral plus x, y, z) was also found to be optimum. This study indicates that there is no significant advantage to using more than six encoding directions as long as an optimum encoding is used for six directions. Future DT-MRI studies are necessary to validate these observations. J. Magn. Reson. Imaging 2001;13:769 -780.

Brain imaging studies find evidence of prefrontal cortical dysfunction in cocaine-dependent subjects. Similarly, cocaine-dependent subjects have problems with behaviors related to executive function and impulsivity. Since prefrontal cortical axonal tracts cross between hemispheres in the corpus callosum, it is possible that white matter integrity in the corpus callosum could also be diminished in cocainedependent subjects. The purpose of this study was to compare corpus callosum white matter integrity as measured by the fractional anisotropy (FA) on diffusion tensor imaging (DTI) between 18 cocaine-dependent subjects and 18 healthy controls. The Barratt Impulsiveness Scale (BIS-11) and a continuous performance test: the Immediate and Delayed Memory Task (IMT/DMT) were also collected. Results of the DTI showed significantly reduced FA in the genu and rostral body of the anterior corpus callosum in cocainedependent subjects compared to controls. Cocaine-dependent subjects also had significantly higher BIS-11 scores, greater impulsive (commission) errors, and reduced ability to discriminate target from catch stimuli (discriminability) on the IMT/DMT. Within cocaine dependent subjects there was a significant negative correlation between FA in the anterior corpus callosum and behavioral laboratory measured impulsivity, and there was a positive correlation between FA and discriminability. The finding that reduced integrity of anterior corpus callosum white matter in cocaine users is related to impaired impulse control and reduced ability to discriminate between target and catch stimuli is consistent with prior theories regarding frontal cortical involvement in impaired inhibitory control in cocainedependent subjects.

Diffusion-tensor imaging allowed for visualization of white matter tracts and was found to be beneficial in the surgical planning for patients with intrinsic brain tumors. The authors' experience with DT imaging indicates that anatomically intact fibers may be present in abnormal-appearing areas of the brain. Whether resection of these involved fibers results in subtle postoperative neurological deficits requires further systematic study.

Brain water may increase in hepatic encephalopathy (HE). Diffusion tensor imaging was performed in patients with cirrhosis with or without HE to quantify the changes in brain water diffusivity and to correlate it with neuropsychological (NP) tests. Thirty-nine patients with cirrhosis, with minimal (MHE) or overt HE, were studied and compared to 18 controls. Mean diffusivity (MD) and fractional anisotropy (FA) were calculated in corpus callosum, internal capsule, deep gray matter nuclei, periventricular frontal, and occipital white matter regions in both cerebral hemispheres. The MD and FA values from different regions in different groups were compared using analysis of variance and Spearman's rank correlation test. In 10 patients with MHE, repeat studies were performed after 3 weeks of lactulose therapy to look for any change in MD, FA, and NP scores.

The major language pathways such as superior longitudinal fasciculus (SLF) pathways have been outlined by experimental and diffusion tensor imaging (DTI) studies. The SLF I and some of the superior parietal lobule connections of the SLF pathways have not been depicted by prior DTI studies due to the lack of imaging sensitivity and adequate spatial resolution. In the current study, the trajectory of the SLF fibers has been delineated on five healthy human subjects using diffusion tensor tractography on a 3.0T scanner at high spatial resolution. We also demonstrate for the first time the trajectory and connectivity of the SLF fibers in relation to other language pathways as well as the superior parietal lobule connections of the language circuit using high spatial resolution diffusion tensor imaging in the healthy adult human brain.