Khader M. Hasan

Analysis of partial volume effects in diffusion-tensor MRI.

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 two‐tensor models depend on the orientations, fractions, and exchange between the two diffusion tensor compartments, as well as the diffusion‐tensor encoding technique and diffusion‐weighting that is used in the measurements. The current single compartment models inaccuracies could cause diffusion‐based 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 ∼ 2.69 × 103 sec/mm2). However, the apparent partial volume effects in white matter decreased significantly when smaller voxel dimensions were used. For diffusion tensor studies obtained using typical diffusion‐weighting values (b ∼ 1 × 103 sec/mm2) partial volume effects are much more difficult to detect and resolve. More accurate measurements of multiple diffusion compartments may lead to improved confidence in diffusion measurements for clinical applications. Magn Reson Med 45:770–780, 2001.

White matter tractography using diffusion tensor deflection

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. Hum. Brain Mapping 18:306–321, 2003.

Comparison of gradient encoding schemes for diffusion-tensor MRI

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.

A geometric analysis of diffusion tensor measurements of the human brain

The degree of diffusion tensor anisotropy is often associated with the organization of structural tissues such as white matter. Numerous measures of diffusion anisotropy have been proposed, which could lead to confusion in interpreting and comparing results from different studies. In this study, a new method for representing the diffusion tensor shape, called the three‐phase (3P) plot, is described. This is a graphical technique based upon a barycentric coordinate system, which weights the tensor shape by a combination of linear, cylindrical, and spherical shape factors. This coordinate system can be used to map and potentially segment different tissues based upon the tensor shape. In addition, the 3P plot can be used to examine the shape properties of existing measures of diffusion anisotropy. In this paper, the 3P plot is used to compare four well‐known anisotropy measures: the anisotropy index, the fractional anisotropy, the relative anisotropy, and the volume fraction. Computer simulations and diffusion tensor images of normal brains were obtained to study the properties of this new mapping technique. Magn Reson Med 44:283–291, 2000.

Diffusion tensor eigenvector directional color imaging patterns in the evaluation of cerebral white matter tracts altered by tumor

To categorize the varied appearances of tumor‐altered white matter (WM) tracts on diffusion tensor eigenvector directional color maps.