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.