A Simplified Method to Measure the Diffusion Tensor from Seven MR Images

Analytical expressions of the diffusion tensor of water, D, and of scalar invariants derived from it, are given in terms of the intensities of seven diffusion-weighted images (DWIs). These formulas simplify the post-processing steps required in diffusion tensor imaging, including estimating D in each voxel (from the set of b-matrices and their corresponding DWIs), and then computing its eigenvalues, eigenvectors, and scalar invariants. In a study conducted using artifact-free DWIs with high diffusion weighting (bmax approximately 900 s/mm2, maps of Trace(D) and the Relative and Lattice Anisotropy indices calculated analytically and by multivariate linear regression showed excellent agreement in brain parenchyma of a healthy living cat. However, the quality of the analytically computed maps degraded markedly as diffusion weighting was reduced. Although diffusion tensor MRI with seven DWIs may be useful for clinical applications where rapid scanning and data processing are required, it does not provide estimates of the uncertainty of the measured imaging parameters, rendering it susceptible to noise and systematic artifacts. Therefore, care should be taken when using this technique in radiological applications.