Characterizing fiber directional uncertainty in diffusion tensor MRI.

Image noise in diffusion tensor MRI (DT-MRI) causes errors in the measured tensor and hence variance in the estimated fiber orientation. Uncertainty in fiber orientation has been described using a circular "cone of uncertainty" (CU) around the principal eigenvector of the DT. The CU has proved to be a useful construct for quantifying and visualizing the variability of DT-MRI parameters and fiber tractography. The assumption of circularity of the CU has not been tested directly, however. In this work, bootstrap analysis and simple theoretical arguments were used to show that the CU is elliptical and multivariate normal in the vast majority of white matter (WM) voxels for typical measurement conditions. The dependence of the cone angle on the signal-to-noise ratio (SNR) and eigenvalue contrast was established. The major and minor cone axes are shown to be coincident with the second and third eigenvectors of the tensor, respectively, in the limit of many uniformly spaced diffusion-encoding directions. The deviation between the major cone axis and the second eigenvector was quantified for typical sets of diffusion-weighting (DW) directions. The elliptical CU provides more realistic error information for fiber-tracking algorithms and a quantitative basis for selecting DT imaging acquisition protocols.