In vivo generalized diffusion tensor imaging (GDTI) using higher‐order tensors (HOT)

Abstract

Generalized diffusion tensor imaging (GDTI) using higher-order tensor (HOT) statistics generalizes the technique of diffusion tensor imaging by including the effect of nongaussian diffusion on the signal of MRI. In GDTI-HOT, the effect of nongaussian diffusion is characterized by higher-order tensor statistics (i.e., the cumulant tensors or the moment tensors), such as the covariance matrix (the second-order cumulant tensor), the skewness tensor (the third-order cumulant tensor), and the kurtosis tensor (the fourth-order cumulant tensor). Previously, Monte Carlo simulations have been applied to verify the validity of this technique in reconstructing complicated fiber structures. However, no in vivo implementation of GDTI-HOT has been reported. The primary goal of this study is to establish GDTI-HOT as a feasible in vivo technique for imaging nongaussian diffusion. We show that probability distribution function of the molecular diffusion process can be measured in vivo with GDTI-HOT and be visualized with three-dimensional glyphs. By comparing GDTI-HOT to fiber structures that are revealed by the highest resolution diffusion-weighted imaging (DWI) possible in vivo, we show that the GDTI-HOT can accurately predict multiple fiber orientations within one white matter voxel. Furthermore, through bootstrap analysis we demonstrate that in vivo measurement of HOT elements is reproducible, with a small statistical variation that is similar to that of diffusion tensor imaging.