{'fraction_non_alphanumeric': 0.035736290819470114, 'fraction_numerical': 0.004929143561306223, 'mean_word_length': 5.683127572016461, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
In vivo generalized diffusion tensor imaging (GDTI) using higher‐order tensors (HOT)

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. Magn Reson Med, 2010. © 2009 Wiley‐Liss, Inc.