Anisotropic anomalous diffusion assessed in the human brain by scalar invariant indices

A new method to investigate anomalous diffusion in human brain, inspired by the stretched-exponential model proposed by Hall and Barrick, is proposed here, together with a discussion about its potential application to cerebral white matter characterization. Aim of the work was to show the ability of anomalous diffusion indices to characterize white matter structures, whose complexity is only partially accounted by diffusion tensor imaging indices. MR signal was expressed as a stretched-exponential only along the principal axes of diffusion; whereas, in a generic direction, it was modeled as a combination of three stretched-exponentials. Indices to quantify the tissue anomalous diffusion and its anisotropy, independently of the experiment reference frame, were derived. Experimental results, obtained on 10 healthy subjects at 3T, show that the new parameters are highly correlated to intrinsic local geometry when compared with Hall and Barrick indices. Moreover, they offer a different contrast in white matter regions when compared with diffusion tensor imaging. Specifically, the new indices show a higher capability to discriminate among areas of the corpus callosum associated to different distribution in axonal densities, thus offering a new potential tool to detect more specific patterns of brain abnormalities than diffusion tensor imaging in the presence of neurological and psychiatric disorders.