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A new method to investigate anomalous diffusion in human brain is proposed.The method has been inspired by both the stretched-exponential model proposedby Hall and Barrick (HB) and DTI. Quantities extracted using HB method wereable to discriminate different cerebral tissues on the basis of theircomplexity, expressed by the stretching exponent gamma and of the anisotropy ofgamma across different directions. Nevertheless, these quantities were notdefined as scalar invariants like mean diffusivity and fractional anisotropy,which are eigenvalues of the diffusion tensor. We hypotesize instead that thesignal may be espressed as a simple stretched-exponential only along theprincipal axes of diffusion, while in a generic direction the signal is modeledas a combination of three different stretched-exponentials. In this way, wederived indices to quantify both the tissue anomalous diffusion and itsanisotropy, independently of the reference frame of the experiment. We testedand compare our new method with DTI and HB approaches applying them to 10healty subjects brain at 3T. Our experimental results show that our parametersare highly correlated to intrinsic local geometry when compared to HB indices.Moreover, they offer a different kind of contrast when compared to DTI outputs.Specifically, our indices show a higher capability to discriminate amongdifferent areas of the corpus callosum, which are known to be associated todifferent axonal densities.

Anisotropic Anomalous Diffusion assessed in the human brain by scalar invariant indices