  A new method to investigate anomalous diffusion in human brain is proposed.
The method has been inspired by both the stretched-exponential model proposed
by Hall and Barrick (HB) and DTI. Quantities extracted using HB method were
able to discriminate different cerebral tissues on the basis of their
complexity, expressed by the stretching exponent gamma and of the anisotropy of
gamma across different directions. Nevertheless, these quantities were not
defined as scalar invariants like mean diffusivity and fractional anisotropy,
which are eigenvalues of the diffusion tensor. We hypotesize instead that the
signal may be espressed as a simple stretched-exponential only along the
principal axes of diffusion, while in a generic direction the signal is modeled
as a combination of three different stretched-exponentials. In this way, we
derived indices to quantify both the tissue anomalous diffusion and its
anisotropy, independently of the reference frame of the experiment. We tested
and compare our new method with DTI and HB approaches applying them to 10
healty subjects brain at 3T. Our experimental results show that our parameters
are 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 among
different areas of the corpus callosum, which are known to be associated to
different axonal densities.
