New invariant indexes to quantify water anomalous diffusion in brain

Introduction Conventional DTI methods are based on the Stejskal-Tanner analysis which predicts for water signal a mono-exponential decay, namely S(b)=S(0)exp(-Db), as function of b-values. The evidence of a non-monoexponential trend which is largely reported in brain, both in animal models and in humans brain [1,2], prompted the search for alternative approaches which take into account the deviation from the Gaussian diffusion conditions. A new method was recently proposed [3,4] which attempted to relate the diffusion decay to the different degrees of structural complexity found in different brain regions. This method is based on the stretched-exponential model, namely S(b)=S(0)exp(-Db). The stretching parameter has been used as a source of contrast revealing the capability to discriminate among cerebrospinal fluid (CSF), white matter (WM) and grey matter (GM). An anisotropy parameter has been also proposed. Even though it showed moderate sensitivity to structure degrees of orientation, Mean γ as defined in ref. [4], cannot be considered a good marker because it is not defined as a scalar invariant (i.e. it is not derived from a tensor) and thus depends on the relative orientation between the structures and the applied encoding gradients. We propose an alternative description which considers the behaviour along each of the three principal diffusive directions as a simple stretched exponential, thus defining three main exponents. The diffusion along a generic direction contains instead a combination of these three exponents. The goals of the present work were: 1) to realize an algorithm for image reconstruction based on the three main exponents mean value and on its anisotropy, in analogy to the conventional DTI analysis and 2) to investigate the potential role of non-Gaussian diffusion parametric maps in discriminating among the different cerebral tissues and in detecting differences into selected ROIs, characterized by a known MR parameters such as mean diffusivity (MD) or fractional anisotropy (FA). Additionally, we aimed at drawing a comparison between the stretching exponent as defined in previous literature and our derived new indexes (Mean γ, Mγ and γ Anisotropy, γA) based on the three principal stretching exponents.