The γ parameter of the stretched-exponential model is influenced by internal gradients: validation in phantoms

In this paper, we investigate the image contrast that characterizes anomalous and non-gaussian diffusion images obtained using the stretched exponential model. This model is based on the introduction of the γ stretched parameter, which quantifies deviation from the mono-exponential decay of diffusion signal as a function of the b-value. To date, the biophysical substrate underpinning the contrast observed in γ maps, in other words, the biophysical interpretation of the γ parameter (or the fractional order derivative in space, β parameter) is still not fully understood, although it has already been applied to investigate both animal models and human brain. Due to the ability of γ maps to reflect additional microstructural information which cannot be obtained using diffusion procedures based on gaussian diffusion, some authors propose this parameter as a measure of diffusion heterogeneity or water compartmentalization in biological tissues. Based on our recent work we suggest here that the coupling between internal and diffusion gradients provide pseudo-superdiffusion effects which are quantified by the stretching exponential parameter γ. This means that the image contrast of Mγ maps reflects local magnetic susceptibility differences (Δχ(m)), thus highlighting better than T(2)(∗) contrast the interface between compartments characterized by Δχ(m). Thanks to this characteristic, Mγ imaging may represent an interesting tool to develop contrast-enhanced MRI for molecular imaging. The spectroscopic and imaging experiments (performed in controlled micro-beads dispersion) that are reported here, strongly suggest internal gradients, and as a consequence Δχ(m), to be an important factor in fully understanding the source of contrast in anomalous diffusion methods that are based on a stretched exponential model analysis of diffusion data obtained at varying gradient strengths g.