Anisotropic fractional diffusion tensor imaging

Abstract

Traditional diffusion tensor imaging (DTI) maps brain structure by fitting a diffusion model to the magnitude of the electrical signal acquired in magnetic resonance imaging (MRI). Fractional DTI employs anomalous diffusion models to obtain a better fit to real MRI data, which can exhibit anomalous diffusion in both time and space. In this paper, we describe the challenge of developing and employing anisotropic fractional diffusion models for DTI. Since anisotropy is clearly present in the three-dimensional MRI signal response, such models hold great promise for improving brain imaging. We then propose some candidate models, based on stochastic theory.

General PFG signal attenuation expressions for anisotropic anomalous diffusion by modified-Bloch equations

“…The results of space-fractional diffusion agree with those obtained by the different modified Bloch equations proposed by other groups [37][38][39]. Ref.…”

Tissue microstructure features derived from anomalous diffusion measurements in magnetic resonance imaging

“…Their findings were based on anomalous or fractal diffusion in time, and not in space, as was the case for our work. Our findings suggest that space fractional anomalous diffusion models have a place in mapping changes in brain microstructure, as has been noted in a previous study [Meerschaert et al, ]. Thereby, in the case of neurological diseases and disorders wherein spatial reorganisation of tissue microstructure is present, the parameters of the space fractional anomalous diffusion model may provide additional insight which may help with diagnosis and prognosis.…”

Exact solutions to the fractional time-space Bloch–Torrey equation for magnetic resonance imaging

“…In recent years, fractional calculus has arisen as a powerful and robust theoretical framework in order to account for the effects of anomalous diffusion in MRI [7][8][9][10][11][12]. The main advantage of such an approach is that insights can A C C E P T E D M A N U S C R I P T be derived from generalisations of the physical principles describing the magnetisation of water protons in MRI: the Bloch-Torrey equation [13].…”

“…However, an important drawback of the fractional setting is the complexity of its associated non-local operators for the derivation of exact solutions for the acquired signal decay. Whereas the purely space fractional setting imposes no real difficulties when using Fourier transforms [10,17], the time fractional setting is much more complicated, and to derive an analytical solution to the full fractional time-space Bloch-Torrey equation still remains as an open challenge [10].…”