Fractional Order Anisotropy at 9.4 T

The fractional order calculus (FC) model applied fractional order differential operators in the Bloch-Torrey equation. Previous studies on the FC model didn't consider the diffusion anisotropy. In this study, the anisotropy property of parameters in fractional order calculus (FC) diffusion model, i.e., the diffusion coefficient ^D, the heterogeneity index β and the spatial parameter μ were investigated. The diffusion-weighted imaging experiments were performed in vitro at 9.4 T using tissue samples of mice brains, hearts and kidneys with the diffusion gradient applied along the three principle axes separately (b-value range: 0–3500 s/mm²). In addition, several diffusion times (12–33 ms) were also used in mice brain experiments. The results showed that the anisotropy of β was much smaller compared to that of D and μ in all the samples studied, indicating that β was not strongly correlated to the diffusional directions compared to D and β. In addition, the diffusion time had little influence on the anisotropy of β in gray matter, while the anisotropy of D and μ changed significantly with increased diffusion time. Due to the direction-insensitive of β, parameter β maps obtained from single-direction diffusion-weighted imaging can give reliable tissue heterogeneity information.