Fractional order NMR reflects anomalous diffusion

Recently, we proposed a new diffusion model in nuclear magnetic resonance (NMR) by solving the Bloch-Torrey equation using fractional order calculus with respect to time and space (Magin, RL, et al, J Magn Reson 2008; 190:255–270). This model yields a new set of parameters to describe anomalous diffusion: diffusion coefficient D, fractional order derivative in space ß, and a spatial variable μ (in units of µm). In this study, we demonstrate that fractional calculus (FC) can be successfully applied to analyze diffusion images of sephadex gels and brain tissues from healthy humans in vivo. Although the biophysical basis of ß and μ remains to be understood, the perspectives of using these parameters to characterize the environment for molecular diffusion may lead to a new way to investigate tissue structural changes in disease.