Fractional motion model for characterization of anomalous diffusion from NMR signals.
Measuring molecular diffusion has been used to characterize the properties of living organisms and porous materials. NMR is able to detect the diffusion process in vivo and noninvasively. The fractional motion (FM) model is appropriate to describe anomalous diffusion phenomenon in crowded environments, such as living cells. However, no FM-based NMR theory has yet been established. Here, we present a general formulation of the FM-based NMR signal under the influence of arbitrary magnetic field gradient waveforms. An explicit analytic solution of the stretched exponential decay format for NMR signals with finite-width Stejskal-Tanner bipolar pulse magnetic field gradients is presented. Signals from a numerical simulation matched well with the theoretical prediction. In vivo diffusion-weighted brain images were acquired and analyzed using the proposed theory, and the resulting parametric maps exhibit remarkable contrasts between different brain tissues.
Center for MRI Research, Academy for Advanced Interdisciplinary Studies, Beijing City Key Lab for Medical Physics and Engineering, Institute of Heavy Ion Physics, School of Physics and McGovern Institute for Brain Research, Peking University, Beijing, China.
Yang
Y
Fan
Center for MRI Research, Academy for Advanced Interdisciplinary Studies, Beijing City Key Lab for Medical Physics and Engineering, Institute of Heavy Ion Physics, School of Physics and McGovern Institute for Brain Research, Peking University, Beijing, China.
Jia-Hong
JH
Gao
D000328:Adult; D001921:Brain / Q000378:metabolism; D003198:Computer Simulation; D004058:Diffusion; D038524:Diffusion Magnetic Resonance Imaging / Q000379:methods; D005260:Female; D006801:Humans; D008297:Male; D008962:Models, Theoretical; D009038:Motion