Characterization of anomalous relaxation using the time-fractional Bloch equation and multiple echo T2 *-weighted magnetic resonance imaging at 7T

Qin, Shanlin, Liu, Fawang, Turner, Ian, Yu, Qiang, Yang, Qianqian, & Vegh, Viktor (2016) Characterization of anomalous relaxation using the time-fractional Bloch equation and multiple echo T2 *-weighted magnetic resonance imaging at 7T. Magnetic Resonance in Medicine. (In Press)

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To study the utility of fractional calculus in modeling gradient-recalled echo MRI signal decay in the normal human brain.


We solved analytically the extended time-fractional Bloch equations resulting in five model parameters, namely, the amplitude, relaxation rate, order of the time-fractional derivative, frequency shift, and constant offset. Voxel-level temporal fitting of the MRI signal was performed using the classical monoexponential model, a previously developed anomalous relaxation model, and using our extended time-fractional relaxation model. Nine brain regions segmented from multiple echo gradient-recalled echo 7 Tesla MRI data acquired from five participants were then used to investigate the characteristics of the extended time-fractional model parameters.


We found that the extended time-fractional model is able to fit the experimental data with smaller mean squared error than the classical monoexponential relaxation model and the anomalous relaxation model, which do not account for frequency shift.


We were able to fit multiple echo time MRI data with high accuracy using the developed model. Parameters of the model likely capture information on microstructural and susceptibility-induced changes in the human brain.

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ID Code: 94667
Item Type: Journal Article
Refereed: Yes
Keywords: magnetic resonance imaging;Bloch equation;ultrahigh field;human brain; anomalous relaxation;fractional derivative
DOI: 10.1002/mrm.26222
ISSN: 0740-3194
Divisions: Current > Research Centres > ARC Centre of Excellence for Mathematical & Statistical Frontiers (ACEMS)
Current > Schools > School of Mathematical Sciences
Deposited On: 08 Apr 2016 04:45
Last Modified: 27 Apr 2016 05:36

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