title: Characterization of anomalous relaxation using the time-fractional Bloch equation and multiple echo T2*-weighted magnetic resonance imaging at 7 T.
abstract: 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. Magn Reson Med 77:1485-1494, 2017. © 2016 International Society for Magnetic Resonance in Medicine.
authors.affiliation: School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld, 4001, Australia.
authors.forename: Shanlin
authors.initials: S
authors.lastname: Qin
authors.affiliation: School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld, 4001, Australia.
authors.forename: Fawang
authors.initials: F
authors.lastname: Liu
authors.affiliation: School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld, 4001, Australia.|ARC Centre of Excellence for Mathematical and Statistical Frontiers, Melbourne, Victoria, Australia.
authors.forename: Ian W
authors.initials: IW
authors.lastname: Turner
authors.affiliation: Centre for Advanced Imaging, the University of Queensland, Brisbane, Queensland, Australia.
authors.forename: Qiang
authors.initials: Q
authors.lastname: Yu
authors.affiliation: School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld, 4001, Australia.
authors.forename: Qianqian
authors.initials: Q
authors.lastname: Yang
authors.affiliation: Centre for Advanced Imaging, the University of Queensland, Brisbane, Queensland, Australia.
authors.forename: Viktor
authors.initials: V
authors.lastname: Vegh
mesh_terms: D000328:Adult; D016477:Artifacts; D001921:Brain / Q000033:anatomy & histology / Q000000981:diagnostic imaging* / Q000502:physiology*; D003198:Computer Simulation; D038524:Diffusion Magnetic Resonance Imaging / Q000379:methods*; D017097:Electric Impedance; D005260:Female; D006801:Humans; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D060526:Magnetic Fields; D008297:Male; D008954:Models, Biological; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity
keywords: 
  T2* anomalous relaxation; Bloch equation; fractional derivative; human brain; magnetic resonance imaging; ultrahigh field