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Anomalous diffusion measured by a twice-refocused spin echo pulse sequence: analysis using fractional order calculus.

Qing Gao1, Girish Srinivasan, Richard L Magin

  • 1School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, China; Center for Magnetic Resonance Research, University of Illinois at Chicago, Chicago, Illinois, USA; Department of Bioengineering, University of Illinois at Chicago, Chicago, Illinois, USA.

Journal of Magnetic Resonance Imaging : JMRI
|April 22, 2011
PubMed
Summary

A new fractional order calculus (FC) diffusion model accurately characterizes anomalous diffusion in brain tissues using a twice-refocused spin-echo (TRSE) sequence. This FC model demonstrates robust performance comparable to conventional methods, offering improved artifact immunity.

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Area of Science:

  • Neuroimaging
  • Biophysics
  • Applied Mathematics

Background:

  • Anomalous diffusion in brain tissues is crucial for understanding neurological conditions.
  • Conventional diffusion models may not fully capture complex diffusion dynamics in biological tissues.
  • Twice-refocused spin-echo (TRSE) sequences offer advantages in minimizing motion and eddy current artifacts.

Purpose of the Study:

  • To develop a theoretical framework using fractional order calculus (FC) for modeling anomalous diffusion.
  • To experimentally validate this FC diffusion model for brain tissue characterization using TRSE sequences.
  • To compare the performance of the FC model with conventional methods across different acquisition strategies.

Main Methods:

  • Generalized the Bloch-Torrey equation to a fractional order calculus (FC) diffusion model.
  • Derived an analytical expression for diffusion-induced signal attenuation in TRSE sequences.
  • Acquired diffusion-weighted (DW) images from healthy human brains using TRSE and Stejskal-Tanner sequences at various b-values.
  • Utilized Levenberg-Marquardt fitting to extract diffusion parameters (D, β, micro) and assessed goodness-of-fit in white matter, gray matter, and CSF ROIs.

Main Results:

  • The FC diffusion model accurately characterized diffusion-induced signal loss in brain tissues, particularly at high b-values.
  • The FC model demonstrated comparable goodness-of-fit and parameter precision for both TRSE and Stejskal-Tanner datasets.
  • Parametric maps generated from TRSE data exhibited reduced artifacts, indicating enhanced immunity to eddy currents.

Conclusions:

  • The fractional order calculus diffusion model effectively describes diffusion-induced signal attenuation in TRSE sequences at high b-values.
  • The FC model provides robust and comparable performance for brain tissue diffusion analysis using both TRSE and conventional Stejskal-Tanner sequences.
  • This approach offers a promising tool for characterizing anomalous diffusion in the brain with improved artifact mitigation.