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Stejskal's formula for multiple-pulsed diffusion MRI.

Jens H Jensen1

  • 1Center for Biomedical Imaging, Medical University of South Carolina, Charleston, SC, USA; Department of Radiology and Radiological Science, Medical University of South Carolina, Charleston, SC, USA.

Magnetic Resonance Imaging
|July 30, 2015
PubMed
Summary
This summary is machine-generated.

This study extends the Stejskal formula for diffusion MRI to multiple-pulsed diffusion MRI (MP-dMRI). The findings express the diffusion-weighted signal using a higher-dimensional Fourier transform for advanced analysis.

Keywords:
Cumulant expansionDiffusion MRIKurtosisMultiple wave vectorPulsed field gradientq-space

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Area of Science:

  • Magnetic Resonance Imaging
  • Quantum Mechanics
  • Biophysics

Background:

  • The Stejskal formula is a cornerstone of diffusion Magnetic Resonance Imaging (dMRI), linking the NMR signal to the Fourier transform of the diffusion displacement probability density function.
  • Extending this fundamental result to more complex diffusion sequences is crucial for advancing dMRI techniques.

Purpose of the Study:

  • To generalize the Stejskal formula for multiple-pulsed diffusion MRI (MP-dMRI).
  • To develop a higher-dimensional q-space formalism for analyzing complex diffusion MRI signals.

Main Methods:

  • Utilized a higher-dimensional q-space formalism.
  • Expressed the diffusion-weighted signal for N diffusion wave vectors.
  • Applied the extended Stejskal's formula to analyze the cumulant expansion of the signal magnitude in MP-dMRI.

Main Results:

  • Successfully extended the Stejskal formula to MP-dMRI.
  • Developed a theoretical framework for relating MP-dMRI signals to a 3N-dimensional diffusion displacement probability density function.
  • Demonstrated the utility of the extended formula through cumulant expansion analysis.

Conclusions:

  • The generalized Stejskal formula provides a powerful theoretical tool for understanding diffusion in MP-dMRI.
  • This work paves the way for more sophisticated analysis of diffusion processes using advanced MRI sequences.
  • The higher-dimensional q-space approach offers new insights into complex diffusion phenomena.