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Analytical solution and verification of diffusion effect in SSFP.

C E Carney1, S T Wong, S Patz

  • 1Brigham and Women's Hospital, Harvard Medical School, Boston, Massachusetts 02115.

Magnetic Resonance in Medicine
|June 1, 1991
PubMed
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This study presents a new method to solve for diffusion effects in steady-state sequences, offering analytical expressions for signal decay. This approach provides a unique sensitivity to b factor changes compared to existing diffusion measurement techniques.

Area of Science:

  • Magnetic Resonance Imaging
  • Diffusion MRI

Background:

  • Steady-state sequences are widely used in MRI.
  • Understanding diffusion effects is crucial for accurate imaging.
  • Existing methods for diffusion measurement have limitations.

Purpose of the Study:

  • To develop analytical expressions for diffusion effects in steady-state sequences.
  • To provide a method for obtaining magnetization responses for various parameters.
  • To investigate the sensitivity of the new method to b factor changes.

Main Methods:

  • Formulating a Fourier series decomposition solution to the Bloch-Torrey equation.
  • Imposing a steady-state condition to derive analytical expressions.
  • Verifying assumptions using finite difference solutions and simulations.

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Main Results:

  • Analytical expressions describing signal decay due to diffusion were developed.
  • Magnetization responses can be obtained for any system and sequence parameters.
  • The method exhibits different sensitivity to b factor changes compared to standard techniques.

Conclusions:

  • The developed method provides a novel analytical solution for diffusion effects in steady-state sequences.
  • This approach offers a new perspective on diffusion measurement in MRI.
  • The findings were validated through simulations and finite difference solutions.