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Related Experiment Videos

Practical pulse synthesis via the discrete inverse scattering transform.

Jeremy Magland1, Charles L Epstein

  • 1Department of Mathematics and LSNI, University of Pennsylvania, Philadelphia, PA, USA.

Journal of Magnetic Resonance (San Diego, Calif. : 1997)
|December 14, 2004
PubMed
Summary

This study introduces the discrete inverse scattering transform (DIST) for designing selective radiofrequency (RF) pulses. DIST offers direct control over magnetization phase, matching the speed of Shinnar-Le Roux (SLR) methods.

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Area of Science:

  • Magnetic Resonance Imaging
  • Applied Physics
  • Signal Processing

Background:

  • Selective radiofrequency (RF) pulse design is crucial for Magnetic Resonance Imaging (MRI).
  • The Shinnar-Le Roux (SLR) algorithm is a common method for designing these RF pulses.
  • Existing methods may lack direct control over magnetization phase during pulse design.

Purpose of the Study:

  • To present the practical implementation of the inverse scattering transform (IST) for designing selective RF pulses.
  • To introduce a novel approach, the discrete inverse scattering transform (DIST), as an alternative to SLR.
  • To demonstrate DIST's ability to provide direct control over the magnetization phase profile.

Main Methods:

  • Utilizing a hard pulse approximation for pulse design, similar to SLR.

Related Experiment Videos

  • Employing full inverse scattering data (reflection coefficient and bound states) instead of flip angle profiles.
  • Developing explicit recursive algorithms based on discretizations of the Marchenko equations.
  • Incorporating both left and right Marchenko equations for enhanced numerical stability when bound states are present.

    • Main Results:

    • The DIST approach allows for direct control over the phase of the magnetization profile.
    • The computational speed of DIST is comparable to the SLR approach.
    • Approximation of the reflection coefficient enables pulses with a prescribed rephasing time.
    • Numerical stability is improved by using both Marchenko equations in the presence of bound states.

    Conclusions:

    • The discrete inverse scattering transform (DIST) provides a viable and efficient alternative for designing selective RF pulses in MRI.
    • DIST offers advantages in controlling magnetization phase compared to traditional methods like SLR.
    • The developed algorithms are practical for implementation and demonstrate robustness, even with amplitude errors.