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High tip angle approximation based on a modified Bloch-Riccati equation.

Nicolas Boulant1, David I Hoult

  • 1CEA, I2BM, NeuroSpin, LRMN, Gif sur Yvette, France. nicolas.boulant@cea.fr

Magnetic Resonance in Medicine
|December 6, 2011
PubMed
Summary
This summary is machine-generated.

Researchers found that scaling radio-frequency pulses to larger flip angles, beyond the small flip angle approximation, yields accurate results. This intuitive method is mathematically justified by a modified Bloch-Riccati equation, improving pulse design in magnetic resonance imaging.

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Area of Science:

  • Physics
  • Magnetic Resonance Imaging
  • Signal Processing

Background:

  • The small flip angle approximation is commonly used in radio-frequency pulse design for magnetic resonance imaging (MRI).
  • This approximation simplifies the relationship between the radio-frequency pulse and the resulting transverse magnetization.
  • Intuitive scaling of pulses to larger flip angles often yields good results despite deviating from the approximation.

Purpose of the Study:

  • To mathematically justify the intuitive approach of scaling radio-frequency pulses to higher flip angles.
  • To analyze the accuracy of higher flip angle approximations in pulse design.
  • To provide a theoretical basis for improved MRI pulse design.

Main Methods:

  • Derivation of a modified Bloch-Riccati equation.
  • Formulation of a differential equation in terms of the flip angle.
  • Analysis of the linear component of the derived equation, relating it to Fourier's equation.
  • Testing the accuracy of the higher flip angle approximation with constant- and variable-phase pulses.

Main Results:

  • A differential equation governing the flip angle was derived from the modified Bloch-Riccati equation.
  • This equation contains a significant linear component, which is an instance of Fourier's equation.
  • The intuitive method of scaling pulses to higher flip angles is mathematically validated.
  • The accuracy of this higher flip angle approximation was demonstrated for various pulse types.

Conclusions:

  • The common practice of scaling radio-frequency pulses to larger flip angles is theoretically sound.
  • The derived differential equation provides a framework for understanding and optimizing pulse design beyond the small flip angle approximation.
  • This work offers a more robust approach to designing radio-frequency pulses for applications in magnetic resonance imaging.