Approximate Fourier domain expression for Bloch-Siegert shift

Purpose: In this study, a newsimple Fourier domain-based analytical expression for the Bloch-Siegert (BS) shift-based B₁ mapping method is proposed to obtain |B₁⁺| more accurately while using short BS pulse durations and small off-resonance frequencies.

Theory and Methods: A new simple analytical expression for the BS shift is derived by simplifying the Bloch equations. In this expression, the phase is calculated in terms of the Fourier transform of the radiofrequency pulse envelope, and thus making the off- and on-resonance effects more easily understandable. To verify the accuracy of the proposed expression, Bloch simulations and MR experiments are performed for the hard, Fermi, and Shinner-Le Roux pulse shapes.

Results: Analyses of the BS phase shift-based B₁ mapping method in terms of radiofrequency pulse shape, pulse duration, and off-resonance frequency show that |B₁⁺| can be obtained more accurately with the aid of this new expression.

Conclusions: In this study, a new simple frequency domain analytical expression is proposed for the BS shift. Using this expression, |B₁⁺| values can be predicted from the phase data using the frequency spectrum of the radiofrequency pulse. This method works well even for short pulse durations and small offset frequencies.