Approximate solutions of the bloch equations for selective excitation

Abstract

Approximate solutions to the Bloch equations for selective excitation are derived using a perturbation method. High-order terms are analyzed, employing some special properties of corresponding multidimensional integrals. It is found that for excitation by a symmetric RF pulse applied in the presence of a field gradient the spin nutation angle as a function of the off-resonance frequency is approximately proportional to the Fourier dine transform of the RF function. This result is more accurate than the common assumption that the transverse magnetization as a function of the off resonance frequency is approximately proportional to the Fourier transform of the RF function. This analysis is useful for understanding the behaviors of both spin-inversion and phase-reversal 180° selective RF pulses as well as selective-excitation pulses, and it also offers insight to the problems of designing better selective RF pulses.