The synthesis of pulse sequences yielding arbitrary magnetization vectors

Area of Science:

• Magnetic Resonance Imaging
• Quantum Control

Background:

• Previous methods for synthesizing spin excitation pulse sequences were limited to symmetric excitations and fixed-axis pulses.
• Arbitrary frequency-dependent spin excitation is crucial for advanced magnetic resonance applications.

Purpose of the Study:

• To develop a generalized procedure and algorithm for synthesizing pulse sequences that generate arbitrary frequency-dependent spin excitation.
• To overcome the limitations of previous methods by removing restrictions on excitation symmetry and pulse axis.

Main Methods:

• The final z-magnetization vector (Mz) is expressed as an Nth order complex Fourier series as a function of off-resonance frequency.
• A consistent Fourier series is formed for the transverse magnetization vector (Mxy).
• Analytic inversion of the Bloch equation is employed to generate pulse sequences yielding desired Mz(f) and Mxy(f).

Main Results:

• The procedure generalizes previous work by allowing arbitrary frequency-dependent spin excitation.
• Up to 2^(2N) different pulse sequences can be generated, all producing the same Mz(f) but varying Mxy(f).
• The method enables the generation of any potentially realizable Mz(f) via pulse sequence synthesis.

Conclusions:

• The presented procedure and algorithm offer a powerful tool for designing sophisticated pulse sequences in magnetic resonance.
• This technique significantly expands the capabilities for controlling spin excitation and magnetization dynamics.
• The analytic inversion of the Bloch equation provides a robust method for achieving desired spin excitation profiles.