Consistent Quadratic Phase Formation in 3D Fast Spin Echo Using Frequency-Modulated RF Pulses

Purpose: Frequency-modulated (FM) RF pulses achieve broadband excitation with low RF peak power, which is required in MRI with inhomogeneous magnetic fields. However, the quadratic phase generated with FM pulses makes it difficult to use them in fast spin echo (FSE), because even and odd refocused echoes have different spatial phase profiles. In this article, we formulate the condition that can generate a consistent quadratic phase in the two echo components in 3D FSE using FM pulses. Methods: The consistent quadratic phase condition in 3D FM-FSE was formulated with the Cayley-Klein parameters. The B₁⁺-dependent phase in FM excitation was compensated by adjusting the initial phase of FM pulses. The consistent quadratic phase in 3D FM-FSE and the impacts from the B₁⁺-dependent phase were simulated with extended phase graph (EPG). The EPG simulation was validated by comparing with experimental results at 3 T. Finally, in vivo brain imaging was conducted with T₁- and T₂-weighted contrasts. Results: In EPG simulation, a consistent quadratic phase was generated in all echoes in 3D FM-FSE under the formulated condition. The EPG simulation matched well with experimental results. The B₁⁺-dependent phase adjustment on FM pulses improved the magnitude profile of the refocused echoes. Despite the presence of large field inhomogeneity, 3D FM-FSE achieved in vivo brain imaging with good T₁- and T₂-contrasts. Conclusion: Achieving consistent quadratic phase in all refocused echoes in 3D FM-FSE makes it possible to use FM pulses in the non-adiabatic regime. 3D FM-FSE is a promising pulse sequence for MRI in inhomogeneous magnetic fields.