# Designing B1 ‐Selective Pulses by Frequency Modulating in a Second Rotating Frame

## TL;DR

This paper introduces a new method for slice selection in MRI that works even when magnetic field inhomogeneities are present, using a novel pulse design.

## Contribution

A new B1-selective pulse design using frequency modulation in a second rotating frame to enable slice selection without B0 gradients.

## Key findings

- AMHS1 simulations showed robust slice inversion despite B0 and B1 inhomogeneities.
- Slice and slab selection was experimentally demonstrated in phantoms and rat brains using surface coils.
- Low-flip angle AMHS1 pulses enabled 3D gradient-echo imaging in vivo at 9.4 T.

## Abstract

To create a frequency‐modulated pulse for slice selection of arbitrary, uniform flip angle even when B
0 and B
1 are inhomogeneous, without utilizing B0 gradients

An amplitude‐modulated hyperbolic secant pulse (AMHS1) was derived from Hoult's B1‐selective imaging method which utilizes one component, B
1y, as a gradient and another, B
1x, for selective excitation. The frequency sweep in AMHS1 was produced by a time‐dependent amplitude‐modulation of B
1x, defining the band of nutation frequencies to select along the B
1y gradient. Resilience of slice selection to B
0 and B
1 inhomogeneities was investigated by simulations. Slice‐ and slab‐selective imaging were demonstrated experimentally in phantoms and rat brain in vivo using surface coils.

Simulations of AMHS1 demonstrated slice inversion despite B
0 and B
1 inhomogeneities. When operating sub‐adiabatically to produce excitation flip angles < 180° with a single coil, the flip angle across the slice varied because both B
1x and B
1y gradients were present. This problem was corrected by scaling B
1x(t) by the normalized frequency‐sweep and phase‐modulation functions. Slice selection using only a B
1 gradient was demonstrated on phantoms using a pair of AMHS1 pulses transmitted with a surface coil. By using a low‐flip angle AMHS1 with B
1y refocusing lobes, slice‐ and slab‐selective excitation was realized in 3D gradient‐echo imaging of rat brain in vivo at 9.4 T.

By implementing frequency modulation in a second rotating frame, B1‐selective excitation and inversion are feasible, even when B
0 and B
1 are nonuniform.