Adiabatic MRI Pulses

Adiabatic radio frequency (RF) pulses are used in magnetic resonance imaging (MRI) to achieve excitation that is insensitive to spatial inhomogeneities in the excitation field or off-resonances in the sampled object.

Nuclear magnetic resonance (NMR) experiments are often performed with surface transceiver coils that have desirable sensitivity, but have the disadvantage of producing an inhomogeneous excitation field.

This inhomogeneous field causes spatial variations in spin flip angles, which, in turn, causes errors and degrades the receiver's sensitivity.

RF pulses can be designed to create low-variation flip-angles or uniform magnetization inversion across a sample, even in the presence of inhomogeneities such as B1-variation and off-resonance.

In the frame rotating at the Larmor frequency, the effective field experienced by the spins is in the transverse plane.

In RF excitation analysis, the effective field is derived in the rotating frame of reference, which depends on the radial frequency of the radio-frequency

In the frame rotating about the z-axis at radial frequency, the effective magnetic field can be derived:

In an “adiabatic passage” process, the parameters A and ω can be varied gradually.

Figure 1 shows how spins track Beffective in an adiabatic passage transition.

is defined as the angle of Beffective with the z-axis in the rotating frame of reference.

Sweep-diagrams plot the trajectory of the effective field for a spin with a particular resonance frequency.

Since the direction of Beffective is largely independent of B1 strength, adiabatic pulses are considered insensitive to B1 inhomogeneities.

An interesting feature of AFP pulses is their insensitivity to off-resonance spins in a particular bandwidth.

The effective field has a trajectory which is shifted upward, but still has a final ending position which points along the –z-axis.

For this reason, AFP pulses are considered insensitive to off-resonance sources, within a certain bandwidth.

Spins with off-resonance outside this bandwidth will not experience an inversion, as shown in the sweep diagram.

As long as adiabaticity is maintained during rotations of Beffective, inhomogeneities in the B1 field strength will not have an effect on the flip-angle of the magnetization after a BIR pulse.

In this sequence, Beffective is applied initially along the +x-axis in the rotating frame, and then adiabatically swept from the +x-axis to the +z-axis.

In the time that it takes the field to sweep, M precesses about the Beffective axis.

In the second half of the pulse, Beffective is applied along the -z-axis and adiabatically swept to point along the -y-axis.

This can be understood by examining how the plane rotates during the second half of the BIR pulse.

Secondly, the initial Beffective for an off-resonance spin can have a significant component pointing along the z-axis of the rotating frame, which causes the spin to track Beffective during the entire adiabatic pulse (known as “spin-locking”).

Spin-locked sources will end up pointing along the -y-axis after a BIR-1 pulse, since that is the final direction for Beffective.

Arbitrary flip angles are achieved by selecting a phase-shift for each of the BIR-1 parts of the pulse.

For a flip-angle of theta, the phase shift of each pulse is set by this design:

Off-resonance spins will exhibit some degree of spin-locking to the Beffective field, similarly to the BIR-1 case.

Many different combinations of phase and amplitude modulated pulses can perform similar adiabatic inversions.

Once a required adiabaticity is defined, the amplitude and phase functions can be optimized against several desired features, such as reduction in the total time of the pulse, insensitivity to off-resonance or constant gradient fields, and reduction in the peak power required in the B1 pulse.

We can examine the cases of AHP and AFP to demonstrate principles in adiabatic pulse design.

These applications include: In addition, several research efforts have demonstrated methods for inverse design of adiabatic pulse sequences[5][6]

Figure 1. Spins precess around B effective , and if B effective meets the adiabatic condition, these spins will track the position of B effective as it changes.
Figure 2. B effective magnitude and phase for the hyperbolic secant adiabatic pulse with different RF peak power. The direction of is relatively independent of RF peak power.
Figure 3. Sweep diagram for on-resonance spins in the case of the hyperbolic secant adiabatic pulse, for different RF peak powers. The direction of B effective is relatively independent of RF peak power. Solid arrows are the final effective fields for AFP; dotted arrows are the final effective fields for AHP.
Figure 4. Adiabatic full-passage (AFP) pulses are off-resonance-insensitive for a certain bandwidth. Sweep diagrams for two off-resonances are shown in red. In the left plot, the off-resonance magnetization will be inverted by the end of the AFP pulse. In the right plot, the off-resonance magnetization will not be inverted by the end of the AFP pulse. Solid arrows are the final effective fields for AFP; dotted arrows are the final effective fields for AHP.
Figure 5. BIR-1 pulse sequence for 90-degree and 45-degree flip-angles.