Effects on signal

To excite the spins in the transverse plane, a carrier frequency tuned to the Larmor frequency is used by the transmit coil. If the frequency of the spins does not match the excitation frequency, it results in a suboptimal tip of the spins in the transverse plane. If the frequency of the spins varies across the ROI, the flip angle is affected differently across the image Wang et al., 2006.

When a signal is acquired, it is demodulated to remove the carrier frequency (Larmor frequency) from the signal. An example of a FID is shown in Figure 5.4. The number of species represent the number of isochromats in the simulation. An isochromat represents an ensemble of spins with the same properties rotating at the same Larmor frequency. For a single isochromat, if the acquired signal and demodulation frequency perfectly match, the T₂ signal can be recovered. If the carrier frequency is different from the expected frequency (such as when there are inhomogeneities), the demodulation introduces low-frequency variations. A non-homogeneous sample is also shown featuring many isochromats. Alternatively, a homogeneous sample with a non-homogeneous B₀ field could be simulated as well and would have a similar shape as the one with multiple species. In that case, the difference from the T₂ curve would reflect T₂^* ($1/T_{2}^{*}=1/T_{2}+1/T_{2}^{'}$) effects. During the relaxation process, spins precessing at different frequencies, due to the presence of B₀ inhomogeneities, will give rise to phase offsets between the spins within a voxel. This intravoxel phase dispersion leads to signal decay.

B₀ inhomogeneities can lead to distorted k-space trajectories during the readout gradient. This effect is worse during further k-space traversal due to the compounding of the errors. When inhomogeneities are present, the frequencies of the spins are altered. The one-to-one relationship between frequency and spatial location (required to obtain accurate spatial correspondence) is broken. This leads to geometric distortions. Figure 5.5 shows an animation of the filing of k-space of an EPI sequence using bi-polar readouts. A theoretical trajectory is shown as well as a trajectory where a constant parasite gradient in the phase encoding direction has been added. One can observe the trajectory differences.

Radiofrequency (RF) pulses can also be affected by an inhomogeneous B₀ field. During slice selection for example, the RF pulse excites a range of frequencies that can be mapped to spatial locations by applying a linearly evolving magnetic field along the slice direction. For a perfectly transverse acquisition, the resulting B₀ field can be expressed by ($G_{z}z+ B_{0}$). If B₀ inhomogeneities are present ($G_{z}z+ B_{0} +\Delta B_{0} (x,y,z)$), the excited slice profile can be distorted or offset from the expected location. When B₀ inhomogeneities are very inhomogeneous, they can also disrupt frequency-selective RF pulses such as fat saturation pulses. There are also other effects such as ringing artifacts, blurring, and ghosting that can occur.

All of these effects can be minimized with B₀ shimming. To do so, a map of the B₀ field can be acquired. In addition to shimming, B₀ mapping is important for other techniques that will be discussed later. The next section will show how to perform B₀ mapping using two echoes.