Transmit and Receive RF field amplitudes

In an MRI experiment, magnetic field amplitude of the radiofrequency field (B₁) is an an important physical parameter that is a product of the interaction between RF coil design and the position (volume and relative position to the coil) and properties (electromagnetic permittivity ε and permeability μ) of the object being imaged. In any MRI experiments, two B₁ fields appear: the transmit RF field amplitude B₁⁺ and the receive RF field amplitude B₁^-. The latter, B₁^-, is often referred to in terms of the receive RF coil sensitivities and this is due to the principle of reciprocity Hoult & Richards, 1976Hoult, 2000 property of RF antennas. In terms of an MRI image, B₁^- is simply a multiplication factor that varies spatially but doesn’t change between pulse sequences if the subject remains motionless, and techniques to “flatten” images by estimating this field numerically have been developed Sled et al., 1998. Additionally, many quantitative MRI techniques calculate the ratio of images, which eliminates this B₁^- component from the resulting image.

B₁⁺, however, impacts the resulting MRI images in a much more complex way and is not a simple multiplication factor. B₁⁺ directly perturbs the system of spins by introducing energy in the system, which practically we quantify as the flip angle of an RF pulse. Two different B₁⁺ values will not have the same impact on voxel for different pulse sequences, as spin dynamics and steady-state conditions will vary. For example, let’s say you acquire a saturation recovery image and also a short TR steady-state gradient echo. For an actual flip angle = $\alpha \cdot B_{1}$, the magnetization after TE will be $M_{z}\text{sin}\left( \alpha \cdot B_{1} \right)\text{exp}\left(-\text{TE}/T_{2} \right)$ and $M_z$ prior to the RF pulse is given by Eq. 2.5. Thus, not only does B₁⁺ not appear as a simple multiplication factor, a change of B₁ will not impact this voxel for both sequences by the same ratio. Thus, knowledge of B₁⁺ through B₁ mapping can help us retroactively understand the dynamics of the spins accurately, and can play the role of a calibration factor for many quantitative MRI techniques (e.g. VFA, T₂/T₂^*, qMT, etc). In addition, B₁ mapping can also map the electromagnetic properties, but this won’t be discussed in this chapter.

In this chapter, we’ll be discussing a simple but widely used class of methods for B₁ mapping, the double angle method. For the sake of simplicity, and for consistency with the quantitative MRI literature, we’ll define B₁ = B₁⁺ and will explicitly state B₁^- when referring to the receive field.