Introduction

The behaviour of electromagnetic fields produced by RF antennas are bound by the laws of physics. The Maxwell equations impose many limitations on how these fields can not only vary spatially and temporally, but how the electric and magnetic fields are linked. While propagating magnetic fields interface of boundary between materials can be discontinuous (a result of Maxwell’s equations), it’s been shown in the context of MRI and tissues that the magnetic field amplitudes are expected to be smoothly varying when using clinical MRIs Sled & Pike, 1998Sled et al., 1998. At ultra-high fields, standing wave artifacts can lead to more B₁ variations and even signal nulls, however the field amplitude nonetheless varies continuously Uğurbil, 2018Vaughan et al., 2001Yang et al., 2002. Thus, for both B₁⁺ and B₁^-, their amplitude is expected to be a smoothly varying multiplicative field, and at clinical field strength it’s also expected to be a slowly or low frequency varying field.

In practice, measured B₁⁺ maps are rarely perfectly smooth over the anatomy-of-interest being imaged. Figure 4.14 shows a comparison of measured B₁ maps in the brain produced by three methods: double angle, actual flip angle imaging (AFI), and Bloch-Siegert shift.

The overall “shape” of the B₁ map is the same for all three maps, and this nonuniformity pattern is expected due to the elliptical shape of the brain and its electromagnetic properties (Sled and Pike 1998). We see in the B₁ maps of Figure 1 that there is some noise, some distinguishable anatomical structures (caused by T₁ sensitivity and/or k-space propagation susceptibility effects), and in one case (AFI) an artifact caused by Gibbs ringing in the acquired images. All of these variations are not present in the actual B₁⁺ field that the spins experience during a pulse sequence, and so using this “raw” B₁ map to calibration flip angles or RF power for other quantitative MRI techniques (eg. variable flip angle T₁ mapping, quantitative magnetization transfer) risks introducing errors during the correction.

Although not a perfect solution, researchers often smoothen their B₁ maps Yarnykh, 2007Lutti et al., 2010Boudreau et al., 2017 in an effort to mitigate the error propagation from the B₁⁺ map noise and artifacts prior to use for other techniques. This chapter will discuss some common ways this B₁ map smoothing is achieved, show some examples of their benefits and weaknesses, and discuss some best practices.