10 - B₁ gradient methods

Summary

Introduction

Although having some distinct limitations (e.g., relatively weak gradients and poor directionality), B₁-based measurements have some particular advantages over B₀ gradient-based methods. However, B₁-based techniques have so far received only limited usage and consequently in this chapter we provide only a cursory coverage of these techniques and the interested reader is referred to the pertinent reviews on the subject.

B₁ gradients

B₁ gradients are more complex than B₀ gradients. Apart from purely technical considerations, there are three main differences between B₀ and B₁ gradients: (i) A B₀ field couples only into the spin system along the z-axis, thus the effective gradient tensor is always truncated into an effective vector (see Section 2.2.2). Radio frequency fields, however, couple into the spin system from any orientation within the transverse plane. As a result the B₁ gradient generally retains its tensor form when it couples into the spin system. (ii) When the same rf coil is used for both excitation and detection, any phase variation is cancelled during the measurement. But when an experiment involves two rf fields at the same frequency this cancellation no longer occurs and phase variations need to be considered. This spatial dependence of the phase difference between the two rf fields presents an additional complication (or opportunity). (iii) The third difference is that B₁ fields are non-secular and so do not commute with internal Hamiltonians. Thus, unlike a B₀ gradient, a B₁ gradient cannot be treated additively with respect to internal Hamiltonians.