Concomitant field terms for asymmetric gradient coils: Consequences for diffusion, flow, and echo‐planar imaging

Abstract

As a consequence of the Maxwell equations, linear field gradients are accompanied by additional spatially dependent field components. A description of the Maxwell field terms is presented which explicitly takes into account the asymmetry of the gradient coil. It is shown both theoretically and experimentally that, in contrast to symmetric coils, an asymmetric coil generates concomitant field terms of zeroth and first order in space. Artifacts induced by concomitant fields can be much more pronounced for asymmetric coil designs than for symmetric ones. For the strong gradient amplitudes available on modern MR systems the effect of these concomitant magnetic fields on the evolution of magnetization has to be taken into consideration in a variety of NMR acquisition techniques. The formalism is used experimentally to compensate for artifacts ob- In MRI, linear magnetic field gradients are used to encode spatial information with the requirement that the gradient coils produce a linear field over the volume of interest. However, this requirement cannot be completely fulfilled as it contradicts the general principle of electromagnetism expressed by Maxwell's equations. For a source-free region they require a zero divergence (div B ϭ 0) and a zero rotation (rot B ϭ 0) of the magnetic flux. Consequently, the linear magnetic fields are accompanied by secondary field terms, which are typically referred to as Maxwell or concomitant fields.Concomitant fields and their effects on NMR images were first described in 1985 (1), but remained mostly unrecognized in routine imaging. Since these early observations, improvement in gradient coil technology has made it possible to significantly increase the amplitude of the applied magnetic field gradients used in NMR imaging studies. This has amplified the influence of the secondary fields and has lead to a new appreciation of their effects. They have subsequently been studied extensively in a series of publications (2-7), which have provided a mathematical description of the concomitant fields and an understanding of some of the associated image artifacts. These studies have focused on the case of cylindrical symmetry, which is appropriate for the symmetrical gradient coils used by most MR systems.However, some systems use an asymmetric coil design, which can be advantageous in some cases. The MRI system used in this work is a human head-only scanner equipped with a short-axis gradient coil of a reduced inner diameter of 36 cm. This compact gradient design increases efficiency and minimizes coil inductance. It reduces the noise level due to a smaller number of coil turns and a shortened length. It also reduces the physiological stimulation dB/dt due to a smaller gradient region size and has a smaller heat generation (see Ref. 8 and references therein). As a result, it provides a better performance for high-speed MRI than coils of a whole body imaging system. Because the patient's head access into the coil is limited by the shoulders, the MRI system uses an asymmetric transverse coil w...

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