Generating unilateral field modulation for MRI using a pyrolytic-graphite-based Halbach array

Richard Bowtell^{1}

A flat Halbach array consisting of an array of long, thin permanent magnets whose magnetization orientation varies linearly with position, has the interesting property of generating a unilateral field perturbation. Such a pattern of field variation could be usefully employed in MRI, for example for attenuating signals from surface structures. Here we show that a Halbach array can be formed by exposing appropriately oriented strips of material with anisotropic magnetic susceptibility to a strong static field, and also validate the predicted behaviour in experiments carried at 3T using a 40-element structure formed from pieces of pyrolytic graphite sheet.

The flat Halbach
array^{1}, which consists of
a planar array of permanent magnets of thickness,* $$$t$$$* , in which the magnetization
in the *x*-*y* plane varies as $$$\textbf M=m\left(\textbf i \cos cx+\textbf k \sin cx \right)$$$ (Figure 1a), generates a spatially varying magnetic field $$\textbf B = \mu_{0} mct\left(\textbf i\cos cx+\textbf k \sin
cx \right)e^{cx} \: \: \: Eq. 1 $$ on one side of the array,where *z*<-*t*/2, and zero field on the
other, where z>*t*/2. This interesting behaviour has led to a diverse range of
applications of planar Halbach arrays which include uses in fridge magnets, free
electron lasers and magnetic levitation.

Planar arrangements that produce a one-sided
local magnetic field variation are also of potential value in MRI where they
could for example be used for selectively eliminating signals^{2,3}
from surface structures (e.g. subcutaneous fat).
Here we show that a Halbach array can be formed by exposing appropriately oriented strips of material with
anisotropic magnetic susceptibility to a strong static field, and also validate the predicted behaviour in
experiments carried at 3T using a 40-element structure formed from pieces of pyrolytic graphite sheet (PGS).

A planar Halbach array can be formed by arranging long, thin pieces of material with anisotropic magnetic susceptibility, characterised by susceptibility tensor $$ \begin{bmatrix}\ \chi_{a}& 0 & 0 \\0 & -\frac{\chi_{a}}{2} & 0\\0 & 0 & -\frac{\chi_{a}}{2}\ \end{bmatrix}$$

in a static magnetic field ,so that the angle, $$$\theta $$$ , that the principal axis of the susceptibility tensor makes with the field varies linearly with $$$x$$$-position (Figure 1b) . When a magnetic field, $$$B_{0}$$$, is applied along the $$$x$$$-direction and $$$\theta = c x/2$$$, the magnetization of the array follows Eq. 1 with $$ m=\frac{3 \chi_{a}B_{0} }{2 \mu_{0}}\: \: \: Eq. 2$$thus generating a one-sided field perturbation of the form shown in Eq. 1. Similar behaviour obtains if the magnetic field is directed along $$$z$$$..

1. Mallinson. JC. One-sided fluxes - magnetic curiosity. IEEE Transactions on Magnetics 1973;MAG9:678-82.

2. Boer VO, van de Lindt T, Luijten PR, Klomp DWJ. Lipid suppression for brain MRI and MRSI by means of a dedicated crusher coil. Magnetic Resonance in Medicine 2015;73:2062-8.

3. Jehenson P, Bloch G. Elimination of surface signals by a surface-spoiling magnetic-field gradient - theoretical optimization and application to human invivo NMR-spectroscopy. Journal of Magnetic Resonance 1991;94:59-72.

4. Wilson JL, Jenkinson M, Jezzard P. Optimization of static field homogeneity in human brain using diamagnetic passive shims. Magnetic Resonance in Medicine 2002;48:906-14.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

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