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      Figure 3.7 Halbach arrays of permanent magnets. Phasing the magnetization from 0 to 4π provides a magnetic dipole with a uniform transverse field inside. Higher-order modes can be obtained by varying the angle to other multiples of 2π. Top left shows the ideal continuous magnetization distribution. Top middle uses key-stone shaped pieces. Top right shows square cross-section pieces, which are readily commercially available. Bottom left shows the possibility of using multiple cubes of differing B_r, chosen to optimize a desired field pattern. The bottom middle takes better advantage of the head geometry by using a portion of a Halbach sphere. The bottom right shows a section of a Halbach sphere used in the “MR Cap” of Figure 3.3.

      The field inside an ideal cylindrical Halbach array (e.g. Figure 3.7, top left) of inner radius r_a and outer radius r_b is given by B = B_r ln(r_b/r_a), where B_r is the remanence of the material used. Thus, for a human head system with r_b/r_a = 50 cm/30 cm and B_r = 1.4 T, we can expect a field of B₀ = 0.72 T in this ideal structure. For a whole-body system with r_b/r_a = 120 cm/80 cm, B₀ = 0.56 T. If the cylinder length is not infinite, but equal to its outer diameter, the estimated weight of rare-earth material for these two systems would be 1500 kg and 18 000 kg – not exactly lightweight. Achieving realistic weights for POC systems necessitates reducing the field, typically to below 0.1 T for adult human imaging systems.

Practical construction necessitates breaking the continuous distribution of material into discrete blocks such as shown in Figure 3.7, coined the NMR-MANDHaLa (nuclear magnetic resonance–magnet arrangements for novel discrete Halbach layout) [39,110]. This has the advantage of using stock NdFeB magnet geometries. Multiple publications have addressed methods to hold the material in place – an important consideration considering there are significant internal forces. Typically some sort of optimization of the configuration is needed for Halbach arrays, which are discretized and of finite length. This is especially important for head magnets where the shoulders are not inside the cylinder, in which case the imaging volume is centered at the brain center, only 18 cm from the end of the magnet. The array geometry is altered to mitigate the truncation effects using some form of optimization. Altering the size or grade of the rare-earth blocks using a genetic algorithm is a popular approach [51,68,111,112] resulting in a homogeneity improvement of 10-fold for a head-sized homogeneous magnet design [111]. The block size can also be treated as a continuous variable for the optimization and later discretized [38] or the angular position can be continuously altered [113,114]. Even with careful optimization, some form of additional shimming has been needed after construction to achieve field target fidelity comparable with superconducting systems. At least two prototype Halbach cylinders, one at 50 mT [20,115] and the other at 80 mT [20,115] have been tested for human brain imaging, in addition to the 72-mT Halbach bulb design of Figure 3.2 [116]. In addition to their lightweight, compact configuration, some of these systems have employed unusual design features such as a gradient field pattern built into the magnet design to eliminate the conventional switched readout gradient [20], or a conventional uniform field design, but with the gradient coils external to the magnet [116].

      3.5.1.6 Other Types of Permanent Magnet Arrays

Several additional geometries have been proposed to create uniform field volumes for MR. The approach of Manz et al. uses a variant of a Halbach sphere using a ring magnet (disk with hole), magnetized along the cylindrical axis and two simple cylinder magnets [117]. A yoked permanent magnet design was introduced for imaging cartilage in the knee at the magic angle, which requires the magnetic field to be rotated relative to the knee about two axes (the Halbach cylinder and conventional dipole are limited to a single rotation axis) [118]. The “Auberg ring” design uses radially magnetized rings on a cylinder to produce a field along the axis of the cylinder [119,120] and has seen increased interest for low-field MRI [25,121–123].

      3.5.2 Other Technological Challenges

      While a suitably compact magnet design constitutes one of the primary challenges to achieving the easy-to-site suite, portable brain MRI, or MR brain monitor discussed, additional technical challenges arise as the system deviates from the canonical high-field system design. Issues include trying to image in a more inhomogeneous field and trying to operate an MRI scanner without the “shielded room” Faraday cage that attenuates external EMI. As mentioned earlier, relaxing the homogeneity constraint benefits compact magnet design and eliminating the shielded room requires an alternative passive or active EMI mitigation strategy.

      3.5.2.1 Image Encoding in an Inhomogeneous Field

The image acquisition strategy and/or the image reconstruction methods will likely need refinement if the homogeneity specifications of the magnet are relaxed to achieve a more desirable POC footprint. Mullins and Garwood review the signal dropout and distortion consequences of inhomogeneities of >10 kHz in conventional sequences and some acquisition approaches [124]. In conventional gradient echo acquisition sequences, simple image reconstructions require that all gradient pulses (slice-select, phase-encoding, and readout) use a gradient strength that dominates the local gradients from the inhomogeneous magnet. Thus, strong gradient fields are desirable for reducing geometric distortions, but at odds with the constraints of portable or POC use where power and cooling infrastructure might be limited. For 3D spin echo sequences, only the readout gradient must dominate since a spin echo can be arranged to refocus the spurious gradients but not the phase-encoding field.

The

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