Читать книгу Magnetic Resonance Microscopy - Группа авторов - Страница 64

The standard dipole magnet described in Section 3.5.1.4, built by placing two blocks of magnetized material above and below the imaging volume can be extended by adding additional blocks around the imaging volume with intermediate magnetization angles. This extension is analogous to expanding two current loop coil dipoles in the “Helmholtz” configuration to a birdcage style structure by adding loops in a circular configuration with the currents phased at intermediate phase angles. In the permanent magnet case, the result is a magnetized annulus commonly referred to as a Halbach array shown in Figure 3.7 [107,108]. The ideal Halbach configurations have the counterintuitive property of not needing a flux return yoke because the flux is returned in the magnets themselves. In linear Halbach arrays there is no flux on one side of the structure. Similarly, the ideal cylindrical (Figure 3.7, top left) and spherical Halbach arrays have no flux outside the structure [109]. This nearly completely eliminates the stray-field footprint, as well as eliminating the heavy iron yoke associated with the open-MRI dipole magnets; two compelling practical advantages to the Halbach configurations.

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].