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advances have been made in cryogenic technology that facilitate maintenance and siting of superconducting high- and mid-field MRI systems in diverse locations. Modern cryocoolers can now remove more heat than previous generations allowing reduction and even elimination of the “bath” of liquid helium (LHe) that has typically surrounded the superconducting wire in the magnet to maintain it at 4.2 K. These cryogenic technologies and those leading up to them have been extensively reviewed [97]. In the earliest superconducting magnets, a two-cryogen system was used; LHe on the inner vessel providing a liquid bath in direct contact with the niobium titanium (NbTi) superconducting wire, and liquid nitrogen (LN) in an outer vessel to reduce heat flow to the environment. The residual heat entering the LHe vessel was countered only by the latent heat of evaporation of helium, about 20.5 kJ/kg. Thus, boiling off ~8 l of Lhe per day (~1 kg per day) compensates for a heat leak of only 0.24 W. The next step was to replace the use of nitrogen with a mechanical refrigeration system (“cold-head”). This is considerably safer, since nitrogen gas poses increased asphyxiation risk compared with helium (which floats up rather than sinking down). In addition to being more convenient, holding a radiation shields outside of the LHe vessel to 20 K and 70 K using cold-heads also decreases the heat flow compared with a similar 77 K LN cooled surface.

      Superconducting MRI systems typically employ Gifford–McMahon (GM) cryocoolers, a variant of the older Stirling cycle. GM cryocoolers have a moving rotary valve in the subsystem attached to the magnet, which makes the familiar steady “washing machine” sound of a nonscanning MRI, and is also a potential source of failure and mechanical vibrations. Current cold-heads can achieve more than 1 W of cooling at 4.2 K and tens of Watts at 12 K. This is enough to not only lessen the entering heat flux, but to fully overcome it, allowing GM cryocooler technology to provide sufficient heat removal at 4 K that helium is liquefied inside the cryostat. The result is a “zero-boiloff” magnet, now the norm for new clinical MRI systems. While not a fully “dry magnet,” current zero-boiloff designs eliminate the need for regular cryogen fills.

The next step is to eliminate the LHe completely, or at least reduce LHe volume to where the system can be safely operated without an emergency quench vent system (<10 l of LHe). This can save significantly on siting costs, especially in a complex hospital setting such as the ED. Elimination of most of the LHe bath requires direct “conduction cooling” of the superconductor by the cold-head (as opposed to bathing the windings in LHe). Although first envisioned as needing more exotic higher temperature superconductors such MgB₂ [98,99], “dry magnets” have recently been introduced by the major clinical MRI manufacturers using standard NbTi wire. The use of high-temperature superconductors that operate well above 4.2 K is attractive because they have an easier cooling target but is currently held back by their increased cost.

      3.5.1.2 Superconducting Solenoid Designs for the Easy-to-Site Suite

Shorter superconducting solenoid magnets have clear benefits for patient acceptance and ease of siting and use in an ED setting. In contrast to the situation for cryogenic equipment, the design of superconducting MRI magnet windings is little changed over the past few decades; see Lvovsky et al. for a thorough review [97]. In standard design optimizations, the position and number of turns of discrete winding groups are optimized on the cylinder. In addition to the primary field-producing windings, counter-wound shielding windings (usually larger-diameter coils at the bore end) attempt to reduce the stray field around the magnet. The optimization seeks a short magnet on a predetermined diameter cylindrical former that achieves the target homogeneity over the imaging region (typically defined as a given diameter spherical volume (DSV) with a minimum wire cost (length of wire). The optimization either assumes a small number of winding groups (e.g. six) [100] or uses linear programming and a sparsity-promoting norm to limit the winding groups [101]. The magnet homogeneity is a relative measure (ppm) and expressing the magnet length in unitless terms (as L/DSV, where DSV is the imaging “diameter spherical volume”) is also helpful. Xu et al. [102] showed that for a 1 ppm target homogeneity, the cost-optimized magnets followed a linear formula: L_optimal = 1.19 DSV + 0.77D, where L_optimal and D are the magnet windings length and diameter, and DSV is the diameter of the spherical homogeneity region. Reducing the magnet length further (<L_optimal) results in skyrocketing wire costs (which are proportional to conductor volume). A similar analysis was also applied to gradient coil lengths [103].

      3.5.1.3 Shorter Supercon Magnets from Relaxed Homogeneity

Because the optimization used by Xu and others is convex, it represents a true optimal solution and we must relax other constraints in order to achieve shorter magnets. In the text that follows, we replicate Xu et al.’s analysis [102] for L_optimal as a function of DSV and magnet diameter for a D = 1.1 m magnet but also examined optimized designs with homogeneity targets between 1 ppm and 10 000 ppm. Figure 3.6 shows the result of this analysis. When a length-optimized design is chosen from the knee of the cost vs. length L-curve, the cost of an optimized design can be plotted as a function of the unitless L/DSV for a given homogeneity target. Figure 3.6 shows this result, which informs the potential improvements in magnet length achievable if imaging could be performed in less homogeneous fields. Unfortunately, substantial relaxation in homogeneity is needed to get a significant reduction in magnet length. For example, relaxing the 1 ppm specification to 1000 ppm reduces the magnet length from 2.92 to 2.15 in normalized units – a 26% reduction. Thus, superconducting solenoid magnets, as they are currently envisioned, are not likely to significantly change in geometry.

Figure 3.6 Tradeoffs in superconducting solenoid optimizations following the optimization of Xu et al.[] The wire cost is seen to rise significantly as the magnet length is shortened (here shown in units of the imaging volume diameter).The left graph shows the wire length–length tradeoff for different homogeneity constraints. Taking the points on the “knee” of these L-curves allows the plot of magnet length vs. homogeneity (right-hand graph).

      3.5.1.4 Permanent Magnets for Portable MRI

      Superconducting solenoids are attractive because of their lack of an external energy source, high stored magnetic field energy, and temporal stability, although with the requirement for a cryogenic subsystem. Permanent magnets offer these capabilities to some degree and do not need cryogenics. Their downside is a reduced field-generating capability; human-sized homogeneous magnets above 0.5 T require a considerable weight of material. They are also less stable, for example drifting with temperature.

Rare-earth magnets made from alloys of neodymium such as NdFeB are the strongest form of permanent magnets readily available. They are a relatively recent development, introduced in 1984 [104,105]. Formed into blocks from sintered powder and then magnetized by applying a pulsed magnetic field, the strength of the permanent magnet is measured by its remanence (B_r), which measures the magnetic field of the residual magnetization present in the absence of an external field. For NdFeB, B_r ranges from 1.0 to 1.4 T. The field of NdFeB changes with temperature, with a temperature coefficient of remanence of about −0.1% per °K (the field goes down as the temperature increases). The coercivity (H_cl) measures the material’s resistance to demagnetization by an external field (or the field of a neighboring block). The tendency of the sintered material to corrode requires that the block be coated, usually with copper-nickel plating, or a coating of epoxy or another polymer. Because of the considerable forces between large NdFeB blocks, handling and assembling the material requires care and expertise.

The most common geometry for MRI use is a simple two-pole-piece dipole magnet. Spacing two magnetized disks with a gap (containing the imaging region) forms a uniform dipole field volume between the pole pieces. Each disk creates a dipole current pattern, and the net effect is like two stacked current loops (each with the current flowing in the same sense). Optimizing the placement of the material in the disks and/or shaping

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