Magnetic Resonance Microscopy

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].

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].

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.

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 distortions induced in the image’s coordinate system are described by the Jacobian matrix formed from the partial spatial derivatives of the B 0field. If the magnet’s B 0field map is known, the Jacobian is fully known and, in principle, can be used to correct the distortions. But no spatial encoding occurs in locations where the magnet’s static gradient is equal and opposite to the applied gradient, and the correction problem is singular. Because of this, it can be desirable to acquire the image twice, for example once with a positive readout gradient and once with the readout gradient current reversed to ensure that all locations are spatially encoded for at least one acquisition. A general approach is to use a “model-based reconstruction” where the “forward model” describes how measured data are produced given any object input to the model. Conversely, given a set of measured data, an inversion of the forward model (generally by some form of iterative search) finds the object giving the “best fit” to the data, possibly subject to some constraints or prior knowledge [125–128].

Acquisition approaches to the magnet inhomogeneity problem include relying on multiple spin echo sequences, which have a long history of use in the oil well-logging industry where NMR is performed in very inhomogeneous fields [129]. This approach was used with phase encoding and the fixed “readout” gradient inherent to an inhomogeneous magnet to image in single-sided devices [49,130] and in a Halbach cylinder with a built-in readout gradient [20,22]. Other approaches include quadratic phase-encoding approaches [131,132] and missing point steady-state free precession (MS-SSFP) methods [133].

If the magnet is inhomogeneous, or has a built-in encoding field, the MR linewidth across the body will be larger than seen in canonical high-field scanners, which typically achieve proton linewidths of a few tens of Hertz over the brain. In addition to the encoding and reconstruction problems described earlier, the Q of the radiofrequency coil is often high enough so that the bandwidth (BW) of the coil is lower than that of the signal, diminishing detection in regions with high-frequency offsets.

On excitation, this could be compensated in the design of the radiofrequency pulse using knowledge of the coil’s response to counteract the effect at the frequencies at the edge of the coil’s response. Alternatively, one could simply damp the resonator with an external resistor switched in during transmit (at the expense of requiring increased radiofrequency power) [134]. But during reception, the high- Q coil will simply be inefficient at detecting spins in locations where the spin frequency exceeds the coil BW. The ability to receive across the full-imaging BW is critical, and becomes more difficult at low field. Low loss reception is important for maintaining the sensitivity of detection, so there is strong motivation to maximize Q by increasing L and reducing resistive losses in the coil. Furthermore, reduced radiofrequency losses in the tissue help keep the Q of head resonators in the 50–200 range across a wide variety of low- to mid-field strengths, since the coil BW (full width at half maximum of coil response) relates to Q through BW = v 0/ Q (where v 0is the Larmor frequency). As Q does not change much, in general the detection BW decreases at lower field. Assuming Q = 100 and an 80-mT magnet ( v 0= 3.4 MHz), the expected BW of the coil is 34 kHz (compared with a 640-kHz BW for a Q = 100 coil at 1.5 T). Even for homogeneous magnets, a typical readout gradient of 10 mT/m will introduce a proton linewidth of 84 kHz over the 20-cm head. Thus, a receive coil constructed with desirable high- Q properties will introduce substantial shading across the FOV.