A multi-circular shim coil (MCSC) [1,2], which consists of a set of localized circular current coils, provides the flexibility to design and produce linear and higher-order magnetic fields that compensate for a given B₀ imhomogeneity both statically and dynamically. However, the concept of the MCSC has currently been realized only for cylindrical base geometries. Here we translated the concept of the multi-circular shimming to a biplanar geometry. To test the concept, a planar-type MCSC was designed and fabricated for an open, 1.0 T permanent magnet system. We verified the validity of the planar MCSC.

Figure 1 shows the MCSC and MRI systems. The planar MCSC consisted of circular coils (24 coils, wire diameter 0.26 mm, 3 turns for each coil) fixed on two fiber-reinforced plastic plates (20 cm × 20 cm, thickness 0.5 mm) (Fig. 1(a)). There is a trade-off between the shimming performance and the maximum coil current, depending on the center diameter of circular coils (Fig. 2). Here the center diameter was determined to be 30 mm. Then the MCSC was fixed on the home-built coplanar gradient coils (Fig. 1(b)). The solenoidal coil (diameter 55 mm, 60 mm long) and the RF shield box (22 cm × 18 cm × 7 cm) made of the brass plates were inserted into the gradient coil and MCSC set. The magnet used was a Halbach 1.0 T permanent magnet (Fig. 1(c); NEOMAX Engineering, Tokyo, Japan; gap 90 mm, homogeneity 7 ppm over 4 cm diameter spherical volume (DSV), weight 980 kg).

The field imhomogeneity over 4 cm DSV at the center of the magnet was corrected using MCSC as follows. The spatial variation of the magnetic field ΔB₀ was measured using a conventional phase shift method with a CuSO4–doped water phantom. Then the constrained leased-squared fitting based on the Levenberg-Marquardt method was applied to decompose the measured field variation into the fields generated by the circular coil elements and to determine the coil currents that were necessary to correct the field variation. The maximum coil current was limited to 1 A. The coil currents were generated by a home-built 24ch current power supply and controlled by a home-written C software run on a laptop windows PC (Fig. 1(d)). For comparison, conventional second-order shim coils (xy, yz, xz, z2, and x2-y2) were fabricated.

Figure 3 shows the center slices of ΔB₀ measured with and without the shimming. The field imhomogeneity was largely compensated for by the planar MCSC with the maximum coil current of 390 mA. Without shimming, the root mean square (RMS) and peak-to-peak (PP) ΔB₀ were 0.91 and 8.2 ppm, and these were largely reduced with the planar MCSC (RMS: 0.56, PP: 4.8 ppm). The measured RMS and PP values with the MCSC were close to the theoretical values (RMS: 0.41 ppm, PP: 4.0 ppm). The performance of the MCSC shimming was compatible with the conventional second-order shimming (RMS: 0.38 ppm, PP: 3.7 ppm). Figure 4 shows the capability of inhomogeneity correction with high-order terms. The theoretical field maps generated by the MCSC agreed with the ideal second and third-order spherical harmonics. The errors were acceptable for the second order terms. They were not small for the third-order terms, but were still acceptable for the practical use. More accurate field correction may be achieved by increasing the maximum coil current or by optimizing the configuration of the circular coils.

In conclusion, the planar MCSC is a useful devise to achieve field homogeneity with reasonable accuracy.