The field inhomogeneities produced by different susceptibilities in biological tissue and air cavities increase linearly with the applied static magnetic field. One of the most promising techniques to minimize field inhomogeneities is to use an array of individual conductive loop elements arranged close to the region of interest^1,2,3. In this paper we describe the synthesis of irregularly shaped coil elements placed in array configuration on a cylinder with the aim to optimized the shim performance, or equivalently, to minimize static field distortion within the human brain. Irregularly shaped coil elements were theoretically considered⁴ and significant benefits over the use of circular loop elements was demonstrated. In our case, individual elements were synthesized by using a genetic algorithm^5,6.

Simulations: The irregular coil geometry was synthesized on the following way. The optimization procedure was based on a B0 field map that was acquired within the brain of a volunteer. The field map was measured (9.4T MR scanner, Siemens, Erlangen, Germany) with a double-echo gradient echo sequence with an echo spacing of 1.39ms and a spatial resolution of 3 x 3 x 3 mm3. The initial configuration consisted of 16 identical randomly generated 8 segment coils arranged in two rows on a cylinder (diameter of cylinder was 360mm and a length of 300mm). The magnetic field produced by the conductive structures was calculated with the Biot-Savart law and the optimization procedure was performed on several slices within the volunteer’s brain. The shape of individual element was optimized in each iteration by using a genetic algorithm based on the Matlab function ga. Once the optimal geometry for the coil element of the shim array was determined, its performance was numerically compared to a 48 channel array of circular loops, which were placed on an identical cylinder.

Coil fabrication: We fabricated 16 channel array shown in Fig. 2. Fig. 2a shows the geometry of the individual element. All array elements have the same geometry and 25 wire turns. The elements were placed in two rows and on cylinder which diameter was 360mm and length 300mm. B0 shim coil was placed around 16ch-transcive coil⁷.

Measurement validations: A spherical phantom filled with KCl and containing an air ball in the center was placed inside of the RF/B0 shim setup. The susceptibility difference of the air in the ball and the surrounding liquid produced a very strong B0 inhomogeneity. B0 maps of the phantom were acquired and in slice shimming was performed. The required currents for the shim coils were calculated with Matlab based on the previously measured B0 fields produced by the individual coil elements. The currents were applied through the voltage supplies connected to each channel. The B0 maps of the shimmed slices were acquired again for validation.

Figure 1 shows B0 maps in a human brain after 2nd order spherical harmonic shim, simulated shimming with a 48 channel loop array and simulated shimming with the 16 channel array with irregular coil geometry. By comparing standard deviations after shimming on specific slices it can be seen that the 16 channel setup with irregular coil geometry outperforms the 48 channel setup with loop elements. Figure 3 shows measured B0 maps in the phantom described above after 2nd order spherical harmonic shimming (Fig. 3a) and a measured B0 map after shimming with 16ch array (Fig. 3b). Shimming with the proposed setup was performed after 2nd order spherical harmonic shim. The inhomogeneity of the respective slice was improved by 40%. The predicted standard deviation of the shimmed slice was 27 Hz while standard deviation of measured slice was 29 Hz, which shows good agreement between predictions and measurements.It is shown by numerical simulations that there is a big advantage of using coils with irregular geometries over traditional arrays based on circular elements. Irregular coil geometries outperformed setups with loop elements. The predicted performance of irregular shim coils were partially verified on phantom measurements. Future work will validate the proposed setup in vivo. In the present work we assumed that all irregular coils in the setup were of the same geometry. Thus we also plan to perform optimization with different geometry of every individual coil.