Multi-target field control for matrix gradient coils

Conventional single-target field control for matrix gradient coils will add control complexity in MRI spatial encoding, such as designing specialized fields and sequences. This complexity can be reduced by multi-target field control, which is realized by optimizing the coil structure according to target fields.

Based on the principle of multi-target field control, the X, Y and Z gradient fields can be set as target fields, and all coil elements can then be divided into three groups to generate these fields. An improved simulated annealing algorithm is proposed to optimize the coil element distribution of each group to generate the corresponding target field. In the improved simulated annealing process, two swapping modes are presented, and randomly selected with certain probabilities that are set to 0.25, 0.5 and 0.75, respectively. The flexibility of the final designed structure is demonstrated by a spherical harmonic basis up to the full second order with single-target field control. An experimental platform is built to measure the gradient fields generated by the designed structure with multi-target target control.

With three probabilities of swapping modes, three similar coil element distributions are optimized, and their maximum magnetic field errors for generating X, Y and Z gradients are all below 5%. The structure selected for the final design is the one with a probability of 0.75, considering the coil performance and structural symmetry. The maximum error for all target fields generated by single-target field control is also below 5%. The experimental results show that the measured gradient fields along the axes have enough strength and high linearity.

With the proposed improved simulated annealing algorithm and swapping modes, multi-target field control for matrix gradient coils is verified and achieved in this study by optimizing the coil element distribution. Moreover, this study provides a solution to simplify the complexity of controlling the matrix gradient coil in spatial encoding.