Design and Optimization of a Novel Multi-Quadrant Spatial Array for Non-Invasive Focalized Magnetic Stimulation of the Deep Brain

As a non-invasive neuromodulation technique, transcranial magnetic stimulation (TMS) has shown great potential in scientific research and clinical application. Using TMS to stimulate the deep brain is important for enhancing the therapeutic effects of mental disorders and explaining the causes of mental disorders. However, the intracranial induced electric field (E-field) generated by conventional magnetic stimulation coils dissipates severely with increasing stimulation depth and the focalized stimulation is limited to superficial areas. In this paper, we first propose a novel multi-quadrant spatial array (MQS array) based on curved-shaped coils. Each coil in the MQS array is tangent to the head and bent away from the human head, which is conducive to reducing the accumulation of non-longitudinal induced E-field components and improving the stimulation focalization in the deep brain. Then, we propose a new spatial magnetic array optimization method based on the BP-NSGA-II algorithm. The predictive models of deep brain transcranial magnetic stimulation characteristics of the spatial array are obtained by the BP neural network and the multi-objective optimization of the stimulation currents applied in the spatial array is performed with the NSGA-II algorithm. Results show that the MQS array can produce an obvious focusing area at 10 cm below the scalp which satisfies the depth requirement of deep brain transcranial magnetic stimulation. Under the same constraint of Joule loss, the optimized MQS array can enhance intracranial stimulation intensity by 131%, increase the longitudinal attenuation ratio to 4.5 times, and reduce the focusing area by 76% compared to the conventional planar magnetic stimulation array. The proposed MQS array has significant advantages in deep brain focalized stimulation, and the spatial array optimization method described in this study may provide a valuable reference for coil or array optimization processes in other application contexts.