Theoretical Analysis and Design of an Innovative Coil Structure for Transcranial Magnetic Stimulation  
[PERSON]  
1 State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, X'an Jiaotong University, Xi'an 710049, China;[EMAIL_ADDRESS] (N.Z.); [EMAIL_ADDRESS] (Z.W.); [EMAIL_ADDRESS] (J.S.); [EMAIL_ADDRESS] (Y.Z.); [EMAIL_ADDRESS] (H.Q.)  
[PERSON]  
1 State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, X'an Jiaotong University, Xi'an 710049, China;[EMAIL_ADDRESS] (N.Z.); [EMAIL_ADDRESS] (Z.W.); [EMAIL_ADDRESS] (J.S.); [EMAIL_ADDRESS] (Y.Z.); [EMAIL_ADDRESS] (H.Q.)  
[PERSON]  
1 State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, X'an Jiaotong University, Xi'an 710049, China;[EMAIL_ADDRESS] (N.Z.); [EMAIL_ADDRESS] (Z.W.); shijinhua@stu.  
despite such advances, the intensity and the stimulated areas are still limited by the signal generator system and the stimulation coil design.  
Traditional magnetic stimulation systems consist of microprocessors, signal generators, and stimulation coils. The strength and focality are the most critical performance indicators of the magnetic stimulation of brain tissue, as the strength of the stimulus should fit the location of the target area, and the stimulus should not affect the neighboring regions around the target nerves. Many studies were carried out to improve the performance of stimulation systems. In 2010, [PERSON] proposed a circular coil array for TMS, that circular coil arrays have significantly larger stimulation intensity in comparison with conventional circular coils [5]. [PERSON] studied the double-butterfly coil for transcranial magnetic stimulation, and the coil's focality proved to be better than that of typical coils [6]. Furthermore, [PERSON] proposed a pulsed magnetic field generator that provided a noncontact way for functional nerve stimulations, where the magnetic field and induced electric field were produced by a figure-8 coil under the excitation of a pulsed discharging current [7]. Based on our previous work, a solenoid was proposed to stimulate the injured sciatic nerves of rats, and the regeneration process of the injured sciatic nerves was facilitated with pulsed magnetic stimulation [8]. [PERSON] compared 50 coil designs and studied the trade-off between the strength and the focality [9]. Despite the great progress of the use of magnetic fields in nerve stimulation, the study on stimulation coil is mainly a study of qualitative theory analysis and lacks in a systems optimization method that is exercisable. To improve the performance of magnetic stimulation, it is necessary to pay attention to both field strength and the focality.  
Herein, to meet the goal of the higher performance of stimulations, the requirements of the TMS coil were analyzed. Based on this research, a novel type of quad structure coil was designed. Moreover, a three-dimensional multilayer human head model was established to simulate the stimulus. The electromagnetic field distribution was calculated and verified by a measurement coil, and a comparison between the typical coils and the proposed coil in this paper was also carried out. The results showed that the proposed coil can obtain higher stimulation strength and better focality. In addition, the influential factors, such as the diameter and the intersection angle, were also analyzed. Thus, this research not only proposes a new structure for high-performance stimulation coils but also provides a method for designing stimulation coils for TMS.