# Helmholtz Coils Based WPT Coupling Analysis of Temporal Interference Electrical Stimulation System
## 5 Conclusions  
The research of interventional treatment modalities is essential in reducing drug dependence in CRPS-I patients. The effectiveness of the CRPS-I foot pain modality through direct sciatic nerve stimulation has been clinically proven. This paper presents further research on the transmission stimulation system and proposes a novel wireless power transmission electrical stimulation system based on temporal interference. It provides a new solution to the miniaturization of implantable devices, easing the medication burden on patients. According to the Bio-Savart law, this paper first solves for the magnetic flux density generated by the Helmholtz coils at any point in space. Combined with the MCR-WPT circuit model based on the Helmholtz coils' structure, the transmission characteristics of the system were investigated by theoretical analysis. Analysis results showed that the Helmholtz transmitting coil could generate a stable magnetic field, and the receiving coil connected to the nerve electrode could obtain a good transmission efficiency. Finally, the uniformity of the magnetic field and the focus of the stimulation location were verified by a finite element analysis. The numerical calculations in free space showed a considerable area near the center of the Helmholtz coil axis where the magnetic flux density is very uniform. The magnetic field distribution remained largely undistorted even in subsequent numerical calculations with the addition of human tissue. The system's uniform magnetic field in the working area provided the basis for an efficient and stable power transmission. A corresponding experimental platform was built to demonstrate that the proposed system could provide the energy required for electrical stimulation through WPT. The experimental results showed that the receiving coil generated an envelope-modulated current with an amplitude of 42.4 mA and a frequency of 10 Hz. The frequency and amplitude were in the range to cause a physiological response from the sciatic nerve, thus demonstrating the feasibility of the method to apply an effective stimulation to the target nerve. When the amplitude of the excitation current passed through the transmitting coils was 0.2 A, the magnitude of the received power of the system was calculated to be 0.98 mW. In fact, the system was not limited to the above power level. The transmitting coil structure and excitation current could be changed according to the target nerve's needs to control the current's intensity on the nerve electrodes, thus enabling a multi-scene electrical stimulation of the sciatic nerve. The peak of the envelope modulation amplitude \(|B_{AM}|\) shifts as the amplitude of the two transmitting coil excitation signals changes, indicating that the temporal interference could achieve a non-physical dynamic adjustment of the stimulation location. Compared to conventional implantable electrical stimulation devices, the proposed electrical stimulation system has the advantage of being miniature and efficient. The alternating magnetic field induces a low-frequency current in the receiving coil, which stimulates the target nerve directly with the help of flexible electrodes implanted in the connected target nerve, thus providing a timely response to pain. This ensures a stable electrical stimulation while reducing the physical burden on the patient, making it a more versatile application. Conceptualization, X.Y. and P.G. ; methodology, C.J. ; software, C.J., P.G. and D.J. ; validation, C.J. and P.G. ; formal analysis, X.Y. and J.S. ; resources C.J. ; data curation, J.S., P.G. and Z.Y. ; writing--original draft preparation, C.J. ; writing--review and editing, P.G., Z.Y. and D.J. ; visualization, C.J., P.G. and X.Y. ; supervision, X.Y. ; project administration, C.J., D.J. and J.S. ; funding acquisition, X.Y. All authors have read and agreed to the published version of the manuscript.