# Helmholtz Coils Based WPT Coupling Analysis of Temporal Interference Electrical Stimulation System
## 1 Introduction
Externally applied electrical stimulation of a specific intensity can cause a series of morphological and physiological changes in the nerve cells at the site of action. The nerve impulses generated are identical to the action potentials induced by natural excitation, thereby modulating the functional response of the nerve circuits and surrounding areas. As the applied electrical stimulation acts directly on the target neuron, it can activate the target neuron while preventing the accidental excitation of other neurons. It has an excellent temporal and spatial resolution and therapeutic effects. Combined with the properties of the neuron itself, below-threshold electrical stimulation can only cause depolarization of the cell membrane. Therefore, only when the intensity of the electrical stimulation reaches the threshold will an effective action potential be excited and produce a therapeutic effect [20]. At the same time, due to the low-frequency nature and fatigue of nerve cells, only a low-frequency alternating \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Continuity of Power Supply** & **Battery Units** & **Signal Processing Modules** & **Coupling Type** \\ \hline Battery Powered & Consumed & Yes & Yes & None \\ \hline Conventional Resonant WPT & Sustainability & Yes & Yes & Magnetically coupled \\ \hline Temporal Interference WPT & Sustainability & None & None & Magnetically coupled \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of the different power supply methods for implantable devices. current or direct current can induce the action potentials. Therefore, the frequency range for electrical nerve stimulation is mainly in the tens to hundreds of hertz levels [21]. The implementation of temporally interfering electric fields to apply stimulation directly to the target region requires acquiring an accurate current density and field strength distribution. However, due to the dispersion of human tissues [22], the dielectric constant becomes smaller when the frequency increases. It will result in the actual electric field waveform and injected current density at different locations in the human body being different from that expected. Moreover, due to the specificity of the individual tissues in the human body, it is often difficult to ensure a high spatial accuracy in practical applications, making the scheme much less operable. The above problems can be avoided using electrical stimulation through induced currents generated in the electrodes by a magnetic field. Since the magnetic permeability of biological tissue is close to a vacuum, the magnetic field can penetrate human tissue without attenuation and distortion [23]. The induced current waveform obtained at the electrodes is stable and independent of depth. Both demonstrate the feasibility of a treatment protocol for targeted electrical stimulation with induced currents in the electrodes. This paper proposes an MCR-WPT electrical stimulation system based on temporal interference in conjunction with the mechanism of action of electrical stimulation signals on nerve cells. In contrast to conventional implantable devices, this system uses temporal interference to generate an envelope-modulated magnetic field at a specific frequency for low-frequency wireless power transfer. The device directly applies electrical stimulation of sufficient intensity to the target nerve using the same frequency current from the electrodes connected to the receiving coil. It eliminates the need for a frequency converter and reduces the implanted device's size while ensuring the effectiveness of the stimulation. It also eliminates the need for implanted batteries, lowering the threshold for the use of implantable neurostimulation devices and reducing the burden on the body. Given the variable position of the receiving coil, this system uses Helmholtz coils as the transmitters. The stability and uniformity of the magnetic field are ensured to the greatest extent possible, thus ensuring a stable electrical stimulation function of the nerve electrodes.