# A Metal Detector for Clip Location Tracking of Stomach and Colon Cancer during Laparoscopic Surgery
## 2 Physical Analysis and Design Planning
### Magnetic Coupling Analysis of Clip-Detection for Tumor Excision  
To locate the clip, magnetic coupling must occur between the clip and detector. Therefore, it is necessary to analyze the characteristics of magnetic coupling. The clip-detector functions based on the inductive current method according to Biot-Savart and lens laws. Accordingly, the clip-detector can be designed using coil and ferrite material [15]. Thus, the magnetic field is generated by the magnetic induction method according to Biot-Savart law that is given by Equation (1). \[\Delta H=\frac{I\Delta_{\mathrm{s}}sin\theta}{4\pi d^{2}}\left[\mathrm{A}/ \mathrm{m}\right] \tag{1}\]  
where \(\mathrm{I_{ext}}\) is the excitation current, \(\Delta_{\mathrm{s}}\) is the infinitesimal of a coil, and \(\theta\) and \(d\) are the phase response and transmission distance between the detector and metal (clip), respectively [15]. The eddy current (\(\mathrm{I_{eddy}}\)) is generated in the metal (clip) when the magnetic field is excited at the coil; the magnetic field is changed by the excitation current (\(\mathrm{I_{ext}}\)) in the coil by [PERSON]'s law, and the excitation current is changed by the induced magnetic field (\(\mathrm{H_{eddy}}\)). Therefore, the induced magnetic field is generated by the magnetic coupling between the coil and metal (clip), wherein the magnetic field of coil is transferred to a metal (clip) as shown in Figure 4. The eddy current (_emf_) (expressed by Equation (2)) is generated in the metal (clip), as illustrated in Figure 4. The metal (clip)-detector operates when the coil frequency (\(f_{Hext}\)) and the metal (clip) frequency (\(f_{Heddy}\)) are equal \(\left(f_{\mathrm{(metal-detection)}}=\sqrt{f_{Hext}-f_{Heddy}}\right)\), where \(B\) is the magnetic flux density. \[emf=-\frac{d}{d_{l}}\int_{s}B\cdot d_{t}\quad\text{\textlesscentered}B:\text { magnetic flux density} \tag{2}\]  
Figure 4: Schematic of magnetic coupling between the clip and detector. In general, the magnetic coupling method for wire transmission exhibits high efficiency (above 90%), and the energy of the magnetic field is efficiently transmitted to the tissue owing to the relative permeability of 1.0 [16; 17]. The frequency and maximum current allowed in the human body according to the standard of KSC IEC 60479-2 and KSC IEC 61200-413 (children reference) are within 20 kHz and 20 mA, respectively [18; 19]. For wireless energy transmission, the dual-loop, helical, and spiral coils are commonly used for magnetic coupling [20; 21; 22]. The helical coil of the clip-detector is used because of its suitable structure. Furthermore, the helical coil can be designed in a compact size, and it has a wide field distribution. In addition, the clip-detector with a helical-type coil can also suitably pass through the working channel of a trocar or endoscope. The coil part and oscillation circuit are important. The coil consists of transmission (TX) and receiving (RX) parts. The oscillator is designed based on Colpitts circuit that has a high-quality factor (\(Q\)) owing to high capacitance. To increase \(Q\), the quality factor is increased. Consequently, the frequency is increased. Therefore, the meta-detection performance is excellent. Moreover, the coil must be enveloped around the ferrite during the coil design, as shown in Figure 5. The coil turn number (\(N\)) is highly important in the metal (clip)-detection circuit, and copper coil is used. At the TX part of ferrite and coil, the ferrite diameter and length are 22.4 mm, as shown in Figure 5. The diameter (\(t_{w}\)), length (\(l_{coil}\)), and turn number (\(N\)) are 0.13 mm, 22 mm, and 50 turns, and the space (\(d_{h}\)) between the coils and air capacitance (\(C_{h}\)) are 0.315 mm and 100 pF, respectively. Moreover, the inductance of coil is 10 mH. In the RX part of ferrite and coil, the ferrite diameter and length are 22 mm.