# A Rectangular Toroidal Current-Based Approach for Lung Biopsy Needle Tracking
## 3 Results  
### System Building  
After establishing the rectangular circulating magnetic field model and deriving the electromagnetic tracking coupling equations, the design of the transmitting coils can be carried out according to the requirements of lung puncture procedures. Based on standard human body dimensions, the 50 th percentile chest width is 280 mm, and the 99 th percentile is 331 mm, while the 50 th percentile chest depth is 212 mm, and the 99 th percentile is 216 mm. Since the abdominal volume is comparable to the thoracic volume, the working area of the transmitting coils is set to 300 mm \(\times\) 300 mm \(\times\) 300 mm directly above the transmitting coils, ensuring complete coverage of the patient's abdomen. Traditional magnetic field generation devices typically use wound coils, where enameled copper wires are tightly wound around an ABS plastic frame using a winding machine. The coil ends are connected to a signal generation and amplification system. The entire magnetic field generation device is box-shaped and suspended above the surgical area. To avoid obstructing the surgeon, a certain distance must be maintained between the device and the patient, which prevents the full utilization of the device's working area. Since the generated magnetic flux density is inversely proportional to the square of the distance, as the receiving coil moves away from the working area, the induced voltage drops rapidly, making signal acquisition and computation difficult. To expand the effective working area, a stronger magnetic field is required, which increases hardware complexity and significantly raises costs. To address these limitations, PCB coils are used as transmitting coils in the design of the magnetic field emission board. Compared to wound coils, PCB coils offer advantages such as simpler fabrication, lower cost, and higher precision. With a line width of 0.5 mm, PCB manufacturing can achieve a precision of 0.02 mm, and PCB coils are significantly thinner, with a thickness of only 1.6 mm. This allows for the magnetic field emission board to be placed directly beneath the patient, in close contact with the body, thereby fully utilizing the working area while reducing hardware requirements for the transmitting coils. We selected planar coils on a single PCB for manufacturability, repeatability, and integration; chose 25 turns to balance signal strength, power consumption, and manufacturability; optimized resistance, inductance, and current for efficiency and stability; and used a single-layer PCB to simplify fabrication, reduce cost, and maintain mechanical stability. The PCB-based magnetic field emission board is designed as shown in Figure 4. The board has an overall size of 300 mm \(\times\) 300 mm with a thickness of 1.6 mm, and the generated magnetic field effectively covers a volume of at least 300 mm \(\times\) 300 mm \(\times\) 300 mm. During lung biopsy procedures, the board can be placed underneath the patient without occupying additional space on the surgical table or interfering with the surgeon's workflow. The outer coils are aligned parallel to the \(X\)-axis, while the middle coils are rotated 45 degrees around the \(Z\)-axis. PCB coils are employed as transmitting coils in the design and fabrication of electromagnetic transmitting boards. These coils offer advantages such as simpler fabrication and lower cost compared to traditional single-layer coils wound with enameled wire. The design parameters for these coils are detailed in Table 1.  
Each coil operates with a distinct frequency AC excitation current, with the frequency range controlled between 68 kHz and 72 kHz. Additionally, to prevent signal degradation due to the filtering process, the signal frequency must be slightly higher than the filter cutoff frequency (by approximately 500 Hz). To mitigate the potential interference from power line noise (50/60 Hz), an analog high-pass filter is implemented using operational amplifiers (op-amps).