# A Rectangular Toroidal Current-Based Approach for Lung Biopsy Needle Tracking
## 1 Introduction  
Early diagnosis is a critical step in the treatment of lung cancer, as earlier detection provides patients with better treatment options and improved outcomes [1]. The five-year survival rate for stage I lung cancer can reach up to 80% following treatment [2]. Currently, lung cancer diagnosis is categorized into two main approaches: imaging-based diagnosis and pathological diagnosis [3]. Pathological diagnosis involves performing a biopsy on a detected lung mass to examine whether cancer cells are present in the tissue, allowing for a definitive confirmation of lung cancer [4]. Visual feedback remains an effective tabletop experimental tracking method and is still applicable in medical procedures where direct visual access to the surgical area is feasible, such as subretinal injections [5]. X-ray imaging is a widely used medical imaging modality due to its high penetration capability, enabling deep tissue visualization [6]. While X-ray imaging provides high-resolution anatomical images (~100 \(\mathrm{\SIUnitSymbolMicro m}\)) with a sufficient refresh rate (30 ms), concerns regarding ionizing radiation exposure pose risks to both patients and physicians [7, 8]. Magnetic resonanceimaging (MRI) is another powerful imaging tool capable of generating detailed images of internal organs and soft tissues. However, its incompatibility with magnetic materials makes it challenging to integrate with magnetic tracking systems [9]. Ultrasound imaging is a bio-friendly, non-invasive imaging technique that has been utilized for real-time tracking of magnetic devices within the vascular system [10]. Nevertheless, ultrasound imaging is highly sensitive to interfaces, making it difficult to visualize tissues located behind rigid structures such as bones. Designing an assisted lung biopsy needle tracking system that ensures high tracking accuracy, aids physicians in puncture path planning, and minimizes the number of CT scans required for patients remains a significant research focus. Various short-range techniques for spatial position tracking include electromagnetic, optical, ultrasonic, mechanical, and inertial navigation systems [10; 11; 12]. The scleral search coil technique is limited to angular position tracking within a small range and is entirely unsuitable for medical biopsy procedures due to its inability to provide precise spatial localization [12; 13; 14]. Among these, optical and electromagnetic tracking are the most commonly used techniques [15]. Optical tracking systems offer high tracking accuracy but are susceptible to occlusion. In contrast, electromagnetic tracking systems can track positions without occlusion, ensuring reliable tracking [16]. Electromagnetic tracking is currently the gold standard for surgical tracking and guided interventions, primarily used in bronchoscopy, urological examinations, orthopedic, and lung puncture procedures [17]. Notably, electromagnetic tracking provides an economical alternative to X-ray fluoroscopy in interventional surgical navigation systems. These methods eliminate radiation requirements and enable three-dimensional and six-degree-of-freedom (6 DOF) navigation in position and orientation. To implement electromagnetic tracking and enhance its accuracy, speed, and robustness, researchers have developed various electromagnetic tracking methods [18]. Optical tracking offers high accuracy (often below 1 mm), but its performance is heavily dependent on maintaining a clear line of sight, which can be difficult in clinical settings due to occlusions and anatomical constraints. Ultrasound-based systems provide real-time imaging and are widely accessible, but they are operator-dependent and generally yield lower spatial resolution, with tracking errors typically in the range of 2-5 mm. Mechanical tracking systems, such as articulated arms or encoders, can offer good repeatability but tend to be bulky and invasive, limiting their applicability during delicate interventions.