Magnetic characteristics of a magnetic marker for localized tumor excision with a handheld magnetic probe

Breast cancer is the most commonly occurring cancer in women and the second most common cancer overall. There are over 2 million new cases worldwide in 2018.¹ According to existing clinical research, one-third of these are non-palpable breast lesions,² which means lesion is not visible by naked eye from the skin surface. For early stage breast cancer, breast conserving surgery is a preferable choice. Surgeon removes the primary tumor with some surrounding breast tissue, leaving as much normal breast as possible to achieve a good cosmetic outcome.

To perform this surgery, since tumor is not visible from skin surface, a marker is necessary to locate the tumor. There are several conventional methods being widely used at the moment. In the Europe and the US, hook wire is the most commonly used localization tool. Under imaging guidance, radiologist inserts a fine needle containing hook wire into the breast tumor. At the desired position, the hook wire in released. Hook wire is long, and therefore the external part of the wire is left out of skin and is taped to the skin, which no doubt lead to patient discomfort. This is also causing the risk of the hook wire migration relative to the tumor location. During operation, surgeons estimate the position of the hook tip by naked eyes, which leads to a re-excision rate as high as 58%.³ 

The magnetic technique is newly developed for its application in breast surgery. A magnetic system consists of a magnetic marker and a magnetometer. The magnetic marker is inserted into the lesion area under ultrasound guidance. In the operation suite, the surgeon detects the location of the marker by the magnetometer.

The limitations for magnetic markers are their detection ranges. There are two magnetic markers commercially available, both of them have detection ranges up to 30 mm, which cannot satisfy applications in all breast size and lesions at all depths.⁴ A novel magnetic marker with extended detection range of 40 mm is in clinical needs. The objective of this study is to develop a numerical calculation tool to calculate the magnetic field strength induced by the marker. Based on a hook shape magnetic marker, the hook length and separation angle between hook and the main body of the marker can be evaluated with the tool and optimal design can be found.

The magnetometer used in this study is a handheld magnetic probe.⁵ The magnetic probe contains a FeNdB permanent magnet, a Hall sensor to detect magnetic field, and a digital display on the main body to indicate field strength detected. The magnetic marker, which is magnetized by the permanent magnet, generates a new magnetic flux that is detected by the hall sensor at the probe head. The sensitivity limit of the Hall sensor is 1μT, owing to the noise attributed to the thermal fluctuations.⁵ Noise level of the probe is around 0.5μT. Therefore, detection threshold of 1μT ensures signal-to-noise ratio is at least 2.

The material of the magnetic marker must satisfy three requirements: It should be magnetic, biocompatible for an implant device and available in wire with diameter less than 1 mm.

Stainless steel (SUS) 304 is widely used in the medical field and satisfies all requirements listed. The magnetic property of SUS 304 is measured using SQUID (superconducting quantum interference device). The magnetic moment generated by SUS 304 sample is recorded when the applied magnetic field varies from −600 mT to 600 mT. Measurement results in both longitudinal and transverse directions are shown in Fig. 1(a).

At 40 mm distance, the magnetic strength generated by the permanent magnet on the magnetic probe was found to be 2.6mT. Magnetic moment is proportional to the applied magnetic field around this field strength. In longitudinal orientation, gradient of the curve is 0.0175 T/Am², while gradient is 1.05x10⁻³T/Am² in the transverse orientation.

Existing magnetic markers are solid cylinder shapes with smooth surface. However, human breast is made up of fatty tissues, which is soft and easy to deform under pressure. To fix the relative position between the marker and the lesion, a hook on the marker is necessary to obtain strong migration resistance. Based on the hook shape design shown in Fig. 1(b), a numerical simulation is developed to look for the optimal dimensions to maximize the magnetic signals at 40 mm distance from all orientation.

The FeNdB magnet on the probe head is in a ring cylinder shape with outer diameter of 12.5 mm, inner diameter of 5 mm and height of 12 mm. The magnet is divided into 1000 small elements in cylindrical coordinate. The magnetization of this FeNdB magnet is defined as 1000 kA/m in the z direction. The origin of this coordinate system is at the center of top surface of the magnet. The hall sensor is placed at the origin. Marker is placed on the z-axis centered at z=40 mm. Fig. 1(c) shows the coordinate system of this simulation. The total length of the magnetic marker is kept at 17 mm and is divided into 17 parts for calculation. Diameter of the marker is 0.8 mm.

The magnetic field (B) generated by the permanent magnet can be derived by equation (1)

where μ₀ is the vacuum permeability, m is the magnetic moment of the permanent magnet element and r is the distance to each element of the permanent magnet.

Magnetization of marker is related to the excitation field by its magnetic susceptibility, descripted with equation (2)

where M is the magnetization of the marker, H is the magnetic field generated by the permanent magnet and χ is the magnetic susceptibility. Magnetic moment of the marker is calculated by multiplying the magnetization of each element by its volume. Then, the induced magnetic field detected by the sensor can be calculated using equation (1) by substituting magnetic moment m of the marker, and r is the distance between marker and the sensor.

There are three variables in the shape of the marker. Firstly, the length of hook part varies between 1 mm and 8 mm, as shown in Fig. 1(d). Secondly, the separation angle between hook and the main body of the marker is defined as ϕ. This angle ranges from 1° to 90° to keep the marker in a backward-facing hook shape, as shown in Fig. 1(e). And lastly, the rotation around y-axis clockwise is defined as θ from 1°to 360°, as shown in Fig. 1(c).

Susceptibility is a magnetic property of the material, and therefore the direction of longitudinal susceptibility χ_l and transverse susceptibility χ_t is fixed to the material. But the xyz coordinate system in the numerical simulation is fixed to the magnet. Therefore, the relationship between magnetization M and magnetic field H is expressed using a susceptibility tensor that contains the rotation of the marker, shown in equation (3) below,

where Mx, My, Mz is the magnetization of the magnetic marker in the xyz coordinate. Hx, Hy, Hz is the magnetic field generated by the permanent magnet at location (x,y,z), and θ is the clockwise rotation of the magnetic marker around the center of the marker.

As shown in Fig. 2(a), the main body of the marker is a rod rotating around its center, therefore the minimum value occurs when the longitudinal orientation of the marker is perpendicular to the z-axis, i.e., when the rotation $Θ$=90° or $Θ$=270°, and maximum value occurs at $Θ$=0° and $Θ$=180°. However, because of the separation angle ϕ, the hook part is angled with the main body. The minimum magnetic field strength generated by the hook shifts towards $Θ$=180°.

As a whole marker, minimum magnetic field over 360° rotation is increased as the hook length become longer (Fig. 2(c)), while the ratio of maximum/minimum magnetic field decreases (Fig. 2(d)). 8 mm is the optimal hook length because of its wider detection range and more even signals from all orientations.

Hook length is set to 8 mm in this simulation. Separation angle ϕ does not affect magnetic flux induced by the main body of the marker, as shown in top figure in Fig. 3(a). The bottom figure in Fig. 3(a) shows the variation of induced magnetic flux from the hook part. Fig. 3(b) shows the induced magnetic field strength for the whole marker. For each separation angle ϕ, the minimum magnetic field strength is plotted in Fig. 3(c), which shows larger ϕ is better for detection. And according to Fig. 3(d), ratio of maximum to minimum magnetic field strength reaches the minimum when ϕ is 75°.

8 mm hook length and 75° separation angle ϕ is the optimal design for this hook shape magnetic marker. As the detection threshold of the handheld magnetic probe is 1 μT, at 40 mm distance, detection of this marker is enabled on 57% of the area.

Results show that, the existence of the hook increase the detection range of the marker, as well as even out the signal from each orientation. Therefore, keeping part of the marker angled with the main body is encouraged. However, the hook shape marker is an asymmetric design, signals from half of the orientations are enhanced, while effects on the other half is limited. For the next step, a symmetric design ‘Y’ shape marker is considered such that the detection can be even closer to an isotropic detection.

The resistance to migration of the marker will be tested in experiments. Phantoms made from agar and silicon, as well as animal tissues will be taken for experiment and statistical test will be carried out to evaluate the migration resistance of our markers compared with existing markers.

Increasing magnetic susceptibility can strengthen the magnetization of the material, according to equation (2), and therefore induce more magnetic moment. Material we considered in this study is only SUS 304, which has an austenitic crystal structure. Ferrite stainless steel material or other materials with stronger magnetic susceptibility can also be potential candidates.

A numerical simulation tool has been developed to evaluate the induced magnetic field from the marker. In this study, magnetic markers made of SUS 304 are simulated based on a backward-facing hook shape design. The induced magnetic field from markers with various hook length and separation angles are evaluated from all orientations numerically. With the goal of detection from all orientations and isotropic signals, a magnetic marker with 8 mm hook length and 75° separation angle is the optimal design. At an extended distance of 40 mm, the detection of this magnetic marker using the handheld magnetic probe can cover 57% of the orientations.

This work was supported by the Project for Medical Device Development of the Japan Agency for Medical Research and Development (AMED).