An experimental apparatus for three-dimensional sensitivity mapping of a handheld magnetic probe with a permanent magnet and a Hall sensor was developed. To optimize the shapes and sizes of the magnets, the sensitivity mappings of two types of magnets, column- and cone-type magnets, were evaluated by the experimental apparatus. The longitudinal sensitivities of column and cone types are 8 and 9 mm, respectively, for 5 μL of magnetic nanoparticles. The measured longitudinal sensitivities agree well with the sensitivities calculated by the finite element method. Furthermore, the maximum lateral resolutions of column and cone types are 4.1 and 3.7 mm, respectively. In terms of the directionality, the sensitivities of column and cone types of the angle of 90° with respect to the probe axis fall approximately to 72% and 50% at 6 mm distance from the probe head, indicating that the cone type has high directionality due to its sharp shape. The measurement of sensitivity mapping revealed that the characteristics of the cone-type magnet are superior to that of the column-type magnet for the identification of sentinel lymph nodes.
I. INTRODUCTION
Sentinel lymph node biopsy (SLNB) is performed in the treatment of breast cancer to detect the presence of metastasis in sentinel lymph nodes (SLNs),1–4 and the radioisotope technique using a gamma probe and radioisotope tracers is clinically utilized for identification of SLNs as a gold standard method.5,6 However, the technique has significant drawbacks. The use of radioactive collides exposes patients as well as workers to radiations. Furthermore, it can only be performed at the hospitals equipped with a radiation facility due to the regulations for handling radioactive materials. Thus, the development of new techniques that can be easily installed in hospitals without the radiations and limitations is required.
Recent studies7–10 have shown that the magnetic technique using superparamagnetic iron oxide (SPIO) nanoparticles and a handheld magnetic probe can be alternatives to the radioisotope technique as a noninvasive and promising method, particularly for hospitals with no radiation facility. In order to detect the SLNs in vivo by transcutaneous measurements, detectable distance of 12 ± 5 mm of the magnetic probe is required11 at least. Furthermore, they are much deeply located from the skin surface in some cases that are attributed to the patient characteristics, such as age and BMI. Thus, in order to develop it as an alternative to the radioisotope technique, the enhancement of the sensitivity of the magnetic probe is essential. In addition, the directionality and spatial resolution of the probe is an important factor to identify just one node in vivo because the SLNs are often clustered in axillary lymph nodes. In terms of the sensitivity, many groups have already reported regarding the demonstrations of the high sensitivity magnetic sensor (e.g. superconducting quantum interference device and flux gate sensor) with the resolution down to 1 nT.12,13 However, their reports describe just as a magnetic sensor.
This paper firstly describes the sensitivity characteristics as a handheld magnetic probe with a permanent magnet and Hall sensor,8 focusing on the sensitivity, spatial resolution, and its directionality. To establish a magnetic technique for the SLNB, the sensitivity mapping of the handheld magnetic probe with respect to two types of magnets was evaluated by utilizing a measurement apparatus.
II. EXPERIMENTAL DEVICE AND METHODS
We developed an experimental apparatus, as shown in Fig. 1(a), in order to measure the three-dimensional (3D) spatial distributions of the sensitivity of the magnetic probe. The sensitivity was evaluated with respect to the relative location between the SPIO sample (5 μL, Resovist14) and the magnetic probe. The SPIO was located at the top of the white pole, and the magnetic probe was fixed above the pole. The actuators (X-LSM100A-E03, Zaber Technologies Inc.) displace the SPIO sample in any direction (Fig. 1(b)) so that the magnetic field at the probe with respect to the 3D position of the SPIO sample is obtained. The SPIO was enclosed in the half sphere of 1.3 mm radius, which corresponds to the volume of 5 μL. The actuators are controlled and the measured magnetic field is obtained by the Igor software in the control PC. As indicated in Fig.1(c), the center of the surface of the probe head was located at the (X, Y, Z) = (0, 0, 0) and the measurement area was (X, Y, Z) = (-10–10, -10–10, 0–20 mm). Note that the displacement error of the actuators is less than 30 μm, which means that it can be negligible because the sensitivity measurement was demonstrated with the spatial resolution of 1mm.
III. RESULTS AND DISCUSSION
Figures 2(a) and 2(b) show the measured sensitivity on the X-Z plane with two types of magnets: column and cone types. The magnet and Hall sensor are enclosed in the probe head (diameter is 18 mm). The diameters of column- and cone-type magnets are 12.5 and 16 mm, respectively, and the lengths of both the magnets are 12 mm.8,15 The gap between the magnet surface and probe surface is approximately 2.0–2.5 mm to isolate the ambient temperature. The strength of the magnetic field measured by the Hall sensor is defined as “sensitivity,” and it expands radially from the center of the probe head as shown in Figs. 2(a) and 2(b). Note that the current sensitivity limit is 1 μT because the readable count on the display of the probe in practical uses is 1 μT. The longitudinal (Z-direction) sensitivity of the probe indicates the ability to detect the presence of the SPIO at a distance. As shown in Fig. 2(c), the detectable distance where the sensitivity is 1 μL is approximately 8 mm in the case of the column-type magnet. Error bars of experimental results represent an average over several measurements (errors are ±0.2 μT at most). The sensitivity falls approximately to 50% between 2 and 3 mm distance, and 65% between 5 and 6 mm distance, that is, the decrement of the sensitivity diminished with a longer distance. For the purpose of validation of the longitudinal sensitivity, numerical simulations were performed using the finite element method (FEM) in the two-dimensional axial symmetry system with the maximum spatial resolution of 0.1 mm. The measured sensitivity corresponds with the sensitivity calculated by numerical simulations using the FEM. Figure 2(d) shows the experimental and numerical results of the sensitivity of the cone-type magnet. The detection limit is approximately 9 mm, which is slightly longer than that of the column-type magnet because the strength of the magnetic fields generated by the cone magnet is larger.15 The results of the cone-type magnet also agree well with the values obtained by numerical simulations using the FEM. To obtain the sensitivity mappings as shown in Figs. 2(a) and 2(b), however, a lot of simulations without the axial symmetry are carried out at each location of the SPIO sample, which requires significant effort and time. Our experimental apparatus can save on effort and time, and display the actual values efficiently. In this paper, we defined 1 μT as the sensitivity limit, for the time being. However, if a sensitivity limit of 0.2 μT can be achieved using a more sensitive sensor, the detection limit could be 15 mm, and the magnetic probe could detect the SLNs of most patients from the skin surface.11
Figures 3(a) show the measured sensitivity of the cone-type on the X-Y plane at Z = 4 mm. It is clear that the sensitivity expands radially from (X, Y) = (0, 0) and mostly has an axial symmetry with respect to the Z-axis. The sensitivities with respect to the X-axis and Y-axis at Z = 4 mm are shown in Fig. 3(b), and correspond well in the range of the measurement errors. The lateral response of the probe indicates the spatial resolutions. For the SLNB, a high spatial resolution is required to detect just one node because the SLNs often assemble in close proximity to other nodes. Figure 3(c) shows the lateral sensitivity that is normalized by the maximum value on the X-axis at Z = 0 mm. Full width at half maximum (FWHM), which is a good quality criterion for the identification of the SLNs, is estimated by curve fitting of the measured values. The FWHM of the column- and cone-type are 4.1 and 3.7 mm, respectively. The result shows that the spatial resolution of the cone-type magnet is slightly higher than that of the column-type magnet. In the case of Z = 4 mm, as shown in Fig. 3(b), the FWHM of both the magnet types are approximately 9 mm, that is, FWHM increases at a greater distance from the probe head. Compared to conventional gamma probes whose resolutions are commonly broader than 10 mm,16,17 the magnetic probe with the permanent magnet has the ability to identify one SLN from the node clusters in actual usages, such as clinical tests or animal experiments.
The directionality of the probe was evaluated as illustrated in Fig. 3(d). R is the distance between the center of the probe head and the SPIO sample, and θ is the angle with respect to the probe axis. Figure 3(e) represents the directionalities of the measured sensitivities of the column- and cone-type magnets. In the case of both the magnets, at R = 2 mm, the sensitivity increases with an increase in the angles. The normalized sensitivities of the column- and cone-type magnets reach approximately to 1.9 and 1.7 at θ = 90°. This result indicates that the SPIO approaches to the magnet and the sensor detects the strong magnetic field of the SPIO at a close distance. On the other hand, at a longer distance, e.g., at R = 6 mm, the normalized sensitivities at θ = 0–70° are almost constant values between 0.95 and 1.15, and they decreases with an increases in the angles at θ > 80°. The sensitivity of the column magnet at θ = 90° is 72%. In particular, for the cone-type magnet, the sensitivity fall approximately to 50% at θ = 90°, which is attributable to the structure of the cone-type magnet having a sharply pointed shape. Hence, these directionality evaluations indicate that the cone-type magnet has a better directionality compared to the column-type magnet. Although the directionality of the magnetic with the permanent magnet is not comparable to that of conventional gamma probes,10,11 these results show that the sharply pointed shape of the magnet leads to the enhancement of the directionality.
IV. CONCLUSION
We have firstly evaluated the sensitivity characteristics of the handheld magnetic probe with a permanent magnet for the detection of the SLNs using the sensitivity mapping measurement system. The longitudinal sensitivity of the column- and cone-type are approximately 8 and 9 mm, respectively, and the measured sensitivities agree well with the sensitivities calculated by the FEM analysis. Compared to the spatial resolution of gamma probes, the magnetic probe shows high spatial resolutions of 4.1 and 3.7 mm in the case of column- and cone-type magnets, respectively. Furthermore, the cone-type magnet has a better directionality due to its sharp shape. Thus, we conclude that the cone-type magnet is more suitable than the column-type magnet for the identification of the SLNs. In this paper, although we could not find significant differences between both the magnets, our experimental apparatus is quite useful for evaluating and optimizing the structure of a magnet for a handheld magnetic probe.
Further work is under way to enhance the sensitivity, spatial resolution, and directionality. Examples are the introduction of a new sensor to enhance the sensitivity, and the optimizing of the structure of the magnet shape to improve the spatial resolution and directionality. We will explore these topics in our future research.
ACKNOWLEDGMENTS
This work was supported by the Project for Medical Device Development of Japan Agency for Medical Research and Development (AMED).