Magnetic immunostaining using a magnet and antibody-labeled fluorescent ferrite (FF) beads is established as a rapid immunostaining. In this study, we proposed the novel configuration of magnets with the large magnetic field gradient and the strong magnetic force for magnetic immunostaining. To confirm the usefulness of the proposed magnet configuration, we performed numerical analysis of the magnetic characteristics of the proposed magnets, and the magnetic immunostaining with FF beads. It was revealed that the proposed magnets generated the strong magnetic force and promoted the immunoreaction rapidly.
Immunostaining is an important tool for diagnosing cancer metastasis by detecting specific proteins (target antigens) in a tissue section using antibodies.1,2 In the metastasis diagnosis of cancer, the presence or absence of cancer metastasis and kinds of cancers are investigated by the expression level of the cancer-related proteins (antigens) corresponding to antibodies in the tissue section. However, the method is not suitable for an intraoperative diagnosis because the method required 2-4 hours to complete the immunoreaction. Therefore a second surgery which is the heavy burden to a patient is necessary if cancer cells metastasize. Hematoxylin and eosin (H&E) staining is a conventional tool with a visual observation by pathologists for the intraoperative diagnosis of cancer metastasis, but micro-metastasis is easily overlooked, compared with the immunostaining. To solve these problems leads to provide a highly accurate intraoperative diagnosis and reduce the patient’s burden. Immunoassays using a magnet and magnetic particles were developed for promoting the immunoreaction.3–6 The magnetic immunostaining using a magnet and antibody-labeled fluorescent ferrite (FF) beads have demonstrated that a 10-min magnetic collection of FF beads enabled the rapid detection of cancer cells.7 The method can increase the chance of the antibodies binding to the antigen or recognizing each other and promote the immunoreaction by attracting the antibody-labeled ferrite toward the antigen using the magnet force.7,8 However, the suitable magnet configuration for magnetic immunostaining has not been examined in any detail.
The Important factor of magnet configuration for rapid immunostaining is to produce a strong magnetic force for attracting the FF beads on the entire tissue section. The magnetic force is expressed as below,
Here, B is the magnetic flux density and rot B is zero because no current source exists in the air. The second and third terms are zero with assuming the uniform magnetization of magnetic moment m. Thus, the magnetic force F is written by
The strong magnetic gradient produces the strong magnetic force. In this paper, we proposed the novel magnet configurations with the large magnetic field gradient for magnetic immunostaining and, performed the numerical calculation of the magnetic force and the magnetic immunostaining using the proposed magnets and FF beads.
II. MAGNET CONFIGURATIONS
We propose two types of novel magnet configurations, the comb-teeth and the N-S magnet as shown in Fig. 1(a), for producing the large magnetic field gradient on the surface of the magnet. Arranging the long (24-mm length) and short (20-mm length) parts of 101 small (2-mm width) neodymium magnets forms the comb-teeth magnet; there are concave and convex patterns on the surface. The N-S magnet consists of N and S poles alternately arrayed of 101 small magnets with the length of 24 mm and width of 2 mm. Entire width and height of both magnets are 22 and 24 mm. Figure 1(b) shows the magnetic flux Ψ of the proposed magnets; the sparse or dense of the lines imply the magnetic field gradient. The field lines are distorted by the concave and convex on the surface of the com-teeth magnet, while in the N-S magnet the field lines significantly concentrate around the surface. Matlab (The Mathworks, Inc., Natick, USA) was used to carry out the calculations.
A. Numerical evaluations of magnetic force
The magnetic flux density B, the magnetic field gradient ∇B, and the magnetic force F applied to the FF beads were calculated by using the magnetic moment method with the spatial resolution of 0.25 mm. The magnet is separated into small magnet elements (0.25mm square) to calculate the magnetic flux density Ba at a point P as shown in Fig. 2(a). The magnetic flux density of the magnets is calculated by
where ri is the distance from a minute magnet to a point P, and Mi is the magnetic moment of magnet separated a small element: the magnetic moment m was calibrated by the measured values along the Z-axis (X = Y = 0).
The magnetic force applied to the FF beads is rewritten by Eq. (1):
where mx, my, and mz are the magnetic moment of the FF beads, and Ba is the magnetic flux density at a point P. The magnetic moment of the FF beads m, that is M-H curve, was measured by a superconducting quantum interference device (SQUID). The saturated moment msat under the 300 mT was approximately 8×10−17 A·m2 per particle.
B. Experiments for magnetic immunostaining
Magnetic immunostaining was carried out for confirming the staining effect using the proposed magnets. Figure 2(b) show the experiment condition. First, the sample and FF beads were treated with 4% skim milk blocking solution for 5 min. Anti-epidermal growth factor receptor (EGFR) antibodies were used as the antibody. The samples included A431 human epidermoid cancer cells, in which EGFR is highly expressed, and H69 which is small-cell lung cancer cell, in which EGFR is not expressed. 200 μL of a FF beads was diluted to 20 times by 4% skim milk blocking solution. After removal of the blocking solution on the sample, 200 μL of antibody-labeled FF beads was casted on the A431 and H69 cells. And then the proposed magnet was moved beneath in order to attract the beads to the cells and FF beads were washed after 1 min of the magnetic immunostaining time and visualized under fluorescence microscope (CKX 53; Olympus). Under ultraviolet exposure, the FF beads emits red fluorescence.7 As shown in Fig. 2(b), the distance from the sample to the surface of the magnet was 1 mm and the beads filled in the distance 1–2 mm from the magnetic surface. The magnet was translationally move below the slide grass by a driving motor for collecting the FF beads uniformly in the staining process. The stroke in the linear reciprocating movement off the magnet was 2 mm, and the rotational speed of the motor was 240 rpm.
IV. RESULTS AND DISCUSSION
A. Numerical analyses
Figure 3 shows the numerical analysis for the comb-teeth magnet, N-S magnet and a conventional flat surface magnet at Z = 1.5 mm and Y = 0 mm. In the comb-teeth magnet, the magnetic flux density Bx and Bz on the X-axis gradually increased and decreased with fluctuating, respectively, with the separation from the center of the magnet (Fig. 3(a)). The undulating curve of Bx and Bz was generated in accordance with the convex parts of the small magnets. As shown in Fig. 3(b), the large magnetic field gradient dBz/dx and dBz/dz on the surface of the comb-teeth magnet are produced: the maximum values of |dBz/dx| and |dBz/dz| are 50 and 100 mT/mm, respectively. The N-S magnet shows that Bx and Bz alternate in sign from the center to the edge of the magnet in accordance with the borders between the N and S poles of the small magnets (Fig. 3(d)), which produces the large magnetic field gradient dBz/dx and dBz/dz (Fig. 3(e). In the contrast, the flat surface magnet shows that Bx and Bz generated in accordance with edge of the magnet, which produces the large magnetic field gradient dBz/dx and dBz/dz only on the edge of the magnet (Fig. 3(g) and (h)). Taking into account that the magnetic flux density By of both magnets is zero on the X-axis at Y = 0 mm (Figs. 3(a), (d) and (g)), the magnetic force is expressed by F = mx dB/dx + mz dB/dz. In the flat surface magnet, the magnetic force focuses only on the edge of the magnet as shown in Fig. 3(i). On the other hand, the comb-teeth magnet and N-S magnet have the many focal points of magnetic force rather than the conventional flat surface magnet, suggests that FF beads are attracted toward the entire surface of the magnet (Figs. 3(c) and (f)). The magnetic force of the comb-teeth is stronger than that of the N-S magnet, indicating that the comb-teeth magnet attracts the FF beads toward the surface of the magnet in shorter time than the N-S magnet. On the other hand, the N-S magnet has the many focal points of magnetic force rather than the comb-teeth magnet. The numerical calculation revealed that the proposed magnets produce the strong magnetic force Fz 4–5 × 10-15 [N] in N-S and 6–9 × 10-15 [N] in comb-teeth magnets, for attracting toward the magnet at multiple points on the surface (Figs. 3(c) and (f)). Note that the gravity force of the FF bead is approximately 10-16 [N],8 which is much smaller than the magnetic force 4–9 × 10-15 [N]. However, the movement of FF beads depends on the magnetic force, the gravity, the buoyance and the viscous resistance on the FF bead in 4% skim milk. The magnetic force depend on the size of magnetic core in FF beads, and the gravity, the buoyance and the viscous resistance depend on the size of FF beads and the viscosity of the medium (4% skim milk). The size of magnetic core in FF beads is 40nm.8 The size of FF beads is 216±22nm.8 The viscosity of 4% skim milk at room temperature measured by a viscosity measuring device (TVE-25L; TOKI SANGYO) is 1.12 mPa·s, which depend on the temperature. We need to take into account that the variation in the movement of FF beads for attracting toward tissue section occurs by the variation of these factors.
We performed the magnetic immunostaining with FF beads using the proposed magnets for confirming the staining effect. Figure 4 shows the staining observation of A431 and H69 by anti-EGFR antibody-labeled FF beads, as described above. A431 are human epidermoid cancer cells, in which EGFR is highly expressed, and H 69 are small-cell lung cancer cells, in which EGFR is not expressed. The samples included A431 showed red fluorescence uniformly by FF beads. By contrast, samples prepared from H69 treated with anti-EGFR antibody-labeled FF beads didn’t produce red fluorescence. The nucleus stained blue by DAPI (4’, 6-diamidino-2-phenylindole) staining. The results indicate that we could diffuse the FF beads uniformly and carry out the magnetic immunostaining in a short time of 1 min using these magnets. We determined that the FF beads diffuse uniformly and the immunoreaction promotes rapidly using both magnets.
We proposed the novel magnet configurations with the large magnetic field gradient and the strong magnetic force for magnetic immunostaining, and performed the numerical calculation of the magnetic force and the magnetic immunostaining using the proposed magnets. The numerical calculation revealed that the proposed magnets produce the large magnetic field gradient and the strong magnetic force for attracting toward the surface of the magnet. In case of this analysis condition, the comb-teeth magnet attracts the FF beads toward the surface of the magnet in shorter time than the N-S magnet. N-S magnet suggests that FF beads are diffused the multiple points of the surface of the magnet. The magnetic immunostaining using the proposed magnets indicates that we could diffuse the FF beads uniformly and carry out the magnetic immunostaining in a short time of 1 min. We determined that the FF beads diffuse uniformly and the immunoreaction promotes rapidly using both magnets. We need to consider optimization of the magnet shape to perform more efficient magnetic staining.
This research was supported by the Project for Medical Device Development from Japan Agency for Medical Research and Development, AMED.