SENSITIVITY AND SPATIAL RESOLUTION OF MNP IMAGING
5.1 Position Identification from B z Measurement
An imaging experiment of one MNP sample was performed using the MNP detection system as shown in Fig. 5.1. Details on the experiment setup and MNP sample properties were already explained in the previous chapter.
Fig. 5.1: Schematic of the MNP detection system. The inset shows its real image.
z
80 5.1.1 Sensitivity of the Measurement System
First, the sensitivity of the imaging system was explored to test the detection limitation of one MNP sample using this system. As a result, Fig. 5.2 shows the detected second harmonic signal in vertical axis, Bz when 100 μg of Resovist MNPs were positioned under the pickup coil (x = y = 0) and the depth z of the sample from the pickup coil was varied from 10 to 30 mm. Both DC and AC excitation currents were fixed at 0.8 A, and AC excitation field frequency was 19.8 kHz. The vertical axes on the left- and right-hand side indicate the output voltage Vz and the magnetic signal Bz at the pickup coil, respectively.
As shown, the 100-μg MNP sample located at z = 30 mm could be detected with Bz = 36.6 pT. As already mentioned in chapter four, the peak-to-peak value of the noise field was 7.2 pT. Therefore, the signal-to-noise ratio (SNR) was approximately 5 in this case. This sensitivity is sufficient for MNP detection in one sentinel lymph node (SLN) for the breast cancer staging.
10
-110
010
110
110
210
310 20 30
Vol ta ge ( μ V) M agn et ic f ie ld (pT)
Depth (mm)
Noise level
Fig. 5.2: Relationship between the detected signal and the depth z. 100 μg of MNP sample was used.
5.1.2 Position Identification in xy Plane (One MNP sample)
Next, the MNP sample was scanned in the xy plane and the magnetic signal from the MNPs was plotted as a contour map. This contour map was used to identify the position of MNP sample in the xy plane. To this end, the sample was moved in the x direction from x = -40 mm to 40 mm at a speed of 20 mm/s. The harmonic signal Bz was detected at intervals of 2 mm from y = -40 mm to 40 mm. x
81 and y were defined as zero when the sample was positioned at the center of the pickup coil.
Figure 5.3(a) shows the measured contour map when the MNPs were located at z = 20 mm. The excitation fields of μ0HAC and μ0HDC were estimated to be approximately 1 mT at the sample position. A clear contour map having a peak value at x = y = 0, corresponding to the real position of the MNPs was successfully obtained. Black circle in the figure represents the position and size of the MNP sample. Therefore, the real position of one MNP sample could be estimated directly from the contour map.
In addition, Fig. 5.3(b) shows the waveform of the detected voltage signal Vz when the sample was moved in the x -direction at y = 0 in which corresponds to the broken line shown in Fig. 5.3(a).
As shown in this figure, Vz had a peak value of 1.65 μV at x = 0, giving the evidence that the sample was placed just under the pickup coil.
(a)
0 0.5 1 1.5 2
-30 -20 -10 0 10 20 30
V z (uV)
x (mm)
(b)
Fig. 5.3: (a) Contour map of Bz signal detected from one MNP sample, and (b) waveform of Vz
along the x-axis at y = 0. The 100-μg MNP sample was located at z = 20 mm under the pickup coil.
82 (a)
0 0.05 0.1 0.15 0.2 0.25 0.3
-30 -20 -10 0 10 20 30
V z (uV)
x (mm)
(b)
Fig. 5.4: (a) Contour map of Bz signal detected from one MNP sample, and (b) waveform of Vz along the x-axis at y = 0. The 100-μg MNP sample was located at z = 30 mm under the pickup coil.
The measured contour map and the MNPs were located at z = 30 mm are shown in Fig. 5.4(a) and (b). The real position of one MNP sample could still be estimated directly from the contour map in this case, however with lower SNR. This can be seen from the blurred image of the contour map in Fig. 5.4(a) supported by the unsmooth waveform of Vz in Fig. 5.4(b).
5.1.3 Position Identification in xy Plane (Two MNP Samples)
Next, imaging experiments using two MNP samples having a separation of Δx were done using the similar imaging system. Figure 5.5 shows two MNP samples with 100 μg Fe were placed into cells with diameter of 6 mm and were separated by Δx. This simulates the situation where MNPs are accumulated at the SLN and the adjacent lymph node. The contour map of Bz was measured to identify and distinguish the positions of MNPs in two samples.
83 Figure 5.6 shows the contour map when two sample of MNPs were located at (a) z = 10 mm, (b) z = 15 mm, (c) z = 20 mm, (d) z = 25 mm, and (e) z = 30 mm under the pickup coil and were separated by Δx = 20 mm. Each sample contained 100 μg of MNPs. In addition, the corresponding waveforms of Vz along the x-axis at y = 0 for each case are also shown in the Fig. 5.7.
Double peaks separated by Δx = 20 mm appeared clearly in the contour map and in the Vz
distribution for the case of MNPs located at z = 10 mm. These might indicate the real position of MNPs in both samples which accumulate in the two SLNs located at z = 10 mm under the body surface. On the other hand, image from the contour maps of MNPs located at other z values became more blurry with the increasing in depths. Moreover, distribution of their Vz also showed a broad peak. Therefore, it was difficult to clearly distinguish the two MNPs using the contour map for the case of z ≧15 mm.
Fig. 5.5: Two MNP samples with 100 μg Fe were placed into cells with diameter of 6 mm and were separated by Δx.
Δx
84 (a) (b)
(c) (d)
(e)
Fig. 5.6: Contour map of Bz signal detected from two MNP samples of similar weight (100 μg) were located at (a) z = 10 mm, (b) z = 15 mm, (c) z = 20 mm, (d) z = 25 mm, and (e) z = 30 mm under the
pickup coil and were separated by Δx = 20 mm.
Δx = 20 mm
85
0 5 10 15 20
-30 -20 -10 0 10 20 30
z10z15 z20z25 z30
Vz ( uV)
x (mm)
Δ x
Fig. 5.7: The corresponding waveform of Vz along the x-axis at y = 0 for MNP samples used in the each case as shown in Fig. 5.6.
5.1.4 Comparison: Experimental and Numerical Simulation Result
The experimental results were compared with a numerical simulation in order to study the precision of the field map. A calculation on magnetic field generated by a MNP sample placed in a cylindrical cell with a diameter of approximately 6 mm and a height of 5 mm (chapter 4: Fig. 4.7) and located at z = 20 mm under the pickup coil was done to estimate voltage induced at pickup coil.
Excitation and pickup coil parameter used during measurement was taken into account for the calculation. MNP sample was moved in the x direction from x = -40 mm to 40 mm and from y = -40 mm to 40 mm. Then, voltage signal was calculated with intervals of 2 mm in both axes.
The calculation was done based on the reciprocity theoerem of voltage signal induction at the pickup coil as indicated in Fig. 5.8. Note that the calculation was done to evaluate the distribution of the voltage signal without emphasizing the voltage strength itself. Therefore, iron concentration c in the MNP sample was neglected during the calculation. Thus, the voltage data obtained was differ from the real ones obtained experimentally.
First, the voltage signal induced at the pickup coil v(t) can be expressed as
( )
)
( B m t
dt t d
v
. (5.1) Then, B
rm
rB
zm
z
v ω
(5.2)86 whereB
is the magnetic field generated at the MNP sample when a unit current flows at the pickup coil, ω is the measurement frequency, Br,Bz,mr,andmzare magnetic field generated and magnetic moment of MNPs in the depth (z) and radius (r) direction. Then, the magnetic moment of MNPs
) (t m
can be written as
2
Be
c
m (5.3) where
e re e
r cB B B
m 2 / (5.4) and
e ze e
z cB B B
m 2 / . (5.5)
B
eis the excitation field with BreandBzeis the excitation field in the r and z direction, respectively.Therefore, total voltage signal induced at the pickup coil from a magnetized MNP sample becomes
Br Be Bre Be Bz Be Bze Be
c
V ω 2 / 2 / . (5.6)
Then, voltage data obtained from the calculation was plotted into a contour map for comparison with the experimental results. For example, Fig. 5.9 shows the simulation result of the contour map of the signal field for the case of (a) one MNP sample located at z = 20, and (b) two MNP samples were located at z = 20 mm and were separated by Δx = 20 mm. As shown, the experimentally obtained contour map shown in Fig. 5.3(a) and Fig. 6(c) agreed well with the numerical simulation.
Next, the solid line in Fig. 5.10 shows the simulation result of the waveform when each MNP sample was moved in the x -direction at y = 0. The experimental result indicated in Fig. 5.3(b) and Fig. 5.7 agreed well with the simulation. These agreements indicate that the field maps from the MNPs were obtained with high precision in the present experiment.
Fig. 5.8: Reciprocity theoerem of voltage signal induction at the pickup coil.
Exc. coil
r z
Pickup coil MNPs
87
(a)
(b)
Fig. 5.9: Simulation result of the contour map of the Bz signal for the case of (a) one MNP sample located at z = 20, and (b) two MNP samples were located at z = 20 mm and were separated by Δx =
20 mm.
88 -30 -20 -10 0 10 20 30
Simulation Experimental
Voltage Signal (a. u.)
x (mm) -30 -20 -10 0 10 20 30
Simulation Experimental
x (mm)
Voltage Signal (a. u.)
(a) (b) Fig. 5.10: Waveform of the Bz signal along the x-axis at y=0 for the case of (a) one MNP sample located at z = 20, and (b) two MNP samples were located at z = 20 mm and were separated by Δx =
20 mm. Solid and dashed lines represent the numerical simulation and experimental result, respectively.