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ISSN 2432-0250

Vol.41 No.4
JournalJournal of the Magnetics Society of Japan
Electronic Journal URL: https://www.jstage.jst.go.jp/browse/msjmag

2017

Biomagnetism / Medical Applications
Evaluation Method of Magnetic Sensors Using the Calibrated Phantom for Magnetoencephalography
発行（公社）日本磁気学会 〠101‒0052 東京都千代田区神田小川町2丁目8番地
三井住友海上小川町ビル5階☎(03)5281-0106
印刷（株）国 際 文 献 社 〠169‒0075 東京都新宿区高田馬場3の8の8☎(03)3362-9741

D. Oyama, Y. Adachi, and G. Uehara…70

Simulation of Extended Source Localization using sLORETA Method for Magnetocardiography

広告◇計測エンジニアリングシステム株式会社

W. Sun and K. Kobayashi…75◇ネオアーク株式会社◇TDK株式会社◇東英工業株式会社

41

HP: http://www.magnetics.jp/ e-mail: msj@bj.wakwak.com
Electronic Journal: http://www.jstage.jst.go.jp/browse/msjmag

4

2017

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Journal of the Magnetics Society of Japan
Vol. 41, No. 4
Electronic Journal URL: https://www.jstage.jst.go.jp/browse/msjmag

CONTENTS
Biomagnetism / Medical Applications
Evaluation Method of Magnetic Sensors Using the Calibrated Phantom for Magnetoencephalography… ……………………………………………………………………… D. Oyama, Y. Adachi, and G. Uehara

70

Simulation of Extended Source Localization using sLORETA Method for Magnetocardiography… …………………………………………………………………………………… W. Sun and K. Kobayashi

Board of Directors of The Magnetics Society of Japan
President:

K. Takanashi

Vice President:

K. Nakagawa, S. Nakamura

Director, General Affairs:

Y. Miyamoto, K. Niiduma

Director, Treasurer:

K. Aoshima, K. Ishiyama

Director, Planning:

Y. Saito, S. Nakagswa

Director, Editorial

K. Kobayashi, T. Ono

Director, Public Relations:

H. Itoh, S. Greaves

Director, International Affairs:

Y. Takemura, M. Nakano

Auditor:Y. Suzuki, R. Nakatani

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J. Magn. Soc. Jpn., 41, 70-74 (2017)<Paper>

Evaluation Method of Magnetic Sensors
Using the Calibrated Phantom for Magnetoencephalography
D. Oyama, Y. Adachi, and G. Uehara

Applied Electronics Laboratory, Kanazawa Institute of Technology, Amaike 3, Kanazawa, Ishikawa 920-1331, Japan

In recent years, many kinds of magnetic sensors have been developed for biomagnetic measurement, such as
magnetocardiography (MCG) and magnetoencephalography (MEG). However, it is difficult to evaluate theirperformance using only actual MCG or MEG measurements. In this paper, we propose the use of the calibrated
MEG phantom for quantitative evaluation of magnetic sensors and present the experimental method. We choose amagneto-impedance (MI) sensor as an example of the magnetic sensor to be evaluated. The magnetic field
distribution near the phantom was measured using the MI sensor and a signal source was localized with different
averaging numbers and different signal source intensities. The results suggest that the MEG signal cannot be
observed in the usual averaging time (i.e., 100), even when the sensor is located near the head; 4.0 mm of source
localization accuracy can be achieved with 400-times averaging if the sensor noise decreases to 1/10. The use of thecalibrated phantom, instead of examination with human subjects, is effective for quantitative evaluation of theperformance of magnetic sensors.
Key words: magnetoencephalography, phantom, magneto-impedance sensor
1. Introduction
Biomagnetic
signalmeasurements,suchasmagnetoencephalography
(MEG)
and
magnetocardiography (MCG) are utilized in clinical applications
and neuroscience studies. The magnetic signals fromthe brain and heart are very weak; therefore,
superconducting quantum interference device (SQUID)
sensors have been used for practical MEG and MCG
systems for which the sensitivity is less than 10 fT/Hz1/2.
On the other hand, SQUID sensors must be cooled byliquidheliumtomaintainsuperconductivity.
Helium-less MCG or MEG systems are importantbecause of the cost and low availability of liquid helium.
In recent years, the development of refrigerant-less orroom-temperature magnetic sensors has advanced, withthe aim of realizing new biomagnetic measurement
systems. Some groups have succeeded in detecting themagnetic signal from the human heart or brain1)-6), andpractical applications are expected.
However, the evaluation of such magnetic sensors isdifficult with actual MCG or MEG measurement,
because there is no guarantee of reproducibility or
reliability of the signal sources. Objective evidence isimportant to prove the effectiveness of newly developed
sensors. Additionally, quantitative evaluation isnecessary for designing the biomagnetic measurement
system using these sensors.
Therefore, the authors propose the use of a phantom
for the evaluation of the newly developed magnetic
sensors. A phantom is an artificial object that imitates
the human body. Quantitative evaluation can beachieved using phantom experiments instead of
examination of a human subject. The authors havedeveloped a new phantom and an associated calibration70

method designed for quantitative evaluation of MEG
systems7). This phantom was calibrated and its
uncertainty was determined so as to ensure
reproducibility and reliability.
In this paper, an evaluation method for aroom-temperature magnetic sensor using the calibrated
phantom is introduced. As an example of theexperimental evaluation with the phantom, we chose amagneto-impedance (MI) sensor that is a candidate forrealizing a helium-less MEG system. The experimental
setup is detailed in Section 2. The measured data arepresented in Section 3. The feasibility of MEG signal
detection by the MI sensor is discussed in Section 4.
2. Method
2.1 Phantom
One popular method to analyze the MEG data is toestimate a magnetic source in a human brain using theSarvas formula8). In the model of the Sarvas formula,
the human brain and the source current are a
conductive sphere and a current dipole, respectively.
There are two types of phantoms: one is the “wetphantom”, composed of two electrodes installed in a
sphere filled with saline, and the other is the “dryphantom”, composed of a triangular wire based on
Ilmonieimi’s suggestion9). We have chosen the dry-type
phantom because it is much easier to handle, maintain,
and calibrate.
Figure 1 shows the schematics of the phantom. Two
individual isosceles triangles were wound around aquadrangular pyramidal bobbin. The isosceles
triangular model has a 5-mm base and 65-mm height.
Twenty-five bobbins were assembled inside a domed
cover that imitates a human skull. The equivalentcurrent dipoles (ECDs) corresponding to fifty triangular

Journal of the Magnetics Society of Japan Vol.41, No.4, 2017

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PHANTOM
5 mm
65 mm

R = 75 mm

q

x

(a)

y

currentz

MI sensor
1 mm≒65 mm
75 mm

z
(b)

Magnetic flux density [pT/Hz1/2]

Fig. 1 Configuration of the MEG phantom. (a)schematic of an isosceles-triangular coil pair. (b)photograph of the MEG phantom7).

y

MI sensor
current

x

Z

76 mm
(a)

100

current

MI sensor

10

sensing
direction
1

0.1

1

10

100

1000

Frequency [Hz]Fig. 2 Noise level of the MI sensor recorded inside amagnetically shielded room.
wires were estimated based on three-dimensional
measurement of the current paths and numericalcalculations. The details of the phantom configurationand calibration are described in Ref. 7.
2.2 Sensor
In this study, we used a commercially available MIsensor(MI-CB-1DH,
Aichi
Micro
Intelligent
Corporation). Figure 2 shows the magnetic noise
spectrum recorded inside a magnetically shielded room
(MSR). The noise level was approximately 10 pT/Hz1/2
at 10 Hz. The noise level of a SQUID sensor for an MEG
system should be of femto-Tesla order. Although thesensitivity of the MI sensor is insufficient, theroom-temperature sensor has the advantage of being
placed at a closer position to the head. Improvement of
the signal-to-noise ratio is expected because of theshorter distance between the sensor and the signal
source.

(b)

Fig. 3 Setup for experimental evaluation of the MI
sensor using the phantom. (a) Schematics of theexperimental setup and (b) photograph of the phantom
and the MI sensor.
2.3 Experimental setup
Figure 3 shows (a) the experimental setup and (b) thephotograph of the phantom and the MI sensor. One
triangular wire was chosen for the experiment and anelectric current was applied to it by a function generator.
The waveform was a sinusoidal burst at a frequency of
11 Hz. The measurement was performed using different
current amplitudes I = 10 and 100 A. The intensity of
the ECD corresponding to an applied current amplitudeof 10 A was approximately 50 nA·m. This ECD
intensity is similar to that estimated from the recorded
data of human auditory evoked responses.
To measure the magnetic field distribution near thephantom, the MI sensor and the phantom were fixed ona three-axial stage and a rotation stage, respectively.
The sensing direction of the MI sensor was indicated byarrows in Fig. 3, therefore, the magnetic field normal tothe phantom surface was detected by the MI sensor.
The total number of measuring points was 54; these

Journal of the Magnetics Society of Japan Vol.41, No.4, 2017

71

INDEX(b) I = 10 A, Nave = 400(a) I = 10 A, Nave = 100

5 pT

5 pT

50 ms

(c) I = 10 A, Nave = 800

(a)

(b)

(c)

(d)

(e)

(f)

50 ms

(d) I = 10 A, Nave = 1200

5 pT

5 pT
50 ms

50 ms

(e) I = 10 A, Nave = 1600(f) I = 100 A, Nave = 100

50 pT

5 pT
50 ms

50 ms

(g)

(h)

(g) I = 100 A, Nave = 400

heightz = 10mm

rotation angle
q = 10 degree

5 A

50 pT
50 ms

50 ms

15

150

10

100

5

50

0

0

-5

-50

-10

-100

-15

-150

signal intensity in pT
left : (a)-(e), right : (f)-(g)Fig. 4 Measured waveforms (a)-(g) with different
current amplitudes (I) and averaging numbers (Nave),and the applied current waveform (h).

Fig. 5 Contour maps with different current amplitudes(I) and averaging numbers (Nave).

points were obtained by rotating the phantom (q = 0°,±4°, ±12°, ±20°, ±28°) and vertically shifting the
MI sensor (z = −20, −10, 0, 10, 20, 30 mm). The
phantom and the MI sensor were placed in an MSR
while measurements were taken.
The output signal of the MI sensor was amplified(×1000) and band-pass filtered (cut-off frequencies = 0.1
Hz and 500 Hz) before recording. The recording was
performed by a 16-bit A/D converter (PCIe-6353,
National Instruments). The sampling frequency was2000 Hz, and the recording time was 440 s for I = 10 A
and 120 s for I = 100 A. After recording, the waveforms
were averaged to reduce noise just as in the case wemeasure a human evoked response. We applieddifferent averaging numbers, namely, 100, 400, 800,
1200, and 1600 for I = 10 A, and 100 and 400 for I =100 A, so as to consider different signal-to-noise ratios.
Moving-average processing was also conducted with awindow length of 16.5 ms to reduce power-line
interference (60 Hz). Then, source localization using theSarvas formula was conducted for each data set.

(a)-(g) correspond to different averaging numbers andapplied current amplitude 100, 400, 800, and 1600 for I= 10 A, and 100 and 400 for I = 100 A, respectively.
The waveform detected at 54 measuring points isoverlapped. The applied current waveform when I = 10
A is shown in Fig. 4 (h).
Figure 5 shows the contour maps of the measured
magnetic field distributions. Figure 5 (a) - (g) are thesame as those of Fig. 4. The time point of the displayed
data was the first peak of the sinusoidal waveform,
indicated by a triangular arrow in Fig. 4(h).
The source estimation was conducted using aleast-mean-square method and the Sarvas formula.
Figure 6 shows the source localization error andgoodness-of-fit (GOF) value in the estimation. Figure6(a)-(g) are the same as those of Figs. 4 and 5. Source
estimation was performed at every four peaks of thesinusoidal waveform; the length of the bar indicates themean value of the source localization error and the GOF.
By increasing the signal-to-noise ratio, the source
localization error decreased and the GOF increased.

3. Result

4. Discussion

Figure 4 shows the waveforms of measured data andapplied current in (h). The measured waveforms in

The amplitude of the magnetic signal from thehuman brain detected by a SQUID-based MEG system

72

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Source localization error [mm]

INDEX

8
6

10 A
(a)

(b)
(c)

100 A
(d)
(e)

4
2
0
100

Goodness of fit [%]

(g)

(f)

(f)

80

(c)

(g)

(e)

(b)

60

40

(d)

(a)

20
0

100

400

800
1200 1600
Averaging number

100

400

Fig. 6 Source localization error and goodness of fit in
ECD analysis.
is typically found to be approximately 1 pT or less.
However, larger waveforms, as shown in Fig. 4(e), canbe detected by a room-temperature sensor that was
located much closer to the target. These results show
the possibility of realizing a room-temperature
sensor-based MEG system.
When a new magnetic sensor is developed or thesensitivity of a magnetic sensor is improved, theaveraging number used to observe the biomagnetic
signal is usually considered a criterion for theevaluation of its performance. As shown in Fig. 6, thesource localization error with different averaging
numbers can be obtained using the phantom. For
example, we conclude that 4.2 mm of accuracy and 80%
of GOF can be achieved with 1600-times averaging for
MEG measurements when using the MI sensor.
In the case of MEG measurement using a
SQUID-based system, the averaging number is usually
set to approximately 100, in consideration of the
trade-off between signal-to-noise ratio and fatigue
and/or the duration of concentration of a subject. In
contrast, we choose 1600-times averaging as a
maximum to obtain a better signal-to-noise ratio. One of
the benefits of using the phantom is highreproducibility of the measurement result with a highsignal-to-noise
ratio
based
on
long-duration
measurement.
Furthermore, we also carried out measurements at acurrent amplitude of 100 A such that the signal
amplitude was 10-times-larger than the human MEG
signal. The obtained signal-to-noise ratio is equivalent
to that with a 100-times-larger averaging number

because the noise decreases in proportion to the squareroot of the averaging number. Therefore, the results in
Fig.6 (f) and (g) correspond to the source localization
errors and GOF values at an averaging number of
10000 and 40000 for I = 10 A, respectively. By
applying a large electric current to the phantom, we canobtain a result equivalent to using a large averaging
number. From these results, another conclusion is
obtained: 4.0 mm of accuracy and over 99% of GOF canbe achieved with 400-times averaging if the sensor
noise decreases to 1/10. These conclusions provide thetarget specifications of the room-temperature magnetic
sensors used to realize MEG measurements.
In addition, we should point out the value of thesource localization error. In this experiment, thesmallest source localization error was 4.0 mm when I =100 A and the averaging number is 400. This error
was much larger than that obtained by the
SQUID-based MEG systems7). A lower signal-to-noise
ratio, smaller measuring points, and a lack of accuracyof sensor positioning are considered to be the causes ofthe larger source localization error. Specifically, theaccuracy of the sensor positioning is supposed to be themajor cause of the source localization error because
there is a large magnetic field gradient near the signal
source comparing with that of SQUID-based MEG
systems10). It is also important to accurately calibrate
the sensor position and orientation to realize the MEG
system.
5. Conclusion
We demonstrated the experimental evaluation of the
MI sensor using the calibrated MEG phantom. The
signal source was estimated from the observed
magnetic field distribution at different signal-to-noise
ratios. The results showed the possibility (anddifficulty) of realizing MEG measurements using the MI
sensor. The use of the calibrated phantom is effective
for evaluating the performance of magnetic sensors.
Acknowledgements This research was partly supportedby The Hokuriku Industrial Advancement Center.
References
1) S. Yabukami, K. Kato, T. Ozawa, N. Kobayashi, and K. I.
Arai: J. Magn. Soc. Jpn., 38, 25 (2014).
2) H. Karo, and I. Sasada: J. Appl. Phys, 117, 17B322 (2015).
3) T. Yamamoto, K. Tashiro, and H. Wakiwaka: The Papers of
Tech. Meeting on “Magnetics”, MAG-15-9, 41 (2015).
4) H. Xia, A. B-A. Baranga, D. Hoffman, and M. V. Romalis:
Appl. Phys. Lett., 89, 211104 (2006).
5) K. Wang, S. Tajima, Y. Asano, Y. Okuda, N. Hamada, C. Cai,
and T. Uchiyama: Proc. of the 8th Intl. Conf. on Sens. Tech.,547 (2014).
6) Y. Ando: Journal of Japan Biomagnetism andBioelectromagnetics Society, 29, 20 (2016)7) D. Oyama, Y. Adachi, M. Yumoto, I. Hashimoto, and G.
Uehara: J. Neurosci. Methods, 251, 24 (2015).
8) J. Sarvas: Physics in Medicine and Biology, 32, 11 (1987)
9) R. J. Illmonieimi, M. S. Hamalainenm, and J. Knuutila: in

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Proc. Biomagnetism: Applications & Theory, New York,
Pergamon, 278 (1985)
10) D. Oyama, Y. Adachi, and G. Uehara: The Papers ofTechnical Meeting on “Magnetics”, IEE Japan, MAG-16-1(2016)
Received Dec. 22, 2016; Revised Mar. 13, 2016; Accepted Apr.
05, 2017

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J. Magn. Soc. Jpn., 41, 75-80 (2017)<Paper>

Simulation of Extended Source Localization using sLORETA Method forMagnetocardiography
W. Sun and K. Kobayashi
Faculty of Engineering, Iwate University, 4-3-5 Ueda, Morioka, Iwate 020-8551, Japan

In this study, cardiac source localization was simulated using the spatial filter method. Three types of spatial
filters were obtained using the standardized low-resolution brain electromagnetic tomography (sLORETA) method,
based on different examination procedures. In Type A filter, the examination was conducted at the front of the torso.
In both Type B and Type C filters, the examinations were conducted at the front and back of the torso; however, thedistance from the frontal observation plane to the center of the heart model was different for each type. In thesimulation experiments, first the goodness of fit (GOF) value was introduced to determine the proper threshold foreach spatial filter. Then, single and multiple dipole sources were simulated at different depths with and without noise.
The extension of the solutions computed using these spatial filters was investigated. Finally, the performances ofthese spatial filters, with the corresponding averaged thresholds, were evaluated using the GOF. Type B and Type C
spatial filters demonstrated reduction in the extension of source dependency on source depth and improvement in theaccuracy of source localization with noisy data.
Key words: Magnetocardiography, sLORETA method, source localization, spatial filter
1. Introduction
Magnetocardiography (MCG) is a noninvasive
technique that detects the magnetic field generated by
the electrical activity in the heart1). Recently, MCG has
been attracting a lot of attention in relation to the early
detection of heart diseases. As MCG is a multichannel
measurement technique and as the signals are notaffected by the shape of the lungs and torso2), it has highpotential for clinical applications. MCG aims at
obtaining functional mapping, starting from thevisualization of signal sources. Because the MCG
inverse problem is ill posed and does not have a uniquesolution, the estimation of MCG signal sources is thebiggest challenge for its application3). MCG signals are
generated by currents flowing within the myocardial
fibers during cardiac activity4). Therefore, we canconsider that an extended source model will be suitablefor estimating MCG sources.
The spatial filter methods5, 6) were developed for
MCG source localization, and could be used to obtain areliable three-dimensional (3D) outline of the heart.
Among the many spatial filter methods, standardized
low-resolution brain electromagnetic tomography(sLORETA)7) is widely used for visualizing brain activity,
as it has zero localization error for a single dipole withnoiseless data. However, it has some limitations,especially under noisy conditions and in case of deep
sources8, 9). For conventional method, MCG examination
is just conducted in the front of the torso, in order toobtain strong signals. In a previous study10), the spatial
filter always favors the sources that are close to themagnetic field sensors and leads to reconstruction of alarge extension for deep sources. Namely, the extensionof the source depends on the source depth. MCG candetect heart signals not only at the front but also at theback of the torso, even though the signals detected at
the back of the torso are very weak11). The assessmentsof the spatial filter based on the different examination
method have not been studied. In order to assess thesource localization abilities of the spatial filters, andinvestigate the dependency of source extension on thesource depth, the simulation study is needed.
In this study, we make sure the distances from thefrontal and back observation planes to the heart are thesame, to reduce the dependency of the source extension
on the source depth, and obtain a spatial filter that canestimate a cardiac source well with noisy data.
2. Simulation ModelIn this study, we simulated MCG source localization
using the sLORETA method based on a conventional
64-channel MCG system. Superconducting quantum
interference device (SQUID) modules were aligned in an
8 × 8 configuration to create a square observation area
sized 175 mm × 175 mm12).

Fig. 1 Frontal and back observation planes and theposition of heart in torso.

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Simulations were carried out for the 64-channel
MCG system within a 168 mm × 168 mm × 120 mmvolume. Six thousand six hundred and fifteen voxels
were divided with the size of each voxel being 8 mm × 8
mm × 8 mm. Fig. 1 shows three types examination
procedures. Type A is the conventional examination
method, which is only conducted at the front of the torso.
In both Type B and Type C, the examinations are
conducted not only at the front but also at the back of
the torso; however, the distance from the frontal
observation plane to the center of the heart model isdifferent for each type. For Type C, in order tocompensate for the varying sensitivities of the sensors
to the current sources at different depths, we make surethe distances from the frontal and back observation
planes to the heart are the same. The distance from thefrontal observation plane to the center of the heartmodel was set as 80 mm for Type A and Type B and as
160 mm for Type C. The distance from the backobservation plane to the center of the heart model was
set as 160 mm for Type B and Type C. For the forward
problem, we calculated the lead-field matrix K using the
Biot–Savart Law.
3. Methods
sLORETA is a spatial filter method used to solve theill posed problem. It can obtain a blurred source image
by using a linear inverse operator7).

(1)Φ  ΚJ  nwhere Ф is the detected signals, K is the lead-field
matrix, J is the original current sources within theheart, and n is the noise at each sensor. Using thewell-known minimum norm estimate (MNE) method,the estimated current sources Ĵ can be written as:Ĵ  GΦ  K T KK T  2 I Φ(2)MNE solution using its variance in the following way:Ĵ sLORETA ,i  Sii

1/2

Ĵ i

(3)

where Sii is the diagonal element of the covariancematrix S withS  GK(4)

In this study, we first calculate the lead-field matrix K
that describes the sensitivity of the sensors to eachcurrent source location. For each current source location,
K includes two columns that represent the X component
and Y component, respectively. Then, Type A, Type B,
and Type C spatial filters are obtained using thesLORETA method.
In the coordinate system, the center point of the top
voxels layer is (0, 0, 20) and the unit is mm. A single
dipole source (0, 0, 20) in the X direction is simulated bychanging the depth in 8 mm increments.
Since the real cardiac sources are considered to beextended sources, simulations with multiple dipoles arealso performed. A normal MCG wave is obtained using
the Iwate create project 64-channel MCG system11). An
isomagnetic field map of the MCG wave at the R peak isshown in Fig. 2(a). The generated magnetic field of themultiple sources is shown in Fig. 2(b). Multiple
sources—(−16, 8, 20) in the X direction, (−8, 8, 20) in the
X direction, and (0, 0, 20) in the Y direction—are
simulated by changing the depth in 8 mm increments.
4. Simulation Results and Discussions
4.1 Simulation without Noise
Fig. 3 shows the simulation results of a single dipole
at different depths (depth = 28 mm, 76 mm, and 124mm). The relative strength was normalized by the
maximum of the solutions. The white rectangle denotes
the maximum of the solutions. All the maximum

where G is a spatial filter matrix, T denotes the matrix
transpose, λ2 is the Tikhonov regularization parameter,and I represents an identity matrix. The sLORETA
solution can be obtained from the standardization of theFig. 2 (a) Isomagnetic field map of MCG wave at R
peak. (b) Isomagnetic field map of multiple dipole
sources. GOF of two patterns is 0.93. One step of theisomagnetic field contour line is 10 pT.

76

Fig. 3 Left column is the true source in the X direction
placed at different depths (from top to bottom depth = 28mm, 76 mm, and 124 mm). The three right columns arecross sections of simulation results using Type A, TypeB, and Type C spatial filters. The white rectangle
denotes the maximum of the solutions.

Journal of the Magnetics Society of Japan Vol.41, No.4, 2017

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solutions are located at real source positions. It meansthat there is no localization error without noise.
However, the solutions have large spatial extensions.
Obviously, the extensions of the solutions computed by
the Type A spatial filter have larger dependencies on thedepths of the true source than that computed by theType B and Type C spatial filters. Because a source thatis far from the sensor contributes less to the measured
data than one that is near the sensor, the solution needs
large extensions to fit the measured data. By contrast,
Type B and Type C spatial filters produce solutions withextensions that have fewer dependencies on the depthsof true sources.
For an extended source, a threshold of relative
strength has to be determined. The full width at half
maximum (FWHM) is used as the threshold13, 14). It
means that only the excess 50% of the maximum
sources are analyzed to avoid influence from the weakinsignificant source estimates. In our study, thegoodness of fit (GOF) value is introduced to determine
the proper threshold. GOF describes the similarities in
the measured and estimated signals at all N sensors15).
GOF is defined as follows:
N

N

i 1

i 1

2
GOF  1   Bmea,i  Bcal,i 2 /  Bcal,
iFig. 4 Left column is the true source in the X
direction placed at different depths (from top tobottom depth = 28 mm, 76 mm, and 124 mm). The
three right columns are cross sections of simulation
results using Type A, Type B, and Type C spatial
filters (threshold = 0.91, 0.90, and 0.93, respectively).
The white rectangle denotes the maximum of thesolutions.

(5)

where Bmea,i denotes the measured magnetic field andTable 1 Threshold of relative strength simulated withthe true source at different depths when thecorresponding GOF is close to 1. (All of the GOF is 0.99
in this study).
depth (mm)Type A

Type B

Type C

20

0.847

0.892

0.940

28

0.830

0.856

0.946

36

0.850

0.860

0.950

44

0.866

0.870

0.940

52

0.902

0.880

0.925

60

0.910

0.883

0.917

68

0.924

0.885

0.911

76

0.934

0.886

0.900

84

0.936

0.910

0.910

92

0.942

0.925

0.920

100

0.942

0.929

0.931

108

0.938

0.938

0.940

116

0.937

0.950

0.952

124

0.927

0.950

0.951

132

0.923

0.947

0.947

average

0.91

0.90

0.93

Fig. 5
Relationship of volume percentage and depthof true source.

Fig. 6 GOFs of solutions computed using Type A,
Type B, and Type C spatial filters when the true
source is placed at different depths.

Journal of the Magnetics Society of Japan Vol.41, No.4, 201777

INDEX

Bcal,i denotes the calculated magnetic field at the i thsensor. A high GOF indicates that the estimated sources
can explain the measured data well. The thresholdvalues with true sources at different depths are shownin Table 1, when the corresponding GOF is close to 1.
The average value is chosen for computing the solutions.
The relative strength, which does not exceed theaverage value of thresholds, is considered to be 0.
In the simulation, a single dipole source in the X
direction is placed at different depths (depth = 28 mm,
76 mm, and 124 mm). Fig. 4 shows the cross sections of
the solutions computed by Type A, Type B, and Type C
spatial filters. The extension of the solution has a large
dependency on the depth of the true source for the TypeA spatial filter because of the varying solid angles
between the dipole at different depths and theobservation plane. In addition, the solutions computedby the Type B and Type C spatial filters show smaller
extensions in the Z direction than that computed by theType A spatial filter, owning to the data measured from

Fig. 7 Left column is the true sources at different
depths (from top to bottom depth = 28 mm, 76 mm,
and 124 mm). The three right columns are crosssections of simulation results using Type A, Type B,
and Type C spatial filters (threshold = 0.91, 0.90, and0.93, respectively). The white rectangle denotes the
maximum of the solutions.

Fig. 8 Relationship of volume percentage and depthsof true sources.

78

Fig. 9 GOFs of solutions computed using Type A,
Type B, and Type C spatial filters when the true
sources are placed at different depths.
the back of torso. Because the distances from the frontal
and back observation planes to the heart model are thesame, the extensions show less dependency on the depthof the true source for the Type C spatial filter.
By computing the volumes of the voxels in which thesolutions are localized, the relationship between thevolume percentage and the true source depth can beobtained as shown in Fig. 5. The extensions of solutions
show less dependency on the depth of the true source for
the Type B and Type C spatial filters. The GOFs of TypeA, Type B, and Type C spatial filters with the proper
thresholds are shown in Fig. 6. The GOF values of theType A and Type B spatial filters are far away from 1
and even drop to negative values for deep sources.
Therefore, the Type C spatial filter shows better
performance.
Fig. 7 shows the cross sections of the solutions
computed using the Type A, Type B, and Type C spatial
filters. By computing the volumes of the voxels in which
the solutions are localized, the relationship between thevolume percentage and the true source depth can beobtained as shown in Fig. 8. Obviously, the Type B andType C spatial filters show extensions that have lessdependency on the depth of the true sources, comparedto the Type A spatial filter. Fig. 9 shows the GOFs of theType A, Type B, and Type C spatial filters simulatedusing sources at different depths. The GOFs of Type A
and Type B spatial filters are far away from 1 and evendrop to negative values for deep sources. It means thatthese two spatial filters cannot fit the measured datawell for deep sources. By contrast, the GOF of the TypeC spatial filter has a good performance despite theslight drop in the case of deep sources.
4.2 Simulation with Noisy Data
Since the MCG inverse problem is ill posed, weaknoise signals can cause large changes in the solution. In
this study, Gaussian white noise is added to thesimulated magnetic field data and the inverse solutions

Journal of the Magnetics Society of Japan Vol.41, No.4, 2017

INDEX

are computed using the above three spatial filters. The
SNR ranges from 0 to 40 in 5 dB increments. The SNR is
defined as:SNR  10log varBexact  / σ 2(6)where Bexact is the variance of the simulated noise-free
measurements and σ2 is the variance of the added
Gaussian white noise. In this study, for a single dipole
source, the localization error is the distance from the
maximum estimated source to the true source. For
multiple sources, the localization error is the distancefrom the maximum estimated source to the center pointof the true sources. The mean value is obtained from100 calculations. In order to obtain the samemeasurement conditions, the same σ value of noise is set
up for these three spatial filters at a certain noise level.
Since the magnitudes of the signals detected at thefrontal and back observation planes are different, the
SNR is different. In this study, the x-axis values of Fig.
10 and Fig. 11 are calculated only using themeasurement data that obtained based on Type A
examination procedure.

Fig. 10 Mean localization error of single dipole
source (depth = 124 mm) with different noise levels.

Fig. 10 and Fig. 11 show the simulation results of asingle dipole source and multiple sources, respectively.
The single dipole source and the multiple sources areplaced at relatively deep positions with a depth of 124
mm. For single dipole source estimation, very weaknoise led to Type A spatial filter generating a large
localization error. By contrast, the localization errors ofType B and Type C spatial filters were stable and about
0 at 20 ~ 40 dB. For multiple sources estimation, thelocalization errors of Type B and Type C spatial filters
were stable at 0 ~ 40 dB. Apparently, the Type B andType C spatial filters have improved source localization
accuracies. It may be owing to the data obtained fromthe back of the torso. In addition, Type B and Type C
spatial filters have good performances for multiple
source localizations even at high noise levels. Hence,
they are fit for estimating multiple sources.
5. Conclusion
In this study, Type A, Type B, and Type C spatial
filters were obtained using the sLORETA method basedon three types of MCG examination procedures. The
GOF was introduced to determine the proper thresholdfor each spatial filter. The extensions of the solutions
computed using these spatial filters with thecorresponding thresholds were investigated. In thesimulation of a single dipole and multiple dipoles placedat different depths, the Type C spatial filter
demonstrated an extension that had less dependency on
the depth of the true source. In addition, the GOF of theType C spatial filter was close to 1 even for deep sources.
It meant that the Type C spatial filter had the best
performance for extended source estimation, compared
to Type A and Type B spatial filters. From the results ofthe simulations with noisy data, we found that the TypeB and Type C spatial filters had improved source
localization accuracies and that they were fit for
estimating extended sources. The reduction of thesource extension for deep sources and the improvementof the source localization accuracies owned to theexamination at the back of the torso. The same distancefrom the frontal and back observation planes led to theless dependency of the source extension on the source
depth. In the future, we hope to detect the real MCG
signals and estimate the cardiac source using Type B
and Type C spatial filters.
Acknowledgements This work was supported by theJapan Society for the Promotion of Science KAKENHI(Grants-in-Aid for Scientific Research (C)) Grant
Number JP26350535.
References

Fig. 11 Mean localization error of multiple sources(depth = 124 mm) with different noise levels.

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Received Jan. 19, 2017; Accepted May 15, 2017.

80

Journal of the Magnetics Society of Japan Vol.41, No.4, 2017

INDEX

Editorial Committee Members・Paper Committee Members
K. Kobayashi and T. Ono (Chairperson),(T. Kato, K. Koike and T. Taniyama (Secretary)
A. Fujita
H. GotoH. Hashino
Y. Hirayama
S. Honda
Y. Kanai
S. Kasai
A. Kikitsu
H. Kikuchi
T. Kimura
K. Miura
T. Nagahama
H. Naganuma
M. Naoe
M. OhtakeY. Sasayama
T. SatoT. SatoS. Seino
K. Sekiguchi
T. Shima
Y. Shiratsuchi
M. Sonehara
T. Tanaka
K. Yamamoto
N. Adachi
N. Inaba
S. Kokado
T. Nakagawa
K. Tajima
K. Yamazaki

K. Bessho
S. Isogami
Y. Kota
H. Nakayama
M. Takezawa
S. Yoshimura

M. DoiK. KamataT. MakiT. Narita
T. Takura

T. DoiH. KatoE. Miyashita
D. Oyama
M. Tsunoda

S.InuiT. Kubota
N. Pham
M. Sekino
H. Yuasa

M. EndoK. KatoT. Morita
T. Saito
S. Yabukami

T. Hasegawa
T. KodaS. Muroga
R. Sugita
T. Yamamoto

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