Signal space separation (SSS) method
for a flat sensor array used in MCG:
Computer simulation study
Kensuke Sekihara1,2
1Tokyo Medical and Dental University
2Signal Analysis Inc.

Motivation and background
High-sensitive magneto-resistive (MR) sensors can lead to development of low-initial-costand maintenance-free MCG systems. A prototype of such systems has been developed byTDK• One problem here is the removal of ambient noise magnetic fields,
called environmental noise.
• This is because, in such new sensor systems, we cannot rely on the(traditional) hardware-based solutions:

Please come to TDK’s booth

They are:1) gradiometer sensors.
It is unknown if “gradiometer-type MR sensors” can be developed.
2) high/medium-quality MSRs.
Use of such MSRs invalidates the goal of developing “low-cost”
systems

My talk addresses the third option, development of software shielding methods, andfocuses on the SSS method for environmental noise cancellation.

So far, SSS has been applied to data from MEG helmet sensor arrays.
What is the problem caused when SSS is applied to flat sensor data used in MCG?
SSS uses spherical harmonics expansion:
LD m (θ , ϕ ) −1rµβ− µ 0 ∑ ∑ α m−B(r ) =m (θ , ϕ )∑∑0m +20 m=0 m=−
−
=
=
r
= Bint (r ) + Bext (r )LCBint (r ) : the internal components, generated from a region closer to the origin
than sensors.
Bext (r ) : the external components, generated from a region farther from the origin
than sensors.

The source region is divided into three regions
Intermediate region:B(r ) has both Bint (r ) and Bext (r ) components.
Externalregion

SensorregionInternal
regionoriginB(r ) has only Bint (r ) components.
B(r ) has only Bext (r ) components.

A key fact: Where the internal and external regions are depends on the origin location,and the origin location is a user-defined parameter.

If clever choices of the origin can make signal sources to be in the internal region,and interference sources to be in the external region, the spherical harmonics
expansion provides a natural separation between the signal and interference.
Such choices of the origin can be found for a helmet sensor arrayexternal region

external region

sensor region
internalregion

originInterference source
Signal source

However, for a flat sensor array….
Since the internal region is very small, wherever the origin is set, most of signal sources arelocated in the intermediate region, and signal magnetic field has both components.
external region

external region
sensor region
internal region
intermediateregion

Interference source
Signal source

originOnly “environmental noise” is considered, and nearby-interference is excluded.
Thus, interference sources are located in the external region.

SSS Computer-Simulation Results for a Helmet Sensor Array
CTF 275-channel array

Signal source (near typical SI area)
Four interference sources:
distances to the sensor array: 2—5m

Signal magnetic field

Interference magnetic fieldinternal

internal

external

external

SSS can remove interference without distorting signal.

SSS Computer-Simulation Results for a Typical MCG Sensor Array
64-channel flat sensor array

8X8 sensors (measuring the normal component) arearranged on a flat plane covering an area of 20cm X20cm.
Signal source (10cm below the sensor plane)
Four interference sources exist.
Distances to the sensor array are 2—5m.

Signal magnetic field

Interference magnetic fieldinternal

internal

externalexternal

SSS can remove interference, but it distorts signal magnetic field.

Signal distortion can be corrected in source space analysis
SignalSignal+interference

Interference

Ground truth

SSS-cleaned datawith normal leadfield

SSS-cleaned data

2D current density image

signal+interference

SSS-cleaned datawith SSS-filteredlead field

Interference is removed,
but signal distortion
exists.

Image obtained withnormal lead field contains
distortion.
Image obtained with SSS
filtered lead field is freeof distortion.

Several numerical parameters affect the SSS performance, and they must be
properly set.
z (cm)Such parameters are:zori: Location (z coordinate) of the origin.
LC and LD : Truncation values of the multipole
order defined such that10zori=9 cm

864LD
 m (θ , ϕ ) −1B(r ) =− µ 0 ∑ ∑ α m
− µ0 ∑ ∑ β mr m (θ , ϕ ) +2=
=0 m=−0 m=−rLCValues of these parameters are determined by computing the performancemeasures below.
Signal gain:

GS =Interference gain:

Noise gain:GI =Pint BSBSPint BI

Proximity to 0 is a measure ofshielding capability.

BI1/ GI is called the shielding factor.

1 M TGε =∑  Pint Pint j,j
M j =1

Pint : SSS internal-subspace projector

Deviation from 1 is a measure ofsignal distortion.

Gε is a measure of noise
amplification through the SSS
procedure.

These performance measures are computed with various parameters values.
Noise gain

Signal gain
Dotted lines:
LD =2Solid lines:
LD =3Interference gain (rI=5m )rISensor plane

Interference gain (rI=20m )Dotted lines:
LD =2
Solid lines:
LD =3

Optimum values are determined such that: zori = 9cm, LC=6 or 7, and LD=2.

Interference gain is then evaluated assuming that sensor calibration errors exist.
Typical existing MCG array
64 (8X8) (normal) sensors
Coverage: 20cmX20cm.

Larger array
100 (10X10) (normal) sensors
Coverage: 24cmX24cm.

Vector sensor array36 (6X6) vector sensors (total 108 sensors)
Coverage: 20cmX20cm.

• The typical existing MCG array and the larger array have similar shielding capabilities.
• In these arrays, shield factor reaches 50 with calibration errors of 0.3%, and 100 with errors of 0.1% .
• Vector arrays have a significantly improved shielding capability. The shield factor reaches 500 with errorsof 1%, and reaches 1000 with errors of 0.3%.
If you do not have a good calibration method, developing a vector sensor array is one choice.

As a summary, SSS is compared with gradiometer methodology• Both provide capability of environmental noise cancellation.
• Both distort signal but the distortion is corrected by using (in someway) modified lead field in source space.
• SSS requires the sensor array to be precisely calibrated, andgradiometers require sensors to be precisely manufactured.
In conclusion, SSS can work as “software” gradiometers for newly-developed sensors
in which the gradiometer configuration is difficult to implement.

Sekihara, K. (2018). Signal Space Separation Method for a Biomagnetic Sensor
Array Arranged on a Flat Plane for Magnetocardiographic Applications: A
Computer Simulation Study. Journal of Healthcare Engineering, 2018.

Please use your smartphone to capture this QR code, and get a link to download the paper.
Thank you very much for your attention.