Keywords

1 Introduction

Currently, the number of patients with mental illness is increasing in developed countries. Near Infra-Red Spectroscopy (NIRS) is used as a diagnostic aid for mental illness in hospital. NIRS is possible to measure brain activity signals with low inversive and low physical restraint. However, measurement weak signal of brain activity such as human intension and recall, is very difficult because noise signal such as heartbeat, respiration and body movement disturb the brain activity signal. Therefore, it is very important to reduce the noise signal to diagnostic aid for mental illness. In our previous study, we succeeded in reducing the artifacts ingredient by the heartbeat, respiration using the Auto-Regressive (AR) model [1]. In this study, we attempt to reduce the effect of the artifacts ingredient by the body movement from the data of NIRS.

2 Experimental Method

In this study, we composed two experiments. In the first experiment, measuring brain activity signal, electrocardiogram (ECG) and the position change of the measurement point were measured by NIRS, Multi-Telemeter and Three-dimensional movement analysis device, when the subject inclined rhythmically the head with up and down. We examined to actively measure changes in blood flow due to body movements, heartbeats and breathing, not changes in blood flow due to cognitive activity.

In the second experiment, signal components for brain activity data were analyzed based on the ECG and Three-dimensional movement analysis device. We reduced the artifacts by the heartbeat and body movement from brain activity data by using analysis result.

2.1 Measurement Principle of NIRS

NIRS is the equipment to measure brain activity signals by using near infrared light. Near infrared light is highly permeable to biological tissue. Irradiated near infrared light from scalp is repeatedly reflected and diffracted while absorbing by Oxygenated Hemoglobin and Deoxygenated Hemoglobin. When brain activity becomes active, Hb concentration is changed to increases blood flow for supplying oxygen. Absorption spectrum characteristics are different in oxyhemoglobin and deoxyhemoglobin. In general, NIRS calculates changes in oxyhemoglobin and deoxyhemoglobin concentration by using near infrared light of different wavelengths such as 780 nm, 805 nm, 830 nm. When brain activity measurement by NIRS, a probe that emits near infrared light and a probe that detects near infrared light are attached to the subject’s scalp. Near infrared light emitted from the light-transmitting probe passes through scalp and skull, is repeatedly absorbed and scattered, and is detected by the detection probe. When the distance between the light-transmitting probe and light-transmitting probe is 30 mm, near infrared light pass through a depth of 25 to 30 mm in the cerebral cortex. Hb concentration changes are calculated Modified Lambert-Beer (MLB) law based on Lambert-Beer (LB) law. The LB law shows the relationship between the attenuation of light and the concentration of light absorbing substance when light is irradiated to a liquid containing the light-absorbing substance. When light is irradiated into a substance that absorbs light but does not scatter, the light intensity decreases exponentially. The relationship between the amount of incident light (I0) and the amount of transmitted light (I) is as shown in Eq. (1).

$$ OD\left( \lambda \right) = Log\left( {I_{o} /I} \right) = \varepsilon \left( \lambda \right) \times c \times L $$
(1)

The OD is absorbance, λ is the wavelength of light, ε is the molar absorbing coefficient (μM−1 ・ cm−1), c is the concentration of the light absorbing substance (mol), L is the optical path length (mm). The optical path length is the same as the thickness of the substance because the light goes straight in a non-scattering substance. However, a substance with light scattering such as biological tissue, the LB law cannot be used because the optical path length longer than the thickness of the substance. Therefore we use Eq. (2).

$$ OD\left( \lambda \right) = Log\left( {I_{o} /I} \right) = \varepsilon \left( \lambda \right) \times c \times \left( {d \times B} \right) + OD\left( \lambda \right)_{R} $$
(2)

The B is the differential path length factor by light scattering. The \( {\text{OD}}\left(\uplambda \right)_{R} \) is a photon that is not detected by light scattering.

$$ \varDelta OD = \varepsilon \left( \lambda \right) \times \varDelta c \times L $$
(3)

The L is the product of D (thickness of the substance) and B. The change in hemoglobin concentration (Δc) can be obtained from Eq. (4) [2].

$$ \varDelta c = \varDelta OD/\left( {\varepsilon \left( \lambda \right) \times L} \right) $$
(4)

2.2 Auto-Regressive (AR) Model

The AR model is a method to estimate future data from past data in time series data. To predict future data in the time series η(t), t = 1, …, S it is necessary to construct a prediction model using information obtained from past data.

$$ \eta \left( t \right) = \sum\nolimits_{i = 1}^{P} {\alpha_{i} \eta \left( {t - i} \right) + \varepsilon \left( t \right)} $$
(5)

Here, α is the AR coefficient and P is the dimension of the model, ε(t) is prediction error (noise according to the normal distribution).

When only the most recent past data is used, we have:

$$ \eta \left( t \right) = \alpha_{1} \eta \left( {t - 1} \right) + \varepsilon \left( t \right) $$
(6)

When using the past two data

$$ \eta \left( t \right) = \alpha_{1} \eta \left( {t - 1} \right) + \alpha_{2} \eta \left( {t - 2} \right) + \varepsilon \left( t \right) $$
(7)

The relationship between the AR coefficient α, frequency f of the stationary vibration and the sampling frequency F_s can be obtained by the following equation.

$$ \alpha_{1} = 2\gamma \cos \left( {2\pi \times \frac{f}{{F_{s} }}} \right) , \alpha_{2} = - \gamma^{2} $$
(8)

Here, γ is constant which corresponds to the attenuation factor. When using actual time series data, AR coefficients can be optimized by the least squares method and Yule-Walker method, and dimension of the model can be determined by Akaike’s information criterion [3, 4].

2.3 Filtering by the AR Model

From (5), the AR model can be deformed as follows.

$$ \varepsilon \left( t \right) = \eta \left( t \right) - \sum\nolimits_{i = 1}^{P} {\alpha_{i} \eta \left( {t - i} \right)} $$
(9)

From (9) is a filter that inputs time series data and outputs prediction error. This prediction error is called innovation. When the frequency to be removed predetermined, the AR coefficient is determined from (8) [3] [4]. When we estimate the AR coefficient by using time series data, the unpredictable signal is included the prediction error (Figs. 1 and 2).

Fig. 1.
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Absorption spectrum of hemoglobin.

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Fig. 2.
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Conceptual diagram of near-infrared light transmission.

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2.4 Measurement of Body Movement by NIRS

We have been thinking about artifact removal. Therefore, artifacts have been removed from resting data with little change in brain activity. The Brain activity data including motion artifacts is measured by NIRS. We confirmed that NIRS data includes at least the effects of the heartbeat and body movement as noise.

We conducted an experiment in sound insulation room. The subjects were adult men aged 20 s, sitting in a chair 60 cm away from the wall and gazing at the markers at eye height. In this experiment, we measured position change of head inclining with a marker attached to the forehead using high speed camera. In this experiment, we tried to remove changes in blood flow due to body movements from brain activity data that mixed changes in body movements and cognitive tasks. Subjects shook their head vertically every second during the experiment. The subject predicts the dice number, throws the dice, and performs the task of confirming dice number at 10 s intervals. Figure 4 shows the procedure of the experiment.

2.5 Artifact Reduction of NIRS Data Using the AR Method

The brain activity measuring data is filtered by the AR model. At this time, AR coefficient was obtained from NIRS data and ECG data. We analyzed the frequency component of the brain activity signals and ECG data. We removed the frequency component by the heartbeat and body movement using AR model. Finally, we analyzed the frequency of the artifact removed data.

We carried out this experiment with informed consent of the subjects following the approval of the Suwa University of Science Ethical Review Board (Fig. 3).

Fig. 3.
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Experimental landscape and NIRS.

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Fig. 4.
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Experimental procedure.

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3 Experimental Result and Discussion

The change of oxygenated hemoglobin of NIRS data and Three dimensional motion data of a subject.

3.1 Measurement of Body Movement by NIRS

Figure 5 shows the result of the position change of the head inclining. Figures 6, 7, 8, 9, 10 and 11 shows the results of the NIRS data of the head inclining. In subject C, changes due to Headshaking are greatly recorded. Signals from cognitive activities cannot be confirmed. An AR model was constructed from the motion of Headshaking and an attempt was made to remove artifacts due to motion. We confirmed 5 peaks in 10 s in NIRS data. We confirmed the artifact based on position change of the head inclining in brain activity signals.

3.2 Artifact Reduction of NIRS Data Using the AR Method

Figure 12, 13, 14, 15, 16 and 17 shows the result of reducing the frequency component of the body movement from the NIRS data using the AR model. The red line is the brain activity data after removal. The orange line is the component of the artifact due to headshake movement. We confirmed a periodic wave of about 0.5 Hz. It can be confirmed that the brain activity during Confirming occurred in some of the subjects. We confirmed the removal of the artifact reduce by a heartbeat and breathing motion and body movement from the NIRS data of all subjects. Thus, we think that it may be possible to measure changes in brain activity due to cognitive tasks even when body motion noise is large

Fig. 5.
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Position change of the head inclining.

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Fig. 6.
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NIRS data of subject A.

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Fig. 7.
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NIRS data of subject B.

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Fig. 8.
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NIRS data of subject C.

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Fig. 9.
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NIRS data of subject D.

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Fig. 10.
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NIRS data of subject E.

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Fig. 11.
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NIRS data of subject F.

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Fig. 12.
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NIRS data of subject A. (Color figure online)

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Fig. 13.
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NIRS data of subject B. (Color figure online)

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Fig. 14.
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NIRS data of subject C. (Color figure online)

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Fig. 15.
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NIRS data of subject D. (Color figure online)

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Fig. 16.
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NIRS data of subject E. (Color figure online)

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Fig. 17.
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NIRS data of subject F. (Color figure online)

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4 Conclusion

In this study, we could show the usefulness of filtering by AR model. We succeeded in removing specific frequency components using the AR model estimated from AR coefficients. From these results, it is considered that high accuracy filter processing is possible using this study method. As a result, this research is highly likely to be useful for measuring signals with low S/N ratio such as intention and memory. This method is considered to be able to measure the cognitive activity even if the artifact is generated strongly. Moreover, by applying the proposed method to previous studies [5, 6], we aim to improve brain region identification and statistical accuracy which could not be clarified by conventional experimental methods.