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An Alpha-Wave-Based Binaural Beat Sound Control System using Fuzzy Logic and Autoregressive Forecasting Model

Sittapong Settapat1 and Michiko Ohkura2 1Department of Electrical Engineering and Computer Science, Graduate School of Engineering,

Shibaura Institute of Technology, Tokyo, Japan (Tel: +81-3-5859-8508; E-mail: m107421@sic.shibaura-it.ac.jp)

2Faculty of Engineering, Shibaura Institute of Technology, Tokyo, Japan (Tel: +81-3-5859-8508; E-mail: ohkura@sic.shibaura-it.ac.jp)

Abstract: We are developing a new real-time control system for customizing auditory stimulus (the binaural beat sound) by judging user alpha waves to entrain a user’s feeling in the most relaxed way. Since brainwave activity provides the necessary predictive information for arousal states, we use an autoregressive forecasting model to estimate the frequency response series of the alpha frequency bands and the inverted-U concept to determine the user’s arousal state. A fuzzy logic controller is also employed to regulate the binaural beat control signal on a forecasting error signal.Our system allows comfortable user self-relaxation. The results of experiments confirm the constructed system’s effectiveness and necessity.

Keywords: Alpha Wave, Binaural Beat, biofeedback, Fuzzy Logic, Autoregressive Model

1. INTRODUCTION Psychological studies of psychoneuroimmunology

(PNI) show that chronic psychological stress and depression have measurable effects on the immune system [1, 2] that can also trigger major psychological and/or physiological disorders. Biosignals monitoring and recording are integral parts of medical diagnosis and treatment control mechanisms [3]. Stress and depression can especially be indicated and interpreted by various biosignals. The most common diagnostic signals are magnetoencephalogram (MEG), electrocardiogram (ECG), heart rate variability (HRV), galvanic skin response (GSR), electromyogram (EMG), and electroencephalogram (EEG). Relaxation is also indicated and interpreted by biosignals, especially, EEG signals.

Several frequency bands are used to describe EEG activities and help describe EEG signals. They include delta (below 4 Hz), theta (4-8 Hz), alpha (8-13 Hz), beta (13-35 Hz), and gamma (36-100 Hz) [4, 5]. In this study, we focus on alpha activity related to three arousal states: relaxed wakefulness with eyes closed, drowsiness, and REM sleep [6-8]. High alpha activity amplitude of alpha activity appears with eyes closed during physical relaxation and relative mental inactivity called the alpha state [9]. Thus, we use the alpha activity level to indicate the level of user’s relaxation.

Appropriate stimulus must be selected to entrain a user’s EEG into the alpha state. Brainwave entrainment using visual and/or auditory stimulation through frequency-following response (FFR) has already been demonstrated to be an effective technique [10-12]. Because that amplitude of alpha activity increases with eyes closed, we selected auditory stimulus as the system’s stimulus. The binaural beat sound is one effective auditory stimulus to entrain brainwave through FFR. Thus, we use a binaural beat sound as the system’s auditory stimulus. Therefore, alpha activity is entrained

with the binaural beat sound in the alpha wave range. To increase and maintain the level of alpha activity, real-time analysis and control of the binaural beat sound are required for proper sound generation.

In this paper, we propose and construct a new single-loop biofeedback control system with the following main features:

• The power spectrum series of all alpha activity is modeled by an autoregressive (AR) forecasting technique.

• The control system employs a fuzzy logic control to regulate the binaural beat control signal on a forecasting error signal.

• An inverted-U concept [13] is also employed for arousal state determination in the control system so that the subject’s arousal state remains in the alpha state.

Our control system allows users to relax more comfortably by a self-regulated binaural beat sound compared with the ordinary binaural beat stimulation system, in which users struggle to select and control the binaural beat sound by themselves.

2. SYSTEM OVERVIEW

The constructed system is based on a single-loop

biofeedback control system. A system overview is shown in Fig 1.

1) The analog EEG signal is detected by electrodes and sent to the brain wave measurement equipment.

2) The analog EEG signal is converted to binary data and sent to the PC through a RS232C cable.

3) The PC receives the EEG binary data and analyzes them to determine the next auditory stimulus, which it generates as a stereo sound signal.

4) The stereo sound signal is sent to the stereo playback system.

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5) The audio signals are sent to the left and right speakers as binaural beat sounds.

Fig. 1 System overview

By repeating the above procedure, the system

attempts to increase the subject’s alpha activity level using auditory stimulus so that the subject’s arousal state remains in the alpha state.

Fig. 2 Modules for Analysis in PC

The process in the PC consists of the following three

modules shown in Fig. 2: Brain Wave Analyzer, Controller, and Binaural Beat Generator.

1) The EEG binary data are analyzed by the Discrete Fourier Transform in the Brain Wave Analyzer module.

2) Alpha activity is processed in the controller in the following procedures: a. Alpha activities are utilized in the AR

forecasting module to determine the model for forecasting alpha activity.

b. The arousal state model module observes the changes in the alpha amplitude and determines the user’s arousal state.

c. The fuzzy logic controller module regulates an appropriate binaural beat sound control signal based on the user’s arousal state.

3) The binaural beat sound is generated by a Binaural Beat Generator module based on the control signal.

3. SYSTEM CONSTRUCTION

3.1 EEG measurement Alpha wave (7.5-13 Hz) emerges when a person

meditates or feels relaxed. To avoid discomfort by attaching too many

electrodes, we simplified the measuring appliance by using the Brain Builder Unit developed by the Brain Function Research Center that consists of sensors and a data processing unit. Sensors Fp1 and Fp2 are attached to the user’s forehead, and ground reference sensor A1 is clipped to the user’s left earlobe [15]. The data processing unit converts the sensor signal to binary data.

We used the FFTW library [16] to compute the alpha wave band spectral power. The forward Discrete Fourier Transform is applied to compute the 128-bit sampling real number EEG series. The spectral composition of the alpha band was found to be state-dependent, which relates to wakefulness, drowsiness, and the REM sleep brain state [8]. 3.2 Auditory Stimulation

The binaural beat sound, which is one auditory stimulation technique for brainwave entrainment [17], consists of two slightly different frequencies of tones presented to each ear. The amount of difference between the two tones should less than 30 Hz. The third frequency, which equals the difference between the two frequencies, is the result of the interaction of the two tones within the auditory brainstem. This interaction result entrains the electrical rhythms of the brain vibration at the same frequency through the frequency following response (FFR). FFR, which is also called brain wave synchronization, is also referred to as brain wave entrainment by repetitive light or sound frequencies. They are stimuli to which brain wave activity reacts and responds. In our work, we employed the binaural beat sound to entrain EEG signals to the alpha state. The binaural beat sound is generated based on a 400-Hz sound. For example, 10 Hz of binaural beat sound are generated by playing a 395 Hz sine wave at the left ear and a 405 Hz sine wave at the right ear.

By evaluating the response to the five binaural beat sounds, which are set as 6, 8, 10, 12, and 14 Hz, respectively, the controller selects the binaural beat sound with the highest alpha activity level as the binaural beat base frequency.

3.3 Arousal State Model

The term arousal defines the level of consciousness of an individual. Our usual behavior is in the arousal range from awake and attentiveness to deep sleep [18]. The study of the relationship between the arousal state and alpha band amplitude defined the state of arousal range from wakefulness, drowsiness period, and REM sleep [8]. Since we focus on increasing and maintaining

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the alpha activity level, the arousal state is considered with the alpha activity level. We use an inverted-U model to determine and monitor the subject’s arousal state. Arousal studies have shown that in individuals who have a prominent alpha rhythm, the alpha amplitude is highest during the relaxed attentiveness stage, and it declines both when the subject becomes drowsy and when the subject is more aroused [13,14,18,19]. This suggests that the alpha rhythm amplitude follows the inverted-U model of arousal theory originally proposed by [13] to relate a subject’s performance to her/his arousal level.

Fig. 3 Inverted-U model represents relationship

between arousal level and alpha band amplitude Figure 3, a schematic representation of the

inverted-U concept, shows the relationship between arousal and alpha band amplitude [19]. The arousal states are represented by an inverted U-shaped curve (A-B-C), where conditions A, B, and C indicate alert attentiveness, relaxed wakefulness, and drowsiness, respectively. The alpha band amplitude varies biphasically between stimulation and resting. A change in the arousal level during resting causes an increase, no change, or a decrease in the alpha band amplitude depending upon whether the subject is at a high, medium, or low level of arousal, respectively. A change in the arousal level during stimulation corresponds to a change of the alpha band amplitude with low, medium or high level of arousal, respectively.

Consequently, we define the changing direction of the arousal state in two directions: Resting Direction and Stimulation Direction; both directions correspond to the change rate of the alpha amplitude with the inverted-U arousal state model. The arousal state changing directions are related to the changing of the alpha amplitude and the current arousal state. Proper changing of the stimulus frequency is required to keep the user’s arousal state in the medium level of the alpha band arousal state.

3.4 AR Forecasting

An autoregressive (AR) model is employed for the

short-term forecasting of an alpha spectral power time series. Because alpha waves are not regular like sine waves, a sample of an alpha wave is not utilized to predict the future fluctuation of alpha waves. The alpha wave’s pattern is non-stationary, but sine waves are described as stationary [22]. So we convert the alpha wave series of the time domain to the spectral power series of the frequency domain for short-term forecasting. From our observation, the alpha activity spectral power series is analyzed every 60 seconds by the standard methods of statistical analysis, frequency analysis, and time-series analysis. In each period, the alpha activity spectral power series, which is considered stationary, was tested by means and variance analysis, autocorrelation, and partial autocorrelation analysis.

Fig. 4 Autocorrelation EEG spectral power series

Fig. 5 Partial Autocorrelation EEG spectral power

series

Figures 4 and 5 show the autocorrelation and the partial autocorrelation coefficients and their respective lag values that are analyzed by plotting a correlogram to identify the relationship between the time series data. The autocorrelation and partial autocorrelation coefficients of the EEG spectral power series range from 7.5 to 13 Hz against a 10-second lag amount. These figures show irregular patterns with amplitude close to zero with 95% confidence limits (Eq. 1) and random correlation:

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Consequently, the alpha activity spectral power series are linear and stationary with 95% confidence limits. The AR model uses the statistical properties of the past behavior of a variable to predict its future behavior. AR (p) model refers to the autoregressive model of order p (Eq. 2):

Here 1, …, p are the parameters of the model, 0 is a constant, t is an error term, Yt-i is the observed value of the Y series at time t-i, and Yt is the predicted value from the model at time t. From the observation, we decided to employ both the random walk model and the AR (1) model to forecast the alpha activity spectral power series. We employed the Box-Jenkins method [20] for the highest possible accuracy and used Gaussian white noise to generate an error term in the model. The forecasting model is calculated every 60 seconds and used to predict the alpha activity spectral power series for the next 30 seconds. The predicted alpha activity spectral power series will be compared with the raw data to determine the change of the alpha amplitude. 3.5 Fuzzy Logic Controller

Figure 6 shows the structure of the fuzzy logic controller that consists of three components: Preprocessing, Fuzzy controller, and Postprocessing.

Fig. 6 Controller components

The controller inputs are the alpha activity spectral

power series and the forecasting series calculated in the AR forecasting module. The preprocessing component calculates the forecasting model error and averages the alpha activity level that ranges from 7.5 to 13 Hz. The error of the forecasting model is the difference between the alpha activity spectral power series and the forecasting series. The processed data are passed and mapped onto the fuzzy controller.

The fuzzy controller component consists of fuzzification, a fuzzy rule, an inference module, and a defuzzification component. The fuzzification unit converts the average alpha activity level and the error of the forecasting model to the degree of membership. A fuzzy rule unit using the if-then format and an inference

unit using MAX-accumulated concludes the results of the fuzzy sets. An appropriate fuzzy rule with the arousal state is selected in the arousal state model module. Defuzzification using a center of gravity method converts the fuzzy quantities into crisp control signals [21]. We designed three membership functions: Forecasting Error, EEG Level, and Control Signal. Forecasting Error and EEG Level membership functions convert the crisp quantities to fuzzy values in the fuzzification process. The Control Signal membership function converts the fuzzy values to crisp control signals ranging from [-1, 1] in the defuzzification process. Fig 7 shows the fuzzy surface of the fuzzy controller, which illustrates the relationship between forecasting error, EEG level, control signal memberships, and the fuzzy rule.

Fig. 7 Fuzzy surface of controller

The crisp control signal is processed in the Postprocessing component. It uses accumulated forecasting error and a weighted crisp control signal to fire an appropriate binaural beat control signal. The binaural beat sound control signal is generated based on the crisp control signal, the accumulated forecasting error, and the arousal state. The binaural beat sound control signal consists of three signals: increase frequency signal (IFS), same frequency signal (SFS), and decrease frequency signal (DFS). Each signal is used to control the binaural beat frequency by increase, no change, or decrease the binaural beat frequency respectively. The appropriate binaural beat sound control signal is fired based on the arousal state, which is determined in the arousal state model and the crisp control signal.

The arousal state model module in the system starts from the changing direction of the arousal state as Resting Direction, based on the assumption that the user is in a resting state by binaural beat base frequency. First, if the crisp control signal is a subset of [-1, -0.5), the DFS signal will be fired to relax the user in the lower arousal state. On the other hand, if the module determines the user’s arousal state as the Stimulation Direction, the IFS signal will be fired to increase the user’s alpha activities level and stimulate the user to a higher arousal state. Second, if the crisp control signal is a subset of (0.5, 1], a SFS signal will be fired. Finally, if the crisp control signal is a subset of [-0.5, 0.5],

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accumulated forecasting error will be used to clarify the proper binaural beat sound control signal. The appropriate fuzzy rule is also selected in the arousal state model module.

4. EVALUATION EXPERIMENTS

We experimentally evaluated the performance of our constructed system. Subjects wore the sensor on their foreheads and listened to five kinds of binaural beat sounds, 60 seconds per one sound, such as 6, 8, 10, 12, and 14 Hz. During this period, the system evaluated each response for the binaural beat sound. From the responses, the AR forecasting model component determined the binaural beat base frequency.

An example of the results during the stimulation period is shown in Fig. 8, which shows average and 60 seconds moving averages of alpha wave responses for the slow alpha band (blue line), the middle alpha band (red line), and the fast alpha band (green line). The arousal states from the arousal state determination component are shown in the blue circles ranging from A (alert attentiveness) to B (relaxed wakefulness) to C (drowsiness) as the corresponding inverted-U model. The changing rate of alpha amplitude from arousal state determination, Resting Direction (Resting), and Stimulation Direction (Stimulation) are also demonstrated.

5. DISCUSSION

As shown in Fig. 8, the results of the evaluation

experiments of the constructed system confirmed that the binaural beat sound successfully boosted the amplitude of the alpha waves of subjects and maintained

the subject’s alpha level, Especially in the middle alpha band that corresponds

to arousal state model that changes from states A (alert attentiveness) to B (relaxed wakefulness). As the inverted-U model, when alpha activity reaches a high level, the alpha activity level will decreases, corresponding to arousal state moving from a relaxed wakefulness state to a drowsiness state. The system automatically detects the changes of alpha activity levels and alters the changing direction of the arousal state to the stimulation direction. In Fig 8, when the middle alpha band decreases, the system attempts to maintain the alpha wave level by increasing the binaural beat sound frequency to stimulate the subject to the arousal B state.

After stimulation direction, increasing the fast alpha band (the green 60-moving average trend line) shows that the higher binaural beat frequency successfully stimulated the subject to a higher arousal state. The alpha band also increased.

The experiment results confirmed that binaural beat sound is an effective auditory stimulus for brainwave entrainment through FFR. We also confirmed the effectiveness of fuzzy logic control with arousal state model determination for appropriate binaural beat sound control.

6. CONCLUSION

We constructed a real-time single-loop biofeedback

control system for customizing the binaural beat sound. The main features of this system are the forecasting of the alpha activity power spectrum series, the arousal state model determination, fuzzy logic control to

Fig. 8 Average alpha wave response and 60- moving average alpha wave response

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regulate the appropriate binaural beat sound for increasing and maintaining the alpha wave level, and determining whether the user is comfortable and relaxed. The results of the experiments confirmed our constructed system’s effectiveness.

The following two points remain as future work: • More precise arousal state model determination • More fitting for AR model selection

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