Keywords

1 Introduction

Over the last years development of brain-machine interfaces (BCI) of different types has become not only like an experimental trend but also more and more of practical use. The first reference to the brain-machine interface creation is primarily connected to the capability development of the electroencephalography and attempts to interpret isolated impulses of brain signals [1]. The basis of all brain-computer interfaces is a biofeedback training method providing information acquisition about current state of this or that physiological function for human training of a conscious brain control and control of this function [2]. Biofeedback utilization involves the use or either positive or negative reinforcement [3].

Electroencephalogram data as well as electromyography or analysis of a human’s ocular motility can be used for the brain-machine interface implementation. Both real and false responses, used for BCI development while patient’s rehabilitation after nervous system damage can be used as brain responses [4].

One of the ways of realization of such systems is the usage of steady-state visual evoked potentials (SSVEP). Registration of the evoked brain potentials (EP) is a non-invasive method of testing functions of the central nervous system [5]. Evoked potentials are brain electrical responses to visual, auditory or sensory stimuli. The important thing is that the signals of the evoked potentials on any irritant are similar to signals generated in case when a person acts as an irritant. SSVEP are evoked potentials of the brain on visual stimuli, where in most cases the following can be used as an irritant: screen image, image in AR goggles or LED glow of different flicker frequencies. Flicker frequency range of an irritant establishes a command set, which can be used for development of brain-computer interfaces or human-machine interactions.

Electroencephalogram (EEG) is a graphical presentation of an oscillatory electrical process registered when electrodes being placed on a brain or a scalp surface. Usually signals are recorded from electrodes to be placed on a scalp surface of a patient. EEG registration required usage of different sets of electrodes from 8 to 75 and different placement on a scalp [6].

The maim problems of using steady-state visual evoked potentials are spontaneous EEG due to external irritants and low signal-to-noise ratio. While the first problem can be solved only by organizational measures – a patient has to be concentrated on an object during the procedure, increase of signal-to-noise ratio often requires coherent integration and/or averaging on a software or hardware level. In addition, it is relevant to reduce an analysis window while highlighting EEG state as it contributes to development of brain-computer interfaces and human-machine interaction systems on the biofeedback basis, which work in real-time mode.

Analysis of research articles and references at scientific conferences in the area of development [7,8,9], implementation [10,11,12] and practical application [13,14,15,16] of human-machine interaction interfaces and development of brain-computer interfaces shows that relevance of recording of steady-state visual evoked potentials only increases with accuracy increase of their highlighting in the EEG signal.

2 Methods and Results

This article looks at the method which shows the highest results from the perspective of various researchers - multivariate synchronization index method [17,18,19,20]. Synchronization principle of multichannel EEG and reference signals, meant to be in line with visual stimulus frequency (photostimulation frequency) is a core of the multivariate synchronization index method. Selection of reference signals are based on Eq. 1.

$$ Y\left( t \right) = \left[ {\begin{array}{*{20}l} {sin(2\pi ft)} \hfill \\ {cos(2\pi ft)} \hfill \\ {...} \hfill \\ {sin(2\pi Nft)} \hfill \\ {cos(2\pi Nft)} \hfill \\ \end{array} } \right],t = \frac{1}{{F_{s} }},\frac{2}{{F_{s} }},...\frac{K}{{F_{s} }} $$
(1)

where N – the harmonic sequence number, K – the number of samples, Fs – the sampling frequency, Y(t) – the reference signal, X(t) – the original EEG signal. Initially, the correlation matrix between two signals is calculated using Eqs. 2–3.

$$ D_{11} = \left( \frac{1}{M} \right)XX^{T} $$
(2)
$$ D_{22} = \left( \frac{1}{M} \right)YY^{T} $$
(3)
$$ D_{21} = D_{12} = \left( \frac{1}{M} \right)XY^{T} $$
(4)

A linear transformation is calculated to eliminate the effect of autocorrelation on the measure of synchronization (Eq. 5).

$$ T = \left[ {\begin{array}{*{20}c} {\frac{1}{{\sqrt {D_{11} } }}} & 0 \\ 0 & {\frac{1}{{\sqrt {D_{22} } }}} \\ \end{array} } \right] $$
(5)

After that the correlation matrix is calculated by the Eq. 6.

$$ S = \left[ {\begin{array}{*{20}c} {I_{1 \times 1} } & {\frac{1}{{\sqrt {D_{11} } }}D_{12} \frac{1}{{\sqrt {D_{22} } }}} \\ {\frac{1}{{\sqrt {D_{22} } }}D_{21} \frac{1}{{\sqrt {D_{11} } }}} & {I_{{2N_{h} \times 2N_{h} }} } \\ \end{array} } \right] $$
(6)

Then multivariate synchronization index is determined by the Eq. 7.

$$ R_{i} = 1 + \frac{{\sum \lambda_{i}^{^{\prime}} \log (\lambda_{i}^{^{\prime}} )}}{\log (P)} $$
(7)

where \(\lambda_{i}^{^{\prime}}\) - normalized eigenvalues S, P = N + Nh и Nh note the number of lines in the reference signal B(t). The frequency of photostimulation is defined as the frequency corresponding to the maximum value of R.

The use of multivariate synchronization index for highlighting of steady-state visual evoked potentials within brain-computer interfaces makes it possible to use signals from several EEG channels at a time that could in perspective contribute to development of human-machine interaction systems of higher quality (Fig. 1).

Fig. 1.
figure 1

Scheme of the use of multivariate synchronization index within brain-computer interfaces.

Full size image

Butterworth filter is a filter that is different in that its amplitude-frequency characteristic (AFC) is max smooth on band pass frequencies [21]. Chebyshev filter is a filter that is different in that its AFC possesses steeper roll-off and more significant pulsations on band-pass frequencies (Chebyshev filter of type I) and stopband frequencies (Chebyshev filter of type II) than those of filters of other types. They can be used, where with the help of the filter of a small order it is required to provide suppression of frequencies from the stopband and at the same time smoothness of AFC on band-pass and stopband frequencies is not of a big importance [22]. Elliptic filter is a filter that is different in that its AFC possesses very steep roll-off, that it why with the help of this filter it becomes possible to achieve more efficient frequency separation in comparison with other filters [23]. Bessel filter is a filter, which specific feature is a maximally smooth group delay such that waveform of a filtrated signal in output of this filter within the band pass remains almost the same [24].

EEG signals with steady-state visual evoked potentials were explored basing on the multivariate synchronization index with the use of the MATLAB [25] application program package. 60 signals of 30 adult patients, men and women of various age groups without contraindications to EEG and photostimulation reading were studied. LED glow was used as a source of photostimulation. All signals were preliminarily subjected to coherent integration in order to increase the signal-to-noise ratio because a big number of noises triggered by the brain spontaneous activity is typical for clear EEG signals. Photostimulation frequency for the signals from the first group amounted to 8 Hz and 14 Hz for the second group. Discretization frequency for all signals amounted to 5 kHz. Each signal was divided into windows of 500, 1000 and 1500 samples, which is equivalent of the analysis epoch of 100, 200 and 300 ms respectively. Band-pass filtering with the usage of the Butterworth filter, Chebyshev filter of type I, Chebyshev filter of type II, elliptic filter and Bessel filter was preliminarily used for each analysis window. Filter order used lay in the range from 1 to 4. Band edges of the filter for signals with required frequency of 8 Hz were set as 4 Hz and 12 Hz. Band edges of the filter for signals with required frequency of 14 Hz were set as 7 Hz and 21 Hz. Recognition accuracy was estimated as a window quantity ratio, where required frequency was correctly defined in regard to the whole number of windows within the signal. All signals were comprised of 15000 samples. The following frequencies were used as competing frequencies in both cases: 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 Hz.

At the first stage of the research signals with 1–4 order filters and without them were processed. As a comparison, the average value of the state recognition accuracy was set as a metrics. It has been noticed that the results for all filters except Bessel filter are getting worse with increase of filter order. In view of this, the use of Butterworth filter, Chebyshev filter and elliptic filter for the fourth order resulted in a situation where almost none of states were correctly recognized. The higher analysis epoch is, the less relevance of the filtering use is, as the recognition accuracy without filtration for the window of 1000 samples and more shows the result of 0.94 and higher. The results of the signal processing within the single-channel mode are presented in the table 1. In the tables below the highest results within one category are bolded.

Table 1. Single-channel mode results.
Full size table

The results obtained within the dual-channel mode of the multivariate synchronization index correspond to the results for the single-channel mode. With increase of the analysis epoch the highest results were obtained without filtration and recognition accuracy for analysis window of 1000 samples showed the result of at least 0.9. The results of the signal processing within the dual-channel mode are presented in the Table 2.

Table 2. Dual-channel mode results.
Full size table

The results obtained within the four-channel mode of the multivariate synchronization index were mixed. With the photostimulation frequency equal to 8 Hz the results correspond to the single-channel and dual-channel modes of filtration. And for the photostimulation frequency equal to 14 Hz with the window of 1000 samples the highest results are obtained with the use of Chebyshev filter and elliptic filter. In the authors’ opinion, it can be ascribed to non-optimal choice of channels for the analysis. For the rest the results correspond to the preceding frequency highlighting modes with the help of the multivariate synchronization index. The results of the signal processing within the four-channel mode are presented in the Table 3.

Table 3. Four-channel mode results.
Full size table

3 Conclusion

This research was made to discover influence of prefiltration of signals when using the multivariate synchronization index to highlight SSVEP in EEG within different MSI modes. Single-channel, dual-channel as well as four-channel modes of the multivariate synchronization index were studied. It is shown that for the current research the use of the prefiltration is required with the analysis window of 500 samples, which is equal to 100 ms. When the analysis epoch increases up to 1000 samples (equal to 200 ms) and higher the use of prefiltration becomes no longer of relevance, except Bessel filter, the use of which shows the results similar to recognition without filtration. Besides, it is relevant to use filters of the first order, because the higher order is, the worse results become. On the basis of the results obtained the authors consider the use of Chebyshev filter of type II as the most efficient as it shows the best results with the analysis window of 500 samples in comparison with elliptic filter and Chebyshev filter of type I, but it also shows higher results when increasing analysis window. In the future it makes sense to examine EEG state recognition with sufficient accuracy on a smaller analysis window, as decrease of analysis window makes it possible to count on integration of human-machine interaction systems running in real-time mode on the basis of the biofeedback. In this case sufficient accuracy is considered as 0.5 and higher because in this case the required frequency will be selected among the competing frequencies.