The article is devoted to the issues of mathematical modeling of electroencephalographic signals for the problem of impaired human communicative function compensation. In particular, the choice of a mathematical model in the form of a piecewise stationary random process, which is adequate to both the physical nature of such signals and the problem, was made, and the method of processing of electroencephalographic signals was developed to identify signs of speech process in their structure. The developed method is based on the application of methods of spectral-correlation analysis of stationary random processes and the sliding window method. According to the developed method, within each broadcast of the sliding window the calculation of the average estimates of the power spectral density distribution is performed. The values of these assessments are compared with the threshold values for the state of rest and the state when the patient tries to say something. These threshold values are obtained at the preparatory stage, which is described in the article. The experimentally selected electroencephalographic signals were processed and it was found that according to the obtained average estimates of power spectral density distribution it is possible to distinguish between state of rest and the state when patient's tries to say something, i.e. the method allows to detect signs of speech process in electroencephalographic signals. Fisher's criterion was used to assess the reliability of the obtained results, which confirmed the high agreement of the experimental results with theoretical assumptions.
The ability to exchange information between people is provided through communicative function,
in the process of which a significant number of organs are involved that form a complex system [
To solve such problem, technical means of speech correction (speech therapy simulators and visualizers) or technical means of partial compensation of the impaired communicative function can be used. However, the disadvantages of such systems are the lack of medical equipment on the market, the high cost of individual orders, and the long time it takes to adapt the software to an individual patient. Accordingly, the development of new technical means of impaired communicative function compensation is urgent.
It is known that the main source of information about the operation of the system is the signal that is
formed during the functioning of this system. Accordingly, it is possible to solve such problem by
properly processing the biosignals that arise during the speech process. The processing methods will
determine the algorithms of the functioning of the software of technical means for impaired
communicative function compensation. With this approach, it is possible to use for subsequent
processing the electroencephalographic (EEG) signals [
A promising method of impaired communicative function compensation is based on the selection and processing of two groups of biosignals: the first are electromyographic signals taken from the surface of the human neck near the vocal folds; the other group is electroencephalographic signals, locally selected from the areas of the patient's head surface, located near the speech centers. In the structure of the last group of signals, electrical images of nerve impulses will be displayed, which these centers will send to the corresponding organs of the vocal apparatus in the process of implementing the communicative function.
This principle is based on the method, proposed in the works [
Taking into account the fact that the structure of EEG signals will reflect the changes in the electrical activity of the brain that is the result of the necessity of providing mechanisms of selfregulation and functioning of all organs and systems of the human body, implementation of the function of adaptation to the variables of external and internal factors affecting the human body, etc., as well as the representation of the EEG signal in the form of a superposition of all potentials of the action of all neurons with varying degrees of influence on the resulting EEG, the article focuses on the evaluation of the results of this group of biosignals processing.
The processing of signals and the functioning of information systems is implemented at the links of
the triad "model - algorithm - software realization" triads [
The structure of EEG signals should show signs of realization of the communicative function. To substantiate the mathematical model of these signals, the following assumptions are made: 1) areas of EEG signals at rest - in the absence of speech process with constant additional factors (emotional state, human position in space, closed eyes, external conditions) - will be stationary; areas of EEG signals when patient tries to implement the communicative function will be stationary, but with different parameters from similar areas for rest (estimates of mathematical expectation, variance, etc.). The task of detecting the signs manifestations of the process of communicative function realization in the structure of EEG signals will be reduced to the task of detecting the changes in the properties of these biosignals characteristic of such a process.
In this case, it is advisable to use a piecewise stationary random process [
If we extend the model of a piecewise stationary random process to the class of EEG signals, so
such biosignals can be given in the form [
, ∝ (1) ( ) = ( ) ∙ ( − ) , where М(·) is the mathematical expectation
In the case of the sliding window method, the sample from the output signal is processed within each broadcast of the sliding window. To form such a sample, the following expression is proposed: = [ + 1, + ), (2) where is sample from the input signal within sliding window, = 0, , is shift of sliding window, is the width of sliding window.
In the developed method of EEG signals processing, the estimations of the speech process
implementation will be intervals (the method makes it possible to determine the time intervals within
which these estimates will be present). The grounding of choosing the width of a sliding window is
given in the papers [
The specialized Matlab software environment was used to process the experimental data. According to the proposed method of impaired human communicative function compensation, it is necessary to determine the time intervals of the beginning and the end of the speech process (time intervals of communicative function implementation) based on the results of EEG signal processing. To do this, EEG signals with signs of increased brain activity when patients mentally try to say something were loaded into the Matlab environment. Figure 2 shows the EEG signal with signs of increased brain activity after 18 seconds (increased signal amplitude). Rectangles conditionally denote a window that is broadcast in time and within which the signal is processed. The amount of shift of the sliding window in time is equal to the width of the window, i.e. the previous and next window do not overlap.
The assumption is made that the averaged PSDD estimates will be indicators of the beginning and the end of the speech process. At the same time, the value of these averaged estimates was postponed at one time axis together with the original EEG signal. The process itself for the formation of averaged PSDD estimates of the EEG signal within a sliding window is shown in Figure 2.
Twindow are marked broadcasts of the sliding window, within which the EEG signal was processed (Figure 3, a). Within each window, the PSDD estimates of the signal were calculated (Figure 3, b). They were then averaged over frequency and power.
The obtained average estimates were plotted on the time axis in the middle of the time interval, which is equal to the width of the sliding window and the position of each individual broadcast of the window in time (Figure 3, c).
Accordingly, the proposed criterion is sensitive and can be used to set the time intervals of attempts to implement the communicative function by the EEG signal.
As noted above, as a criterion for establishing time intervals of attempts to implement the
communicative function, it is proposed to use it is proposed to use the values of the variation of
averaged PSDD estimates the samples from the EEG signal. In this case, the zero hypothesis H0 is put
forward, that in a state of rest (the communicative function is not realized) the value of variation the
averaged PSDD estimates will have a value of dξ1. For the alternative hypothesis H1, we made the
assumption that at the time interval of attempts to implement the communicative function the values of
variation will have a value of dξ2, however dξ1 ≠ dξ2. That is, on segments of the stationary EEG
signal, the sampled variations of the averaged PSDD estimates will be almost identical and differ for
different pieces of stationary. To evaluate the statistical significance of the processing results and their
reliability, the Fisher's criterion was used [
By this value, using the table data, we can assess the significance of the results of the EEG signals processing, construct the axis of significance, form the conclusion of accepting the hypothesis H0 or rejecting it in favor of the hypothesis H1 and, accordingly, assessing the reliability of the decision.
At the statistical processing of data is usually asked by some level of significance α, which
characterizes the probability of appearance the error of first kind. Applying Fisher's criterion, we can
estimate the level of significance of the processing results. If we denote the probability of error in the
second kind through β, then the value of 1-β is called the power of the criterion [
To use Fischer's criterion, the sample variations of the sequence of averaged PSDD estimates was evaluated. In Figure 5 marked by d1 – d5 the sample variations with volume of 10 values, and: d1=4,2465 uV2, d2=4,4063 uV2, d3=34,1038 uV2, d4=94,3297 uV2, d5=103,507 uV2. By the requirement of the process of calculating the value of Fisher's criterion is the ratio of the greater value of the variation to the smaller. Four values of Fischer's criterion were calculated:
F d2 1,0376; F2 d3 7,7398; F3 d4 2,7659; F d5 1,0973; 1 d1 d2 d3 4 d4
The value of criterion F1 was calculated for two sample variations, corresponding to the region of the EEG signal in the state of rest. In this case, the null hypothesis about the insignificant difference between the two variations must be confirmed.
The value of criterion F2 was calculated for two sample variations, the first of which corresponds to the region of the EEG signal in the state of rest, and the second - in the state of implementation the communicative function. In this case, the null hypothesis should be rejected in favor of the alternative since the difference between the values of sample variances is significant.
The values of criterion F3 and F4 were calculated for sample variations corresponding to the region of the EEG signal in the state of implementation the communicative function. In this case, the null hypothesis about the insignificant difference between these variations must also be confirmed.
To confirm the made assumptions, it is necessary that the values F , F3 and F4 fell into the zone 1 of insignificance of the Fischer's criterion, and value F2 – into the zone of significance. For this purpose, an axis of significance of the Fischer's criterion was constructed (Figure 6).
For the degrees of freedom n-1=9 and m-1=9 (n=m=10) of the samples according to the tabular
data [
In Figure 7 the calculated criteria values F1 - F4 are delayed and it was found that the values of the criteria F1 , F3 and F4 fall into the zone of insignificance, and value F2 – into the zone of significance of Fisher's criterion.
Accordingly, the use of the proposed criterion for determining the time intervals of implementation the communicative function by the variation of averaged PSDD estimates of the samples from the EEG signals gives the possibility with the reliability of 1-α=1-0,01=0,99 or in relative units - 99% increase brain activity in the process of communicative function implementing.
Previously, the assumption was made that the accuracy of determining the state of the process of communicative function implementation would increase if the next and previous windows, within which the averaged PSDD estimates are calculated, will be overlapped by the value tau. To confirm this assumption, an estimation of the decision-making reliability using Fisher's criterion was made, for which the estimation of sample variations was calculated for the averaged PSDD estimates at tau=0,2 Twindow . variations d1 – d3 at tau=0,2 Twindow
In this case, the volume of samples was 100 values. For this number of freedom degrees by the
tabular data [
2
F1 dd12 5,7698; F2 dd23 1,0701;
The obtained values are deferred to the significance axis (Figure 8).
From Figure 8 it can be concluded that the value of F1 is much further on the axis of the value Fcr at р=0,01 and accordingly, at larger volumes of samples, for which sample variations are calculated, the reliability of the decision is increasing.
In accordance with a grounded mathematical model of EEG signals in the form of a piecewise stationary random process, the method of statistical processing of such signals is developed for the task of detecting the time intervals of implementation the communicative function. The developed method is based on the application of methods of spectral correlation analysis and the method of a sliding window.
To establish the time intervals of implementation the communicative function by the EEG signal, a calculation of PSDD estimates was performed within each broadkast of a sliding window. Then the averaging of these estimates was calculated. It is established that the proposed averaged PSDD estimates are sensitive to manifestations of changes in brain activity in the structure of EEG signals in the implementation of the human communicative function. As a criterion for determining the time intervals of implementation the communicative function, the variation of the averaged PSDD estimates is used. It is established that the values of variation increase by more than an order of magnitude with the presence of signs of brain activity. The proposed criterion is sensitive.
The reliability of obtained results is evaluated on the basis of Fisher's criterion. It was established that the use of the proposed criterion for determining the time intervals of implementation the communicative function by the values of variation of the averaged PSDD estimates of the samples from the EEG signals gives an opportunity to establish with 99% reliability the state of increasing brain activity in the process of implementing the communicative function.