Method for assessing the extent of neurodegeneration by measuring brain signal complexity

Abstract

The invention relates to a method for determining neurodegeneration of the brain by reading bioelectrical brain data. Brain signals are obtained. The obtained signals are digitized, unless already digitized. A digitized brain signal from each sensor is converted into a topological space object in the form of a piecewise linear curve of the trace of each digitized signal from each corresponding sensor. The rank of the curves is calculated as the maximum number of eigenvalues of the scattering matrix of a curve such that the other eigenvalues can be neglected. The number of active sources of each obtained brain signal is determined according to the rank of the corresponding curve, wherein if the number of such sources for at least one brain signal is less than a given number, this indicates neurodegeneration. The invention makes it possible to increase the speed of determining neurodegeneration and assessing the extent thereof by measuring brain signal complexity, while also maintaining a high level of accuracy.

Description

[0001] A METHOD FOR ASSESSING THE DEGREE OF NEURODEGENERATION BY MEASURING SIGNAL COMPLEXITY IN THE BRAIN

[0002] AREA OF TECHNOLOGY

[0003] The invention relates to the field of detecting brain states, in particular to equipment and methods for detecting neurodegeneration of the brain by reading its bioelectrical data.

[0004] LEVEL OF TECHNOLOGY

[0005] A brain-computer interface (BCI) is known from prior art (Russian Patent No. 2823580) and includes a specialized input device for obtaining electromagnetic or other information about the brain. The BCI includes an analog-to-digital converter, microcontrollers for processing information, and may contain software and hardware data converters, such as modules for obtaining frequency spectra and spatial and temporal domain data in the brain signal, a GPU / TPU / CPU / neuromorphic processor for training and operating a classifier, which may be integrated into the BCI or located separately, including on a training server, a hardware module for storing and operating the trained / trained / customized classifier, and a neural network.In this case, neural networks are used to process the received brain signals. An additional computing device containing a GPU / TPU / CPU / neuromorphic processor, or a training server, is used for training and operation. Incorporating these additional modules into the interface device significantly increases energy consumption and signal processing time, thereby preventing real-time processing and classification of brain signals. This system configuration also prevents the entire neural interface from being placed on the user's head, thereby ensuring wearable mobility and autonomy. Therefore, the disadvantage of this solution is the use of a graphics processor (or other additional computing devices) for its operation and, consequently, the low data recognition speed, which precludes real-time signal processing. Furthermore, the interface in question suffers from low energy efficiency, limited mobility, and limited autonomy.The proposed technical solution is aimed at eliminating the shortcomings of the current state of technology and differs from previously known ones in that it provides higher signal processing speed, autonomy, mobility, and increased energy efficiency while maintaining or increasing the accuracy of brain signal recognition, compared to other solutions of the current state of technology.

[0006] The proposed technical solution offers a solution for expanding the functionality of current technology and differs from previously known ones in that it allows for the storage and activation of mental states through the use of a neural interface with feedback.

[0007] DISCLOSURE OF THE INVENTION

[0008] The technical problem solved by the claimed invention is to increase the speed of assessing the degree of neurodegeneration by measuring the complexity of the signal in the brain while achieving high accuracy.

[0009] The technical result of the claimed invention is to increase the speed of determining neurodegeneration and assessing its degree by measuring the complexity of the signal in the brain while achieving high accuracy.

[0010] The claimed technical result is achieved by receiving brain signals; digitizing the received signals if such signals are not digitized; transforming the digitized brain signal from each sensor into a topological space object—a piecewise linear Buchstaber unfolding curve of each digitized signal from the corresponding sensor; calculating the rank of such curves as the maximum number of eigenvalues ​​of the scattering matrix of the curve such that the remaining eigenvalues ​​can be neglected; determining the number of active sources of each received brain signal based on the rank of the corresponding curve; and if the number of such sources for at least one brain signal is less than a given number corresponding to the number of active sources of brain signals for a given brain state for a person without neurodegeneration, then neurodegeneration occurs. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] The invention will be better understood from the description, which is not limiting in nature and is given with reference to the accompanying drawings.

[0012] Fig. 1 illustrates the logarithmic scale of eigenvalues ​​for a signal from a sensor located in the left and front part of the head of a healthy person in a waking state (on the ordinate axis is the binary logarithm of the eigenvalues ​​of the scattering matrix, and on the abscissa axis is the number of eigenvectors);

[0013] Fig. 2 illustrates the logarithmic scale of eigenvalues ​​for a signal from a sensor located in the right parietal part of the head of a healthy person in a waking state (on the ordinate axis is the binary logarithm of the eigenvalues ​​of the scattering matrix, and on the abscissa axis is the number of eigenvectors).

[0014] Fig. 3 illustrates the comparison of the original series f with the series f' r=2 , reconstructed from the first two components of the signal of a healthy person in a waking state;

[0015] Fig. 4 illustrates a comparison of the original series f with the series f' r=4 , reconstructed from the first four components of the signal of a healthy person in a waking state;

[0016] Fig. 5 illustrates a comparison of the original series f with the series f' r=8 , reconstructed from the first eight components of the signal of a healthy person in a waking state;

[0017] Fig. 6 illustrates the logarithmic scale of eigenvalues ​​for the signal from a sensor located in the left and front part of the head of a person diagnosed with alcoholism in the waking state (on the ordinate axis is the binary logarithm of the eigenvalues ​​of the scattering matrix, and on the abscissa axis is the number of eigenvectors);

[0018] Fig. 7 illustrates a comparison of the original series f with the series f' r=4 , reconstructed from the first four components of the signal of a person diagnosed with alcoholism in a waking state.

[0019] The figures indicate: 1 - the inflection point for a healthy person in a waking state (left and front parts of the head);

[0020] 2 - the initial series f of a healthy person in a waking state;

[0021] 3 - time series f2 of a healthy person in a waking state; 4 - the difference between the time series f and f2 of a healthy person in a waking state;

[0022] 5 - the difference between the time series f and

[0023]

[0024] 4a healthy person in a waking state;

[0025] 6 - the difference between time series f and f в a healthy person in a waking state;

[0026] 7 - the inflection point for a person diagnosed with alcoholism in a waking state;

[0027] 8 - the difference between the time series f and

[0028]

[0029] 4 people diagnosed with alcoholism in a waking state;

[0030] 9 is the inflection point for a healthy person in a waking state.

[0031] IMPLEMENTATION OF THE INVENTION

[0032] The following detailed description of the invention includes numerous implementation details intended to provide a clear understanding of the present invention. However, one skilled in the art will readily appreciate how the present invention may be utilized with or without these implementation details. In other instances, well-known methods, procedures, and components have not been described in detail to avoid unnecessarily obscuring the features of the present invention.

[0033] Furthermore, it will be clear from the foregoing description that the invention is not limited to the embodiment described. Numerous possible modifications, changes, variations, and substitutions, while preserving the spirit and form of the present invention, will be apparent to those skilled in the art.

[0034] The proposed method is implemented using a hardware and software system for detecting signs of neurodegeneration in signals received from at least one electromagnetic signal source in the brain. The data can be presented as time series obtained from the electromagnetic signal.

[0035] The system may comprise a neural interface (input device). The neural interface (input device) is a hardware and software complex and comprises a data acquisition unit with 8 (or 16, or 32, depending on the counting number) gold-plated electrodes with a spring mechanism, arranged according to the international 10-10 / 10-20 schemes. The neural interface comprises a power source, which may be a battery or other means. The neural interface also comprises means for converting an analog signal into digital form; for example, the neural interface may comprise 2 data digitization units with microcontrollers featuring an ADS1299 analog-to-digital converter (ADC). The neural interface may comprise data packaging means, for example, 3 data packaging units according to the author's protocol, which includes adding to the time series of digitized data marks indicating the beginning and end of a packet, a hash function, a numerical value of the time series length, and service information about the device.

[0036] The neural interface also has a data conversion and evaluation unit implemented on programmable logic integrated circuits, such as the Xilinx family, or on microcontrollers, such as the ESP32.

[0037] To transmit data from the neural interface, a data transmission unit / units are used via wireless communication, such as Bluetooth. One implementation of the present invention may utilize a data transmission unit using an ESP microcontroller with an integrated BLE 5.2 module. The neural interface may also include a memory unit for storing a state database. Data obtained in the evaluation unit can be sent to a mobile computer via the BLE protocol for visualization and further analysis of the classified data.

[0038] The system may additionally comprise a mobile (smartphone, laptop) or desktop (desktop, server) computing device. The smartphone may have the following specifications: Android version 12 (>= 12 recommended), Android API level >= 31, NPU support, 4 GB RAM (8 GB recommended), and a screen >= 7 inches. The mobile computing device receives data obtained in the evaluation unit via the BLE protocol. The mobile computing device can also receive a vector of values ​​and transmit data, for example, via a gigabit Wi-Fi protocol to other devices, and display the evaluation results and other data via display elements (e.g., a smartphone screen). An application implementing the above functions may be installed on the mobile device. The desktop computing device may be equipped with a graphics processing unit (GPU) and a central processing unit (CPU).The stationary computer has data storage with a RAID 5 data loss protection unit. The stationary computer can be a desktop computer or a server. The stationary and mobile computers can operate in tandem. Moreover, both the stationary and mobile computers are designed with the ability to receive brain signal data, for example, via the internet.

[0039] In humans, 1-25 electromagnetic signal generators (EMGs) can be identified in the brain. These generators are located in the cortical and subcortical structures of the brain. These generators represent a morphofunctional agglomeration of neurons that simultaneously perform a common brain function, which is represented by the generation of a quasi-periodic signal. The number and arrangement of EMGs varies depending on the brain's state and is individualized. When the brain is in a certain state at a given moment in time, a certain number of oscillators (EMGs) are active. Each oscillator is represented by a sum of smaller EMGs (neurons). The signals received from each neurointerface sensor represent a combination of signals from active oscillators in the brain. Thus, brain states are characterized by a combination of oscillator activity.This representation of brain signals as a sum of signals from nearly periodic signal generators makes it possible to describe the brain signal as a set of harmonic signals described by nearly periodic functions.

[0040] The authors proposed approximating electromagnetic signals on the surface of the cerebral cortex with harmonic signals propagating across the surface of the cerebral cortex from sources of electromagnetic activity—oscillators. Brain states can be described by changes in the number and nature of oscillators.

[0041] The authors of the invention proposed to approximate the electromagnetic signal arriving at the sensors of the neural interface on the surface of the head with a system of differential equations with constant coefficients for each sensor of the following type: y(t) =

[0042]

[0043] Yn a n (t)e Ant sin( <i) n t + <р п ), where an (t) - polynomials, m is the number of oscillators.

[0044] The authors of the invention have established that the complexity of brain signals can be estimated as the number of harmonic components in the signal received by the neural interface sensors, which corresponds to the number of active signal sources (oscillators) in the brain. Moreover, the number of harmonic components in the signal (the number of active signal sources (oscillators) in the brain) differs between healthy individuals and individuals with neurodegeneration. (Further, healthy individuals are defined as individuals who have not been diagnosed with any disorders of the nervous system.) Accordingly, by estimating the number of active signal sources (oscillators) in the human brain, it is possible to assess the degree of neurodegeneration. The proposed invention proposes assessing the degree of neurodegeneration by determining the number of oscillators in the read brain signal.

[0045] The analog signals from the brain read by the neurointerface sensors have a range of 5-100 microvolts (μV) and 1-100 x 10 Л (-15) Tesla (T). According to the results of biophysics, the frequency spectrum of the physiological electromagnetic signal of the brain is located in the range of 1-100 Hz and 1-100 x 10 Л(-15) Tesla (T). Selecting a frequency of 250 Hz is sufficient for signal analysis. The ADC converts the analog signal with a sampling frequency of 250 Hz. One measurement is packed into a 32-bit vector, of which 26 bits are informative and 6 bits are service. The signal error is 3 bits. Analysis of real data shows that all 26 bits are used significantly. The vector of values ​​is packed every 100 milliseconds (ms) in the data packing block and sent to the evaluation block. In the evaluation block, the number of oscillators of the brain signal is determined and the degree of neurodegeneration is assessed. For this purpose, the digitized physiological electromagnetic signal of the brain is represented as an object of topological space, the topological properties of the resulting time series scans are evaluated, and the number of oscillators is determined. As stated earlier, to determine the number of oscillators, the brain signal (time series) from each sensor is converted into an object of topological space and analyzed in this space.The analysis is based on the transition from a time series to a multidimensional unfolding—a piecewise linear curve in a multidimensional space, the points of which correspond to segments of the original series—and the analysis of the projections of this curve onto the subspaces spanned by the principal components (vectors) of the corresponding scattering matrix.

[0046] A time series f = (f1, ..., fN) is a sequence of values ​​f(t), with a fixed time interval At.

[0047] It is necessary to determine the number of oscillators in each digitized physiological electromagnetic signal from the brain, obtained from a sensor or sensors as a time series (digitized sequence). This requires transforming the brain signal using the method described below.

[0048] A digitalized discrete brain signal is obtained in the form of real-valued time series f 1 = (f 1 i, TN), f s = (f s i, f sN) of fixed length N, where s is the number of neural interface sensors. The sampling frequency of the neural interface's analog-to-digital converter, according to Kotelnikov's theorem, imposes a limit on the signal frequencies available for analysis.

[0049] Next, from each time series, a multidimensional (n-dimensional) scan is obtained in the form of a Hankel matrix using the Buchstaber method.

[0050] If there is no a priori information about the expected number of signal sources, the maximum possible scan window n is selected. The maximum possible initial value n = Q((N + 1) / 2), where Q is the integer part. This results in a Hankel matrix of size n x p, where p = N - n + 1, with rank r < n.

[0051] In this case, the n-dimensional scan Xf = Xf(N, n) of the time series f = (f1, ..., fN) in the n-dimensional Euclidean space is an oriented piecewise linear curve obtained by successively connecting the vectors Xi, X2, Xp, where Xi = (fi, fi+1, f i+n-1). Thus, the piecewise linear curve can be represented as a set of column vectors as Xf = { X1... X р}.

[0052] From s time series (obtained from s sensors), time series scans are obtained in the form of Xf curves (namely, Xf curves 1 .. Xf s taking into account the index with the sensor number) with nodes that are described by the Hankel matrix. Thus, the piecewise linear curve Xf of the Buchstaber unfolding of each time series of the corresponding sensor can be written as a matrix, where the columns of the matrix are n-dimensional vectors or nodes of the curve Xf, and the resulting matrix of p columns and n rows is a Hankel matrix of the form:

[0053]

[0054] Next, scattering matrices W (one matrix for each sensor) of the Xf curves (obtained from the sensors) are formed. Moreover, the scattering matrix W = W j of the curve Xf = { Xi... X р} is called the Gram matrix of the population X =

[0055] {Xfc}, where / ( y =< Xi, Xj > is the standard scalar product, X L = X^ —

[0056] X, where X = 1(X1+ +X2+...+X р ).

[0057] Obtain the eigenvalues ​​of the scattering matrix W and the eigenvectors for the Buchstaber scans from each channel (sensor) of the neural interface data.

[0058] The rank r of the curves Xf is calculated as the maximum number of eigenvalues ​​such that the remaining eigenvalues ​​can be neglected, as follows:

[0059] a) Filter the scan Xf using the subspaces M г(n, p), spanned by r eigenvectors, r ∈ {1, n}. The output of this step is r x p-matrices that describe the nodes of the projections of the unfolding Xf onto the subspaces spanned by r eigenvectors. Consequently, r x p-matrices are obtained from the elements of the matrix Hf such that all elements that do not lie in the subspace M г (p,r), are discarded.

[0060] b) Reconstruct the time series using the previously obtained ghr matrices using the Buchstaber formula below:1 k

[0061] TZ ai.k-i+1 1 < k < n

[0062] Ki=l

[0063] 1 p

[0064] - Z a-kk-i+in < k < p

[0065] n i=l

[0066] IN—k+1

[0067] . N - n + 1 D a i+kp,p-i+lP k < N

[0068]

[0069] where a 0

[0070] The output of this step is a time series f'= (f'i, FN), the scans of which lie in r-dimensional subspaces of M г (п,р). The resulting r-th time series f' is considered the r-th model (approximation) of the original series f. Thus, for different r (for example, for r = 2, 4, 6, or 8), different models (approximations) of f are obtained. r

[0071]

[0072] =2 ; f' r=4 ; f' r=6 ; f' r=Q original series f.

[0073] c) A comparison is made between the original series f and the reconstructed time series of the r-th model f', whose piecewise linear curve lies entirely in r-dimensional space. The difference between these series is assessed for compliance with noise criteria.

[0074] At this step, a minimax problem is solved, which selects r (the spatial dimension) based on a compromise: we obtain the minimum r such that the difference between the reconstructed and original time series satisfies the noise criteria. As mentioned earlier, when working with neural interfaces, the limiting factor in signal accuracy is the operating characteristics of the analog-to-digital converter (ADC). The manufacturer provides information on noise characteristics in the neural interface ADC specification. The noise amplitude is taken into account when solving the minimax problem.

[0075] The noise component may have values ​​of 2 decibels or lower, so the difference between the reconstructed and original time series should be less than 2 decibels. However, other noise criterion values ​​may be selected differently in other embodiments of the invention; for example, the noise criterion may be specified by the user via an app on a mobile computing device or otherwise. The rank r (or ε-rank r) corresponds to the number of active signal sources (oscillators) as follows: m = r / k, where k is the dimension of the space in which the signal arriving at a given sensor is generated.

[0076] When modeling a signal in two-dimensional space, for example, reflecting the propagation of a signal over the surface of the cerebral cortex, the formula for the honor of brain oscillators has the form: m = r / 2.

[0077] When modeling a signal in three-dimensional space, for example, reflecting the propagation of a signal from deep brain structures to neural interface sensors on the surface of the head, the formula for calculating brain oscillators is: m = r / 3.

[0078] The output of the step is the number of active oscillators m for a given sensor.

[0079] The calculated oscillator count is then compared with the oscillator count of a healthy individual in a quiet, waking state to determine the degree of neurodegeneration. If the subject's number of activated oscillators is lower than that of a healthy individual, neurodegeneration has occurred, the degree of which can be assessed by the difference between the healthy individual's oscillator count and the subject's activated oscillators.

[0080] Example 1 of the invention shows the determination of the signal complexity (number of oscillators) of a healthy person by obtaining data through the neural interface described above.

[0081] In this example, a neurointerface with 16 electrodes (sensors) was arranged according to the international 10-20 scheme.

[0082] 1) Data were recorded on 20 healthy subjects (without diagnosed nervous system disorders). Each subject provided 120 1-second recordings. These recordings corresponded to a calm, waking state. The recordings were digitized using data digitization units. The digitized data consisted of 1-second time series with a signal sampling frequency of 256 Hz, meaning the time series consisted of 256 values. Thus, the signal from the neural interface was obtained as a real-valued time series f with a length of N = 256 samples.

[0083] 2) Next, we obtained the scans of the time series f = (f1, ..., fN) for N = 256, n = 16. We calculated the scattering matrix, calculated the eigenvalues ​​of the scattering matrix W, and obtained the eigenvectors for the scans from each channel (sensor) of the neural interface data.

[0084] By analyzing the data (including a priori information about the signal), we established a threshold for the eigenvalues ​​of the scattering matrix W (the dimension of the information subspace). This information could include the approximate number of oscillators generating the signal, the presence of noise in the signal, and the results of previous analysis of similar signals. The threshold value for the eigenvalues ​​limits the number of obtained r-th time series f' r, considered as the r-th model (approximation) of the original series f, such that the maximum r corresponds to the threshold for the eigenvalues. The threshold can be set by default to 8 (the value of r for a healthy person) to reduce calculations and improve performance, and in case of a discrepancy between the differences in the values ​​of the series f and f' r=maxThe noise criterion is adjusted upward. The threshold for the eigenvalues ​​can also be established by analyzing the logarithmic scale of the eigenvalues ​​for a signal from a specific sensor, where the ordinate axis is the binary logarithm of the eigenvalues ​​of the scattering matrix, and the abscissa axis is the number of eigenvectors. Figure 1 shows the logarithmic scale of the eigenvalues ​​for a signal from a sensor located in the left and frontal parts of the head, and Figure 2 shows the signal from a sensor located in the right parietal part. As can be seen from these dependencies, eight eigenvectors on the graph correspond to an inflection point (Figs. 1, 2, pos. 1, 9), indicating that the eigenvalues ​​of the scattering matrix W with more than 8 eigenvectors can be ignored, since the corresponding brain signal components clearly do not meet the noise criterion (less than 2 dB).

[0085] The above graphs can be displayed on a mobile or stationary device (smartphone or computer screen), and the user can be prompted to set a threshold based on the x-axis value corresponding to the inflection point (Figs. 1 and 2, pos. 1), or the threshold can be set automatically by calculating the inflection point by the system. This eliminates the need for redundant calculations, for example, for Гмах=9, 10, 16, which increases the performance of the method. In this implementation example, the information subspace (eigenvalue threshold) has a dimension of 8 (Figs. 1 and 2, pos. 1). Accordingly, it is assumed that Гмах=8, and the NUMBER of oscillators ГПмах= Гмах / k.

[0086] 3) Next, we filtered the scan data using the subspace M г(n,p), spanned by 8 eigenvectors for n = 16. This yields matrices that describe the nodes of the projections of the unfolding Xf onto the subspaces spanned by the eigenvectors. This reduces the dimensionality of the data.

[0087] We reconstruct the time series by estimating the contribution of each pair of signal components lying in the corresponding subspaces formed by the eigenvectors. We obtain the time series f' r=2 ; f' r=4 ; f' r=8 which are models (approximations) of the original series f.

[0088] Fig. 3 shows a comparison of the original series f with the series f' r=2 , reconstructed from the first two components of the signal (lying in a two-dimensional subspace formed by 2 eigenvectors), where pos. 2 denotes the original series f, pos. 3 denotes the time series f' r=2 , pos. 4 is their difference. Fig. 4 shows a comparison of the original series f with the series f

[0089]

[0090] reconstructed from the first four components of the signal (lying in the four-dimensional subspace formed by 4 eigenvectors), where pos. 5 shows their difference.

[0091] Comparison during restoration by eight components (Fig. 5) showed that the signal residues (the difference between the original series f and the series f' r=8 , pos. 6) can be considered noise, i.e. the difference between all the values ​​of the series fnf' r=8 less than 2 dB. Then, the time series sweep is located with acceptable accuracy in an eight-dimensional space formed by 8 eigenvectors, and r = 8. Consequently, the required number of active sources of this signal (the number of oscillators) is m = r / 2 = 4 (k = 2, since the signal propagates over the surface of the cerebral cortex). Thus, the number of oscillators m = 4 corresponds to a healthy person (without neurodegenerative diseases) in a calm, waking state.

[0092] By means of the method it is also possible to determine neurodegeneration of the nervous system and to assess its degree by measuring the recorded brain signal. In example 2 of the implementation of the present invention, the data on the brain signals of 87 study participants measured by electroencephalography were obtained from the study “A large EEG database with users’ profile information for motor imaging brain-computer interface research” (Internet address) https: / / www.nature.com / articles / s41597-023-02445-z#Sec16. Participants

[0093]

[0094] The subjects of the study had no diagnosed disorders in the functioning of the nervous system, i.e., they were healthy. The obtained data were converted to the time series format f = (f1, ..., fN) with N = 256, n = 16. A similar noise criterion (2 dB) was also set. Time series scans were obtained. The scattering matrix was calculated, the eigenvalues ​​of the scattering matrix W were calculated, and eigenvectors for scans from each channel (sensor) of the neural interface data were obtained. In this example of implementation, the dimension of the information subspace (the threshold of eigenvalues) was also set equal to 8. Accordingly, it is assumed that Rmax = 8. Next, the scans were filtered using the subspace M г (n, p), spanned by the eigenvectors for n = 16, and reconstructed the time series by estimating the contribution of each pair of signal components. The time series f' were obtained r=2 ; f'

[0095]

[0096] f' r=8which are models (approximations) of the original series f. Comparison of the original series f with its models f' showed that when reconstructed using eight components, the signal residues can be considered noise, i.e. the difference between all the values ​​of the series fnf' r=8 less than 2 dB. Then r = 8, the required number of active sources of this signal (the number of oscillators) is m = r / 2 = 4 (k = 2, since the signal propagates along the surface of the cerebral cortex). Thus, in this example, the number of oscillators in a healthy person (without neurodegenerative diseases) in a quiet, waking state is also equal to 4.

[0097] Example 3 of the invention demonstrates the determination of the signal complexity (number of oscillators) of people diagnosed with alcoholism in a waking state, by obtaining data using a neural interface.

[0098] In this example, a neurointerface with 16 electrodes (sensors) was arranged according to the international 10-20 scheme.

[0099] 1) The data were recorded on 27 subjects (with diagnosed alcoholism). Each subject provided 120 1-second recordings. The recordings corresponded to the waking state. The recordings were digitized using data digitization units. The digitized data represent 1-second time series with a signal sampling frequency of 256 Hz, i.e., the time series was represented by 256 values. Thus, a signal from the neural interface was obtained in the form of real-valued time series f with a length of N = 256 samples. Next, time series scans f = (fi, fisi) were obtained for N = 256, n = 16. The scattering matrix was calculated, the eigenvalues ​​of the scattering matrix W were calculated, and the eigenvectors for the scans from each channel (sensor) of the neural interface data were obtained. At the inflection point, the threshold for the eigenvalues ​​of the scattering matrix W was set to 4 (see Fig. 6, pos. 7). Accordingly, it is assumed that Гмах=4.Next, the scans are filtered using the subspace M. г (n,p), spanned by the eigenvectors for n = 16. We reconstruct the time series by estimating the contribution of each pair of signal components. We obtain the time series / , г=2 ; / , г=4 ;which are models (approximations) of the original series f.

[0100] Comparison during restoration by four components showed that the signal residues can be considered noise, i.e. the difference between all the values ​​of the faf' series r =4 is less than 2 dB (Fig. 7, pos. 8). Then, the time series scan is located with acceptable accuracy in a four-dimensional space formed by 4 eigenvectors, and r=4. Consequently, the required number of active sources of this signal (the number of oscillators) m=r / 2=2 (k=2, since the signal propagates over the surface of the cerebral cortex). Thus, the number of active sources of brain signals in people diagnosed with alcoholism is 2.

[0101] In Example 4 of the present invention, the brain signal data of 122 study participants, measured by electroencephalography, were obtained from the database (Internet address) https: / / archive.ics.uci.edu / dataset / 121 / eeg+database. Half of the participants

[0102]

[0103] The study participants had no diagnosed disorders in the nervous system, while the other half had diagnosed alcoholism. The obtained data were converted to a time series format f = (f1, ..., fN) with N = 256, n = 16. A noise criterion of 2 dB was set. It was found that the number of active brain signal sources during wakefulness was 4 for participants in the group without diagnosed alcoholism, while the number of active sources during wakefulness was 2 for participants in the group with diagnosed alcoholism. The signal complexity (number of oscillators) was also determined for people with diagnosed Alzheimer's disease during wakefulness. After calculation using the proposed method, it was found that the number of signal sources during wakefulness for people with diagnosed Alzheimer's disease is 1-2, depending on the severity of the disease.

[0104] Thus, the presented examples demonstrated how the patented method can be used to determine neurodegradation in the nervous system and assess its severity. Moreover, unlike other signal analysis technologies (fully convolutional, convolutional, recurrent neural networks, generative networks, transformers, and spiking networks), the method can be implemented on programmable gate arrays (FPGAs) and application-specific integrated circuits (ASICs) in the form of efficient matrix calculations, with an accuracy no worse than the required level (no worse than other technologies). It also avoids the energy-intensive training associated with other technologies (e.g., neural networks) and the use of additional devices (in most cases, a graphics processing unit (GPU)) for such training and operation, which also significantly increases energy consumption.Accordingly, FPGAs and specialized integrated circuits can be located within the neural interface itself, significantly increasing the speed of signal processing and determining neurodegeneration and its severity. The proposed solution also improves the neural interface's energy efficiency, ensuring its mobility and autonomy. This technology, by eliminating the need for additional devices (such as a GPU) for signal analysis, also improves the speed of neurodegeneration detection and assessment while maintaining high accuracy on mobile and desktop computing devices.

[0105] Although the invention has been described with reference to the disclosed embodiments, it will be apparent to those skilled in the art that the specific experiments described in detail are provided merely for the purpose of illustrating the present invention and should not be construed as limiting the scope of the invention in any way. It will be understood that various modifications can be made without departing from the scope of the invention.

Claims

FORMULA 1. A method for determining neurodegeneration and assessing its degree, including the following steps: receive signals from the brain; carry out digitalization of the received signals if such signals are not digitalized; transform the digitalized brain signal from each sensor into an object of topological space - a piecewise linear sweep curve of each digitalized signal of the corresponding sensor; the rank of such curves is calculated as the maximum number of eigenvalues ​​of the scattering matrix of the curve such that the remaining eigenvalues ​​can be neglected; The number of active sources of each received brain signal is determined by the rank of the corresponding curve, and if the number of such sources for at least one brain signal is less than a given number corresponding to the number of active sources of brain signals for a given brain state for a person without neurodegeneration, then neurodegeneration occurs.

2. The method according to claim 1, in which brain signals are received by means of neurointerface sensors placed on the head, wherein the sensors are electrodes and are designed with the ability to record an electroencephalogram of the human brain.

3. The method according to paragraphs 1-2, in which, when converting a digitized brain signal into an object of topological space, the time series of the digitized signal is converted into a piecewise linear curve - a sweep, which is representable by a Hankel matrix; a scattering matrix is ​​obtained, sets of eigenvalues ​​and sets of eigenvectors are obtained.

4. The method according to paragraphs 1-3, in which, when calculating the rank of curves, time series are obtained that are approximations of the digitalized received signal, a comparison of such approximations is carried out with the time series of the received signal, and if the difference in the values ​​of the time series of the signal and the time series of the approximation corresponds to the noise criterion, then the dimension of the subspace in which the scan of the time series of such an approximation is located corresponds to the desired rank of the curve - the maximum number of eigenvalues ​​of the scattering matrix of the curve such that the remaining eigenvalues ​​can be neglected.

5. The method according to paragraph 4, in which a threshold value is set for the eigenvalues ​​of the scattering matrix of the curve, limiting the number of obtained approximations of the digital received signal.

6. The method according to claim 5, in which the threshold value for the eigenvalues ​​of the scattering matrix of the curve is set by using the dependence of the eigenvalues ​​of the scattering matrix of the curve on the number of eigenvectors.

7. The method according to paragraphs 1-6, in which the number of active sources of each received brain signal is equal to the ratio of the numerical value of the rank of the corresponding curve to the dimension of the space in which the signal is formed.

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