Detection of eeg signal based on mfdma and fractal dimension

Abstract

This invention discloses an EEG signal detection method based on MFDMA and fractal dimension. The invention uses MFDMA, Hurst exponent, and fractal dimension to characterize the dynamic properties of EEG. It also considers the MFDFA method to obtain the Hurst exponent, and then uses Hall-Wood and Robust Genon estimators to calculate the fractal dimension D. Finally, based on the fractal dimension D and the Hurst exponent, a new combined measure CI is proposed to assess the nonlinear EEG TS of epilepsy patients and healthy subjects. This invention avoids the limitations found when selecting a single index, improving the effectiveness and rationality of the algorithm.

Description

Technical Field

[0001] This invention relates to the field of heuristic algorithms, and in particular to a method for detecting electroencephalogram (EEG) signals based on MFDMA and fractal dimension. Background Technology

[0002] Normal physiology in biological systems requires a complex network to achieve effective control functions. These networks combine integration, differentiation, feedback loops, and other regulatory mechanisms, enabling organisms to perform a variety of activities, making them typical complex systems with time-dependent adaptive characteristics. Various techniques related to complexity theory have been employed to describe and quantify the dynamic properties of biological systems.

[0003] The analysis of complex systems and the assessment of their complexity have become important aspects of mathematics and physics. Complexity can be roughly defined as the difficulty encountered in describing a signal or predicting its future behavior. The historical development of the concept of complexity has focused on measuring regularity based on various measures of nonlinear time series (TS) analysis. Correlation dimension, entropy, and Lyapunov exponent are commonly used metrics to measure the randomness and predictability of a given TS. An alternative approach is to calculate the fractal complexity of the TS. The Hurst exponent (H) and fractal dimension (D) are measures of the fractal complexity or persistence of fractal processes such as fractional Gaussian noise or Brownian motion.

[0004] Due to the complex structure of its neural networks, the brain is considered one of the most complex dynamic systems. Recording brain electrical activity is achieved through electroencephalography (EEG). EEG is actually a non-invasive technique, as it is performed using disc-shaped electrodes placed on the patient's scalp. EEG is the bioelectrical representation of neural activity. Typically, EEG aims to identify specific problems, such as detecting the location of epileptic foci from abnormal electrical activity in certain areas of the brain. Epilepsy is a serious neurological disorder that affects people of all ages, sexes, and races. According to the World Health Organization, epilepsy is a serious brain disorder affecting approximately 50 million people (about 1% of the world's population), 80% of whom live in developing or underdeveloped countries. The problems revealed by the occurrence of epileptic seizures directly impact a patient's quality of life in most aspects. Epilepsy is a central nervous system disorder characterized by spontaneous, recurrent, and unpredictable interruptions of normal brain function, known as epileptic seizures. An epileptic seizure is defined as a transient occurrence of signs and / or symptoms caused by synchronous or excessive abnormal brain activity.

[0005] Some studies focus on using nonlinear methods to detect epilepsy from EEG signals. These methods can detect and quantify linear and nonlinear mechanisms, thus reflecting the characteristics of the EEG to some extent. Nonlinear features can extract the hidden complexity in EEG TS. One of the earliest studies was developed by Babloyantz et al., who used nonlinear parameters such as correlation dimension and maximum Lyapunov exponent to study sleep wave signals. These studies have expanded the potential applications of nonlinear EEG analysis methods, but epilepsy identification remains a relevant area of ​​research. Dynamic TS analysis of EEG signals can reveal complex phenomena related to long-range correlations and different types of nonlinear interactions. This type of analysis can provide useful diagnostic and prognostic information. Nevertheless, most papers on EEG found in the literature consider a single index. Furthermore, when multiple indices are used, information fusion is not considered; each index is analyzed separately. Analysis based on a single index is insufficient to capture EEG properties, thus leading to limited results.

[0006] To address the above problems, this application proposes a solution. Summary of the Invention

[0007] Purpose of the invention: The purpose of this invention is to provide an EEG signal detection method based on MFDMA and fractal dimension, which eliminates the limitations that may occur when using a single indicator for EEG analysis, and can diagnose normal people and patients with epilepsy.

[0008] Technical solution: The EEG signal detection based on MFDMA and fractal dimension described in this invention specifically includes the following steps:

[0009] S1: Acquire brainwave signals, obtain EEG datasets, and analyze the characteristics of brainwave signals;

[0010] S2: Obtain EEG fragments and employ data segmentation techniques to minimize analysis time and cost;

[0011] S3: Extract the generalized Hearst exponent from the EEG signal using MFDMA. Specifically:

[0012] S3.1: Given a time series of EEG signals , , To construct a new sequence for the total number of data points:

[0013] ;

[0014] S3.2: The value of scale is Calculate the moving average function within the moving window. The formula is:

[0015]

[0016] in, Indicates less than or equal to The largest non-negative integer, Indicates greater than or equal to The smallest non-negative integer, This represents the position of the moving average within the moving window;

[0017] S3.3: Calculate the residuals The residuals are used as a new data sequence Specifically:

[0018] , ,

[0019]

[0020] The total number of data is ;

[0021] will sequence Divided into equal sizes Each interval is a set of non-overlapping intervals. One data point, , Then the sequence After reversing the partition once, we get Each interval segment;

[0022] S3.4: Calculate the local root mean square value and the global root mean square value. The root mean square value, specifically:

[0023] Calculate the local root mean square value: the first Root mean square function in each interval It can be calculated using the following formula:

[0024]

[0025]

[0026] in For the new data sequence, The total number of data points. These are disjoint intervals;

[0027] Calculate global Root mean square value, when When, the calculation formula is:

[0028]

[0029] when When, the calculation formula is:

[0030]

[0031] S3.5: Change the value of scale. , to obtain the corresponding If the signal sequence is a scale-invariant signal with a power-law relationship, then:

[0032]

[0033] in yes Hurst exponent;

[0034] S4: Extract the fractal dimension of the EEG signal Specifically:

[0035] S4.1: Analyzing Fractal Dimension Properties in nonlinear time series (TS);

[0036] S4.2: The fractal dimension is obtained using the Hall-Wood estimator, i.e., the HW estimator. Quantity;

[0037] S4.3: Calculate the fractal dimension using the Robust Genon estimator, i.e., the RG estimator. Quantity;

[0038] S5: Define the joint index CI for calculating the nonlinear time series EEG (TS); based on the Hurst index. and fractal dimension To represent the randomness and long-term dependence of nonlinear time series (TS), a joint index CI is proposed, with the following formula:

[0039]

[0040] in and These are respectively the Hearst index and fractal dimension The expected value of the related random walk phenomenon, yes The estimated value, Depend on Received, among which and Calculated by S4.2 and S4.3 respectively;

[0041] S6: Calculate the CI index of the EEG data segment and use the Wilcoxon signed-rank test principle to detect epilepsy.

[0042] Preferably, the EEG dataset in S1 is obtained through an open-source database.

[0043] Preferably, the data segmentation technique in S2 is as follows: each EEG signal is divided into 15 non-overlapping segments, each segment containing a time series of 256 samples.

[0044] Preferably, the generalized Hearst exponent in S3.5 Specifically: searching and Scale-free regions with linear relationships are obtained by calculating the mesoscale within the scale-free region. sum function The first-order polynomial fitting coefficients between the logarithmic values ​​are used to calculate the slope of the linear regression line, which is... .

[0045] Preferably, in S3.5... At that time, the generalized Hearst index The exploration can prove good performance, and H = H(−2) is selected as the component for calculating the CI exponent of EEG nonlinear time series TS.

[0046] Preferably, S4.1 specifically refers to: fractal dimension. As a measure of local memory in nonlinear time series (TS), for univariate series, The fractal dimension Connected to the long-term memory of the nonlinear time series TS, enabling That is, from the fractal dimension Fractal dimension is reflected in long-term memory. The properties of nonlinear time series TS are as follows:

[0047] (a) ;

[0048] (b) when At that time, the nonlinear time series TS exhibits a random walk phenomenon;

[0049] (c) When At this time, it corresponds to a persistent process and leads to a non-random walk;

[0050] (d) when Then, an anti-persistence process occurs.

[0051] Preferably, the HW estimator in S4.2 is a box-counting estimator that considers a small scale, where the area of ​​the boxes covers the curves, not their sum, and formally, there is a scale. ,in The aforementioned area is:

[0052]

[0053] in yes The integer part of the HW estimator is given by the expression:

[0054]

[0055] in To avoid limitations, Hall-Wood uses L = 2, which gives:

[0056]

[0057] Preferably, the moment estimation scale of the RG method in S4.3 is not robust. To avoid this problem, a robust estimator developed by Genton is used, which is the fractal dimension. The component used to calculate the CI index yields the following result:

[0058]

[0059] Similar to HW, the RG estimator is:

[0060]

[0061] in To avoid limitations, Hall-Wood uses L = 2, which gives:

[0062]

[0063] Preferably, the joint index CI in S5 is close to zero, indicating that the distance between the measured value and the random signal value is small, that is, the deviation is small; the further away from random behavior, the lower the complexity of the recorded signal.

[0064] Preferably, S6 specifically involves: selecting a significance level of 0.05 and obtaining the result through a Wilcoxon signed-rank test. Value, if This indicates that the CI index cannot distinguish between EEG signals; This indicates that the CI index can distinguish EEG signals; This indicates that the CI index can significantly distinguish EEG signals.

[0065] Beneficial effects: This application employs MFDMA, Hurst exponent, and fractal dimension. To characterize the dynamic properties of EEG, the MFDFA method was considered to obtain... Exponent; fractal dimension is calculated using HW and RG estimators. ;exist and Based on the existing metrics, a novel combined measure CI is proposed to evaluate EEG nonlinearity TS in different datasets of epilepsy patients and healthy subjects. This application also avoids the limitations found when selecting a single index alone, improving the effectiveness and rationality of the algorithm. Attached Figure Description

[0066] Figure 1 This is a flowchart of this application. Detailed Implementation

[0067] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0068] like Figure 1 The diagram shown is a flowchart of this application. In this embodiment, the application specifically includes the following steps:

[0069] S1: Acquire electroencephalogram (EEG) signals, obtain an EEG dataset, and analyze the characteristics of the EEG signals. In this embodiment, the data in the EEG dataset comes from the artifact-free EEG time series of the Department of Epilepsy at the University of Bonn. This open-source database has been widely used to test various methods related to identifying patients with continuous or intermittent epilepsy from healthy patients with epilepsy, and is often considered a high-quality benchmark in this field. In this embodiment, the data consists of four groups, including:

[0070] Group A: Extracranial recordings of healthy subjects with their eyes open;

[0071] Group B: Extracranial recording of a healthy subject with eyes closed;

[0072] Group C: Intracranial recordings of hippocampal formation in the brain hemispheres during the interictal period in patients;

[0073] Group D: Intracranial recordings of the epileptogenic zone in patients without seizure intervals;

[0074] Each data set consists of 30 EEG signals, each lasting 23.6 seconds, with a sampling frequency of 173.61 Hz.

[0075] S2: Obtain EEG segments. To minimize analysis time and cost, data segmentation technology is used. Specifically, each EEG signal is divided into 15 non-overlapping segments, each containing a time series of 256 samples. That is, each group of EEG signals yields... One EEG signal, four sets of data were obtained. .

[0076] S3: Extract the generalized Hearst exponent from the EEG signal using MFDMA. Specifically:

[0077] S3.1: Given a time series of EEG signals , , To construct a new sequence for the total number of data points:

[0078] ;

[0079] S3.2: The value of scale is Calculate the moving average function within the moving window. The formula is:

[0080]

[0081] in, Indicates less than or equal to The largest non-negative integer, Indicates greater than or equal to The smallest non-negative integer, This represents the position of the moving average within the moving window;

[0082] S3.3: Calculate the residuals The residuals are used as a new data sequence Specifically:

[0083] , ,

[0084]

[0085] The total number of data is ;

[0086] will sequence Divided into equal sizes Each interval is a set of non-overlapping intervals. One data point, , Then the sequence After reversing the partition once, we get Each interval segment;

[0087] S3.4: Calculate the local root mean square value and the global root mean square value. The root mean square value, specifically:

[0088] Calculate the local root mean square value: the first Root mean square function in each interval It can be calculated using the following formula:

[0089]

[0090]

[0091] in For the new data sequence, The total number of data points. These are disjoint intervals;

[0092] Calculate global Root mean square value, when When, the calculation formula is:

[0093]

[0094] when When, the calculation formula is:

[0095]

[0096] S3.5: Change the value of scale. , to obtain the corresponding If the signal sequence is a scale-invariant signal with a power-law relationship, then:

[0097]

[0098] in yes Hurst exponent;

[0099] Specifically: Search and Scale-free regions with linear relationships are obtained by calculating the mesoscale within the scale-free region. sum function The first-order polynomial fitting coefficients between the logarithmic values ​​are used to calculate the slope of the linear regression line, which is... .

[0100] because At that time, the generalized Hearst index The exploration has demonstrated good performance, therefore, in this embodiment, H = H(−2) is selected as the component for calculating the CI exponent of the EEG nonlinear time series TS.

[0101] S4: Extract the fractal dimension of the EEG signal Specifically:

[0102] S4.1: Analyzing Fractal Dimension Properties of nonlinear time series (TS):

[0103] fractal dimension As a measure of local memory in nonlinear time series (TS), for univariate series, The fractal dimension Connected to the long-term memory of the nonlinear time series TS, enabling That is, from the fractal dimension Fractal dimension is reflected in long-term memory. The properties of nonlinear time series TS are as follows:

[0104] (a) ;

[0105] (b) when At that time, the nonlinear time series TS exhibits a random walk phenomenon;

[0106] (c) When At this time, it corresponds to a persistent process and leads to a non-random walk;

[0107] (d) when Then, an anti-persistence process occurs.

[0108] S4.2: The fractal dimension is obtained using the Hall-Wood estimator, i.e., the HW estimator. Quantity:

[0109] The HW estimator is a box-counting estimator that considers a small scale, where the area of ​​the boxes covers the curves, not their sum, and formally, there is a scale. ,in The aforementioned area is:

[0110]

[0111] in yes The integer part of the HW estimator is given by the expression:

[0112]

[0113] in To avoid limitations, Hall-Wood uses L = 2, which gives:

[0114]

[0115] S4.3: Calculate the fractal dimension using the Robust Genon estimator, i.e., the RG estimator. Quantity:

[0116] The moment estimation scale of the RG method is not robust. To avoid this problem, a robust estimator developed by Genton is used, which measures the fractal dimension. The component used to calculate the CI index yields the following result:

[0117]

[0118] Similar to HW, the RG estimator is:

[0119]

[0120] in To avoid limitations, Hall-Wood uses L = 2, which gives:

[0121]

[0122] S5: Define the joint index CI for calculating nonlinear time series (TS) in electroencephalography (EEG); the randomness of biological nonlinear time series (TS) is a common response observed in healthy organisms. The complexity of an organism's biological / physiological signals reflects its most adaptive (healthy) state; the more adaptive an organism, the more complex the signals it may produce. A persistent loss of complexity is typically observed in pathological conditions, including aging (debilitating) syndromes and diseases, taking into account the Hurst index. and fractal dimension To represent the randomness and long-term dependence of nonlinear time series (TS), a joint index CI is proposed, with the following formula:

[0123]

[0124] in and These are respectively the Hearst index and fractal dimension The expected value of the related random walk phenomenon, yes The estimated value, Depend on Received, among which and Calculated by S4.2 and S4.3 respectively;

[0125] A joint index (CI) close to zero indicates that the measured value is close to the random signal value, i.e., the deviation is small; the further away from random behavior, the lower the complexity of the recorded signal.

[0126] S6: Calculate the CI index of the EEG data segment and use the Wilcoxon signed-rank test to detect epilepsy. Specifically: select a significance level of 0.05 and obtain the CI index through the Wilcoxon signed-rank test. Value, if This indicates that the CI index cannot distinguish between EEG signals; This indicates that the CI index can distinguish EEG signals; This indicates that the CI index can significantly distinguish EEG signals.

[0127] Table 1. Wilcoxon signed-rank test of four groups of EEG signals value

[0128]

[0129] Although embodiments of the invention have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the invention, and such modifications and variations all fall within the scope defined by the appended claims.

Claims

1. A method for detecting electroencephalogram (EEG) signals based on MFDMA and fractal dimension, characterized in that: Specifically, the following steps are included: S1: Acquire brainwave signals, obtain EEG datasets, and analyze the characteristics of brainwave signals; S2: Obtain EEG fragments and employ data segmentation techniques to minimize analysis time and cost; S3: Extract the generalized Hearst exponent from the EEG signal using MFDMA. Specifically: S3.1: Given a time series of EEG signals , , To construct a new sequence for the total number of data points: ； S3.2: The value of scale is Calculate the moving average function within the moving window. The formula is: in, Indicates less than or equal to The largest non-negative integer, Indicates greater than or equal to The smallest non-negative integer, This represents the position of the moving average within the moving window; S3.3: Calculate the residuals The residuals are used as a new data sequence Specifically: ， , The total number of data is ; will sequence Divided into equal sizes Each interval is a set of non-overlapping intervals. One data point, , Then the sequence After reversing the partition once, we get Each interval segment; S3.4: Calculate the local root mean square value and the global root mean square value. The root mean square value, specifically: Calculate the local root mean square value: the first Root mean square function in each interval It can be calculated using the following formula: in For the new data sequence, The total number of data points. These are disjoint intervals; Calculate global Root mean square value, when When the time is right, the calculation formula is: when When the time is right, the calculation formula is: S3.5: Change the value of scale. , to obtain the corresponding If the signal sequence is a scale-invariant signal with a power-law relationship, then: in yes Hurst exponent; S4: Extract the fractal dimension of the EEG signal Specifically: S4.1: Analyzing Fractal Dimension Properties in nonlinear time series (TS); S4.2: The fractal dimension is obtained using the Hall-Wood estimator, i.e., the HW estimator. Quantity; S4.3: Calculate the fractal dimension using the Robust Genon estimator, i.e., the RG estimator. Quantity; S5: Define the joint index CI for calculating the nonlinear time series EEG (TS); based on the Hurst index. and fractal dimension To represent the randomness and long-term dependence of nonlinear time series (TS), a joint index CI is proposed, with the following formula: in and These are respectively related to the Hearst index and fractal dimension The expected value of the related random walk phenomenon, yes The estimated value, Depend on We obtained, among which and Calculated by S4.2 and S4.3 respectively; S6: Calculate the CI index of the EEG data segment and use the Wilcoxon signed-rank test principle to detect epilepsy.

2. The EEG signal detection method based on MFDMA and fractal dimension according to claim 1, characterized in that: The EEG dataset in S1 was obtained through an open-source database.

3. The EEG signal detection method based on MFDMA and fractal dimension according to claim 1, characterized in that: The data segmentation technique in S2 specifically involves dividing each EEG signal into 15 non-overlapping segments, each segment containing a time series of 256 samples.

4. The EEG signal detection method based on MFDMA and fractal dimension according to claim 1, characterized in that: The generalized Hearst exponent in S3.5 Specifically: searching and Scale-free regions with linear relationships are obtained by calculating the mesoscale within the scale-free region. sum function The first-order polynomial fitting coefficients between the logarithmic values ​​are used to calculate the slope of the linear regression line, which is... .

5. The EEG signal detection method based on MFDMA and fractal dimension according to claim 1, characterized in that: In S3.5 At that time, the generalized Hearst index The exploration can prove good performance, and H = H(−2) is selected as the component for calculating the CI exponent of EEG nonlinear time series TS.

6. The EEG signal detection method based on MFDMA and fractal dimension according to claim 1, characterized in that: Specifically, S4.1 refers to: fractal dimension. As a measure of local memory in nonlinear time series (TS), for univariate series, The fractal dimension Connected to the long-term memory of the nonlinear time series TS, enabling That is, from the fractal dimension Fractal dimension is reflected in long-term memory. The properties of nonlinear time series TS are as follows: (a) ； (b) when At that time, the nonlinear time series TS exhibits a random walk phenomenon; (c) When At this time, it corresponds to a persistent process and leads to a non-random walk; (d) when Then, an anti-persistence process occurs.

7. The EEG signal detection method based on MFDMA and fractal dimension according to claim 1, characterized in that: The HW estimator in S4.2 is a box-counting estimator that considers a small scale, where the area of ​​the boxes covers the curves, not their sum, and formally, there is a scale. ,in The aforementioned area is: in yes The integer part of the HW estimator is given by the expression: in To avoid limitations, Hall-Wood uses L = 2, which gives: 。 8. The EEG signal detection method based on MFDMA and fractal dimension according to claim 1, characterized in that: The moment estimation scale of the RG method in S4.3 is not robust. To avoid this problem, a robust estimator developed by Genton is used, which measures the fractal dimension. The component used to calculate the CI index yields the following result: Similar to HW, the RG estimator is: in To avoid limitations, Hall-Wood uses L = 2, which gives: 。 9. The EEG signal detection method based on MFDMA and fractal dimension according to claim 1, characterized in that: In S5, the joint index CI is close to zero, indicating that the distance between the measured value and the random signal value is small, that is, the deviation is small; the further away from random behavior, the lower the complexity of the recorded signal.

10. The EEG signal detection method based on MFDMA and fractal dimension according to claim 1, characterized in that: Specifically, S6 involves selecting a significance level of 0.05 and obtaining the result through the Wilcoxon signed-rank test. Value, if This indicates that the CI index cannot distinguish between EEG signals; This indicates that the CI index can distinguish EEG signals; This indicates that the CI index can significantly distinguish EEG signals.

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