Resting state gastric-brain electrical signal coupling method

Abstract

The application discloses a resting state stomach-brain electro signal coupling method, comprising the following steps: obtaining the raw brain electro signal and the raw stomach electro signal of a user in a resting state collected by a multi-lead acquisition device; preprocessing the raw stomach electro signal and the raw brain electro signal; determining the phase information, the second phase amplitude information and the artifact information according to the preprocessed stomach electro signal; determining the first target analysis phase and the second target phase amplitude information according to the artifact information; performing phase-phase coupling and phase-amplitude coupling on the first target analysis phase and the second target phase amplitude information, and performing amplitude-amplitude coupling on the preprocessed stomach electro signal and the preprocessed brain electro signal; and determining the transfer entropy according to the preprocessed stomach electro signal and the preprocessed brain electro signal. The application provides effective data support for analyzing the interaction between the stomach and the brain, and improves the accuracy and comprehensiveness of the analysis of the interaction between the stomach and the brain.

Description

Technical Field

[0001] This invention belongs to the field of electrical signal processing technology, specifically relating to a method for coupling gastrobrain electrical signals in a resting state. Background Technology

[0002] There is a close interaction between the stomach and the brain, and they jointly participate in the regulation of cognitive and digestive functions. This interaction is achieved through the gastrobrain neural axis, which includes three main neural pathways: the vagus nerve, the sympathetic nervous system, and the gastrointestinal nervous system. The vagus nerve is the most important, as it transmits sensory signals from the stomach to motor signals from the brain bidirectionally, thus influencing appetite, mood, and cognition. The sympathetic nervous system is mainly activated under stress; it can inhibit gastric activity and increase the sensitivity of the gastric mucosa. The gastrointestinal nervous system is an independent neural network within the digestive tract; it can autonomously regulate the movement and secretion of the digestive tract and also exchange information with the central nervous system.

[0003] Gastric electrical signals and electroencephalogram (EEG) signals are important bioelectrical signals reflecting the function of the gastro-brain neural axis. They exhibit coupling relationships at different frequencies, known as cross-frequency coupling (CFC). CFC is a biosignal analysis method first proposed in the 1980s to study the coupling phenomenon between theta and gamma rhythms in the hippocampus of the brain. Later, CFC was widely applied to the analysis of various biosignals, including EEG and electromyography (EMG). CFC can quantify the degree of interaction between bioelectrical signals of different frequencies, thereby revealing the dynamic changes of physiological systems. Gastric electrical signals are generated by the electrical activity of gastrointestinal muscles. Its low-frequency component (0.033-0.067 Hz) can be transmitted to the brainstem and cerebral cortex via the vagus nerve, thus affecting the high-frequency component (0.5-45 Hz) of the EEG signal. Conversely, the high-frequency component of the EEG signal can also feed back to the gastrointestinal tract via the vagus nerve, thus influencing the basic rhythm of the gastric electrical signal. This bidirectional CFC is particularly evident during eating or digestion, and it may be related to various cognitive functions, such as multi-item representation, remote communication, and stimulus interpretation. Therefore, the CFC between gastric and brain electrical signals is of great significance for revealing the relationship between human cognitive and digestive functions.

[0004] Our understanding of cross-frequency coupling between gastric and brain electrical signals is still relatively limited. Cross-frequency coupling is mainly used to explore the interaction between different frequency bands of brain signals, revealing the synchronization of neural signals at different time scales and the functional mechanisms in neural information processing and cognition. For example, the phase of low-frequency oscillations can modulate the amplitude of high-frequency activities, thereby achieving coordination and integration between neuronal groups. Cross-frequency coupling can also reflect the adaptive regulation of the nervous system to external stimuli and internal states, as well as abnormal patterns associated with certain neurological and psychiatric diseases. Existing methods for coupling gastric and brain signals do not provide comprehensive and accurate coupling data, thus affecting the analysis results of the interaction between the stomach and brain. Summary of the Invention

[0005] To address the aforementioned problems in the prior art, this invention provides a method for coupling gastric and brain electrical signals in a resting state. The technical problem to be solved by this invention is achieved through the following technical solution:

[0006] A method for coupling gastric and brain electrical signals in a resting state includes the following steps:

[0007] Acquire raw EEG and raw Gastrointestinal signals of the user in a resting state, simultaneously collected by a multi-channel acquisition device;

[0008] The raw gastric electrical signal is preprocessed to obtain a preprocessed gastric electrical signal;

[0009] The first analytical phase and gastric electrical phase artifact information are determined based on the preprocessed gastric electrical signal;

[0010] The raw EEG signal is preprocessed to obtain a preprocessed EEG signal;

[0011] The second phase amplitude information and EEG artifact information are determined based on the preprocessed EEG signals;

[0012] Based on the first analytical phase, the gastric electrical phase artifact information, the second phase amplitude information, and the electroencephalogram artifact information, the first target analytical phase and the second target phase amplitude information are determined;

[0013] Phase-phase coupling and phase-amplitude coupling are performed on the phase resolution of the first target and the phase amplitude information of the second target, and amplitude coupling is performed on the preprocessed gastric electroencephalogram signal and the preprocessed electroencephalogram signal.

[0014] The transfer entropy is determined based on the preprocessed gastric electroencephalogram (GEG) signal and the preprocessed electroencephalogram (EEG) signal.

[0015] In one embodiment of the present invention, the preprocessing of the raw gastric electrical signal to obtain a preprocessed gastric electrical signal includes:

[0016] Calculate the power spectrum of the raw gastric electrical signal;

[0017] Determine the lead signal corresponding to the maximum power based on the power spectrum;

[0018] The lead signal is filtered to obtain a preprocessed gastric electrical signal.

[0019] In one embodiment of the present invention, determining the first analytical phase and gastric electrical phase artifact information based on the preprocessed gastric electrical signal includes:

[0020] The first analytical phase is determined based on the preprocessed gastric electrical signal;

[0021] Based on the first analytical phase, determine the gastric electrical phase artifact information;

[0022] The second phase amplitude information includes: the second analytical phase and the second instantaneous amplitude;

[0023] The step of determining the second phase amplitude information and EEG artifact information based on the preprocessed EEG signal includes:

[0024] The second analytical phase and the second instantaneous amplitude are determined based on the preprocessed EEG signals;

[0025] Brain artifact information is determined based on the preprocessed EEG signals.

[0026] In one embodiment of the present invention, determining the gastric electrical phase artifact information based on the first resolved phase includes:

[0027] Obtain multiple edges where the phase derivative change of the first analytical phase is greater than -1, and calculate the period length between each edge;

[0028] The period threshold is determined based on the mean and standard deviation of the multiple period lengths;

[0029] The second time point corresponding to the period lengths greater than the period threshold and less than the period threshold is determined based on the period threshold;

[0030] Obtain the third time point corresponding to the non-monotonic increasing period length among the multiple period lengths;

[0031] The second time point and the third time point are extracted as gastric electrical phase artifact information.

[0032] In one embodiment of the present invention, determining the EEG artifact information based on the preprocessed EEG signal includes:

[0033] The preprocessed EEG signal of each channel is divided into multiple sub-segments;

[0034] The Z-Score matrix is ​​determined based on the average amplitude difference and the maximum absolute value of the amplitude of each sub-segment signal.

[0035] The time points of the sub-segment signals corresponding to the elements in the Z-Score matrix that are greater than a preset score threshold are extracted as EEG artifact information.

[0036] In one embodiment of the present invention, the second target phase amplitude information includes: the second target analytical phase and the second target instantaneous amplitude;

[0037] The step of determining the first target analytical phase and the second target phase amplitude information based on the first analytical phase, the gastric electrical phase artifact information, the second phase amplitude information, and the electroencephalogram artifact information includes:

[0038] The first target analytical phase is obtained by removing the phase corresponding to the gastric electrical phase artifact information from the first analytical phase.

[0039] The second target analytical phase and the second target instantaneous amplitude are obtained by removing the phase and amplitude corresponding to the EEG artifact information from the second analytical phase and the second instantaneous amplitude.

[0040] In one embodiment of the present invention, the step of performing phase-phase coupling and phase-amplitude coupling on the phase amplitude information of the first target and the second target, and performing amplitude coupling on the preprocessed gastric electroencephalogram signal and the preprocessed electroencephalogram signal, includes:

[0041] Phase-to-phase coupling is performed based on the first target analytical phase and the second target analytical phase to obtain the phase-locked value;

[0042] Amplitude coupling was performed on the preprocessed gastric electroencephalogram (GEG) signal and the preprocessed electroencephalogram (EEG) signal to obtain the average Pearson correlation coefficient.

[0043] Phase-amplitude coupling is performed based on the analytical phase of the first target and the instantaneous amplitude of the second target to obtain the coupling strength value.

[0044] In one embodiment of the present invention, phase-to-phase coupling is performed based on the first target resolved phase and the second target resolved phase to obtain a phase-locked value, including:

[0045] The analytical phase of the envelope is determined based on the analytical phase of the second target;

[0046] The phase-locked value is calculated based on the resolved phase of the envelope and the resolved phase of the first target.

[0047] In one embodiment of the present invention, the step of amplitude coupling of the preprocessed gastric electroencephalogram (GEG) signal and the preprocessed electroencephalogram (EEG) signal to obtain the average Pearson correlation coefficient includes:

[0048] The preprocessed gastric electrical signal is divided into multiple consecutive first time windows;

[0049] Perform a Fast Fourier Transform on the signal in each of the first time windows at different frequency bands to obtain the first amplitude to be coupled in different frequency bands;

[0050] The preprocessed EEG signal is divided into multiple consecutive second time windows;

[0051] Perform a Fast Fourier Transform on the signal in each of the second time windows at different frequency bands to obtain the second power spectrum to be coupled in different frequency bands;

[0052] The average Pearson correlation coefficient is calculated based on the values ​​of the first amplitude to be coupled and the second power spectrum to be coupled.

[0053] In one embodiment of the present invention, determining the transfer entropy based on the preprocessed gastric electroencephalogram (GEG) signal and the preprocessed electroencephalogram (EEG) signal includes:

[0054] The gastric electrical vector is determined based on the preprocessed gastric electrical signal;

[0055] The brainwave vector is determined based on the gastric electrical vector and the preprocessed brainwave signal;

[0056] The corresponding marginal probability distribution and joint probability distribution are determined based on the gastric electrical vector and the brain electrical vector;

[0057] Determine the conditional entropy and joint entropy based on the marginal probability distribution and the joint probability distribution;

[0058] The transition entropy is determined based on the conditional entropy and the joint entropy.

[0059] The beneficial effects of this invention are:

[0060] This invention can effectively extract phase-amplitude coupling, phase-phase coupling, and amplitude-amplitude coupling indices between raw gastric electroencephalogram (GEG) signals and raw brain electroencephalogram (EEG) signals at different frequency bands, reflecting the degree of dynamic correlation between them. These three different coupling indices respectively reflect the phase-amplitude coupling, phase-phase coupling, and amplitude-amplitude coupling between the raw GEG and EEG signals, thereby improving the comprehensiveness and richness of the data. Simultaneously, this invention utilizes transfer entropy to calculate the directed information transfer amount from the raw GEG signal to the raw EEG signal, reflecting the degree of bidirectional influence between the two signals. This provides effective data support for analyzing the interaction between the stomach and brain, improving the accuracy and comprehensiveness of the analysis.

[0061] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0062] Figure 1 This is a flowchart illustrating a method for coupling gastric and brain electrical signals in a resting state, as provided in an embodiment of the present invention.

[0063] Figure 2 This is a schematic diagram of the electrode positions for acquiring raw gastric electrical signals provided in an embodiment of the present invention;

[0064] Figure 3 This is a schematic diagram of the electrode positions for acquiring raw EEG signals provided in an embodiment of the present invention;

[0065] Figure 4 The PPC coupling degree and causal interaction diagram of different frequency bands of the stomach and brain provided in the embodiments of the present invention;

[0066] Figure 5 A diagram showing the degree of AAC coupling and causal interaction in different frequency bands of the stomach and brain, provided for embodiments of the present invention;

[0067] Figure 6 The PAC coupling degree and causal interaction diagram of different frequency bands of the stomach and brain provided in the embodiments of the present invention;

[0068] Figure 7 The simulation experiment provided for the embodiments of the present invention is based on the multiple comparison results of mean rank. Detailed Implementation

[0069] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0070] Example 1

[0071] like Figure 1 As shown, a method for coupling gastric and brain electrical signals in a resting state includes the following steps:

[0072] Step 10: Acquire the raw EEG and gastric electrical signals of the user in a resting state, simultaneously acquired by the multi-channel acquisition device. In this step, the multi-channel acquisition device includes a PSG and an EEG lead localization system. During signal acquisition, gastric and EEG signals are acquired simultaneously, and the raw signals are time-domain signals.

[0073] Specifically, PSG (Polysomnography) was used to acquire gastric electrical data. Since the amplitude of the gastric electrical signal is affected by the distance between the stomach and the skin surface, and EGG acquired while seated typically has a lower amplitude, to obtain a higher signal-to-noise ratio, the user needs to lie at a 45° angle on a recliner. This makes it easier to access the gastric electrical pacing area, and the user is required to avoid any voluntary movement. Movement or electrode line disturbances can cause numerous artifacts during acquisition; these artifact data segments were identified and excluded from further analysis. The electrode placement during gastric electrical data acquisition is described below:

[0074] The first electrode 1 is placed 2 cm above the umbilicus. The second electrode 2 and the third electrode 3 are located on the midline at one-third and two-thirds of the distance between the first electrode 1 and the xiphoid process, respectively, both above the first electrode 1. The longitudinal positions of the other two electrodes, the sixth electrode 6 and the seventh electrode 7, are determined by a vertical line passing through the midpoint of the left clavicle, and their horizontal positions are the same as those of the first electrode 1 and the second electrode 2. Since the seventh electrode 7 may fall above the thoracic cavity, in this case, it can be moved towards the midline to improve the signal-to-noise ratio. Finally, the fourth electrode 4 and the fifth electrode 5 are placed at the horizontal position of the vertical midpoint between the first electrode 1 and the second electrode 2, and between the second electrode 2 and the third electrode 3. The reference electrode is placed symmetrically with the fifth electrode 5. Finally, the ground electrode is placed on the left abdomen, above the iliac crest, as shown in the figure. Figure 2 As shown.

[0075] To ensure data quality and result validity, this embodiment employs a standard EEG lead localization system to acquire raw EEG signals. Specifically, 16 electrodes were placed on the scalp, with positioning strictly adhering to the standard 10-20 localization system. The system provides selectable channel modes, allowing for channel selection and analysis based on actual needs. The 16 acquisition electrodes were positioned at Fp1, Fp2, F3, F4, C3, C4, P3, P4, O1, O2, F7, F8, CP5, CP6, M1, and M2, with the reference electrode at Cz and the ground electrode at Fpz. The electrode placement is as follows. Figure 3 As shown.

[0076] Step 20 involves preprocessing the raw gastric electrical signal to obtain a preprocessed gastric electrical signal. Specifically, step 20 includes steps 21-23:

[0077] Step 21: Calculate the power spectrum of each channel of the raw gastric electrical signal.

[0078] The power spectrum of the raw gastric electrical signal was approximated using a multi-window spectral estimation method. The basic idea of ​​this method is to obtain a cluster of data window functions by minimizing frequency leakage outside half the bandwidth, based on the Rayleigh-Ritz minimization problem. This cluster of window functions replaces the single window function. These window functions are mutually orthogonal, and each window function samples the signal differently. Information lost by one window function can be recovered by another, thus maintaining the offset at an acceptable level. Using a cluster of orthogonal window functions to process random signals can reduce spectral leakage caused by the limited data length.

[0079] When using a computer to perform direct signal processing, it is impossible to measure and calculate infinitely long signals. Therefore, this embodiment analyzes a finite time segment of the signal. Specifically, a time segment is extracted from the signal, and then this segment is periodically extended to obtain a virtual infinitely long signal. Finally, a Fourier transform is performed on this signal. Truncation of an infinitely long signal causes spectral distortion. The energy originally concentrated at f(0) is dispersed into two wider frequency bands. To reduce this spectral energy leakage, this embodiment uses different truncation functions, i.e., window functions, to truncate the signal.

[0080] The specific calculation steps are as follows:

[0081] (1) Parameter settings

[0082] Based on the length N of the original gastric electrical signal and the sampling rate f s Determine the frequency resolution f that satisfies the Nyquist theorem. n .

[0083] (2) Generate data window

[0084] A Slepian sequence is a data window used in multi-window spectral estimation methods. It is a set of orthogonal functions, also known as a discrete spherical sequence. Let represent the k-th raw gastric electrical signal sequence sample, abbreviated as This sequence satisfies the following two conditions.

[0085] 1) Each window function has a unit energy, i.e.

[0086]

[0087] 2) These window functions are mutually orthogonal, that is...

[0088]

[0089] To satisfy the above two conditions, the Slepian sequence can be generated using the following formula:

[0090]

[0091] Where n represents the starting point of the data window in the original gastric electrical signal, and k represents the number of data windows, which is determined by the bandwidth parameter p of the data windows.

[0092] k = |p+1|

[0093]

[0094] (3) Calculation of characteristic coefficients

[0095] The raw gastric electrical signal is multiplied by the Slepian sequence to obtain a windowed data sequence X(t), and the characteristic coefficients are obtained by performing the following discrete Fourier transform:

[0096]

[0097] (4) Adaptive weighting

[0098] For the characteristic coefficient y k (f) Perform adaptive average weighting, using the ratio of the characteristic coefficients of each characteristic coefficient to b. k (f) can be used as weighting coefficients to obtain the power spectrum estimate p. x (f).

[0099]

[0100]

[0101] Step 22: Determine the lead signal corresponding to the maximum power based on the power spectrum. Under normal circumstances, high-quality electrogastrography (EGG) recordings exhibit unique spectral characteristics, with similar peak frequencies at most recording locations. The lead signal with the highest power corresponding to the peak frequency is selected for further analysis.

[0102] Step 23: Filter the lead signal to obtain a preprocessed gastric electrical signal.

[0103] The phase characteristics of the raw gastric electrical signal reflect the slow wave rhythm and propagation pattern generated by the pacemaker cells in the gastrointestinal tract. To ensure that the phase is not distorted, this embodiment uses a zero-phase filter for bidirectional filtering in the processing of the gastric electrical signal. That is, the signal is first filtered in the forward direction, and then the forward-filtered signal is filtered in the reverse direction. This can not only effectively remove high-frequency noise and DC offset, but also does not affect the phase characteristics of the gastric electrical signal, thus maintaining the integrity of the signal.

[0104] The original gastric electrical signal has a full frequency band of 0.016-0.15 Hz. Based on the degree of disturbance in the gastric electrical rhythm, it can be further divided into: slow wave (0.016-0.033 Hz), normal wave (0.034-0.068 Hz), and fast wave (0.068-0.15 Hz). A third-order FIR filter and a zero-phase filter were used for bidirectional filtering, applying bandpass filtering to the three different frequency bands with a transition bandwidth of 0.15.

[0105] Step 30: Determine the first resolved phase and gastric electrical phase artifact information based on the preprocessed gastric electrical signal. Step 30 includes steps 31-32:

[0106] Step 31: Determine the first analytical phase based on the preprocessed gastric electrical signal.

[0107] To better analyze the amplitude and phase changes of the preprocessed gastric electrical signal, this embodiment uses Hilbert transform to convert the one-dimensional preprocessed gastric electrical signal into an analytic signal on a two-dimensional complex plane. The magnitude and amplitude of the analytic signal represent the amplitude and phase of the signal, respectively. That is, the envelope (instantaneous amplitude) and analytic phase are calculated through the analytic signal, and then the instantaneous frequency is obtained.

[0108] The Hilbert transform is widely used in signal processing, and its physical meaning is very clear: it delays the phase of all frequency components of a signal by 90 degrees. The Hilbert transform of a preprocessed gastric electrical signal is calculated using the following formula:

[0109]

[0110] The analytical process of the Hilbert transform is as follows:

[0111]

[0112] in, This represents an analytic signal; the process has the following characteristics: the power spectra of the real and imaginary parts are the same, and the autocorrelation functions are the same; the cross-correlation function of the real and imaginary parts is an odd function; the power spectrum of the analytic signal only has a positive frequency band, and the intensity is 4 times that of the original (the amplitude is 2 times that of the original).

[0113] The formula for calculating the first analytical phase is as follows:

[0114]

[0115] The formula for calculating instantaneous amplitude is as follows:

[0116]

[0117] The formula for calculating instantaneous frequency is as follows:

[0118]

[0119] Step 32: Determine the gastric electrical phase artifact information based on the first analytical phase.

[0120] Specifically, artifact identification can be based on two parts: large amplitude caused by body motion and non-monotonic phase changes introduced by nonlinear interference. Since amplitude is not used in the subsequent coupling process, only phase artifacts need to be considered. Because the physiological processes such as contraction and relaxation of gastrointestinal smooth muscle are relatively stable, the amplitude and frequency of gastric electrical signals also remain relatively stable, so they can be approximated as linear. The Hilbert transform is essentially a linear operator, and the analytic phase is calculated based on the amplitude and phase of the new function. Since linear operators satisfy the superposition principle, the analytic phase of the Hilbert transform can also be obtained by calculating the analytic phase of each frequency component separately and then adding them together to obtain the analytic phase of the entire function, thus satisfying the linear property. When the analytic phase of the signal changes nonlinearly, it indicates that there is a nonlinear component in the signal. This nonlinear component may come from various factors, such as the nonlinear dynamic mechanism of the signal source, the influence of noise or interference, etc. The specific implementation steps are as follows: Step 32 includes steps 321-325:

[0121] Step 321: Obtain multiple edges where the phase derivative change of the first analytical phase is greater than -1, and calculate the period length between each edge. Calculate the distribution of period lengths based on the first analytical phase to determine the period threshold. Obtain multiple edges in the signal where the derivative change of the first analytical phase is greater than -1, and calculate the time difference between each edge, i.e., the period length.

[0122] Step 322: Determine the period threshold based on the mean and standard deviation of multiple period lengths. Calculate the mean and standard deviation of all period lengths, and set the period threshold to the mean minus or plus three times the standard deviation.

[0123] Step 323: Determine the second time point corresponding to the period lengths greater than and less than the period threshold based on the period threshold.

[0124] Step 324: Obtain the third time point corresponding to the non-monotonic increasing period length among multiple period lengths.

[0125] Based on phase time series detection, artifacts are identified, periods that are too short or too long (period lengths greater than or less than the period threshold) and non-monotonic increasing periods in the signal are marked with red areas in the graph, and the time point information corresponding to the artifacts is extracted.

[0126] Step 325: Extract the second and third time points as gastric electrical phase artifact information.

[0127] Step 40: Preprocess the raw EEG signal to obtain a preprocessed EEG signal.

[0128] Specifically, the raw EEG signal is filtered to obtain a preprocessed EEG signal.

[0129] Based on different frequency bands, EEG can be divided into 5 parts:

[0130] Delta waves: with a frequency range of 0.5Hz-4Hz, are associated with deep sleep and restorative sleep.

[0131] Theta waves: with a frequency range of 4Hz-8Hz, are associated with dreams, hypnosis, and deep emotions.

[0132] Alpha waves: with a frequency range of 8Hz-13Hz, are associated with relaxation, focus, and creativity.

[0133] Beta waves: with a frequency range of 13Hz-40Hz, are associated with alertness, thinking, and cognition.

[0134] Gamma waves: with a frequency range of 40Hz-100Hz, are associated with information processing, learning, and memory.

[0135] First, a notch filter of 49-51Hz is used to perform band-stop filtering on the raw EEG signal to remove 50Hz power frequency interference. Then, the frequency band is divided into 0.5-70Hz with a passband of 1Hz, resulting in 0.5-1Hz, 1-2Hz, ... 69-70Hz. Bandpass filtering is then performed on each of these 70 frequency bands, followed by bidirectional filtering.

[0136] Step 50: Determine the second phase amplitude information and EEG artifact information based on the preprocessed EEG signals. The second phase amplitude information includes: the second analytical phase and the second instantaneous amplitude. Step 50 includes steps 51-52:

[0137] Step 51: Determine the second analytical phase and the second instantaneous amplitude based on the preprocessed EEG signal.

[0138] The preprocessed EEG signal was subjected to Hilbert transform to obtain the second analytic phase and the second instantaneous amplitude. The instantaneous amplitude and analytic phase of different frequency bands of the preprocessed EEG signal were extracted using Hilbert transform. The processing procedure was the same as the feature extraction procedure in step 31 of the preprocessed gastric EEG signal, and will not be repeated here.

[0139] Step 52: Determine EEG artifact information based on preprocessed EEG signals. Detect and extract artifacts containing outliers, eye movements, electromyography (EMG), electrocardiogram (ECG), and other non-neural sources from the segmented data. This embodiment uses the average amplitude difference of each segment and the Z-score to identify artifacts. The specific implementation steps are as follows: Step 52 includes steps 521-523:

[0140] Step 521: Divide the preprocessed EEG signal of each channel into multiple sub-segments. The original EEG signal consists of 16 channels, and each channel is processed accordingly. The preprocessed EEG signal of each channel can be segmented into multiple sub-segments, with each segment lasting ten seconds.

[0141] Step 522: Determine the Z-Score matrix based on the average amplitude difference and maximum absolute value of each sub-segment signal. Specifically, the average amplitude difference is obtained by calculating the absolute value of the difference between each amplitude data point in each sub-segment signal and the mean amplitude of that sub-segment signal, and then averaging the result. Simultaneously, the maximum absolute value of the amplitude data for each sub-segment is also calculated. Then, a Z-transform is performed on the average amplitude difference of each sub-segment signal. This is done by subtracting the mean amplitude of each sub-segment signal from the average amplitude difference of each sub-segment signal and dividing by the standard deviation of the amplitude of each sub-segment signal, thus obtaining the transformed amplitude. The Z-Score matrix is ​​a two-dimensional matrix that includes the transformed amplitude and the maximum absolute value of the amplitude for all sub-segments.

[0142] Step 523: Extract the time points of the sub-segment signals corresponding to elements in the Z-Score matrix that are greater than a preset score threshold as EEG artifact information. In this step, the preset score threshold includes a first threshold and a second threshold. Extract the sub-segment signals corresponding to the transform amplitudes greater than the first threshold and the sub-segment signals corresponding to the maximum absolute values ​​of the amplitudes greater than the second threshold. The time points of the extracted sub-segment signals are used as EEG artifact information. That is, for each sub-segment signal, if either the transform amplitude or the maximum absolute value of the amplitude exceeds the threshold, the sub-segment signal is identified as an artifact.

[0143] Step 60: Based on the first analytical phase, gastric electroencephalogram (GEG) phase artifact information, the second phase amplitude information, and EEG artifact information, determine the first target analytical phase and the second target phase amplitude information. The second target phase amplitude information includes: the second target analytical phase and the second target instantaneous amplitude. Step 60 includes steps 61-62:

[0144] Step 61: Remove the phase corresponding to the gastric electrical phase artifact information from the first analytical phase to obtain the first target analytical phase.

[0145] Step 62: Remove the phase and amplitude corresponding to the EEG artifact information from the second analytical phase and the second instantaneous amplitude to obtain the second target analytical phase and the second target instantaneous amplitude.

[0146] To remove artifacts, simply remove the signal information (phase and amplitude) in the phase and amplitude that corresponds to the time point indicated by the artifact information.

[0147] Step 70: Perform phase-phase coupling and phase-amplitude coupling on the phase and amplitude information of the first target and the second target, and perform amplitude coupling on the preprocessed gastric electroencephalogram signal and the preprocessed electroencephalogram signal.

[0148] Cross-frequency coupling is a neural phenomenon reflecting the interaction between physiological signals of different frequencies. This interaction may be an effective mechanism enabling the brain to coordinate and integrate information across different temporal and spatial scales. Cross-frequency coupling between the stomach and brain refers to the dynamic interaction between neural oscillations of different frequency bands, which may coordinate neural dynamics on spatial and temporal scales and is related to higher cognitive functions such as sensory information integration and spatial and temporal memory encoding. Cross-frequency coupling often occurs between low-frequency and high-frequency oscillating signals; in fact, this cross-frequency coupling relationship also exists between low-frequency signals.

[0149] Cross-frequency coupling analysis methods can be broadly classified into three coupling modes: phase-phase coupling, amplitude-amplitude coupling, and phase-amplitude coupling. The following will describe these in detail: Step 70 includes steps 71-73:

[0150] Step 71: Perform phase-to-phase coupling based on the first target's analytical phase and the second target's analytical phase to obtain the phase-locked value.

[0151] Both gastric electroencephalogram (GEG) signals and electroencephalogram (EEG) signals can be viewed as periodic or quasi-periodic signals composed of multiple superimposed sine waves, thus possessing distinct frequency and phase characteristics. A causal relationship or information transmission exists between them, leading to phase consistency or amplitude modulation within certain frequency ranges or across frequencies. Phase coupling indices can quantitatively describe the degree of phase correlation between gastric and EEG signals, thereby reflecting the interaction between gastrointestinal motility and neural activity. Specifically, step 71 includes steps 711-712:

[0152] Step 711: Determine the resolved phase of the envelope based on the resolved phase of the second target. Phase-phase coupling refers to the consistency between the phases of two signals at the same or different frequencies. In this embodiment, the phase-locked value (PLV) is calculated based on circular statistical phase synchronization. When calculating the phase-phase coupling relationship between the gastric electroencephalogram (GEG) signal and the electroencephalogram (EEG) signal, the phase of the EEG signal is generally not used directly, but rather the phase of the EEG signal envelope is extracted. In this step, a Hilbert transform is performed on the resolved phase of the second target to obtain the resolved phase of the envelope.

[0153] Step 712: Calculate the phase-locked value based on the resolved phase of the envelope and the resolved phase of the first target. The degree of phase coupling between the stomach and brain is quantified using the following formula:

[0154]

[0155] Where N is the length of time, and These are the resolved phase of the envelope and the resolved phase of the first target, respectively, for different frequency bands. The analytical phase of the envelope, The phase is analyzed for the first target.

[0156] The degree of PPC coupling and causal relationship in different frequency bands of the gastrobrain complex were calculated using phase-locked loop values ​​based on circular statistics. Figure 4 As shown, Figure 4 The top image in the diagram illustrates the degree of coupling, while the bottom image shows the causal relationship. The horizontal axis represents the 70 frequency bands of the EEG signal after division, and the vertical axis represents the 3 frequency bands of the gastric electrical signal. Figure 4 In the image above, the shades of color reflect the degree of coupling between gastric and brain signals in the corresponding frequency band; the darker the color, the stronger the coupling. Figure 4 In the image below, black arrows indicate information transmission from the stomach to the brain, while white arrows indicate information transmission from the brain to the stomach. The intensity of the color reflects the amount of information transmitted. The results obtained below are explained in the same way.

[0157] Step 72: Amplitude coupling is performed on the preprocessed gastric electroencephalogram (GEG) signal and the preprocessed electroencephalogram (EEG) signal to obtain the average Pearson correlation coefficient.

[0158] Amplitude-amplitude coupling (AAC) in the gastro-brain domain refers to the correlation between the amplitudes of gastric electrical signals and electroencephalogram (EEG) signals across different frequency ranges. It reflects the synchronization or coordination between gastrointestinal motility and neural activity. AAC can be categorized into two types: low-frequency-high-frequency coupling and high-frequency-high-frequency coupling. Low-frequency-high-frequency coupling refers to the variation in amplitude between the low-frequency components of one signal and the high-frequency components of another signal. High-frequency-high-frequency coupling refers to the correlation between the amplitudes of the high-frequency components of two signals.

[0159] In this embodiment, cooperative modulation (CM) is used to quantify the amplitude coupling of gastric electroencephalogram (GEG) signals at different frequency bands, that is, decomposing the time-domain signal into single, continuous, adjacent, and non-overlapping time windows. A fast Fourier transform is performed on the signal in each time window to obtain the spectral density function of that time window, and multiplying it by its complex conjugate yields its power spectrum S(f). The specific implementation steps are as follows: Step 72 includes steps 721-725:

[0160] Step 721: Divide the preprocessed gastric electrical signal into multiple consecutive first time windows.

[0161] Step 722: Perform Fast Fourier Transform (FFT) on the signal in each first time window at different frequency bands to obtain the first amplitude to be coupled in different frequency bands. The first amplitude to be coupled is obtained by taking the modulus after the FFT.

[0162] Step 723: Divide the preprocessed EEG signal into multiple consecutive second time windows.

[0163] Step 724: Perform Fast Fourier Transform (FFT) on the signal in each second time window at different frequency bands to obtain the second power spectrum to be coupled in different frequency bands. Obtain the amplitude by taking the modulus after the FFT, and calculate the square of the amplitude to obtain the power.

[0164] Step 725: Calculate the average Pearson correlation coefficient based on the values ​​of the first to be coupled amplitude and the second to be coupled power spectrum.

[0165] First, define the size and step size of the time window. The size of the time window represents how many seconds of data are contained in each time window, for example, 1 second. The step size of the time window represents how many seconds are between each time window, for example, 0.5 seconds. Use a Fast Fourier Transform with 1000 points to obtain the amplitude of different frequency bands of the gastric electroencephalogram (GEO) signal and the power of different frequency bands of the electroencephalogram (EEG) signal in each time window. Then, calculate the Pearson correlation coefficient of the current time window in different frequency bands and average the Pearson correlation coefficients of different time windows in the frequency band as the amplitude-amplitude coupling factor.

[0166] The coupling (mean Pearson correlation coefficient) between different frequency bands of the amplitude of gastric electroencephalogram (GEG) and the power of EEG is calculated using the following formula:

[0167]

[0168] Where, x i and y i This represents the values ​​of the first uncoupled amplitude of the preprocessed gastric electroencephalogram (GEG) signal and the second uncoupled power spectrum of the preprocessed electroencephalogram (EEG) signal for the i-th sample. This represents the average value of the first amplitude to be coupled. This represents the average power of the second power spectrum to be coupled.

[0169] In this embodiment, the AAC coupling degree and causal interaction diagram of different frequency bands of the stomach and brain obtained by co-modulation calculation are as follows: Figure 5 As shown.

[0170] Step 73: Perform phase-amplitude coupling based on the analytical phase of the first target and the instantaneous amplitude of the second target to obtain the coupling strength value.

[0171] Phase-amplitude coupling (PAC) is the relationship between the phase of one frequency band and the power of another. PAC is an indicator that reflects how the amplitude of a high-frequency signal changes with the phase of a low-frequency signal. It can reveal the interaction between neural oscillations of different frequencies, potentially related to information processing and integration in the brain. Binning-variance analysis is a method for calculating phase-amplitude coupling. Its basic idea is to divide the phase signal into several equally wide intervals, each called a bin. Then, the average amplitude signal within each bin is calculated. Finally, using variance analysis, the ratio of the between-group mean squared error to the within-group mean squared error, i.e., the F-statistic, is used as an indicator of the strength of phase-amplitude coupling. The advantage of this method is its simplicity and ease of implementation, as it does not require the assumption that the relationship between phase and amplitude is linear or sinusoidal.

[0172] The following describes the specific implementation steps for phase-amplitude coupling calculation in binning-variance analysis:

[0173] First, the phase signal of the gastric electroencephalogram (GEG) is divided into n equally wide intervals, each called a bin, and the boundary values ​​of each bin are calculated. Then, for each bin, the index of the phase signal belonging to that bin is found. Based on these indices, the corresponding amplitude signals are extracted from the EEG amplitude, and their average values ​​are calculated to obtain the average amplitude of each bin. Finally, the overall average of the average amplitudes of all bins is calculated, called the global mean.

[0174] The first target's analytical phase is: The instantaneous amplitude of the second target is a. t Soon Divided into n bin The system is divided into several equally spaced intervals (bins). To simplify calculations, n... bin The value is 18, and the boundary of each interval is... Where k = 1, 2, ..., n bin .

[0175] Then calculate the interval 'a' corresponding to each interval in the instantaneous amplitude of the second target. t The average value, that is:

[0176]

[0177] Where, n k This represents the number of time points belonging to the k-th interval.

[0178] Then, using the principles of analysis of variance, the between-group sum of squares (the sum of squares of the differences between the average amplitude of each bin and the global mean) and the within-group sum of squares (the sum of squares of the differences between the amplitude of each bin and its average amplitude) are calculated. Next, the between-group degrees of freedom (the number of bins minus one) and the within-group degrees of freedom (the number of data points minus the number of bins) are calculated. Then, the between-group and within-group root mean squares (RMS) and the between-group sum of squares (RMS) and the within-group sum of squares (RMS) are calculated, respectively. Finally, the F-statistic (the between-group MMS divided by the within-group MMS) is calculated. This value reflects the degree of modulation of the amplitude signal by the phase signal, that is, the strength of the phase-amplitude coupling.

[0179] The degree of PAC coupling in different frequency bands of the gastrobrain and the causal relationship diagram obtained by binning-variance analysis are shown below. Figure 6 As shown.

[0180] Step 80: Determine the transfer entropy based on the preprocessed gastric electroencephalogram (GE) signal and the preprocessed electroencephalogram (EEG) signal. Step 80 includes steps 81-85:

[0181] Step 81: Determine the gastric electrical vector based on the preprocessed gastric electrical signal.

[0182] To calculate the information content and causality between the gastrobrain time series, the data first needs to be transformed into points in a multidimensional space. This allows for better capture of the dynamic characteristics within the data. Specifically, starting from the first point in the preprocessed gastric electroencephalogram (GEG) signal, a value is taken every t points until M values ​​are collected, resulting in an M-dimensional vector. This process is repeated starting from the second point to obtain a second M-dimensional vector. This process continues until all points are collected, resulting in an M-dimensional GEG vector sequence. The length of this vector sequence is N-(M-1)*t, where N is the length of the signal x.

[0183] Step 82: Determine the EEG vector based on the gastric electrical vector and the preprocessed EEG signal.

[0184] For preprocessing EEG signals, the dimension of the gastric electroencephalogram (GEG) vector can be determined starting from the (M-1)*t+1th point, taking a value at every other point until all points are taken, thus obtaining a one-dimensional EEG vector sequence. The length of this vector sequence is also N-(M-1)*t.

[0185] Step 83: Determine the corresponding marginal probability distribution and joint probability distribution based on the gastric electrical vector and the electroencephalogram (EEG) vector. Construct a two-dimensional joint probability distribution based on the last column of the gastric electrical vector sequence and the EEG vector sequence.

[0186] Step 84: Determine the conditional entropy and joint entropy based on the marginal probability distribution and joint probability distribution. The formulas for calculating the joint entropy H(x) and conditional entropy H(x|y) are as follows:

[0187]

[0188]

[0189] Where p(x) represents the marginal probability distribution of the last vector of the gastric electrical vector, p(y) represents the marginal probability distribution of the last vector of the electroencephalogram (EEG) vector, and p(x,y) represents the joint probability distribution of the last vector of the gastric electrical vector and the current value of the EEG vector.

[0190] Step 85: Determine the transfer entropy based on the conditional entropy and joint entropy.

[0191] Finally, a formula is needed to calculate the transfer entropy, which is expressed using the entropy of two random variables: the conditional entropy and the joint entropy.

[0192]

[0193] in, It is the joint entropy of the current value of the EEG vector and the last vector of the Gastrointestinal vector. It is the conditional entropy of the current value of the EEG vector under the condition of the last vector of the given Gastroelectroencephalogram, where M represents the length of the vector.

[0194] Transition entropy measures the influence of one random variable on the future state of another random variable, essentially indicating causality. Specifically, it uses the current state of one random variable and the past states of another to predict the future state of the third, and then examines how much uncertainty this prediction reduces. If the prediction significantly reduces uncertainty, it indicates that the first random variable has a large influence on the second, meaning it has high transition entropy; conversely, if the prediction does not significantly reduce uncertainty, it indicates that the first random variable has little influence on the second, meaning it has low transition entropy.

[0195] In this embodiment, cross-frequency coupling is applied to the analysis of gastric electroencephalogram (GEG) and electroencephalogram (EEG) signals, thereby revealing the complexity and diversity of gastrobrain coupling. Three different coupling indices are used to reflect phase-amplitude coupling, phase-phase coupling, and amplitude-amplitude coupling between GEG and EEG signals, respectively, thus improving the comprehensiveness and richness of the data. Transfer entropy is used to reflect the directional information transfer from GEG to EEG, thereby revealing the degree of influence of GEG on EEG and the direction of information transfer along the gastrobrain neural axis.

[0196] The reliability of the method of the present invention will be verified and illustrated through simulation experiments below:

[0197] To verify the reliability of the calculation results, three sets of alternative data with different phases and amplitudes were first generated. The original phase and amplitude data were then shuffled by shifting along 60, 120, and 180 seconds to ensure that the variance and mean of the data remained unchanged, thus preserving the characteristics of the original signal. The Kruskal-Wallis test and multiple comparisons were used to statistically test the four sets of results to demonstrate their reliability.

[0198] However, the hypothesis made using only the Kruskal-Wallis test can only determine whether the medians of each group are equal or unequal, but it cannot reveal differences in other indicators between pairs of groups. Therefore, multiple comparisons are used to return a very specific matrix of values ​​compared between each pair of groups, as well as a graph plotting the confidence intervals of the sample means for each group using line segments. The comparison rule is that if there is no overlap between two line segments, it indicates that the means of the corresponding two groups are significantly different, thus verifying the reliability of the algorithm's results. By analyzing various information from nonparametric analysis of variance, such as sample size, mean, rank, mean squared error, and degrees of freedom, it is possible to determine whether the difference between the control group and the experimental group is significant.

[0199] This invention uses the Tukey-Kramer method for multiple comparisons. This method can control the overall error rate and is suitable for situations with unequal sample sizes. The principle of the Tukey-Kramer method is that for each pair of samples, their mean difference and confidence interval are calculated, and a standardized t-statistic is used to determine whether there is a significant difference. If the confidence intervals of the two samples do not overlap, it indicates that there is a significant difference between them.

[0200] By calculating the transfer entropy of gastric electrical rhythms to brain electrical rhythms and vice versa, and then taking the difference, the causal direction between different frequency bands of the gastric and brain electrical rhythms can be determined; that is, which rhythm has a greater influence on the amplitude of the other. If the difference is greater than 0, it indicates that the gastric electrical rhythm has a greater influence on the amplitude of the brain electrical rhythm; conversely, it indicates that the brain electrical rhythm has a greater influence on the amplitude of the gastric electrical rhythm. The difference is only used to indicate the causal direction and does not represent the causal strength or time delay.

[0201] The results obtained through the Kruskal-Wallis test and multiple comparisons are shown in the figure below. Figure 7 As shown in Table 1:

[0202]

[0203] Table 1. Results of the Kruskal-Wallis test

[0204] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0205] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0206] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for coupling gastric and brain electrical signals in a resting state, characterized in that, Includes the following steps: Acquire raw EEG and raw Gastrointestinal signals of the user in a resting state, simultaneously collected by a multi-channel acquisition device; The raw gastric electrical signal is preprocessed to obtain a preprocessed gastric electrical signal; The first analytical phase and gastric electrical phase artifact information are determined based on the preprocessed gastric electrical signal; The raw EEG signal is preprocessed to obtain a preprocessed EEG signal; The second phase amplitude information and EEG artifact information are determined based on the preprocessed EEG signals; The first target analytical phase is obtained by removing the phase corresponding to the gastric electrical phase artifact information from the first analytical phase. The phase and amplitude corresponding to the EEG artifact information are removed from the second phase amplitude information to obtain the second target phase amplitude information; The second target phase amplitude information includes: the resolved phase of the second target and the instantaneous amplitude of the second target; Phase-phase coupling and phase-amplitude coupling are performed on the phase resolution of the first target and the phase amplitude information of the second target, and amplitude coupling is performed on the preprocessed gastric electroencephalogram signal and the preprocessed electroencephalogram signal. The transfer entropy is determined based on the preprocessed gastric electroencephalogram (GEG) signal and the preprocessed electroencephalogram (EEG) signal.

2. The method for coupling gastric and brain electrical signals in a resting state according to claim 1, characterized in that, The preprocessing of the raw gastric electrical signal to obtain a preprocessed gastric electrical signal includes: Calculate the power spectrum of the raw gastric electrical signal; Determine the lead signal corresponding to the maximum power based on the power spectrum; The lead signal is filtered to obtain a preprocessed gastric electrical signal.

3. The method for coupling gastric and brain electrical signals in a resting state according to claim 1, characterized in that, The step of determining the first analytical phase and gastric phase artifact information based on the preprocessed gastric electrical signal includes: The first analytical phase is determined based on the preprocessed gastric electrical signal; Based on the first analytical phase, determine the gastric electrical phase artifact information; The second phase amplitude information includes: the second analytical phase and the second instantaneous amplitude; The step of determining the second phase amplitude information and EEG artifact information based on the preprocessed EEG signal includes: The second analytical phase and the second instantaneous amplitude are determined based on the preprocessed EEG signals; Brain artifact information is determined based on the preprocessed EEG signals.

4. The gastroencephalometric signal coupling method under resting state according to claim 3, characterized in that, The step of determining the gastric electrical phase artifact information based on the first resolved phase includes: Obtain multiple edges where the phase derivative change of the first analytical phase is greater than -1, and calculate the period length between each edge; The period threshold is determined based on the mean and standard deviation of the multiple period lengths; The second time point corresponding to the period lengths greater than the period threshold and less than the period threshold is determined based on the period threshold; Obtain the third time point corresponding to the non-monotonic increasing period length among the multiple period lengths; The second time point and the third time point are extracted as gastric electrical phase artifact information.

5. The gastroencephalometric signal coupling method under resting state according to claim 3, characterized in that, The step of determining EEG artifact information based on the preprocessed EEG signals includes: The preprocessed EEG signal of each channel is divided into multiple sub-segments; The Z-Score matrix is ​​determined based on the average amplitude difference and the maximum absolute value of the amplitude of each sub-segment signal. The time points of the sub-segment signals corresponding to the elements in the Z-Score matrix that are greater than a preset score threshold are extracted as EEG artifact information.

6. The method for coupling gastric and brain electrical signals in a resting state according to claim 1, characterized in that, The step of performing phase-phase coupling and phase-amplitude coupling on the phase and amplitude information of the first target and the second target, and performing amplitude coupling on the preprocessed gastric electroencephalogram (GEG) signal and the preprocessed electroencephalogram (EEG) signal, includes: Phase-to-phase coupling is performed based on the first target analytical phase and the second target analytical phase to obtain the phase-locked value; Amplitude coupling was performed on the preprocessed gastric electroencephalogram (GEG) signal and the preprocessed electroencephalogram (EEG) signal to obtain the average Pearson correlation coefficient. Phase-amplitude coupling is performed based on the analytical phase of the first target and the instantaneous amplitude of the second target to obtain the coupling strength value.

7. The gastroencephalometric signal coupling method under resting state according to claim 6, characterized in that, Phase-to-phase coupling is performed based on the first target resolved phase and the second target resolved phase to obtain the phase-locked value, including: The analytical phase of the envelope is determined based on the analytical phase of the second target; The phase-locked value is calculated based on the resolved phase of the envelope and the resolved phase of the first target.

8. The method for coupling gastric and brain electrical signals in a resting state according to claim 6, characterized in that, The step of amplitude coupling of the preprocessed gastric electroencephalogram (GEG) signal and the preprocessed electroencephalogram (EEG) signal to obtain the average Pearson correlation coefficient includes: The preprocessed gastric electrical signal is divided into multiple consecutive first time windows; Perform a Fast Fourier Transform on the signal in each of the first time windows at different frequency bands to obtain the first amplitude to be coupled in different frequency bands; The preprocessed EEG signal is divided into multiple consecutive second time windows; Perform a Fast Fourier Transform on the signal in each of the second time windows at different frequency bands to obtain the second power spectrum to be coupled in different frequency bands; The average Pearson correlation coefficient is calculated based on the values ​​of the first amplitude to be coupled and the second power spectrum to be coupled.

9. The method for coupling gastric and brain electrical signals in a resting state according to claim 1, characterized in that, The step of determining the transfer entropy based on the preprocessed gastric electroencephalogram (GEG) signal and the preprocessed electroencephalogram (EEG) signal includes: The gastric electrical vector is determined based on the preprocessed gastric electrical signal; The brainwave vector is determined based on the gastric electrical vector and the preprocessed brainwave signal; The corresponding marginal probability distribution and joint probability distribution are determined based on the gastric electrical vector and the brain electrical vector; Determine the conditional entropy and joint entropy based on the marginal probability distribution and the joint probability distribution; The transition entropy is determined based on the conditional entropy and the joint entropy.

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