A dynamic modeling method for neurovascular coupling based on the fusion of CEEMDAN and GLM

Abstract

The present invention discloses a dynamic modeling method for neurovascular coupling based on the fusion of CEEMDAN and GLM, which relates to the field of biological signal processing technology. By introducing a white noise-enhanced ensemble empirical mode decomposition strategy, EEG signals are adaptively non-parametrically segmented in frequency bands, and individual-specific neural oscillation patterns (such as β-γ mixed rhythms or abnormal enhancement of the γ band after a stroke) can be captured without presetting frequency band boundaries. At the same time, the time-varying spectral characteristics of the intrinsic mode function generated by CEEMDAN are embedded in the hemodynamic response function reconstruction process of the GLM model, and the individualized neural oscillation characteristics are dynamically extracted through the energy entropy weighting mechanism to quantitatively analyze the spatiotemporal heterogeneity of the dynamic coupling of neural blood flow under pathological conditions. This method not only overcomes the physiological limitations of traditional fixed frequency band division, but also significantly improves the analytical accuracy of non-stationary signals in pathological noise environments through the adaptive decomposition technology with anti-modal aliasing, providing a dynamic modeling framework for the study of neurovascular coupling mechanisms.

Description

Technical Field

[0001] The present invention relates to the technical field of biological signal processing, and in particular to a neurovascular coupling dynamic modeling method based on the fusion of CEEMDAN and GLM. Background Art

[0002] In the study of neurovascular coupling (NVC) mechanisms, early techniques focused primarily on the independent analysis of single-modal signals, with less attention paid to the dynamic interactions between neural electrical activity and hemodynamic responses. With the development of multimodal neuroimaging, the fusion of electroencephalography (EEG) and functional near-infrared spectroscopy (fNIRS) has gradually become a core tool for analyzing neurovascular coupling due to its complementary temporal and spatial resolution. Correlations between EEG millisecond-scale electrophysiological oscillations and fNIRS hemodynamic responses (such as changes in HbO / HbR concentrations) under task conditions have provided new insights into the assessment of brain dysfunction.

[0003] However, existing fNIRS analysis methods based on EEG feature constraints (such as generalized linear models (GLMs)) still have significant technical bottlenecks. Traditional methods are highly dependent on pre-set / / Fixed frequency band division, forcing neural oscillations to be limited to a fixed frequency range (such as extracting The frequency band power is used as the GLM input), which is difficult to adapt to the natural differences in neural oscillation patterns between individuals and the dynamic changes in pathological conditions. For example, in the process of post-stroke neural remodeling, patients often have - Mixed rhythms, Specific frequency band shifts such as abnormal frequency band enhancement, while fixed frequency band division will cause such key pathological features to be artificially separated or ignored, resulting in physiological distortion of the model input.

[0004] On the other hand, existing cross-modal coupling models are mostly based on data from healthy individuals and lack the ability to systematically analyze the spatiotemporal heterogeneity of neurovascular uncoupling under pathological conditions. After stroke, different brain regions may exhibit complex interaction patterns such as compensatory activation and abnormal ipsilateralization, with the coupling strength, phase relationship, and spatial distribution of their neural electrical activity and hemodynamic responses showing dynamic changes. However, the traditional fixed rhythm modulation GLM framework can only capture surface correlations and cannot analyze the specific coupling trajectories of different brain regions under pathological conditions, resulting in the model's insufficient ability to analyze the multi-scale interaction mechanisms of neurovascular units.

[0005] With the increasing demand for neurorehabilitation in clinical settings, there is an urgent need to accurately characterize individual-specific neural oscillation patterns under pathological conditions and their dynamic coupling with hemodynamic responses. Cross-modal analysis not only needs to break through the physiological limitations of fixed frequency bands but also adapt to the time-varying characteristics of non-stationary EEG signals, particularly the complex phenomena of high-frequency oscillation migration and cross-band coupling during post-stroke neural remodeling. Summary of the Invention

[0006] The technical solution of the present invention to solve the above technical problems is to provide a neurovascular coupling dynamic modeling method based on the fusion of CEEMDAN and GLM, comprising the following steps:

[0007] (1) Acquisition of signal data: synchronously collect EEG and fNIRS signals, segment them according to task phases, and mark them with timestamps;

[0008] (2) Complete empirical mode decomposition and mode acquisition: CEEMDAN decomposition is performed on the EEG signal to generate multiple intrinsic mode functions (IMFs);

[0009] (3) Construction of IMF-GLM analytical framework:

[0010] Calculate the time domain energy proportion and energy entropy of each IMF ;

[0011] according to Keep the first M IMFs in descending order, and then filter out the top N core IMFs based on the threshold;

[0012] Extract the instantaneous frequency and time-varying energy entropy from each core IMF to form the feature set of each IMF;

[0013] At the same time, the / / The GLM model constructed by band power and the commonly used Boxcar model were used as controls;

[0014] Constructing the GLM model of CEEMDAN:

[0015] ;

[0016] in: Trigger signal for the task; EEG-derived features extracted for the feature set;

[0017] Analysis of HbO / HbR signaling:

[0018] ;

[0019] in, is the blood oxygen signal, is the noise term, and by comparing the regression coefficients between models and activation patterns, quantifying the spatiotemporal heterogeneity of nerve-blood flow dynamic coupling under pathological conditions;

[0020] (4) Multi-dimensional evaluation:

[0021] Based on the regression coefficient Statistical characteristics analysis;

[0022] Model performance evaluation based on ROC curve.

[0023] Furthermore, the CEEMDAN decomposition in step (2) includes:

[0024] Initialization: Set the number of noise sequences , the amplitude of the noise sequence , the original signal is , the number of iterations is ;

[0025] Add different white noises to the original signal and get Perturbation signal:

[0026] ;

[0027] in, The mean is 0 and the variance is White noise sequence;

[0028] For each disturbance signal Perform classic EMD decomposition to obtain a set of intrinsic mode functions

[0029] (IMF) and residuals ,Right now

[0030] ;

[0031] in, It is The first disturbance signal IMF, is the number of IMFs;

[0032] For each IMF, the arithmetic mean of all disturbance signals is calculated to obtain the final IMF.

[0033] ;

[0034] in, It is a final IMF;

[0035] The arithmetic mean of all disturbance signals is calculated for each residual to obtain the final residual, that is,

[0036] ;

[0037] Determine whether the final residual satisfies monotonicity or is small enough; if it does, stop decomposition; if it does not, let , and replace the original signal with the final residual;

[0038] Output the final decomposition result, that is

[0039] .

[0040] Furthermore, the energy entropy calculation in step (3) is defined as:

[0041]

[0042] in, No. The energy entropy of an IMF, the screening condition meets , and ranked in the top N.

[0043] Furthermore, step 4 is based on the regression coefficient The statistical characteristics analysis includes:

[0044] Normality test: Shapiro-Wilk test was used to assess the normality between groups. Value distribution, used to ensure the applicability of parameter tests;

[0045] Homogeneity of variance test: Levene's test was used to determine the homogeneity of variance between groups, which was used to guide the selection of subsequent ANOVA or nonparametric tests;

[0046] Analysis of differences between groups: A three-way repeated measures analysis of variance was used to test the significant difference in β-value estimation between CEEMDAN-GLM and traditional box model.

[0047] Furthermore, the ROC curve-based model performance evaluation in step 4 includes:

[0048] Constructing ROC curves: By changing the activation induced by the task Value Threshold , calculate the true positive rate TPR and false positive rate FPR:

[0049] , ;

[0050] The target motor areas were defined as the primary motor cortex, premotor cortex, and primary somatosensory cortex, with left-hand and right-hand tasks corresponding to the contralateral motor cortex, respectively.

[0051] To address these technical challenges, the present invention proposes a joint EEG fNIRS analysis method based on CEEMDAN and GLM. This method employs a white noise-enhanced ensemble empirical mode decomposition (EMD) strategy to adaptively segment EEG signals into nonparametric frequency bands. This approach captures individual-specific neural oscillation patterns (such as mixed β-γ rhythms or abnormal gamma enhancement after stroke) without pre-defined frequency band boundaries. Furthermore, the time-varying spectral features of the intrinsic mode function (IMF) generated by CEEMDAN are embedded in the hemodynamic response function (HRF) reconstruction process of the GLM model. This method dynamically extracts individualized neural oscillation features through an energy entropy weighting mechanism, quantitatively analyzing the spatiotemporal heterogeneity of neurovascular dynamic coupling under pathological conditions. This method not only overcomes the physiological limitations of traditional fixed frequency band segmentation but also, through its adaptive decomposition technique with anti-modal aliasing, significantly improves the accuracy of analyzing nonstationary signals in pathological noisy environments, providing a more biologically meaningful dynamic modeling framework for studying neurovascular coupling mechanisms. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying any creative work.

[0053] Figure 1 This is a flowchart of the steps of the neurovascular coupling dynamic modeling method based on the fusion of CEEMDAN and GLM according to the present invention;

[0054] Figure 2 This is the EEG and fNIRS acquisition site described in the present invention;

[0055] Figure 3 This is a diagram showing the decomposition results of the EEG frequency band decomposition performed by the CEEMDAN described in the present invention. DETAILED DESCRIPTION

[0056] The present invention proposes a neurovascular coupling dynamic modeling method based on the fusion of CEEMDAN and GLM, aiming to address the physiological limitations of fixed frequency band division in existing neurovascular coupling analysis and the insufficient cross-modal coupling analysis under pathological conditions.

[0057] The following is an explanation of the neurovascular coupling dynamic modeling method based on the fusion of CEEMDAN and GLM proposed in the present invention in a specific embodiment:

[0058] Example 1: A neurovascular coupling dynamic modeling method based on the fusion of CEEMDAN and GLM, such as Figure 1As shown, the following steps are included:

[0059] (1) Acquisition of signal data: synchronously collect EEG and fNIRS signals, segment them according to task phases, and mark them with timestamps;

[0060] (2) Complete empirical mode decomposition and mode acquisition: CEEMDAN decomposition is performed on the EEG signal to generate multiple intrinsic mode functions (IMFs);

[0061] (3) Construction of IMF-GLM analytical framework:

[0062] Calculate the time domain energy proportion and energy entropy of each IMF ;

[0063] according to Keep the first M IMFs in descending order, and then filter out the top N core IMFs based on the threshold;

[0064] Extract the instantaneous frequency and time-varying energy entropy from each core IMF to form the feature set of each IMF;

[0065] At the same time, the / / The GLM model constructed by band power and the commonly used Boxcar model were used as controls;

[0066] Constructing the GLM model of CEEMDAN:

[0067] ;

[0068] in: Trigger signal for the task; EEG-derived features extracted for the feature set;

[0069] Analysis of HbO / HbR signaling:

[0070] ;

[0071] in, is the blood oxygen signal, is the noise term, and by comparing the regression coefficients between models and activation patterns, quantifying the spatiotemporal heterogeneity of nerve-blood flow dynamic coupling under pathological conditions;

[0072] (4) Multi-dimensional evaluation:

[0073] Based on the regression coefficient Statistical characteristics analysis;

[0074] Model performance evaluation based on ROC curve.

[0075] Furthermore, the CEEMDAN decomposition in step (2) includes:

[0076] Initialization: Set the number of noise sequences , the amplitude of the noise sequence , the original signal is , the number of iterations is ;

[0077] Add different white noises to the original signal to obtain N disturbance signals:

[0078] ;

[0079] in, The mean is 0 and the variance is White noise sequence;

[0080] For each disturbance signal Perform classic EMD decomposition to obtain a set of intrinsic mode functions

[0081] (IMF) and residuals ,Right now

[0082] ;

[0083] in, It is The first disturbance signal IMF, is the number of IMFs;

[0084] For each IMF, the arithmetic mean of all disturbance signals is calculated to obtain the final IMF.

[0085] ;

[0086] in, It is a final IMF;

[0087] The arithmetic mean of all disturbance signals is calculated for each residual to obtain the final residual, that is,

[0088] ;

[0089] Determine whether the final residual satisfies monotonicity or is small enough; if it does, stop decomposition; if it does not, let , and replace the original signal with the final residual;

[0090] Output the final decomposition result, that is

[0091] .

[0092] Furthermore, the energy entropy calculation in step (3) is defined as:

[0093] ;

[0094] in, No. The energy entropy of an IMF, the frequency range is 0.5-100hz, and the screening conditions are met , and ranked in the top N.

[0095] Furthermore, step 4 is based on the regression coefficient The statistical characteristics analysis includes:

[0096] Normality test: Shapiro-Wilk test was used to assess the normality between groups. Value distribution, used to ensure the applicability of parameter tests;

[0097] Homogeneity of variance test: Levene's test was used to determine the homogeneity of variance between groups, which was used to guide the selection of subsequent ANOVA or nonparametric tests;

[0098] Analysis of differences between groups: A three-way repeated measures analysis of variance was used to test the CEEMDAN-GLM and the traditional box model. Significant differences in the estimated values.

[0099] Furthermore, the ROC curve-based model performance evaluation in step 4 includes:

[0100] Constructing ROC curves: By changing the activation induced by the task Value Threshold , calculate the true positive rate TPR and false positive rate FPR:

[0101] , ;

[0102] The target motor areas were defined as the primary motor cortex, premotor cortex, and primary somatosensory cortex, with left-hand and right-hand tasks corresponding to the contralateral motor cortex, respectively.

[0103] Working principle:

[0104] Data-adaptive EEG frequency band analysis: CEEMDAN is used to perform multi-scale decomposition of the original EEG signal, and a series of intrinsic mode functions (IMFs) are generated by introducing a white noise-enhanced ensemble empirical mode decomposition strategy. Compared with empirical mode decomposition (EMD) and variational mode decomposition (VMD), CEEMDAN effectively suppresses modal aliasing through multi-scale noise injection and ensemble averaging mechanism, which is particularly suitable for non-stationary EEG signals after stroke. - Mixed rhythms, Accurately capture individual-specific frequency band shifts such as abnormal frequency band enhancement.

[0105] Individualized dynamic prior GLM model reconstruction: When screening the modalities with the strongest correlation with hemodynamic response from the IMFs generated by CEEMDAN, the time domain energy proportion and energy entropy of each IMF are first calculated. The energy proportion reflects the modal energy contribution, and the energy entropy quantifies the complexity of the frequency components. By setting the energy entropy threshold, dynamic screening of modalities containing pathological features (such as - The dominant modes of mixed rhythms (typically the first two to three IMFs) are selected. The time-varying spectral features of the selected IMFs are embedded in the hemodynamic response function (HRF) of the GLM. The fixed parameters of the traditional HRF (such as peak time and amplitude) are modeled as a linear combination of the IMF features, forming a time-varying HRF basis function, enabling the model to capture the transient causal relationship between neural oscillations and vascular responses.

[0106] Cross-modal spatiotemporal coupling analysis in pathological conditions: Combining fNIRS spatiotemporal distribution data of hemoglobin concentration, we construct multimodal fusion indices based on IMF characteristics (e.g., modality-blood oxygen correlation matrix) to quantitatively assess functional reorganization patterns in the motor cortex after stroke (e.g., synchronous increases in IMF power and HbO concentration in compensatory activated regions). This cross-modal spatiotemporal joint analysis reveals pathologically specific coupling patterns that are not captured by traditional fixed rhythm models (e.g., IMF phase lags behind HbR response in abnormally ipsilateralized brain regions).

[0107] Example 2: A neurovascular coupling dynamic modeling method based on the fusion of CEEMDAN and GLM, comprising the following steps:

[0108] Step 1: Get signal data:

[0109] Synchronously collected EEG and fNIRS signals were used as input data. The two signals were sampled at 1000 Hz and 11 Hz, respectively. A synchronization box was used to ensure data synchronization and reduce errors. During the experiment, timestamps were used to mark the start and end time of the action. The collected EEG and fNIRS signals were divided according to the preparation phase, movement execution phase, and rest phase, and labeled accordingly according to different phases to ensure that the neural and vascular activities in each phase can be fully reflected. EEG and fNIRS acquisition positions are as follows: Figure 2 shown.

[0110] Step 2, complete empirical mode decomposition and mode acquisition:

[0111] CEEMDAN is used to decompose the EEG signal. Decompose into multiple modes. CEEMDAN is an adaptive non-parametric decomposition technology enhanced by white noise. It adaptively decomposes the EEG signal into multiple intrinsic mode functions (IMFs) by iteratively adding Gaussian white noise to the original signal and performing ensemble averaging. Each IMF has a band-limited characteristic within a specific frequency band, and the frequencies between modes are separated from each other. Compared with the traditional fixed frequency band division method, CEEMDAN does not require preset frequency band boundaries and can capture individual-specific neural oscillation patterns (such as abnormally enhanced oscillation patterns under pathological conditions). - Mixed rhythm or frequency band response), which is particularly suitable for analyzing the dynamic characteristics of non-stationary EEG signals.

[0112] The core advantages of CEEMDAN lie in its ability to resist modal aliasing and noise robustness. Through a white noise-assisted set decomposition strategy, it significantly suppresses the endpoint effects and modal aliasing of traditional EMD algorithms. Even in pathological noise environments (such as strong background interference after a stroke), it can still achieve refined separation of neural oscillation components in different frequency bands. Each IMF not only reflects the dynamic characteristics of the signal in a specific frequency band, but its time-varying spectral characteristics can be directly embedded in the GLM hemodynamic response function (HRF) reconstruction process. The algorithm flow of CEEMDAN is as follows:

[0113] (1) Initialization: Set the number of noise sequences , the amplitude of the noise sequence , the original signal is , the number of iterations is .

[0114] (2) Add different white noises to the original signal to obtain Perturbation signal:

[0115] ;

[0116] in The mean is 0 and the variance is white noise sequence.

[0117] (3) For each disturbance signal Perform classic EMD decomposition to obtain a set of intrinsic mode functions

[0118] (IMF) and residuals ,Right now

[0119] ;

[0120] in It is The first disturbance signal IMF, is the number of IMFs;

[0121] (4) Calculate the arithmetic mean of all disturbance signals for each IMF to obtain the final IMF,

[0122] ;

[0123] in It is The final IMF.

[0124] (5) Take the arithmetic mean of all disturbance signals for each residual to obtain the final residual, that is,

[0125] ;

[0126] (6) Determine whether the final residual satisfies monotonicity or is small enough. If yes, stop decomposition; if not, let , and replace the original signal with the final residual, and repeat steps (2)-(6).

[0127] (7) Output the final decomposition result, that is

[0128] ;

[0129] The core of CEEMDAN is steps (4) and (5), and the decomposition results are demonstrated using 3s EEG data. Figure 3 As shown;

[0130] Step 3: Construction of IMF-GLM analysis framework:

[0131] As a statistical linear model, GLM analyzes data through a linear combination of explanatory variables and error terms. Because it focuses on the time-varying pattern of the signal rather than the absolute amplitude, it has good robustness in estimating changes in brain activation.

[0132] set up for The cerebral blood oxygen concentration signal (HbO / HbR) of each channel, is the sequence length ( ). The GLM calculation expression is:

[0133] ;

[0134] in, is the design matrix, is the regression coefficient matrix ( is the number of explanatory variables), is the noise. The GLM analysis of all channels can be expressed as:

[0135] ;

[0136] in, for The identity matrix of order, is the Kronecker product, It is a vectorized operation. Model estimation coefficients ( is a transposed matrix) reflects the brain activation pattern of the subjects under specific tasks, and is tested by statistical tests (such as value) to determine the active channels related to the task.

[0137] The construction process of EEG-derived regressor based on CEEMDAN:

[0138] (1) Channel selection and signal preprocessing:

[0139] The motor-related brain area channels (such as C3 / C4) were selected, and the EEG signals of each motor task were averaged 20 times to obtain stable event-related potential (ERP) characteristics.

[0140] (2) CEEMDAN adaptive decomposition and feature extraction:

[0141] Apply CEEMDAN decomposition to the preprocessed EEG signal to generate a series of intrinsic mode functions (IMFs):

[0142] ;

[0143] in is the total number of IMFs, For the The time domain energy ratio of each IMF, is the number of signal time points, Calculate the time domain energy proportion and energy entropy of each IMF:

[0144] Energy share primary election: ;

[0145] according to The top three modes (IMF1, IMF2, IMF3) are retained in descending order.

[0146] Energy entropy verification:

[0147] Among them The energy entropy of an IMF (measures the complexity of frequency components), : Frequency range (0.5-100Hz), : No. The power spectral density of the IMF is set to the threshold ,filter The first two modes of are the core modes (denoted as ).

[0148] (3) Multi-band neural oscillation feature extraction:

[0149] The following features are extracted from the core mode: 1. Time-varying spectrum features: Energy entropy sequence: The time-varying energy entropy is calculated using a 500ms sliding window and is recorded as , ; Instantaneous frequency: Obtain the instantaneous frequency sequence of the core mode through Hilbert transform, denoted as , ; Traditional band power: calculation Band power, denoted as 2. Feature Matrix Construction: Forming Feature Set The dimension is ( is the number of time points).

[0150] (4) GLM design matrix for EEG modulation:

[0151] The traditional task correlation matrix and CEEMDAN features are combined to construct the design matrix:

[0152] ;

[0153] in: Trigger signal for the task (box function, dimension , including preparation / exercise / rest phases); The 7-dimensional EEG derived features extracted by (3) have a total design matrix dimension of .

[0154] (5) Neurovascular coupling analysis:

[0155] Six GLM models (five EEG modulation models + one traditional box model) were used to analyze HbO / HbR signals:

[0156] ;

[0157] in is the blood oxygen signal (dimension , is the number of channels), is the noise term, and by comparing the regression coefficients between models and activation patterns, quantifying the spatiotemporal heterogeneity of nerve-blood flow dynamic coupling under pathological conditions.

[0158] Step 4: Multi-dimensional evaluation system of CEEMDAN-EEG modulation GLM model:

[0159] A dual-index evaluation framework was constructed to verify the effectiveness and performance improvement of the CEEMDAN-EEG modulation GLM model in brain activation analysis.

[0160] (1) Statistical analysis of regression coefficient β:

[0161] The regression coefficient β reflects the intensity of the task design's regulation of blood oxygen signal (HbO / HbR), and its absolute value is positively correlated with the degree of brain activation. Multi-dimensional statistical tests were performed on the β value:

[0162] Normality test: The Shapiro-Wilk test was used to evaluate the distribution of beta values ​​between groups to ensure the applicability of the parametric test;

[0163] Homogeneity of variance test: Levene's test was used to determine the homogeneity of variance between groups and to guide the selection of subsequent ANOVA or nonparametric tests;

[0164] Analysis of inter-group differences: A three-way repeated measures analysis of variance (task type × subject group × model type) was used to test the significant difference in β-value estimation between the CEEMDAN-GLM and the traditional box-hatch model.

[0165] (2) Model performance evaluation based on ROC curve:

[0166] The area under the receiver operating characteristic curve (AUC) was used to quantify the model performance. The specific process is as follows:

[0167] ROC curve construction: by changing the task-induced activation Value Threshold , calculate the true positive rate (TPR) and false positive rate (FPR):

[0168] ; ;

[0169] The target motor areas were defined as the primary motor cortex (M1-BA4), premotor cortex (PM-BA6), and primary somatosensory cortex (S1-BAs1-3), with the left and right hand tasks corresponding to the contralateral motor cortex, respectively.

[0170] AUC calculation and comparison: AUC value The higher the value, the higher the TPR and the lower the FPR of the model. A one-way repeated measures ANOVA test was used to evaluate the performance difference between CEEMDAN-GLM and the traditional model. The specific steps are as follows:

[0171] Anderson-Darling normality test confirmed data distribution;

[0172] Fisher's least significant difference (LSD) post hoc test was used to compare differences between any pairs of models.

[0173] This application achieves accurate analysis of the dynamic coupling between nerve and blood flow under pathological conditions through adaptive modal decomposition enhanced by white noise and dynamic embedding of individualized neural oscillation characteristics. This method breaks through the physiological limitations of traditional fixed frequency band division and uses the anti-modal aliasing properties of CEEMDAN to perform non-parametric frequency band segmentation on EEG signals to capture individual-specific neural oscillation patterns (such as post-stroke - Mixed rhythm abnormalities), and the time-varying spectral characteristics are integrated into the hemodynamic response function reconstruction of GLM through the energy entropy weighting mechanism to quantitatively analyze the spatiotemporal heterogeneity of neurovascular coupling.

[0174] Verification test:

[0175] The experiment was designed to collect EEG-fNIRS data from volunteers in two action paradigms: arm flexion and rest. The data of three healthy subjects, three patients in the subacute stage, and three patients in the recovery stage were collected to complete the left and right upper limb movement tasks. The pre-processed EEG signals were decomposed into intrinsic mode functions (IMFs) with band-limited characteristics by CEEMDAN, and the energy-dominant modes and traditional / / The frequency band features are used to construct the EEG derived design matrix, which is then embedded into the GLM model for cerebral blood oxygen signal analysis. The experimental results are as follows. Table 1 shows the energy and center frequency of each IMF decomposed by CEEMDAN for different subjects. The results show that this method can successfully capture the reorganization of neural oscillation patterns after stroke, such as the IMF1 in the recovery period of the affected side. Frequency band migration, present in subacute phase - Mixed rhythm, Table 2 shows the average AUC difference comparison of different GLM models, comparing the IMF1 / IMF2 model extracted by CEEMDAN with the traditional model ( / / / Boxcar) in the healthy group (HC) and the contralateral side of stroke patients (SP-HS). The results showed that the IMF-based GLM design matrix (especially IMF2) was significantly better than the traditional model in brain activation detection ( / Boxcar, etc.), demonstrating higher AUC values ​​compared to traditional box-shaped models. A one-way ANOVA test showed a statistically significant difference in AUC between the IMF2-DM and Boxcar models (p<0.05). In summary, the CEEMDAN-GLM model improves the accuracy of identifying activation patterns in target motor areas and can effectively distinguish the dynamic differences in neurovascular coupling between pathological and normal states. It exhibits particularly strong noise robustness and feature resolution capabilities in non-stationary signal environments.

[0176] Table 1. EEG intrinsic mode function (IMF) energy (µV²) versus center frequency (Hz) for the four groups of subjects.

[0177] IMF HC SP–HS SP–AS–Rec SP–AS–SubA Energy / Freq Energy / Freq Energy / Freq Energy / Freq IMF1 35.2 / 1.54 44.88 / 3.52 37.52 / 3.09 62.55 / 4.27 IMF2 22.54 / 11.05 23.69 / 15.85 36.94 / 52.56 34.67 / 23.12 IMF3 6.22 / 26.57 8.15 / 47.62 15.24 / 97.25 15.43 / 51.94 IMF4 5.12 / 50.43 7.14 / 73.06 8.11 / 15.47 6.05 / 76.75

[0178] Table 2. Area under the curve (AUC) values ​​of the GLM model for HbO and HbR signals under different experimental conditions.

[0179] Model Signal HC SP–HS SP–AS–Rec SP–AS–SubA Alpha-DM HbO 0.763 0.715 0.553 0.536 Alpha-DM HbR 0.752 0.747 0.532 0.571 Beta-DM HbO 0.796 0.813 0.690 0.743 Beta-DM HbR 0.778 0.821 0.712 0.725 Gamma-DM HbO 0.657 0.616 0.775 0.718 Gamma-DM HbR 0.642 0.625 0.792 0.686 IMF1-DM HbO 0.819 0.806 0.844 0.839 IMF1-DM HbR 0.821 0.817 0.825 0.795 IMF2-DM HbO 0.848 0.857 0.808 0.787 IMF2-DM HbR 0.852 0.853 0.807 0.768 BoxcarModel HbO 0.658 0.706 0.611 0.556 BoxcarModel HbR 0.646 0.680 0.582 0.533

[0180] Note. HC = healthy controls; SP–HS = stroke patients, healthy-side movement; SP–AS–Rec = affected-side movement during recovery phase; SP–AS–SubA = affected-side movement during subacute phase. DM = Design Matrix.

[0181] This patent also compares the classification performance of CEEMDAN with EMD and VMD under the same experimental conditions. Combining technical characteristics with clinical needs, a comparison scheme is designed from the dimensions of decomposition accuracy, anti-aliasing ability and model adaptability. The algorithm parameters in the experiment are as follows: CEEMDAN: noise amplitude = 0.2, number of collections = 50; VMD: preset number of modes = 3, quadratic penalty factor = 2000; EMD: default parameters (termination condition: standard deviation < 0.2). The results are shown in Table 3. Decomposition accuracy: CEEMDAN It is only 1 / 3 of VMD and 1 / 5 of EMD, indicating that it is more sensitive to time-varying frequency bands (such as pathological conditions). - More accurate capture of mixed rhythms; Anti-aliasing ability: The MFI of CEEMDAN is 62% lower than that of VMD and 81% lower than that of EMD, verifying its effective suppression of modal aliasing through the noise injection-integrated averaging mechanism; Model adaptability: When the IMF extracted by CEEMDAN is used in GLM, the AUC improvement rate is 1.9 times that of VMD and 5.5 times that of EMD, indicating that its characteristics can better reflect the true dynamics of neurovascular coupling. Through the above comparison, we can systematically demonstrate the technical advantages of CEEMDAN over VMD and EMD in neurovascular coupling analysis, especially the significant improvement in the decomposition accuracy of pathological non-stationary signals and the clinical adaptability of the model.

[0182] Table 3. Performance parameter comparison of CEEMDAN, VMD, and EMD algorithms (ΔAUC = IMF model AUC - comparison model AUC):

[0183] Algorithm Δf(Hz) MFI SNR(dB) ΔAUC CEEMDAN 0.32 0.08 12.5 +28.7% VMD 0.89 0.21 9.2 +15.3% EMD 1.56 0.43 7.1 +5.2%

[0184] The CEEMDAN feature embedding mechanism constructed in this paper combines the time-frequency features of adaptive decomposition with the statistical modeling advantages of GLM, addressing the physiological information loss caused by fixed frequency band division in traditional methods. This provides a new technical approach for cross-modal correlation analysis between neural oscillations and hemodynamic responses. The white noise-enhanced ensemble decomposition strategy not only suppresses modal aliasing and endpoint effects but also dynamically modulates individual-specific neural features through energy entropy weighting, enabling the model to more accurately capture neurovascular coupling abnormalities in pathological conditions.

[0185] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A neurovascular coupling dynamic modeling method based on the fusion of CEEMDAN and GLM, characterized by: The following steps are involved: (1) Acquisition of signal data: synchronously collect EEG and fNIRS signals, segment them according to task phases, and mark them with timestamps; (2) Complete empirical mode decomposition and mode acquisition: CEEMDAN decomposition is performed on the EEG signal to generate multiple intrinsic mode functions (IMFs); (3) Construction of IMF-GLM analytical framework: Calculate the time domain energy proportion and energy entropy of each IMF ; according to Keep the first M IMFs in descending order, and then filter out the top N core IMFs based on the threshold; Extract the instantaneous frequency and time-varying energy entropy from each core IMF to form the feature set of each IMF; At the same time, the / / The GLM model constructed by band power and the commonly used Boxcar model were used as controls; Constructing the GLM model of CEEMDAN: ； in: Trigger signal for the task; EEG-derived features extracted for the feature set; Analysis of HbO / HbR signaling: ； in, is the blood oxygen signal, is the noise term, and by comparing the regression coefficients between models and activation patterns, quantifying the spatiotemporal heterogeneity of nerve-blood flow dynamic coupling under pathological conditions; (4) Multi-dimensional evaluation: Based on the regression coefficient Statistical characteristics analysis; Model performance evaluation based on ROC curve.

2. The neurovascular coupling dynamic modeling method based on the fusion of CEEMDAN and GLM according to claim 1, characterized in that: The CEEMDAN decomposition in step (2) includes: Initialization: Set the number of noise sequences , the amplitude of the noise sequence , the original signal is , the number of iterations is ; Add different white noises to the original signal and get Perturbation signal: ； in, The mean is 0 and the variance is White noise sequence; For each disturbance signal Perform classic EMD decomposition to obtain a set of intrinsic mode functions (IMF) and residuals ,Right now ； in, It is The first disturbance signal IMF, is the number of IMFs; For each IMF, the arithmetic mean of all disturbance signals is calculated to obtain the final IMF. ； in, It is a final IMF; The arithmetic mean of all disturbance signals is calculated for each residual to obtain the final residual, that is, ； Determine whether the final residual satisfies monotonicity or is small enough; if it does, stop decomposition; if it does not, let , and replace the original signal with the final residual; Output the final decomposition result, that is 。 3. The neurovascular coupling dynamic modeling method based on the fusion of CEEMDAN and GLM according to claim 1, characterized in that: The energy entropy calculation in step (3) is defined as: ;in, No. The energy entropy of an IMF, the screening condition meets , and ranked in the top N; T is the number of signal time points; is the threshold.

4. The neurovascular coupling dynamic modeling method based on the fusion of CEEMDAN and GLM according to claim 3, characterized in that: Step 4 based on the regression coefficient The statistical characteristics analysis includes: Normality test: Shapiro-Wilk test was used to assess the normality between groups. Value distribution, used to ensure the applicability of parameter tests; Homogeneity of variance test: Levene's test was used to determine the homogeneity of variance between groups, which was used to guide the selection of subsequent ANOVA or nonparametric tests; Analysis of differences between groups: A three-way repeated measures analysis of variance was used to test the CEEMDAN-GLM and the traditional box model. Significant differences in the estimated values.

5. The neurovascular coupling dynamic modeling method based on the fusion of CEEMDAN and GLM according to claim 4, characterized in that: The ROC curve-based model performance evaluation in step 4 includes: Constructing ROC curves: By changing the activation induced by the task Value Threshold , calculate the true positive rate TPR and false positive rate FPR: ， ； The target motor areas were defined as the primary motor cortex, premotor cortex, and primary somatosensory cortex, with left-hand and right-hand tasks corresponding to the contralateral motor cortex, respectively; The performance of CEEMDAN-GLM was evaluated using one-way repeated measures ANOVA test.

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