A Hybrid EEG-Based Stress State Classification Model Using Multi-Domain Transfer Entropy and PCANet.

This paper proposes a new hybrid model for classifying stress states using EEG signals, combining multi-domain transfer entropy (TrEn) with a two-dimensional PCANet (2D-PCANet) approach. The aim is to create an automated system for identifying stress levels, which is crucial for early intervention and mental health management. A major challenge in this field lies in extracting meaningful emotional information from the complex patterns observed in EEG. Our model addresses this by initially applying independent component analysis (ICA) to purify the EEG signals, enhancing the clarity for further analysis. We then leverage the adaptability of the fractional Fourier transform (FrFT) to represent the EEG data in time, frequency, and time-frequency domains. This multi-domain representation allows for a more nuanced understanding of the brain's activity in response to stress. The subsequent stage involves the deployment of a two-layer 2D-PCANet network designed to autonomously distill EEG features associated with stress. These features are then classified by a support vector machine (SVM) to determine the stress state. Moreover, stress induction and data acquisition experiments are designed. We employed two distinct tasks known to trigger stress responses. Other stress-inducing elements that enhance the stress response were included in the experimental design, such as time limits and performance feedback. The EEG data collected from 15 participants were retained. The proposed algorithm achieves an average accuracy of over 92% on this self-collected dataset, enabling stress state detection under different task-induced conditions.

Identifying Effective Connectivity between Stochastic Neurons with Variable-Length Memory Using a Transfer Entropy Rate Estimator.

Information theory explains how systems encode and transmit information. This article examines the neuronal system, which processes information via neurons that react to stimuli and transmit electrical signals. Specifically, we focus on transfer entropy to measure the flow of information between sequences and explore its use in determining effective neuronal connectivity. We analyze the causal relationships between two discrete time series, X:=Xt:t∈Z and Y:=Yt:t∈Z, which take values in binary alphabets. When the bivariate process (X,Y) is a jointly stationary ergodic variable-length Markov chain with memory no larger than k, we demonstrate that the null hypothesis of the test-no causal influence-requires a zero transfer entropy rate. The plug-in estimator for this function is identified with the test statistic of the log-likelihood ratios. Since under the null hypothesis, this estimator follows an asymptotic chi-squared distribution, it facilitates the calculation of p-values when applied to empirical data. The efficacy of the hypothesis test is illustrated with data simulated from a neuronal network model, characterized by stochastic neurons with variable-length memory. The test results identify biologically relevant information, validating the underlying theory and highlighting the applicability of the method in understanding effective connectivity between neurons.

Land surface temperature and transboundary air pollution: a case of Bangkok Metropolitan Region.

In a rapidly urbanizing world, heavy air pollution and increasing surface temperature pose significant threats to human health and lives, especially in densely populated cities. In this study, we took an information theory perspective to investigate the causal relationship between diel land surface temperature (LST) and transboundary air pollution (TAP) from 2003 to 2020 in the Bangkok Metropolitan Region (BMR), which includes Bangkok Metropolis and its five adjacent provinces. We found an overall increasing trend of LST over the study region, with the mean daytime LST rising faster than nighttime LST. Evident seasonal variations showed high aerosol optical depth (AOD) loadings during the dry period and low loadings at the beginning of the rainy season. Our study revealed that TAP affected diel surface temperature in Bangkok Metropolis significantly. Causality tests show that air pollutants of two adjacent provinces west of Bangkok, i.e., Nakhon Pathom and Samut Sakhon, have a greater influence on the LST of Bangkok than other provinces. Also, the bidirectional relationship indicates that air pollution has a greater impact on daytime LST than nighttime LST. While LST has an insignificant influence on AOD during the daytime, it influences AOD significantly at night. Our study offers a new approach to understanding the causal impact of TAP and can help policymakers to identify the most relevant locations that cause pollution, leading to appropriate planning and management.

EEG Information Transfer Changes in Different Daily Fatigue Levels During Drowsy Driving.

A significant issue for traffic safety has been drowsy driving for decades. A number of studies have investigated the effects of acute fatigue on spectral power; and recent research has revealed that drowsy driving is associated with a variety of brain connections in a specific cortico-cortical pathway. In spite of this, it is still unclear how different brain regions are connected in drowsy driving at different levels of daily fatigue. This study identified the brain connectivity-behavior relationship among three different daily fatigue levels (low-, median- and high-fatigue) with the EEG data transfer entropy. According to the results, only low- and medium-fatigue groups demonstrated an inverted U-shaped change in connectivity from high performance to poor behavioral performance. In addition, from low- to high-fatigue groups, connectivity magnitude decreased in the frontal region and increased in the occipital region. These study results suggest that brain connectivity and driving behavior would be affected by different levels of daily fatigue.

Respiratory modulation of the heart rate: A potential biomarker of cardiorespiratory function in human.

In recent decade, wearable digital devices have shown potentials for the discovery of novel biomarkers of humans' physiology and behavior. Heart rate (HR) and respiration rate (RR) are most crucial bio-signals in humans' digital phenotyping research. HR is a continuous and non-invasive proxy to autonomic nervous system and ample evidence pinpoints the critical role of respiratory modulation of cardiac function. In the present study, we recorded longitudinal (7 days, 4.63 ± 1.52) HR and RR of 89 freely behaving human subjects (Female: 39, age 57.28 ± 5.67, Male: 50, age 58.48 ± 6.32) and analyzed their dynamics using linear models and information theoretic measures. While HR's linear and nonlinear characteristics were expressed within the plane of the HR-RR directed flow of information (HR→RR - RR→HR), their dynamics were determined by its RR→HR axis. More importantly, RR→HR quantified the effect of alcohol consumption on individuals' cardiorespiratory function independent of their consumed amount of alcohol, thereby signifying the presence of this habit in their daily life activities. The present findings provided evidence for the critical role of the respiratory modulation of HR, which was previously only studied in non-human animals. These results can contribute to humans' phenotyping research by presenting RR→HR as a digital diagnosis/prognosis marker of humans' cardiorespiratory pathology.

Altered Cortical Information Interaction During Respiratory Events in Children with Obstructive Sleep Apnea-Hypopnea Syndrome.

Obstructive sleep apnea-hypopnea syndrome (OSAHS) significantly impairs children's growth and cognition. This study aims to elucidate the pathophysiological mechanisms underlying OSAHS in children, with a particular focus on the alterations in cortical information interaction during respiratory events. We analyzed sleep electroencephalography before, during, and after events, utilizing Symbolic Transfer Entropy (STE) for brain network construction and information flow assessment. The results showed a significant increase in STE after events in specific frequency bands during N2 and rapid eye movement (REM) stages, along with increased STE during N3 stage events. Moreover, a noteworthy rise in the information flow imbalance within and between hemispheres was found after events, displaying unique patterns in central sleep apnea and hypopnea. Importantly, some of these alterations were correlated with symptom severity. These findings highlight significant changes in brain region coordination and communication during respiratory events, offering novel insights into OSAHS pathophysiology in children.

Cross-frequency cortex-muscle interactions are abnormal in young people with dystonia.

Sensory processing and sensorimotor integration are abnormal in dystonia, including impaired modulation of beta-corticomuscular coherence. However, cortex-muscle interactions in either direction are rarely described, with reports limited predominantly to investigation of linear coupling, using corticomuscular coherence or Granger causality. Information-theoretic tools such as transfer entropy detect both linear and non-linear interactions between processes. This observational case-control study applies transfer entropy to determine intra- and cross-frequency cortex-muscle coupling in young people with dystonia/dystonic cerebral palsy. Fifteen children with dystonia/dystonic cerebral palsy and 13 controls, aged 12-18 years, performed a grasp task with their dominant hand. Mechanical perturbations were provided by an electromechanical tapper. Bipolar scalp EEG over contralateral sensorimotor cortex and surface EMG over first dorsal interosseous were recorded. Multi-scale wavelet transfer entropy was applied to decompose signals into functional frequency bands of oscillatory activity and to quantify intra- and cross-frequency coupling between brain and muscle. Statistical significance against the null hypothesis of zero transfer entropy was established, setting individual 95% confidence thresholds. The proportion of individuals in each group showing significant transfer entropy for each frequency combination/direction was compared using Fisher's exact test, correcting for multiple comparisons. Intra-frequency transfer entropy was detected in all participants bidirectionally in the beta (16-32 Hz) range and in most participants from EEG to EMG in the alpha (8-16 Hz) range. Cross-frequency transfer entropy across multiple frequency bands was largely similar between groups, but a specific coupling from low-frequency EMG to beta EEG was significantly reduced in dystonia [P = 0.0061 (corrected)]. The demonstration of bidirectional cortex-muscle communication in dystonia emphasizes the value of transfer entropy for exploring neural communications in neurological disorders. The novel finding of diminished coupling from low-frequency EMG to beta EEG in dystonia suggests impaired cortical feedback of proprioceptive information with a specific frequency signature that could be relevant to the origin of the excessive low-frequency drive to muscle.

Causal connectivity measures for pulse-output network reconstruction: Analysis and applications.

The causal connectivity of a network is often inferred to understand network function. It is arguably acknowledged that the inferred causal connectivity relies on the causality measure one applies, and it may differ from the network's underlying structural connectivity. However, the interpretation of causal connectivity remains to be fully clarified, in particular, how causal connectivity depends on causality measures and how causal connectivity relates to structural connectivity. Here, we focus on nonlinear networks with pulse signals as measured output, e.g., neural networks with spike output, and address the above issues based on four commonly utilized causality measures, i.e., time-delayed correlation coefficient, time-delayed mutual information, Granger causality, and transfer entropy. We theoretically show how these causality measures are related to one another when applied to pulse signals. Taking a simulated Hodgkin-Huxley network and a real mouse brain network as two illustrative examples, we further verify the quantitative relations among the four causality measures and demonstrate that the causal connectivity inferred by any of the four well coincides with the underlying network structural connectivity, therefore illustrating a direct link between the causal and structural connectivity. We stress that the structural connectivity of pulse-output networks can be reconstructed pairwise without conditioning on the global information of all other nodes in a network, thus circumventing the curse of dimensionality. Our framework provides a practical and effective approach for pulse-output network reconstruction.

The effective connectivity analysis of fMRI based on asymmetric detection of transfer brain entropy.

It is important to explore causal relationships in functional magnetic resonance imaging study. However, the traditional effective connectivity analysis method is easy to produce false causality, and the detection accuracy needs to be improved. In this paper, we introduce a novel functional magnetic resonance imaging effective connectivity method based on the asymmetry detection of transfer entropy, which quantifies the disparity in predictive information between forward and backward time, subsequently normalizing this disparity to establish a more precise criterion for detecting causal relationships while concurrently reducing computational complexity. Then, we evaluate the effectiveness of this method on the simulated data with different level of nonlinearity, and the results demonstrated that the proposed method outperforms others methods on the detection of both linear and nonlinear causal relationships, including Granger Causality, Partial Granger Causality, Kernel Granger Causality, Copula Granger Causality, and traditional transfer entropy. Furthermore, we applied it to study the effective connectivity of brain functional activities in seafarers. The results showed that there are significantly different causal relationships between different brain regions in seafarers compared with non-seafarers, such as Temporal lobe related to sound and auditory information processing, Hippocampus related to spatial navigation, Precuneus related to emotion processing as well as Supp_Motor_Area associated with motor control and coordination, which reflects the occupational specificity of brain function of seafarers.

Direct lingam and visibility graphs for analyzing brain connectivity in BCI.

The brain-computer interface (BCI) is a direct pathway of communication between the electrical activity of the brain and an external device. The present paper was aimed to investigate directed connectivity between different areas of the brain during motor imagery (MI)-based BCI. For this purpose, two methods were implemented including, Limited Penetrable Horizontal Visibility Graph (LPHVG) and Direct Lingam. The visibility graph (VG) is a robust algorithm for analyzing complex systems such as the brain. Direct Lingam uses a non-Gaussian model to extract causal links which is appropriate for analyzing large-scale connectivity. First, LPHVG map MI-EEG (electroencephalogram) signals into networks. After extracting the topological features of the networks, a support vector machine classifier was applied to categorize multi-classes MI. The network of all classes was found to be different from one another, and the kappa value of classification was 0.68. The degree sequence of LPHVG was calculated for each channel in order to obtain the direction of brain information flow. Transfer entropy (TE) is used to compute the relations of the channel degree sequence. Therefore, the directed graph between channels was formed. This method is called LPHVG_TE directed graph. The Bayesian network, also known as the Direct LiNGAM model, was implemented for the second method. Finally, images of the LPHVG and Direct Lingam were classified by convolutional neural network (CNN). In this study, Data sets 2a of BCI competition IV was used. The outcomes reveal that the brain network developed by LPHVG (92.7%) might be more effective to distinguish 4 classes of MI than the Direct Lingam (90.6%) and it was shown that graph theory has the potential to get better efficiency of BCI.

Disrupted properties of functional brain networks in major depressive disorder during emotional face recognition: an EEG study via graph theory analysis.

Previous neuroimaging studies have revealed abnormal brain networks in patients with major depressive disorder (MDD) in emotional processing. While any cognitive task consists of a series of stages, little is yet known about the topology of functional brain networks in MDD for these stages during emotional face recognition. To address this problem, electroencephalography (EEG)-based functional brain networks of MDD patients at different stages of facial information processing were investigated in this study. First, EEG signals were collected from 16 patients with MDD and 18 age-, gender-, and education-matched normal subjects when performing an emotional face recognition task. Second, the global field power (GFP) method was employed to divide group-averaged event-related potentials into different stages. Third, using the phase transfer entropy (PTE) approach, the brain networks of MDD patients and normal individuals were constructed for each stage in negative and positive face processing, respectively. Finally, we compared the topological properties of brain networks of each stage between the two groups using graph theory approaches. The results showed that the analyzed three stages of emotional face processing corresponded to specific neurophysiological phases, namely, visual perception, face recognition, and emotional decision-making. It was also demonstrated that depressed patients showed abnormally decreased characteristic path length at the visual perception stage of negative face recognition and normalized characteristic path length in the stage of emotional decision-making during positive face processing compared to healthy subjects. Furthermore, while both the MDD and normal groups' brain networks were found to exhibit small-world network characteristics, the brain network of patients with depression tended to be randomized. Moreover, for patients with MDD, the centro-parietal region may lose its status as a hub in the process of facial expression identification. Together, our findings suggested that altered emotional function in MDD patients might be associated with disruptions in the topological organization of functional brain networks during emotional face recognition, which further deepened our understanding of the emotion processing dysfunction underlying MDD.

Enhanced Hippocampus-Nidopallium Caudolaterale Interaction in Visual-Spatial Associative Learning of Pigeons.

Learning the spatial location associated with visual cues in the environment is crucial for survival. This ability is supported by a distributed interactive network. However, it is not fully understood how the most important task-related brain areas in birds, the hippocampus (Hp) and the nidopallium caudolaterale (NCL), interact in visual-spatial associative learning. To investigate the mechanisms of such coordination, synchrony and causal analysis were applied to the local field potentials of the Hp and NCL of pigeons while performing a visual-spatial associative learning task. The results showed that, over the course of learning, theta-band (4-12 Hz) oscillations in the Hp and NCL became strongly synchronized before the pigeons entered the critical choice platform for turning, with the information flowing preferentially from the Hp to the NCL. The learning process was primarily associated with the increased Hp-NCL interaction of theta rhythm. Meanwhile, the enhanced theta-band Hp-NCL interaction predicted the correct choice, supporting the pigeons' use of visual cues to guide navigation. These findings provide insight into the dynamics of Hp-NCL interaction during visual-spatial associative learning, serving to reveal the mechanisms of Hp and NCL coordination during the encoding and retrieval of visual-spatial associative memory.

Enhancing Exchange-Traded Fund Price Predictions: Insights from Information-Theoretic Networks and Node Embeddings.

This study presents a novel approach to predicting price fluctuations for U.S. sector index ETFs. By leveraging information-theoretic measures like mutual information and transfer entropy, we constructed threshold networks highlighting nonlinear dependencies between log returns and trading volume rate changes. We derived centrality measures and node embeddings from these networks, offering unique insights into the ETFs' dynamics. By integrating these features into gradient-boosting algorithm-based models, we significantly enhanced the predictive accuracy. Our approach offers improved forecast performance for U.S. sector index futures and adds a layer of explainability to the existing literature.

An improved hierarchical variational autoencoder for cell-cell communication estimation using single-cell RNA-seq data.

Analysis of cell-cell communication (CCC) in the tumor micro-environment helps decipher the underlying mechanism of cancer progression and drug tolerance. Currently, single-cell RNA-Seq data are available on a large scale, providing an unprecedented opportunity to predict cellular communications. There have been many achievements and applications in inferring cell-cell communication based on the known interactions between molecules, such as ligands, receptors and extracellular matrix. However, the prior information is not quite adequate and only involves a fraction of cellular communications, producing many false-positive or false-negative results. To this end, we propose an improved hierarchical variational autoencoder (HiVAE) based model to fully use single-cell RNA-seq data for automatically estimating CCC. Specifically, the HiVAE model is used to learn the potential representation of cells on known ligand-receptor genes and all genes in single-cell RNA-seq data, respectively, which are then utilized for cascade integration. Subsequently, transfer entropy is employed to measure the transmission of information flow between two cells based on the learned representations, which are regarded as directed communication relationships. Experiments are conducted on single-cell RNA-seq data of the human skin disease dataset and the melanoma dataset, respectively. Results show that the HiVAE model is effective in learning cell representations, and transfer entropy could be used to estimate the communication scores between cell types.

Separation of responsive and unresponsive patients under clinical conditions: comparison of symbolic transfer entropy and permutation entropy.

Electroencephalogram (EEG)-based monitoring during general anesthesia may help prevent harmful effects of high or low doses of general anesthetics. There is currently no convincing evidence in this regard for the proprietary algorithms of commercially available monitors. The purpose of this study was to investigate whether a more mechanism-based parameter of EEG analysis (symbolic transfer entropy, STE) can separate responsive from unresponsive patients better than a strictly probabilistic parameter (permutation entropy, PE) under clinical conditions. In this prospective single-center study, the EEG of 60 surgical ASA I-III patients was recorded perioperatively. During induction of and emergence from anesthesia, patients were asked to squeeze the investigators' hand every 15s. Time of loss of responsiveness (LoR) during induction and return of responsiveness (RoR) during emergence from anesthesia were registered. PE and STE were calculated at -15s and +30s of LoR and RoR and their ability to separate responsive from unresponsive patients was evaluated using accuracy statistics. 56 patients were included in the final analysis. STE and PE values decreased during anesthesia induction and increased during emergence. Intra-individual consistency was higher during induction than during emergence. Accuracy values during LoR and RoR were 0.71 (0.62-0.79) and 0.60 (0.51-0.69), respectively for STE and 0.74 (0.66-0.82) and 0.62 (0.53-0.71), respectively for PE. For the combination of LoR and RoR, values were 0.65 (0.59-0.71) for STE and 0.68 (0.62-0.74) for PE. The ability to differentiate between the clinical status of (un)responsiveness did not significantly differ between STE and PE at any time. Mechanism-based EEG analysis did not improve differentiation of responsive from unresponsive patients compared to the probabilistic PE.Trial registration: German Clinical Trials Register ID: DRKS00030562, November 4, 2022, retrospectively registered.

Computational Insights into Prostaglandin E2 Ligand Binding and Activation of G-Protein-Coupled Receptors.

G-protein coupled receptors (GPCRs) are eukaryotic integral membrane proteins that regulate signal transduction cascade pathways implicated in a variety of human diseases and are consequently of interest as drug targets. For this reason, it is of interest to investigate the way in which specific ligands bind and trigger conformational changes in the receptor during activation and how this in turn modulates intracellular signaling. In the present study, we investigate the way in which the ligand Prostaglandin E2 interacts with three GPCRs in the E-prostanoid family: EP1, EP2, and EP3. We examine information transfer pathways based on long-time scale molecular dynamics simulations using transfer entropy and betweenness centrality to measure the physical transfer of information among residues in the system. We monitor specific residues involved in binding to the ligand and investigate how the information transfer behavior of these residues changes upon ligand binding. Our results provide key insights that enable a deeper understanding of EP activation and signal transduction functioning pathways at the molecular level, as well as enabling us to make some predictions about the activation pathway for the EP1 receptor, for which little structural information is currently available. Our results should advance ongoing efforts in the development of potential therapeutics targeting these receptors.

Study on the sentimental influence on Indian stock price.

The rapidly increasing scientific research on the stock market and the visible impact of media on equity prices are nowadays in limelight. To a greater extent, causal analysis can reckon the sentimental effect of the broadcasted content on stock valuation. We propose a four stage model to detect the direction of information flow between the news sentiment and stock price. Whilst web scraping explores and extracts the news datasets, the modified VADER algorithm finds the sentiments of the aired media. The associational causal analysis determines the cause effect between the news and stock price. The results suggest that the non parametric Shannon and Renyi's entropy approach supersedes the Granger test, a parametric study which is constrained to Gaussian time series with linear causation. Since Renyi's Entropy can perfectly identify the deluge of information during quick leaps, it is regarded as a beneficial formulation for investors when evaluating stocks with a fewer number of news mentions. The impact of news during the COVID-19 pandemic over the pharmaceutical sector was also done. The study infers an explicit information flow and direction of causality between news sentiment and stock price movement, which can be used to devise future investment and consumption strategies.

Classification of Right/Left Hand Motor Imagery by Effective Connectivity Based on Transfer Entropy in Electroencephalogram Signal.

Introduction: The right and left-hand motor imagery (MI) analysis based on the electroencephalogram (EEG) signal can directly link the central nervous system to a computer or a device. This study aims to identify a set of robust and nonlinear effective brain connectivity features quantified by transfer entropy (TE) to characterize the relationship between brain regions from EEG signals and create a hierarchical feature selection and classification for discrimination of right and lefthand MI tasks. Methods: TE is calculated among EEG channels as the distinctive, effective connectivity features. TE is a model-free method that can measure nonlinear effective connectivity and analyze multivariate dependent directed information flow among neural EEG channels. Then four feature subset selection methods namely relief-F, Fisher, Laplacian, and local learningbased clustering (LLCFS) algorithms are used to choose the most significant effective connectivity features and reduce redundant information. Finally, support vector machine (SVM) and linear discriminant analysis (LDA) methods are used for classification. Results: Results show that the best performance in 29 healthy subjects and 60 trials is achieved using the TE method via the Relief-F algorithm as feature selection and support vector machine (SVM) classification with 91.02% accuracy. Conclusion: The TE index and a hierarchical feature selection and classification can be useful for the discrimination of right- and left-hand MI tasks from multichannel EEG signals. Highlights: Effective connectivity features were extracted from electroencephalogram (EEG) to analyze relationships between regions.Four feature selection methods used to select most significant effective features.Support vector machine (SVM) used for discrimination of right and left hand motor imagery (MI) task. Plain Language Summary: In this study, we investigated brain activity using effective connectivity during MI task based on EEG signals. The motor imagery task can accomplish the same goal as motor execution, since they are both activated by the same brain area. Transfer entropy, coherence, and Granger casualty were employed to extract the features. Differential patterns of activity between the left vs. right MI task showed activity around the motor area rather than other areas. In order to reduce redundant information and select the most significant effective connectivity features, four feature subset selection algorithms are used: Relief-F, Fisher, Laplacian, and learning-based clustering feature selection (LLCFS). Then, support vector machine (SVM) and linear discriminant analysis (LDA) are used to classify left and right hand MI task. Comparison of three different connectivity methods showed that TE index had the highest classification accuracy, and could be useful for the discrimination of right and left hand MI tasks from multichannel EEG signals.

Confounding Factor Analysis for Vocal Fold Oscillations.

This paper provides a methodology to better understand the relationships between different aspects of vocal fold motion, which are used as features in machine learning-based approaches for detecting respiratory infections from voice recordings. The relationships are derived through a joint multivariate analysis of the vocal fold oscillations of speakers. Specifically, the multivariate setting explores the displacements and velocities of the left and right vocal folds derived from recordings of five extended vowel sounds for each speaker (/aa/, /iy/, /ey/, /uw/, and /ow/). In this multivariate setting, the differences between the bivariate and conditional interactions are analyzed by information-theoretic quantities based on transfer entropy. Incorporation of the conditional quantities reveals information regarding the confounding factors that can influence the statistical interactions among other pairs of variables. This is demonstrated on a vector autoregressive process where the analytical derivations can be carried out. As a proof of concept, the methodology is applied on a clinically curated dataset of COVID-19. The findings suggest that the interaction between the vocal fold oscillations can change according to individuals and presence of any respiratory infection, such as COVID-19. The results are important in the sense that the proposed approach can be utilized to determine the selection of appropriate features as a supplementary or early detection tool in voice-based diagnostics in future studies.

Multiscale information interaction at local frequency band in functional corticomuscular coupling.

The multiscale information interaction between the cortex and the corresponding muscles is of great significance for understanding the functional corticomuscular coupling (FCMC) in the sensory-motor systems. Though the multiscale transfer entropy (MSTE) method can effectively detect the multiscale characteristics between two signals, it lacks in describing the local frequency-band characteristics. Therefore, to quantify the multiscale interaction at local-frequency bands between the cortex and the muscles, we proposed a novel method, named bivariate empirical mode decomposition-MSTE (BMSTE), by combining the bivariate empirical mode decomposition (BEMD) with MSTE. To verify this, we introduced two simulation models and then applied it to explore the FCMC by analyzing the EEG over brain scalp and surface EMG signals from the effector muscles during steady-state force output. The simulation results showed that the BMSTE method could describe the multiscale time-frequency characteristics compared with the MSTE method, and was sensitive to the coupling strength but not to the data length. The experiment results showed that the coupling at beta1 (15-25 Hz), beta2 (25-35 Hz) and gamma (35-60 Hz) bands in the descending direction was higher than that in the opposition, and at beta2 band was higher than that at beta1 band. Furthermore, there were significant differences at the low scales in beta1 band, almost all scales in beta2 band, and high scales in gamma band. These results suggest the effectiveness of the BMSTE method in describing the interaction between two signals at different time-frequency scales, and further provide a novel approach to understand the motor control. Supplementary Information: The online version contains supplementary material available at 10.1007/s11571-022-09895-y.