Multiscale Transfer Spectral Entropy for Quantifying Corticomuscular Interaction

Multiscale Canonical Coherence for Functional Corticomuscular Coupling Analysis

Functional corticomuscular coupling (FCMC) probes multi-level information communication in the sensorimotor system. The canonical Coherence (caCOH) method has been leveraged to measure the FCMC between two multivariate signals within the single scale. In this paper, we propose the concept of multiscale canonical Coherence (MS-caCOH) to disentangle complex multi-layer information and extract coupling features in multivariate spaces from multiple scales. Then, we verified the reliability and effectiveness of MS-caCOH on two types of data sets, i.e., a synthetic multivariate data set and a real-world multivariate data set. Our simulation results showed that compared with caCOH, MS-caCOH enhanced coupling detection and achieved lower pattern recovery errors at multiple frequency scales. Further analysis on experimental data demonstrated that the proposed MS-caCOH method could also capture detailed multiscale spatial-frequency characteristics. This study leverages the multiscale analysis framework and multivariate method to give a new insight into corticomuscular coupling analysis.

Analysis of Cortico-Muscular Coupling and Functional Brain Network under Different Standing Balance Paradigms

Maintaining standing balance is essential for people to engage in productive activities in daily life. However, the process of interaction between the cortex and the muscles during balance regulation is understudied. Four balance paradigms of different difficulty were designed by closing eyes and laying sponge pad under feet. Ten healthy subjects were recruited to stand for ten 15 s trials in each paradigm. This study used simultaneously acquired electroencephalography (EEG) and electromyography (EMG) to investigate changes in the human cortico-muscular coupling relationship and functional brain network characteristics during balance control. The coherence and causality of EEG and EMG signals were calculated by magnitude-squared coherence (MSC) and transfer entropy (TE). It was found that changes in balance strategies may lead to a shift in cortico-muscular coherence (CMC) from the beta band to the gamma band when the difficulty of balance increased. As subjects performed the four standing balance paradigms, the causality of the beta band and the gamma band was stronger in the descending neural pathway than that in the ascending neural pathway. A multi-rhythmic functional brain network with 19 EEG channels was constructed and analyzed based on graph theory, showing that its topology also changed with changes in balance difficulty. These results show an active adjustment of the sensorimotor system under different balance paradigms and provide new insights into the endogenous physiological mechanisms underlying the control of standing balance.

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.

Upper Limb Cortical-Muscular Coupling Analysis Based on Time-Delayed Back Maximum Information Coefficient Model

In musculoskeletal systems, describing accurately the coupling direction and intensity between physiological electrical signals is crucial. The maximum information coefficient (MIC) can effectively quantify the coupling strength, especially for short time series. However, it cannot identify the direction of information transmission. This paper proposes an effective time-delayed back maximum information coefficient (TDBackMIC) analysis method by introducing a time delay parameter to measure the causal coupling. Firstly, the effectiveness of TDBackMIC is verified on simulations, and then it is applied to the analysis of functional cortical-muscular coupling and intermuscular coupling networks to explore the difference of coupling characteristics under different grip force intensities. Experimental results show that functional cortical-muscular coupling and intermuscular coupling are bidirectional. The average coupling strength of EEG → EMG and EMG → EEG in beta band is 0.86 ± 0.04 and 0.81 ± 0.05 at 10% maximum voluntary contraction (MVC) condition, 0.83 ± 0.05 and 0.76 ± 0.04 at 20% MVC, and 0.76 ± 0.03 and 0.73 ± 0.04 at 30% MVC. With the increase of grip strength, the strength of functional cortical-muscular coupling in beta frequency band decreases, the intermuscular coupling network exhibits enhanced connectivity, and the information exchange is closer. The results demonstrate that TDBackMIC can accurately judge the causal coupling relationship, and functional cortical-muscular coupling and intermuscular coupling network under different grip forces are different, which provides a certain theoretical basis for sports rehabilitation.

Analysis of corticomuscular-cortical functional network based on time-delayed maximal information spectral coefficient

Objective. The study of brain networks has become an influential tool for investigating post-stroke brain function. However, studies on the dynamics of cortical networks associated with muscle activity are limited. This is crucial for elucidating the altered coordination patterns in the post-stroke motor control system.Approach. In this study, we introduced the time-delayed maximal information spectral coefficient (TDMISC) method to assess the local frequency band characteristics (alpha, beta, and gamma bands) of functional corticomuscular coupling (FCMC) and cortico-cortical network parameters. We validated the effectiveness of TDMISC using a unidirectionally coupled Hénon maps model and a neural mass model.Main result. A grip task with 25% of maximum voluntary contraction was designed, and simulation results demonstrated that TDMISC accurately characterizes signals' local frequency band and directional properties. In the gamma band, the affected side showed significantly strong FCMC in the ascending direction. However, in the beta band, the affected side exhibited significantly weak FCMC in all directions. For the cortico-cortical network parameters, the affected side showed a lower clustering coefficient than the unaffected side in all frequency bands. Additionally, the affected side exhibited a longer shortest path length than the unaffected side in all frequency bands. In all frequency bands, the unaffected motor cortex in the stroke group exerted inhibitory effects on the affected motor cortex, the parietal associative areas, and the somatosensory cortices.Significance. These results provide meaningful insights into neural mechanisms underlying motor dysfunction.

A novel delay estimation method for improving corticomuscular coherence in continuous synchronization events

OBJECTIVE

While the corticomuscular coupling between motor cortex and muscle tissue has received considerable attention, which is typically quantitative measure to evaluate neural signals synchronization in the motor control system, little work has been published regarding the effect of underlying delay of two coupled physiological signals on coherence.

METHODS

In this study, we developed a novel delay estimation method, named rate of voxels change (RVC), detecting time delay in two coupled physiological signals. Based on RVC framework, delay compensation was used to adjust magnitude squared coherence (MSC) image. To illustrate the effectiveness of the RVC method, we compared the estimated delays and the adjusted MSC results based on RVC method and corticomuscular coherence with time lag (CMCTL) method.

RESULTS

The simulation results suggested that RVC method was not only superior to the CMCTL method in estimating different time delays, but also has better optimization effect on MSC image. The experimental results further confirmed that delay estimated by the proposed RVC method was more in line with the underlying physiology (controls: 22.8 ms vs patients: 34.5 ms). Meanwhile, RVC-based delay compensation could significantly optimize the MSC of specific regions.

SIGNIFICANCE

This study proved that RVC has remarkably higher reliability in detecting time delay between coupled neurophysiological signals, and the application of RVC was an improvement on the previous studies that mainly focused on biased MSC estimation.