Multiplex recurrence networks

Clinical significance of dynamical network indices of surface electromyography for reticular neuromuscular control assessment

BACKGROUND

There is currently no objective and accurate clinical assessment of reticular neuromuscular control in healthy subjects or patients with upper motor neuron injury. As a result, clinical dysfunctions of neuromuscular control could just be semi-quantified, efficacies and mechanisms of various therapies for neuromuscular control improving are difficult to verify.

METHODS

Fourteen healthy participants were required to maintain standing balance in the kinetostatics model of Gusu Constraint Standing Training (GCST). A backward and upward constraint force was applied to their trunk at 0°, 20° and 25°, respectively. The multiplex recurrence network (MRN) was applied to analyze the surface electromyography signals of 16 muscles of bilateral lower limbs during the tests. Different levels of MRN network indices were utilized to assess reticular neuromuscular control.

RESULTS

Compared with the 0° test, the MRN indices related to muscle coordination of bilateral lower limbs, of unilateral lower limb and of inter limbs showed significant increase when participants stood in 20° and 25° tests (P < 0.05). The indices related to muscle contribution of gluteal, anterior thigh and calf muscles significantly increased when participants stood in 20° and 25° tests (P < 0.05).

CONCLUSIONS

This study applied the dynamical network indices of MRN to analyze the changes of neuromuscular control of lower limbs of healthy participants in the kinetostatics model of GCST. Results showed that the overall coordination of lower limb muscles would be significantly enhanced during performing GCST, partly by the enhancement of neuromuscular control of single lower limb, and partly by the enhancement of joint control across lower limbs. In particular, the muscles in buttocks, anterior thighs and calves played a more important role in the overall coordination, and their involvement was significantly increased. The MRN could provide details of control at the bilateral lower limbs, unilateral lower limb, inter limbs, and single muscle levels, and has the potential to be a new tool for assessing the reticular neuromuscular control. Trial registration ChiCTR2100055090.

Multivariate joint order recurrence networks for characterization of multi-lead ECG time series from healthy and pathological heartbeat dynamics

Analysis of nonlinear dynamic characteristics of cardiac systems has been a hot topic of clinical research, and the recurrence plots have earned much attention as an effective tool for it. In this paper, we propose a novel method of multivariate joint order recurrence networks (MJORNs) to evaluate the multi-lead electrocardiography (ECG) time series with healthy and psychological heart states. The similarity between time series is studied by quantifying the structure in a joint order pattern recurrence plot. We take the time series that corresponds to each of the 12-lead ECG signals as a node in the network and use the entropy of diagonal line length that describes the complex structure of joint order pattern recurrence plot as the weight to construct MJORN. The analysis of network topology reveals differences in nonlinear complexity for healthy and heart diseased heartbeat systems. Experimental outcomes show that the values of average weighted path length are reduced in MJORN constructed from crowds with heart diseases, compared to those from healthy individuals, and the results of the average weighted clustering coefficient are the opposite. Due to the impaired cardiac fractal-like structures, the similarity between different leads of ECG is reduced, leading to a decrease in the nonlinear complexity of the cardiac system. The topological changes of MJORN reflect, to some extent, modifications in the nonlinear dynamics of the cardiac system from healthy to diseased conditions. Compared to multivariate cross recurrence networks and multivariate joint recurrence networks, our results suggest that MJORN performs better in discriminating healthy and pathological heartbeat dynamics.

Autonomic nervous activity analysis based on visibility graph complex networks and skin sympathetic nerve activity

Background: Autonomic nerve system (ANS) plays an important role in regulating cardiovascular function and cerebrovascular function. Traditional heart rate variation (HRV) and emerging skin sympathetic nerve activity (SKNA) analyses from ultra-short-time (UST) data cannot fully reveal neural activity, thereby quantitatively reflect ANS intensity.

Methods: Electrocardiogram and SKNA from sixteen patients (seven cerebral hemorrhage (CH) patients and nine control group (CO) patients) were recorded using a portable device. Ten derived HRV (mean, standard deviation and root mean square difference of sinus RR intervals (NNmean, SDNN and RMSSD), ultra-low frequency (<0.003 Hz, uLF), very low frequency ([0.003 Hz, 0.04 Hz), vLF), low frequency ([0.04 Hz, 0.15 Hz), LF) and high frequency power ([0.15 Hz, 0.4 Hz), HF), ratio of LF to HF (LF/HF), the standard deviation of instantaneous beat-to-beat R-R interval variability (SD1), and approximate entropy (ApEn)) and ten visibility graph (VG) features (diameter (Dia), average node degree (aND), average shortest-path length (aSPL), clustering coefficient (CC), average closeness centrality (aCC), transitivity (Trans), average degree centrality (aDC), link density (LD), sMetric (sM) and graph energy (GE) of the constructed complex network) were compared on 5-min and UST segments to verify their validity and robustness in discriminating CH and CO under different data lengths. Besides, their potential for quantifying ANS-Load were also investigated.

Results: The validation results of HRV and VG features in discriminating CH from CO showed that VG features were more clearly distinguishable between the two groups than HRV features. For effectiveness evaluation of analyzing ANS on UST segment, the NNmean, SDNN, RMSSD, LF, HF and LF/HF in HRV features and the CC, Trans, Dia and GE of VG features remained stable in both activated and inactivated segments across all data lengths. The capability of HRV and VG features in quantifying ANS-Load were evaluated and compared under different ANS-Load, the results showed that most HRV features (SDNN, LFHF, RMSSD, vLF, LF and HF) and almost all VG features were correlated to sympathetic nerve activity intensity.

Conclusions: The proposed autonomic nervous activity analysis method based on VG and SKNA offers a new insight into ANS assessment in UST segments and ANS-Load quantification.

Dynamic Linkages among Carbon, Energy and Financial Markets: Multiplex Recurrence Network Approach

It has become a hot issue to integrate the carbon market, energy market, and financial market into one system and explore the relationship among them. Considering that the carbon market, energy market, and financial market all have chaotic characteristics to varying degrees, this paper proposes a theoretical framework to study the linkage relationship among the three markets on the basis of the method of the Multiplex recurrence network. Firstly, we built a multiplex recurrence network of carbon-energy-financial market. Then, based on the connection relationship among nodes of the recurrence network of each market, the degree distribution of nodes of each market, and the information entropy theory, we put forward several metric indicators to explore the correlativity and mutual guidance relation among carbon market, energy market and financial market from micro and macro perspectives. Using the data generated by the deterministic system, the effectiveness of the defined index was confirmed by numerical simulation. The empirical analysis of the carbon market, energy market, and financial market revealed the evolution process of the increasingly close connection between the three markets, and we found that the carbon market plays an increasingly important role in the world capital market system. Based on the research results, we propose some suggestions for market decision-makers, enterprises, and investors.

Early Warning Signals in Phase Space: Geometric Resilience Loss Indicators From Multiplex Cumulative Recurrence Networks

The detection of Early Warning Signals (EWS) of imminent phase transitions, such as sudden changes in symptom severity could be an important innovation in the treatment or prevention of disease or psychopathology. Recurrence-based analyses are known for their ability to detect differences in behavioral modes and order transitions in extremely noisy data. As a proof of principle, the present paper provides an example of a recurrence network based analysis strategy which can be implemented in a clinical setting in which data from an individual is continuously monitored for the purpose of making decisions about diagnosis and intervention. Specifically, it is demonstrated that measures based on the geometry of the phase space can serve as Early Warning Signals of imminent phase transitions. A publicly available multivariate time series is analyzed using so-called cumulative Recurrence Networks (cRN), which are recurrence networks with edges weighted by recurrence time and directed towards previously observed data points. The results are compared to previous analyses of the same data set, benefits, limitations and future directions of the analysis approach are discussed.

Being in a crowd bonds people via physiological synchrony

Collective events can generate intense emotions, shape group identities, and forge strong bonds. Do these effects extend to remote participation, and what are the psychological mechanisms underpinning their social power? We monitored psycho-physiological activity among groups of basketball fans who either attended games in-person (in a stadium) or watched games live on television in small groups. In-person attendance was associated with greater synchronicity in autonomic nervous system activation at the group level, which resulted in more transformative experiences and contributed to stronger identity fusion. Our findings suggest that the social effects of sports depend substantially on the inter-personal dynamics unfolding among fans, rather than being prompted simply by watching the game itself. Given the increasing prevalence of virtual experiences, this has potentially wide-reaching implications for many domains of collective human interaction.

Fast reconstruction of an original continuous series from a recurrence plot

We propose an algorithm to refine the reconstruction of an original time series given a recurrence plot, which is also referred to as a contact map. The refinement process calculates the local distances based on the Jaccard coefficients with the neighbors in the previous resolution for each point and takes their weighted average using local distances. We demonstrate the utility of our method using two examples.

Functional Muscle Network in Post-stroke Patients during Quiet Standing. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2021;2021:874-877. [PMID: 34891429 DOI: 10.1109/embc46164.2021.9630003]

The overall muscle activation of post-stroke patients during standing has not been well understood. Functional muscle network provides a tool to quantify the functional synchronization across a large number of muscles. In order to investigating the functional muscle network of stroke survivors during quiet standing, we recruited 8 post-stroke hemiplegic patients and required them to stand still for 30 s with eyes open and closed. Surface electromyography signals were recorded from 16 muscles in abdomen, buttocks and lower limbs. The functional muscle networks of paretic side and healthy side were built by multiplex recurrence network approach. The topological characteristics of functional muscle network was quantified by parameters of multiplex network and weighted network. The results showed that the dynamical similarities of muscles on paretic side were reduced, and the dynamical connections of muscles on paretic side were weakened. Without visual feedback, the muscles activated in a more similar mode. The stroke led to lower synchronization of the muscle activation, and decreased efficiency of information transmission between muscles. When subjects stood with eyes closed, the muscles activated in a more deterministic pattern. The research opens new horizons to detect the overall muscle activation when stroke patients stand quietly, and can provide a theoretical basis for understanding the motor dysfunction caused by stroke.

Multiplex Recurrence Network Analysis of Inter-Muscular Coordination During Sustained Grip and Pinch Contractions at Different Force Levels

Production of functional forces by human motor systems require coordination across multiple muscles. Grip and pinch are two prototypes for grasping force production. Each grasp plays a role in a range of hand functions and can provide an excellent paradigm for studying fine motor control. Despite previous investigations that have characterized muscle synergies during general force production, it is still unclear how intermuscular coordination differs between grip and pinch and across different force outputs. Traditional muscle synergy analyses, such as non-negative matrix factorization or principal component analysis, utilize dimensional reduction without consideration of nonlinear characteristics of muscle co-activations. In this study, we investigated the novel method of multiplex recurrence networks (MRN) to assess the inter-muscular coordination for both grip and pinch at different force levels. Unlike traditional methods, the MRN can leverage intrinsic similarities in muscle contraction dynamics and project its layers to the corresponding weighted network (WN) to better model muscle interactions. Twenty-four healthy volunteers were instructed to grip and pinch an apparatus with force production at 30%, 50%, and 70% of their respective maximal voluntary contraction (MVC). The surface electromyography (sEMG) signals were recorded from eight muscles, including intrinsic and extrinsic muscles spanning the hand and forearm. The sEMG signals were then analyzed using MRNs and WNs. Interlayer mutual information ( I ) and average edge overlap ( ω ) of MRNs and average shortest path length ( L ) of WNs were computed and compared across groups for grasp types (grip vs. pinch) and force levels (30%, 50% and 70% MVC). Results showed that the extrinsic, rather than the intrinsic muscles, had significant differences in network parameters between both grasp types ( ), and force levels ( ), and especially at higher force levels. Furthermore, I and ω were strengthened over time ( ) except with pinch at 30% MVC. Results suggest that the central nervous system (CNS) actively increases cortical oscillations over time in response to increasing force levels and changes in force production with different sustained grasping types. Muscle coupling in extrinsic muscles was higher than in intrinsic muscles for both grip and pinch. The MRNs may be a valuable tool to provide greater insights into inter-muscular coordination patterns of clinical populations, assess neuromuscular function, or stabilize force control in prosthetic hands.

Multiplex recurrence networks from multi-lead ECG data

We present an integrated approach to analyze the multi-lead electrocardiogram (ECG) data using the framework of multiplex recurrence networks (MRNs). We explore how their intralayer and interlayer topological features can capture the subtle variations in the recurrence patterns of the underlying spatio-temporal dynamics of the cardiac system. We find that MRNs from ECG data of healthy cases are significantly more coherent with high mutual information and less divergence between respective degree distributions. In cases of diseases, significant differences in specific measures of similarity between layers are seen. The coherence is affected most in the cases of diseases associated with localized abnormality such as bundle branch block. We note that it is important to do a comprehensive analysis using all the measures to arrive at disease-specific patterns. Our approach is very general and as such can be applied in any other domain where multivariate or multi-channel data are available from highly complex systems.

Fractal analysis of recurrence networks constructed from the two-dimensional fractional Brownian motions

In this study, we focus on the fractal property of recurrence networks constructed from the two-dimensional fractional Brownian motion (2D fBm), i.e., the inter-system recurrence network, the joint recurrence network, the cross-joint recurrence network, and the multidimensional recurrence network, which are the variants of classic recurrence networks extended for multiple time series. Generally, the fractal dimension of these recurrence networks can only be estimated numerically. The numerical analysis identifies the existence of fractality in these constructed recurrence networks. Furthermore, it is found that the numerically estimated fractal dimension of these networks can be connected to the theoretical fractal dimension of the 2D fBm graphs, because both fractal dimensions are piecewisely associated with the Hurst exponent H in a highly similar pattern, i.e., a linear decrease (if H varies from 0 to 0.5) followed by an inversely proportional-like decay (if H changes from 0.5 to 1). Although their fractal dimensions are not exactly identical, their difference can actually be deciphered by one single parameter with the value around 1. Therefore, it can be concluded that these recurrence networks constructed from the 2D fBms must inherit some fractal properties of its associated 2D fBms with respect to the fBm graphs.

Construction of Multiplex Muscle Network for Precision Pinch Force Control

Muscle synergy is a fundamental mechanism of motor control. Despite a number of studies focusing on muscle synergy during power grip and pinch at high-level force, relatively less is known about the functional interactions between muscles within low-level force production during precision pinch. Traditional analytical tools such as nonnegative matrix factorization or principal component analysis have limitations in processing nonlinear dynamic electromyographic signals and have confined sensitivity particularly for the low-level force production. In this study, we developed a novel method - multiplex muscle networks, to investigate the dynamical coordination of muscle activities at low-level force production during precision pinch. The multiplex muscle network was constructed based on multiplex limited penetrable horizontal visibility graph (MLPHVG). Seven forearm and hand muscles, including brachioradialis (BR), flexor carpi ulnaris (FCU), flexor carpi radialis (FCR), flexor digitorum superficialis (FDS), extensor digitorum communis (EDC), abductor pollicis brevis (APB) and first dorsal interosseous (FDI), were examined using surface electromyography (sEMG). Eight healthy subjects were instructed to perform a visuomotor force tracking task by producing higher (10% MVC) and lower (1% MVC) precision pinch. Interlayer mutual information I, average edge overlap ω weighted clustering coefficient C^W, weighted characteristic path length L^W were selected as network metrics. We assessed the undirected weighted network generated from multiplex muscle network after taking the I between paired muscle network layers as edge. There are significant differences between higher and lower force level with higher I, ω, C^W and lower L^W at higher force level. Advanced efficiency of information processing in the regional and global perspective indicated dynamical alterations when human faces the higher force tracking task. It suggested that ω may be an important characteristic to classify different force control states with the average classification accuracy of 82.21%. These findings reveal related alterations of functional interactions between muscles involved in precision pinch. The novel method for constructing multiplex muscle network may provide insights into muscle synergies during precision pinch force control.

Dynamic Analysis of Muscle Coordination at Different Force Levels during Grip and Pinch with Multiplex Recurrence Network

Muscle synergistic contraction to produce force has been recognized as an important neurophysiological mechanism in neuromuscular system. Despite a range of approaches, such as nonnegative matrix factorization or principal component analysis that have been widely used, limitations still exist in analysis of dynamic coordination of multiple muscles. In addition, it is still less studied about the potential difference of muscle dynamic coordination at different force levels during grip and pinch within the same framework. With this aim, this study analyzed the dynamic coordination of multiple upper-limb muscles at low, medium and high force levels during pinch and grip with multiplex recurrence network (MRN). Twenty-four healthy subjects participated in the experiment. Subjects were instructed to grip an apparatus to match the target force as stably as they could for 10 s. Surface electromyographic (sEMG) signals were recorded from 8 upper-limb muscles and analyzed by the MRN. The interlayer mutual information (I) and the average edge overlap (ω) of MRNs were calculated to quantify muscle correlation and muscle synchronization, respectively. Results showed that I and ω values of extrinsic muscles' MRNs during grip were significantly higher than that during grip at medium and high force. Furthermore, the I and ω values of extrinsic muscle networks during grip increased with augmented force levels. No significant changes were found for the intrinsic muscles with force output levels. These findings indicate that the muscles coordination patterns between grip and pinch were different and higher co-contraction of extrinsic muscles is favorable to synergistic force production. With the force output increased, muscles' coordination was augmented in extrinsic muscles, but no change in intrinsic muscles because of independent and complicated control of fingers. This study provides an analytical tool for dynamic muscles coordination and provides insights into the mechanisms of synergistic control of muscle contractions for force production.Clinical Relevance-This study provides a novel analytical tool for muscle coordination during force production, which may facilitate the evaluation of neuromuscular function or serve as indicators for neuromuscular disorders.

A Brief Introduction to Nonlinear Time Series Analysis and Recurrence Plots

Nonlinear time series analysis gained prominence from the late 1980s on, primarily because of its ability to characterize, analyze, and predict nontrivial features in data sets that stem from a wide range of fields such as finance, music, human physiology, cognitive science, astrophysics, climate, and engineering. More recently, recurrence plots, initially proposed as a visual tool for the analysis of complex systems, have proven to be a powerful framework to quantify and reveal nontrivial dynamical features in time series data. This tutorial review provides a brief introduction to the fundamentals of nonlinear time series analysis, before discussing in greater detail a few (out of the many existing) approaches of recurrence plot-based analysis of time series. In particular, it focusses on recurrence plot-based measures which characterize dynamical features such as determinism, synchronization, and regime changes. The concept of surrogate-based hypothesis testing, which is crucial to drawing any inference from data analyses, is also discussed. Finally, the presented recurrence plot approaches are applied to two climatic indices related to the equatorial and North Pacific regions, and their dynamical behavior and their interrelations are investigated.

A recurrence network-based convolutional neural network for fatigue driving detection from EEG

Driver fatigue is an important cause of traffic accidents, which has triggered great concern for detecting drivers' fatigue. Numerous methods have been proposed to fulfill this challenging task, including feature methods and machine learning methods. Recently, with the development of deep learning techniques, many studies achieved better results than traditional feature methods, and the combination of traditional methods and deep learning techniques gradually received attention. In this paper, we propose a recurrence network-based convolutional neural network (RN-CNN) method to detect fatigue driving. To be specific, we first conduct a simulated driving experiment to collect electroencephalogram (EEG) signals of subjects under alert state and fatigue state. Then, we construct the multiplex recurrence network (RN) from EEG signals to fuse information from the original time series. Finally, CNN is employed to extract and learn the features of a multiplex RN for realizing a classification task. The results indicate that the proposed RN-CNN method can achieve an average accuracy of 92.95%. To verify the effectiveness of our method, some existing competitive methods are compared with ours. The results show that our method outperforms the existing methods, which demonstrate the effect of the RN-CNN method.