Postural control is a primary request of standing balance maintenance and is vulnerable to stroke. Post-stroke patients usually exhibit increased body sway, weight-bearing asymmetry, decreased limits of stability, body tilting and even falls [1,2,3]. The motor system, involving muscles, bones and joints, can generate a corrective, stabilizing torque to maintain the postural stability and orientation within the base of support [4]. To understand the mechanisms underlying postural control would help develop more indicators of motor functions relevant to impaired standing balance control and improve the efficiency of standing recovery after a stroke.
Postural control requires temporal and spatial coordination of multiple muscles. However, the damage to the pyramidal system and (or) extrapyramidal system in stroke survivors leads to interruption of descending motor paths and decreased common motoneuronal drives, ultimately manifesting as altered multi-muscle coordination [5, 6]. As one of the main motor behaviors for postural control, muscle synergies during walking has been studied in some depth. Asymmetric gait occurs after a stroke, as evidenced by differences in muscle synergies between sides. Compared with the affected side, muscle synergies related to unaffected side of hemiplegic patients were more similar to those of healthy individuals [7]. Besides, muscle synergies may merge after a stroke. It has been verified that fewer muscle synergies were needed to account for the whole muscle activity on the affected side when compared to the unaffected side [8], and rehabilitation training could significantly increase the number of muscle synergies during walking [9]. Upright standing can be approximated to a single inverted pendulum, with high demand on the coordination of muscles on trunk, hips, thighs and calves to counter gravity [10]. Surface electromyography (sEMG) studies in the standing position of post-stroke patients mainly focused on single-muscle activation and two-muscle coupling. Specifically, post-stroke patients have lower muscle activation and greater synchronous control between the antagonistic muscles on the affected lower limb [11, 12]. Stroke-related characteristics in muscle coordination during standing has been relatively less studied. Most of the research on muscle synergies during standing in post-stroke patients are generally combined with other tasks, such as reaching from standing, sit-to-stand transition and standing under disturbance [13,14,15]. The multi-muscle coordination of hemiplegic patients performing simple standing task is in urgent need of study.
Quantification of multi-muscle coordination relies on appropriate analytical tools. Previous studies about multi-muscle coordination are mostly based on non-negative matrix factorization (NMF), principal component analysis (PCA) and spectral coherence [6, 16, 17]. Tasks that are better analyzed by NMF and PCA are dynamic tasks, such as walking, running, pedaling and standing under perturbation [15, 18, 19]. These tasks satisfy the requirement of variation in activation amplitude for NMF and PCA to correctly identify synergy vectors of muscles [20,21,22]. When processing relatively steady sEMG signals, the role of NMF and PCA are very limited [23]. Besides, NMF and PCA are sensitive to the data length and signal quality of sEMG, thereby showing low robustness and repeatability in experimental studies [24]. Linear spectral coherence analysis assumes that a variety of muscles are coupled by linear relation, omitting the synchronizations between muscle complex. Therefore, some nonlinear analytical tools that are not based solely on signal amplitude and frequency variability, such as recurrence-based analysis, were proposed to assess the dynamical coordination of nonlinear, nonstationary neurophysiological signals [25, 26]. Recurrence-based analysis methods showed unique advantages in detection of the state changes in drifting dynamical motor systems and measurement of the rule-obeying structures in motor commands, especially for movements with little variation in sEMG signal amplitude [25,26,27]. By a careful choice of the setup parameters, recurrence-based analysis methods are relatively immune to noise [26]. However, these recurrence-based analysis methods had difficulty in describing detailed changes in specific muscles. In the examination of postural control during standing, there is a need to develop novel methods that can provide holistic and detailed information on intermuscular coordination.
Network analysis has its origins in graph theory and describes the spatiotemporal relationships between system elements through holistic and detailed characteristics, enabling in-depth exploration of the structure, behavior and function of systems [28, 29]. In the analysis of human electrophysiological signals, network analysis has been widely used to characterize the organization of distributed brain activity [30]. In the last decade, muscle networks have been gaining attention and have provided powerful tools for monitoring the spatiotemporal synergetic relationships of multiple muscles [31,32,33,34,35]. Most of existing literature decodes functional muscle connectivity by linear spectral coherence and NMF [31, 33, 34, 36]. Recently, a novel multiplex recurrence network (MRN) approach has be proposed by combining dynamical recurrence with a multiplex network [37]. The MRN is suitable for the analysis of neurophysiological dynamics. It maps multivariate time series into phase space simultaneously to obtain trajectories and reveals the interactions of multiple subsystems through subtle recurrence features between trajectories, providing a new way to identify the structural and temporal characteristics of intermuscular dynamical coordination [25, 38]. In one of our previous studies, we employed the MRN to assess the intermuscular coordination for both grip and pinch at different force levels, and found that MRN could better explore the tiny changes of muscle coordination within a short time muscle contraction (less than 500 ms) compared with the NMF and PCA [39]. An intriguing issue is whether the MRN could provide insights into the intermuscular coordination of multiple muscles responsible for postural control and promote the evaluation of balance capacity for post-stroke patients.
Strongly shaped by the anatomical constraints of the musculoskeletal system and affected by tasks, the muscles of the functional network usually show unbalanced contributions [33]. Identifying the responsible muscles for abnormal coordinated actions may aid in developing more effective treatment programs of rehabilitation for patients with stroke. Using metrics that could measure the importance of nodes in the network, such as the degree of centrality (DC), the specific contributions of nodes in a network would be quantified and the abnormal function of nodes could be identified [40]. Unfortunately, little is known whether the contributions of multiple muscles involved in postural control during standing could be indexed, or the stroke-related impaired muscles could be identified.
The aim of this study was to evaluate the multi-muscle coordination for postural control during standing and to identify the abnormal muscle functions due to stroke. A weighted recurrence network (WRN) was constructed to analyze the dynamical coordination of multiple muscles responsible for standing balance. The DC was implemented to index the contributions of specific muscles in WRN. It was hypothesized that stroke would affect the dynamical coordination patterns for postural control, and it was also hypothesized that responsible muscles for impaired coordination after a stroke could be identified by using this novel method.
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Yogev Koren
Simona Bar-Haim
Noy Goldhamer1,3
Lior Shmuelof
Marialuisa Gandolfi
Nicola Valè
Eleonora Dimitrova1,2, 
Marcello Beccari
Christian Geroin
Alessandro Picelli
Nicola Smania