Noise-assisted Multivariate Empirical Mode Decomposition based Causal Decomposition for brain-physiological network in bivariate and multiscale time series

Detection of intermuscular coordination based on the causality of empirical mode decomposition

Considering the stochastic nature of electromyographic (EMG) signals, nonlinear methods may be a more accurate approach to study intermuscular coordination than the linear approach. The aims of this study were to assess the coordination between two ankle plantar flexors using EMG by applying the causal decomposition approach and assessing whether the intermuscular coordination is affected by the slope of the treadmill. The medial gastrocnemius (MG) and soleus muscles (SOL) were analyzed during the treadmill walking at inclinations of 0°, 5°, and 10°. The coordination was evaluated using ensemble empirical mode decomposition, and the causal interaction was encoded by the instantaneous phase dependence of time series bi-directional causality. To estimate the mutual predictability between MG and SOL, the cross-approximate entropy (XApEn) was assessed. The maximal causal interaction was observed between 40 and 75 Hz independent of inclination. XApEn showed a significant decrease between 0° and 5° (p = 0.028), between 5° and 10° (p = 0.038), and between 0° and 10° (p = 0.014), indicating an increase in coordination. Thus, causal decomposition is an appropriate methodology to study intermuscular coordination. These results indicate that the variation of loading through the change in treadmill inclination increases the interaction of the shared input between MG and SOL, suggesting increased intermuscular coordination.

Matlab Open Source Code: Noise-Assisted Multivariate Empirical Mode Decomposition Based Causal Decomposition for Causality Inference of Bivariate Time Series

Causality inference has arrested much attention in academic studies. Currently, multiple methods such as Granger causality, Convergent Cross Mapping (CCM), and Noise-assisted Multivariate Empirical Mode Decomposition (NA-MEMD) are introduced to solve the problem. Motivated by the researchers who uploaded the open-source code for causality inference, we hereby present the Matlab code of NA-MEMD Causal Decomposition to help users implement the algorithm in multiple scenarios. The code is developed on Matlab2020 and is mainly divided into three subfunctions: na_memd, Plseries, and cd_na_memd. na_memd is called in the main function to generate the matrix of Intrinsic Mode Functions (IMFs) and Plseries can display the average frequency and phase difference of IMFs of the same order in a matrix which can be used for the selection of the main Intrinsic Causal Component (ICC) and ICCs set. cd_na_memd is called to perform causal redecomposition after removing the main ICC from the original time series and output the result of NA-MEMD Causal Decomposition. The performance of the code is evaluated from the perspective of executing time, robustness, and validity. With the data amount enlarging, the executing time increases linearly with it and the value of causal strength oscillates in an ideally small interval which represents the relatively high robustness of the code. The validity is verified based on the open-access predator-prey data (wolf-moose bivariate time series from Isle Royale National Park in Michigan, USA) and our result is aligned with that of Causal Decomposition.

Noise-assisted Multivariate Empirical Mode Decomposition based Causal Decomposition for Detecting Upper Limb Movement in EEG-EMG Hybrid Brain Computer Interface

EEG-EMG based hybrid Brain Computer Interface (hBCI) utilizes the brain-muscle physiological system to interpret and identify motor behaviors, and transmit human intelligence to automated machines in AI applications such as neurorehabilitations and brain-like intelligence. The study introduces a hBCI method for motor behaviors, where multiple time series of the brain neuromuscular network are introduced to indicate brain-muscle causal interactions, and features are extracted based on Relative Causal Strengths (RCSs) derived by Noise-assisted Multivariate Empirical Mode Decomposition (NA-MEMD) based Causal Decomposition. The complex process in brain neuromuscular interactions is specifically investigated towards a monitoring task of upper limb movement, whose 63-channel EEGs and 2-channel EMGs are composed of data inputs. The energy and frequency factors counted from RCSs were extracted as Core Features (CFs). Results showed accuracies of 91.4% and 81.4% with CFs for identifying cascaded (No Movement and Movement Execution) and 3-class (No Movement, Right Movement, and Left Movement) using Naive Bayes classifier, respectively. Moreover, those reached 100% and 94.3% when employing CFs combined with eigenvalues processed by Common Spatial Pattern (CSP). This initial work implies a novel causality inference based hBCI solution for the detection of human upper limb movement.