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Abstract-Recent studies have investigated bilateral gaits based on the causality analysis of kinetic (or kinematic) signals recorded using both feet. However, these approaches have not considered the influence of their simultaneous causation, which might lead to inaccurate causality inference. Furthermore, the causal interaction of these signals has not been investigated within their frequency domain. Therefore, in this study we attempted to employ a causal-decomposition approach to analyze bilateral gait. The vertical ground reaction force (VGRF) signals of Parkinson's disease (PD) patients and healthy control (HC) individuals were taken as an example to illustrate this method. To achieve this, we used ensemble empirical mode decomposition to decompose the left and right VGRF signals into intrinsic mode functions (IMFs) from the high to low frequency bands. The causal interaction strength (CIS) between each pair of IMFs was then assessed through the use of their instantaneous phase dependency. The results show that the CISes between pairwise IMFs decomposed in the high frequency band of VGRF signals can not only markedly distinguish PD patients from HC individuals, but also found a significant correlation with disease progression, while other pairwise IMFs were not able to produce this. In sum, we found for the first time that the frequency specific causality of bilateral gait may reflect the health status and disease progression of individuals. This finding may help to understand the underlying mechanisms of walking and walking-related diseases, and offer broad applications in the fields of medicine and engineering.

Objective: Multivariate signal (MS) analysis, especially the assessment of its information transmission (for example, from the perspective of network science), is the key to our understanding of various phenomena in biology, physics and economics. Although there is a large amount of literature demonstrating that MS can be decomposed into space-timefrequency domain information, there seems to be no research confirming that multivariate information transmission (MIT) in these three domains can be quantified. Therefore, in this study, we attempted to combine dynamic mode decomposition (DMD) and parallel communication model (PCM) together to realize it. Methods: We first regarded MS as a large-scale system and then used DMD to decompose it into specific subsystems with their own intrinsic oscillatory frequencies. At the same time, the transition probability matrix (TPM) of information transmission within and between MS at two consecutive moments in each subsystem can also be calculated. Then, communication parameters (CPs) derived from each TPM were calculated in order to quantify the MIT in the space-time-frequency domain. In this study, multidimensional electroencephalogram (EEG) signals were used to illustrate our method. Results: Compared with traditional EEG brain networks, this method shows greater potential in EEG analysis to distinguish between patients and healthy controls. Conclusion:This study demonstrates the feasibility of measuring MIT in the space-time-frequency domain simultaneously. Significance: This study shows that MIT analysis in the spacetime-frequency domain is not only completely different from the MS decomposition in these three domains, but also can reveal many new phenomena behind MS that have not yet been discovered.