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      Rhythmic Dynamics and Synchronization via Dimensionality Reduction: Application to Human Gait

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          Abstract

          Reliable characterization of locomotor dynamics of human walking is vital to understanding the neuromuscular control of human locomotion and disease diagnosis. However, the inherent oscillation and ubiquity of noise in such non-strictly periodic signals pose great challenges to current methodologies. To this end, we exploit the state-of-the-art technology in pattern recognition and, specifically, dimensionality reduction techniques, and propose to reconstruct and characterize the dynamics accurately on the cycle scale of the signal. This is achieved by deriving a low-dimensional representation of the cycles through global optimization, which effectively preserves the topology of the cycles that are embedded in a high-dimensional Euclidian space. Our approach demonstrates a clear advantage in capturing the intrinsic dynamics and probing the subtle synchronization patterns from uni/bivariate oscillatory signals over traditional methods. Application to human gait data for healthy subjects and diabetics reveals a significant difference in the dynamics of ankle movements and ankle-knee coordination, but not in knee movements. These results indicate that the impaired sensory feedback from the feet due to diabetes does not influence the knee movement in general, and that normal human walking is not critically dependent on the feedback from the peripheral nervous system.

          Author Summary

          Complex physiological rhythms arise from a large variety of biological systems that include natural pacemakers as well as feedback mechanisms, from the heartbeat to the rhythmic movement of human walking. Accurately extracting and characterizing the fluctuations underlying the biological rhythms is a fundamental problem which holds the key to understanding the mechanisms that govern the dynamics of biological systems. Usually such signals demonstrate certain oscillatory patterns, with each period displaying irregular fluctuation, or nontrivial dynamics, over time. This renders traditional spectral methods and nonlinear techniques less effective. We propose a novel approach to highlight the intrinsic fluctuations masked by the periodic component and noise through advanced dimension-reduction techniques, and apply it to human gait data from healthy subjects and diabetics. We find that this approach is capable of extracting the intrinsic dynamics and identifying the subtle synchronization pattern between knee and ankle. We find that although the two groups of individuals demonstrate remarkable differences in the dynamics of ankle movement and ankle-knee synchronization, the knee movement of both groups show similar dynamics. These results suggest that sensory feedback from a peripheral nerve system (like the feet) does not play an important role in regulating the motor control of human walking.

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          Most cited references29

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          Dynamic causal modelling.

          In this paper we present an approach to the identification of nonlinear input-state-output systems. By using a bilinear approximation to the dynamics of interactions among states, the parameters of the implicit causal model reduce to three sets. These comprise (1) parameters that mediate the influence of extrinsic inputs on the states, (2) parameters that mediate intrinsic coupling among the states, and (3) [bilinear] parameters that allow the inputs to modulate that coupling. Identification proceeds in a Bayesian framework given known, deterministic inputs and the observed responses of the system. We developed this approach for the analysis of effective connectivity using experimentally designed inputs and fMRI responses. In this context, the coupling parameters correspond to effective connectivity and the bilinear parameters reflect the changes in connectivity induced by inputs. The ensuing framework allows one to characterise fMRI experiments, conceptually, as an experimental manipulation of integration among brain regions (by contextual or trial-free inputs, like time or attentional set) that is revealed using evoked responses (to perturbations or trial-bound inputs, like stimuli). As with previous analyses of effective connectivity, the focus is on experimentally induced changes in coupling (cf., psychophysiologic interactions). However, unlike previous approaches in neuroimaging, the causal model ascribes responses to designed deterministic inputs, as opposed to treating inputs as unknown and stochastic.
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            Evaluating causal relations in neural systems: granger causality, directed transfer function and statistical assessment of significance.

            We consider the question of evaluating causal relations among neurobiological signals. In particular, we study the relation between the directed transfer function (DTF) and the well-accepted Granger causality, and show that DTF can be interpreted within the framework of Granger causality. In addition, we propose a method to assess the significance of causality measures. Finally, we demonstrate the applications of these measures to simulated data and actual neurobiological recordings.
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                Author and article information

                Contributors
                Role: Editor
                Journal
                PLoS Comput Biol
                plos
                ploscomp
                PLoS Computational Biology
                Public Library of Science (San Francisco, USA )
                1553-734X
                1553-7358
                December 2010
                December 2010
                16 December 2010
                : 6
                : 12
                : e1001033
                Affiliations
                [1 ]Center for Computational Systems Biology, Fudan University, Shanghai, People's Republic of China
                [2 ]Department of Electronic and Information Engineering, Hong Kong Polytechnic University, Hong Kong, People's Republic of China
                [3 ]Life Science Division, Lawrence Berkeley National Laboratory, Berkeley, California, United States of America
                [4 ]Department of Computer Science and Mathematics, Warwick University, Coventry, United Kingdom
                University of Potsdam, Germany
                Author notes

                Conceived and designed the experiments: JZ KZ JF MS. Analyzed the data: JZ KZ. Contributed reagents/materials/analysis tools: JZ KZ JF MS. Wrote the paper: JZ KZ JF MS.

                Article
                10-PLCB-RA-2354R2
                10.1371/journal.pcbi.1001033
                3002994
                21187907
                5573252f-bafe-4930-992d-60421c5fed07
                This is an open-access article distributed under the terms of the Creative Commons Public Domain declaration which stipulates that, once placed in the public domain, this work may be freely reproduced, distributed, transmitted, modified, built upon, or otherwise used by anyone for any lawful purpose.
                History
                : 10 June 2010
                : 11 November 2010
                Page count
                Pages: 11
                Categories
                Research Article
                Physics/Interdisciplinary Physics

                Quantitative & Systems biology
                Quantitative & Systems biology

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