Mathematical Biosciences and Engineering, 2011, 8(4): 1085-1097. doi: 10.3934/mbe.2011.8.1085.

Primary: 92C55, 92C10; Secondary: 93C70.

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Empirical mode decomposition/Hilbert transform analysis of postural responses to small amplitude anterior-posterior sinusoidal translations of varying frequencies

1. Department of Electrical and Computer Engineering, Clarkson University, Potsdam, NY 13699
2. Deptartments of Mathematics, Computer Science, and Physics, Clarkson University, Potsdam, NY 13699
3. Department of Electrical and Computer Engineering & Center for Rehabilitation, Science and Technology (CREST), Clarkson University, Potsdam, NY 13699

Bursts of 2.5mm horizontal sinusoidal anterior-posterior oscillations of sequentially varying frequencies (0.25 to 1.25 Hz) are applied to the base of support to study postural control. The Empirical Mode Decomposition (EMD) algorithm decomposes the Center of Pressure (CoP) data (5 young, 4 mature adults) into Intrinsic Mode Functions (IMFs). Hilbert transforms are applied to produce each IMF’s time-frequency spectrum. The most dominant mode in total energy indicates a sway ramble with a frequency content below 0.1 Hz. Other modes illustrate that the stimulus frequencies produce a ‘locked-in’ behavior of CoP with platform position signal. The combined Hilbert Spectrum of these modes shows that this phase-lock behavior of APCoP is more apparent for 0.5, 0.625, 0.75 and 1 Hz perturbation intervals. The instantaneous energy profiles of the modes depict significant energy changes during the stimulus intervals in case of lock-in. The EMD technique provides the means to visualize the multiple oscillatory modes present in the APCoP signal with their time scale dependent on the signals’s successive extrema. As a result, the extracted oscillatory modes clearly show the time instances when the subject’s APCoP clearly synchronizes with the provided sinusoidal platform stimulus and when it does not.
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Keywords Center of Pressure; Empirical Mode Decomposition; Induced Oscillations.; Posture and Balance; Sinusoidal Per- turbations

Citation: Rakesh Pilkar, Erik M. Bollt, Charles Robinson. Empirical mode decomposition/Hilbert transform analysis of postural responses to small amplitude anterior-posterior sinusoidal translations of varying frequencies. Mathematical Biosciences and Engineering, 2011, 8(4): 1085-1097. doi: 10.3934/mbe.2011.8.1085


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