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

Rakesh Pilkar; Erik M. Bollt; Charles Robinson

doi:10.3934/mbe.2011.8.1085

Article Contents

2011, Volume 8, Issue 4: 1085-1097. Doi: 10.3934/mbe.2011.8.1085

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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

Received: September 30, 2010

Revised: April 30, 2011

Published: July 2011

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Abstract

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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Mathematics Subject Classification: Primary: 92C55, 92C10; Secondary: 93C70.

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References

[1]	A. M. Nunzio, A. Nardone and M. Schieppati, Head stabilization on a continuously oscillating platform: The effect of proprioceptive disturbance on the balance strategy, Experimental Brain Research, 165 (2005), 261-272.
[2]	B. Boashash, Estimating and interpreting the instantaneous frequency of a signal - Part 1: Fundamentals, Proceedings of the IEEE, 80 (1992), 520-538.
[3]	C. Tokuno, A. Cresswell, A. Thorstensson and M. Carpenter, Age-related changes in postural responses revealed by support-surface translations with a long acceleration-deceleration interval, Clinical Neurophysiology, 121 (2010), 109-117.
[4]	C. Robinson, M. Purucker and L. Faulkner, Design, control and characterization of a sliding linear investigative platform for analyzing lower limb stability (SLIP-FALLS), IEEE Transactions on Rehabilitation Engineering, 6 (1998), 334-350.
[5]	F. King, "Hilbert Transforms," Volume 1, Encyclopedia of Mathematics and its Applications, 124, Cambridge University Press, Cambridge, 2009.
[6]	L. Cohen, Time frequency distributions - review, IEEE Transactions on Neural Systems and Rehabilitation Engineering, 77 (2002), 941-981.
[7]	L. Cohen and C. Lee, Instantaneous frequency, its standard deviation and multicomponent signals, in "Advanced Algorithms and Architectures for Signal Processing III" (ed. Franklin T. Luk), Proc. SPIE, 975 (1988), 186-208.
[8]	N. Huang, Z. Shen, S. Long, M. Wu, H. Shih, Q. Zheng, N. Yen, C. Tung and H. Liu, The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis, Royal Society London Proc. Ser. A Math. Phys. Eng. Sci., 454 (1998), 903-995.
[9]	N. Bugnariu and H. Sveistrup, Age-related changes in postural responses to externally- and self-triggered continuous perturbations, Archives of Gerontology and Geriatrics, 42 (2006), 73-89.
[10]	P. Loughlin and M. Redfern, Spectral characteristics of visually induced postural sway in healthy elderly and healthy young subjects, IEEE Transactions on Neural Systems and Rehabilitation Engineering, 9 (2001), 24-30.doi: 10.1109/MEMB.2003.1195699.
[11]	P. Loughlin, M. Redfern and J. Furman, Nonstationarities pf postural sway, IEEE Engineering in Medicine and Biology Magazine, 22 (1998), 69-75.
[12]	P. Sparto, J. Jasko and P. Loughlin, Detecting postural responses to sinusoidal sensory inputs: A statistical approach, IEEE Transactions on Neural Systems and Rehabilitation Engineering, 12 (2004), 360-366.
[13]	R. Pilkar, E. Bollt and C. Robinson, "Empirical Mode Decomposition/ Hilbert Transform Analysis of Induced Postural Oscillations," BMES Anual Meeting, 2010.
[14]	R. Schilling and C. Robinson, A phase-locked looped model of the response of the control system to periodic platform motion, IEEE Transactions on Neural Systems and Rehabilitation Engineering, 18 (2010), 274-283.
[15]	R. Soames and J. Atha, The Spectral characteristics of postural sway, European Journal of Applied Physiology and Occupational Physiology, 49 (1982), 169-177.
[16]	S. Richerson, L. Faulkner, C. Robinson, M. Redfern and M. Purucker, Acceleration threshold detection during short anterior and posterior perturbations on a translating platform, Gait and Posture, 18 (2003), 11-19.
[17]	S. Nakappan, C. Robinson, V. Dharbe, C. Storey and K. O'Neal, Variations in anterior -posterior COP patterns in elderly adults between psychophysically detected and non-detected short horizontal perturbations, IEEE-EMBS 27th Anual International Conference, (2005), 5427-5430.
[18]	V. Dietz, M. Trippel, I. Ibrahim and W. Berger, Human Stance on a sinusoidally translating platform: Balance control by feedforward and feedback mechanisms, Experimental Brain Research, 93 (1993), 352-362.