Analysis of Heart Beat Dynamics through Singularity Spectrum
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32870
Analysis of Heart Beat Dynamics through Singularity Spectrum

Authors: Harish Kumar, Hussein Yahia, Oriol Pont, Michel Haissaguerre, Nicolas Derval, Meleze Hocini


The analysis to detect arrhythmias and life-threatening conditions are highly essential in today world and this analysis can be accomplished by advanced non-linear processing methods for accurate analysis of the complex signals of heartbeat dynamics. In this perspective, recent developments in the field of multiscale information content have lead to the Microcanonical Multiscale Formalism (MMF). We show that such framework provides several signal analysis techniques that are especially adapted to the study of heartbeat dynamics. In this paper, we just show first hand results of whether the considered heartbeat dynamics signals have the multiscale properties by computing local preticability exponents (LPEs) and the Unpredictable Points Manifold (UPM), and thereby computing the singularity spectrum.

Keywords: Microcanonical Multiscale Formalism (MMF), UnpredictablePoints Manifold (UPM), Heartbeat Dynamics.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1487


[1] M. Malik and A. Camm, and Members of the Task Force, Heart rate variability: standards of measurement, physiological interpretation, and clinical use, Circulation, vol. 93, pp. 10431065, 1996.
[2] P. Ivanov, L. Amaral, A. Goldberger, S. Havlin, M. Rosenblum, Z. Struzik, H. Stanley, Multifractality in human heartbeat dynamics, Nature 399, pp. 461465, 1999.
[3] P. Ivanov, Long-range dependence in heartbeat dynamics, In G. Rangarajan, M. Ding (eds.) Processes with Long-Range Correlations, Lecture Notes in Physics, Springer Berlin / Heidelberg, vol. 621, pp. 339372, 2003.
[4] S. Kozaitis, Improved feature detection in ecg signals through denoising, International Journal of Signal and Imaging Systems Engineering, 1(2), pp. 108114, 2008.
[5] R. Klabunde, Cardiovascular Physiology Concepts, Lippincott Williams Wilkins, Hagerstwon, 2005.
[6] C. Peng, J. Mietus, J. Hausdorff, S. Havlin, H. Stanley, and A. Goldberger, Long-Range Anticorrelations and Non-Gaussian Behavior of the Heartbeat, Phys. Rev. Lett., 70, pp. 1343-1346, 1993.
[7] S. Thurner, M. Feurstein, and M. Teich, Multiresolution Wavelet Analysis of Heartbeat Intervals Discriminates Healthy Patients from Those with Cardiac Pathology, Phys. Rev. Lett., 80, pp. 1544-1547, 1998.
[8] L. Amaral, P. Ivanov, N. Aoyagi, I. Hidaka, S. Tomono, A. Goldberger, H. Stanley, and Y. Yamamoto, Behavioral-Independent Features of Complex Heartbeat Dynamics, Phys. Rev. Lett., 86, pp. 6026-6029, 2001.
[9] Y. Ashkenazy, P. Ivanov, S. Havlin, C. Peng, A. Goldberger, and H. Stanley, Magnitude and Sign Correlations in Heartbeat Fluctuations, Phys. Rev. Lett., 86, pp. 1900-1903, 2001.
[10] P. Bernaola-Galvan, P. Ivanov, L. Amaral, and H. Stanley, Scale Invariance in the Nonstationarity of Human Heart Rate, Phys. Rev. Lett., 87, 168105, 2001.
[11] P. Ivanov, L. Amaral, A. Goldberger, S. Havlin, M. Rosenblum, H. Stanley, and Z. Struzik, From 1/f Noise to Multifractal Cascades in Heartbeat Dyamics, Chaos 11, pp. 641-652, 2001.
[12] V. Ribeiro, R. Riedi, M. Crouse, R. Baraniuk, Multiscale queuing analysis of long-range-dependent network traffic, In: INFOCOM (2), pp. 10261035, 2000.
[13] O. Pont, A. Turiel, C. Perez-Vicente, Application of the microcanonical multifractal formalism to monofractal systems, Physical Review E 74, 061110061123, 2006.
[14] A. Turiel, H. Yahia, C. Perez-Vicente, Microcanonical multifractal formalism: a geometrical approach to multifractal systems. Part I: Singularity analysis, Journal of Physics A, 41, 015501, 2008.
[15] S. Mallat, W. Huang, Singularity detection and processing with wavelets, IEEE Trans. in Inf. Th. 38, pp. 617643, 1992.
[16] S. Mallat, S. Zhong, Wavelet transform maxima and multiscale edges, In: et al, M.B.R. (ed.) Wavelets and their applications, Jones and Bartlett, Boston, 1991.
[17] O. Pont, A. Turiel, C. Perez-Vicente, On optimal wavelet bases for the realization of microcanonical cascade processes, Int. J. Wavelets Multi., IJWMIP, 9(1), pp. 3561 , 2011.
[18] A. Turiel, C. Perez-Vicente, J. Grazzini, Numerical methods for the estimation of multifractal singularity spectra on sampled data: a comparative study, Journal of Computational Physics, 216(1), pp. 362390, 2006.
[19] S. Jaffard, Multifractal formalism for functions. I. Results valid for all functions, SIAM Journal of Mathematical Analysis 28(4), 944-970, 1997.
[20] I. Simonsen, A. Hansen, O. Magnar, Determination of the hurst exponent by use of wavelet transforms, Phys. Rev. E, 58(3), pp. 2779-2787, 1998.
[21] C. Jones, G. Lonergan, D. Mainwaring, Wavelet packet computation of the hurst exponent, J. Phys. A: Math. Gen, 29(10), 2509, 1996.
[22] A. Turiel, N. Parga, The multi-fractal structure of contrast changes in natural images: from sharp edges to textures, Neural Computation 12, 763-793, 2000.
[23] S. Mallat, A Wavelet Tour of Signal Processing, Academic Press, 2nd Edition, 1999.
[24] K. Falconer, Fractal Geometry: Mathematical Foundations and Applications, John Wiley and sons, Chichester, 1990.
[25] A. Arneodo, F. Argoul, E. Bacry, J. Elezgaray, J. Muzy, Ondelettes multifractales et turbulence, Diderot Editeur, Paris, France, 1995.
[26] G. Parisi, U. Frisch, On the singularity structure of fully developed turbulence, in: M. Ghil, R. Benzi, G. Parisi (Eds.), Turbulence and Predictability in Geophysical Fluid Dynamics. Proc. Intl. School of Physics E. Fermi, North Holland, Amsterdam, pp. 84-87, 1985.
[27] O. Pont, A. Turiel, H. Yahia, An Optimized Algorithm for the Evaluation of Local Singularity Exponents in Digital Signals, IWCIA, 6636, pp, 346- 357, 2011.