Multifractal application on electrocardiogram

References

• Kantelhardt, J.W., 2008, Fractal and multifractal time-series. Physica A, 1, 1–59
   Google Scholar
• Webster, J.G., 2008, Medical Instrumentation: Application and Design, 3rd edn. (Singapore: John Wiley & Sons Pte. Ltd.), pp. 10
   Google Scholar
• Ocak, H., 2008, Optimal classification of epileptic seizures in EEG using wavelet analysis and genetic algorithm. Signal Processing, 88, 1858–1867
   Web of Science ®Google Scholar
• Ocak, H., 2009, Automatic detection of epileptic seizures in EEG using discrete wavelet transform and approximate entropy. Expert Systems with Applications, 36, 2027–2036
   Web of Science ®Google Scholar
• Butler, G.C., Yamamoto, Y., and Hughson, R.L., 1994, Fractal nature of short-term systolic BP and HR variability during lower body negative pressure. American Journal of Physiology, Regulatory Integrative and Comparative Physiology, 267, R26–33
   Google Scholar
• Elbert, T., Ray, W.J., Kowalik, Z.J., Skinner, J.E., Graf, K.E., and Birbaumer, N., 1994, Chaos and physiology: Deterministic chaos in excitable cell assemblies. Physiological Reviews, 74, 1–47
   PubMed Web of Science ®Google Scholar
• Easwaramoorthy, D., and Uthayakumar, R., 2010, Analysis of biomedical EEG signals using Wavelet Transforms and Multifractal Analysis. IEEE International Conference for Communication Control and Computing Technologies, Oct 7-9 2010; Ramanathapuram; pp. 544–549
   Google Scholar
• Falconer, K., 2003, Fractal Geometry: Mathematical Foundations and Applications, 2nd edn. (England: John Wiley & Sons Ltd)
   Google Scholar
• Ghashghaie, S., Breymann, W., Peinke, J., Talkner, P., and Dodge, Y., 1996, Turbulent cascades in foreign exchange market. Nature, 381, 767–770
   Web of Science ®Google Scholar
• Mandelbrot, B.B., and Van Ness, J., 1968, Fractional Brownian motion, fractional noises and applications. SIAM Review, 10, 422–437
   Web of Science ®Google Scholar
• Jiang-dong, C.A.I., and Qing, Y.O.U., 2010, Fractal theory and its application in studying the feature of landforms. International Workshop on Chaos-Fractal Theory and its Applications; 2010; Kunming, Yunnan: pp. 440–444
   Google Scholar
• Ihlen, E.A.F., 2012, Introduction to multifractal detrended fluctuation analysis in matlab. Frontiers in Physiology, 3, 1–18. Available online at: http://www.frontiersin.org/Fractal_Physiology/10.3389/fphys.2012.00141/full. doi: 10.3389/fphys.2012.00141
   Google Scholar
• Hurst, H.E., 1951, Long-term storage capacity of reservoirs. The American Society of Civil Engineers, 116, 770–799
   Google Scholar
• Ivanov, P.C., Amaral, L.A.N., Goldberger, A.L., Havlin, S., Rosenblum, M.G., Struzik, Z.R., and Stanley, H.E., 1999, Multifractality in human heart beat dynamics. Nature, 399, 461–465
   PubMed Web of Science ®Google Scholar
• Stanley, H.E., Buldyrev, S.V., Goldberger, A.L., Havlin, S., Peng, C.K., and Simons, M., 1993, Long-range power-law correlations in condensed matter physics and biophysics. Physica A, 200, 4–24
   Web of Science ®Google Scholar
• Lavinia, S., Catalina, N., Anca, S., Liviu, A., Constantin, C., and Grosu, I., 2001, Investigations of cardiac rhythm fluctuation using the DFA method. Proceedings of the 23rd Annual International Conference for Engineering in Medicine and Biology Society, 1, 530–533
   Google Scholar
• Goldberger, A.L., Amaral, L.A.N., Glass, L., Hausdorff, J.M., Ivanov, P.C., Mark, R.G., Mietus, J.E., Moody, G.B., Peng, C.K., and Stanley, H.E., 2000, PhysioBank, PhysioToolkit, and PhysioNet: Components of a new research resource for complex physiologic signals. Circulation, 101, e215–e220
   PubMed Web of Science ®Google Scholar
• Peng, C.K., Buldyrev, S.V., Havlin, S., Simons, M., Stanley, H.E., and Goldberger, A.L., 1994, Mosaic Organization of DNA Nucleotides. Physical Review E, 49, 1685–1689
   PubMed Web of Science ®Google Scholar
• Kantelhardt, J.W., Konscienly-Bunde, E., Rego, H.H.A., Havlin, S., and Bunde, A., 2001, Detecting long range correlations with detrended fluctuation analysis. Physica A, 295, 441–454
   Web of Science ®Google Scholar
• Kantelhardt, J.W., Zschiegner, S.A., Konscienly-Bunde, E., Havlin, S., Bunde, A., and Stanley, H.E., 2002, Multifractal detrended fluctuation analysis of non-stationary time-series. Physica A, 316, 87–114
   Web of Science ®Google Scholar
• Telesca, L., Colangelo, G., Lapenna, V., and Macchiato, M., 2004, Fluctuation dynamics in geoelectrical data: An investigation by using multifractal detrended fluctuation analysis. Physics Letters A, 332, 398–404
   Web of Science ®Google Scholar
• Beran, J., 1994, Statistics for Long-Memory Processes. Monographs on Statistics & Applied Probability (New York: Chapman & Hall/CRC)
   Google Scholar
• Eke, A., Herman, P., Bassingthwaighte, J.B., Raymond, G.M., Percival, D.B., Cannon, M., Balla, I., and Ikrenyi, C., 2000, Physiological time-series: Distinguishing fractal noises from motions. Pflugers Archiv, 439, 403–415
   PubMed Web of Science ®Google Scholar
• Eke, A., Herman, P., Sanganahalli, B.G., Hyder, F., Mukli, P., and Nagy, Z., 2012, Pitfalls in fractal time-series analysis: fMRI BOLD as an exemplary case. Frontiers in Physiology, 3, 1–24. Available online at: http://www.frontiersin.org/Fractal_Physiology/10.3389/fphys.2012.00417/full. doi: 10.3389/fphys.2012.00417
   Google Scholar
• Heneghan, C., and McDarby, G., 2000, Establishing the relation between detrended fluctuation analysis and power spectral density analysis for stochastic processes. Physical Review E, 62, 6103–6110
   PubMed Web of Science ®Google Scholar
• Mandelbrot, B.B., 1985, Self-affine fractals and fractal dimension. Physica Scripta, 32, 257–260
   Web of Science ®Google Scholar
• Hardstone, R., Poil, S.S., Schiavone, G., Jansen, R., Nikulin, V.V., Mansvelder, H.D., and Linkenkaer-Hansen, K., 2012, Detrended fluctuation analysis: A scale-free view on neuronal oscillations. Frontiers in Physiology, 3, 1–13. Available online at: http://www.frontiersin.org/Fractal_Physiology/10.3389/fphys.2012.00450/full. doi: 10.3389/fphys.2012.00450
   Google Scholar
• Lashermes, B., Abry, P., and Chainais, P., 2004, New insight on the estimation of scaling exponents. Wavelets Multiresolution and Information Processing, 2, 497–523
   Google Scholar
• Bassingthwaighte, J.B., and Raymond, G.M., 1994, Evaluating rescaled range analysis for time series. Annals of Biomedical Engineering, 22, 432–444
   PubMed Web of Science ®Google Scholar