Multifractality in human heartbeat dynamics

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There is evidence that physiological signals under healthy conditions may have a fractal temporal structure1. Here we investigate the possibility that time series generated by certain physiological control systems may be members of a special class of complex processes, termed multifractal, which require a large number of exponents to characterize their scaling properties2,3,4,5,6. We report onevidence for multifractality in a biological dynamical system, the healthy human heartbeat, and show that the multifractal character and nonlinear properties of the healthy heart rate are encoded in the Fourier phases. We uncover a loss of multifractality for a life-threatening condition, congestive heart failure.

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Figure 1: Visualization of multifractality in the hearbeat.
Figure 2: Heartbeat time series contain densely packed, non-isolated singularities which unavoidably affect each other in the time-frequency decomposition.
Figure 3: Multifractality in healthy dynamics.
Figure 4: Discrimination method based on the multifractal formalism.
Figure 5: Nonlinearity and Fourier phases.


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We thank A. Bunde, U. Frisch, J. M. Hausdorff, V. Horváth, H. Kallabis, R.G. Mark, J. Mietus, C.-K. Peng, K. R. Sreenivasan and B. J. West for discussions. We are especially grateful to A. Arneodo and T. Vicsek for advice on the analytical technique and on the text and R. Goldsmith for providing the blind test data. This work was supported by NASA, NIH, FCT/Portugal, and The G. Harold and Leila Y. Mathers Charitable Foundation.

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Correspondence to Plamen Ch. Ivanov.

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