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Homeodynamic complexity: multifractal analysis of physiological instability


Physiological instability is a common clinical problem in the critically ill. Physiological adaptation can be regarded as a dynamic process, with stability being conferred by a number of apparently complex, fluctuating homeokinetic processes [1]. Many natural systems are nonlinear, and seemingly random fluctuations may result as a consequence of their underlying dynamics. Fractal geometry offers a method to characterize the underlying nonlinear state, providing a technique for monitoring complex physiology in real time, which may be of clinical importance.


We employ the wavelet modulus maxima technique to characterize the multifractal properties of physiological time series such as heart rate (HR) and mean arterial pressure (MAP) under conditions of clinical physiological instability. We calculated point estimates for the dominant Hölder exponent (hm) and multifractal spectrum width-at-half-height (WHH). We investigated how these parameters changed with pharmacological interventions such as vasoconstriction.


Hypotensive patients showed lower values of hm for MAP, consistent with a more highly fluctuating, antipersistent and complex behavior. Blood pressure support with pharmacological vasoconstriction led to a transient increase in hm for MAP (Figure 1) revealing the appearance of longer-range correlations, but did not affect hm as estimated for HR. On the other hand, supporting the heart rate with atropine had no effect on hm for MAP, but did tend to increase hm for HR.

Figure 1

abstract P229


We demonstrate increasing signal complexity under physiological challenge consistent with the activation of homeokinetic processes. Differential fractal behavior for HR and MAP suggests that the homeokinetic systems are recruited in a targeted way depending on the physiological challenge. Pharmacological restoration of homeostasis leads to system decomplexification suggesting that homeokinetic mechanisms are derecruited as physiology is restored. We suggest fractal geometry provides a method for characterizing physiological instability and measuring the homeokinetic stress response during physiological challenges.


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    Goldberger AL, Amaral LAN, Hausdorff JM, Ivanov PC, Peng C-K, Stanley HE: Proc Natl Acad Sci USA. 2002, 99: 2466-2472. 10.1073/pnas.012579499

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Correspondence to A Ercole.

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Ercole, A., Bishop, S., Yarham, S. et al. Homeodynamic complexity: multifractal analysis of physiological instability. Crit Care 16, P229 (2012).

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  • Mean Arterial Pressure
  • Fractal Geometry
  • Modulus Maximum
  • Multifractal Analysis
  • Multifractal Spectrum