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Anesthesiology. 2012 Oct;117(4):810-21.

Multifractal analysis of hemodynamic behavior: intraoperative instability and its pharmacological manipulation.

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Division of Anaesthesia, School of Clinical Medicine, University of Cambridge, Cambridge, United Kingdom.



Physiologic instability is a common clinical problem in the critically ill. Many natural feedback systems are nonlinear, and seemingly random fluctuations may result from the amplification of external perturbations or even arise de novo as a consequence of their underlying dynamics. Characterization of the underlying nonlinear state may be of clinical importance, providing a technique to monitor complex physiology in real-time, guiding patient care and improving outcomes.


We employ the wavelet modulus maxima technique to characterize the multifractal properties of heart rate and mean arterial pressure physiology retrospectively for four patients during open abdominal aortic aneurysm repair. We calculated point-estimates for the dominant Hölder exponent (hm, hm) and multifractal spectrum width-at-half-height for both heart rate and mean arterial pressure signals. We investigated how these parameters changed with the administration of an intravenous vasoconstrictor and examined how this varied with atropine pretreatment.


Hypotensive patients showed lower values of hm, consistent with a more highly fluctuating and complex behavior. Treatment with a vasoconstrictor led to a transient increase in hm, revealing the appearance of longer-range correlations, but did not impact hm. On the other hand, prior treatment with atropine had no effect on hm behavior but did tend to increase hm.


Hypotension leads to a reduction in dominant Hölder exponents for mean arterial pressure, demonstrating an increasing signal complexity consistent with the activation of important homeokinetic processes. Conversely, pharmacological interventions may also alter the underlying dynamics. Pharmacological restoration of homeostasis leads to system decomplexification, suggesting that homeokinetic mechanisms are derecruited as homeostasis is restored.

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