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Fluctuation-Dissipation Theorem (FDT) Provides a Simple Analytical Relationship between

Fluctuation-Dissipation Theorem (FDT) Provides a Simple Analytical Relationship between Post-Stress Heart Rate Recovery (HRR) and Heart Rate Variability (HRV) During the Stress Anton Burykin 1 , Yan Lu 2 , Michael W. Deem 2 , Timothy G. Buchman 1 1 Washington University, Saint Louis, MO;

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Fluctuation-Dissipation Theorem (FDT) Provides a Simple Analytical Relationship between

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  1. Fluctuation-Dissipation Theorem (FDT) Provides a Simple Analytical Relationship between Post-Stress Heart Rate Recovery (HRR) and Heart Rate Variability (HRV) During the Stress Anton Burykin1, Yan Lu2, Michael W. Deem2, Timothy G. Buchman1 1Washington University, Saint Louis, MO; 2Rice University, Houston, TX Lu Y., Burykin A., Deem M. W., Buchman T. G. Predicting Clinical Physiology: A Markov Chain Model of Heart Rate Recovery after Spontaneous Breathing Trials in Mechanically Ventilated Patients. Journal of Critical Care (2009) 24, 347–361. [see Appendix A]

  2. Outline: • Hart Rate Variability (HRV) • Exercise (Treadmill) Stress Test and Heart Rate Recovery (HRR) Time; • Relationship between Heart Rate Recovery (HRR) and Heart Rate Variability. Onsager Regression Hypothesis (Fluctuation Dissipation Theorem, FDT); • Clinical Data: Spontaneous Breasting Trial (SBT) as a Stressor; • Results

  3. HRV (SD) (msec) Electrocardiogram (ECG) Heart Rate Kleiger RE, Miller JP, Bigger JT, Moss AJ, Decreased heart rate variability and its association with increased mortality after acute myocardial infarction. Am J Cardiol. 1987;59:256-262 time (msec) time (sec) Hart Rate Variability (HRV)- microscopic fluctuations of HR at rest Reduced HRV as a predictor of mortality

  4. Post-Exercise (Treadmill) Heart Rate Recovery (HRR) STRESS AFTER BEFORE Heart Rate exponential fit ~exp(-t/Toff) Hart Rate Recovery (HRR) – macroscopic change of HR after exercise

  5. n=9454 n=509 n=484 Prolonged HRR as a predictor of mortality Imai, K., H. Sato, M. Hori, H. Kusuoka, H. Ozaki, H. Yokoyama, H. Takeda, M. Inoue, T. Kamada, Vagally mediated heart rate recovery after exercise is accelerated in athletes but blunted in patients with chronic heart failure. J Am Coll Cardiol, 1994. 24(6): p. 1529-1535. Nishime, E.O., C.R. Cole, E.H. Blackstone, F.J. Pashkow, M.S. Lauer, Heart Rate Recovery and Treadmill Exercise Score as Predictors of Mortality in Patients Referred for Exercise ECG. JAMA, 2000. 284(11): p. 1392-1398. Lu L-Y, Kuo H-K, Lai L-P, Lin J-L, Tseng C-D, Hwang J-J. Inversecorrelation between heart rate recovery and metabolic risks in healthychildren and adolescents. Diabetes Care 2008;31(5):1015-9.

  6. Hypothesis: • The autonomic nervous system (ANS) modulates both the dynamics of heart rate (HR) recovery (HRR) after an exercise stress test as well as HR variability (HRV) under steady-state conditions. • reduced HRV as well as prolonged HRR are believed to be predictors of mortality our hypothesis is that the HRR time is inversely proportional to some index or measure of HRV: previous studies have employed conventional statistical tools (parametric or nonparametric correlation coefficients) to explore empirical correlations between HRR time constants and different measures of HRV during (or after) the exercise Buchheit, M., Y. Papelier, P.B. Laursen, S. Ahmaidi, Noninvasive assessment of cardiac parasympathetic function: postexercise heart rate recovery or heart rate variability? Am J Physiol Heart Circ Physiol, 2007. 293(1): p. H8-10. Javorka, M., I. Zila, T. Balharek, K. Javorka, On- and off-responses of heart rate to exercise - relations to heart rate variability. Clinical Physiology and Functional Imaging, 2003. 23(1): p. 1-8. Javorka, M., I. Zila, T. Balharek, K. Javorka, Heart rate recovery after exercise: relations to heart rate variability and complexity. Brazilian Journal of Medical and Biological Research, 2002. 35(8): p. 991-1000. • We adopt an alternative strategy, deriving this relationship theoretically rather than empirically (statistically) infer it from the data.

  7. Onsager Regression Hypothesis The relaxation of macroscopic disturbances is governed by the same laws as the regression of spontaneous microscopic fluctuations in an equilibrium system FDT:

  8. Fluctuation-Dissipation Theorem (FDT) - Stress Intensity - “Thermal Energy” (width of the distribution)

  9. Fluctuation-Dissipation Theorem (FDT)

  10. Connection between HRV <f(t)> & HRR F, Hz II 3.0 III IV I 2.5 2.0 1.5 1.0 0.5 0.0 0 2000 4000 6000 8000 Patient “Relaxation Time” Poincare Plot (return map) Recovery time after stress-test is related to the correlation coefficient of hart rate fluctuation during the stress-test

  11. sedative antibiotic monitor BP med ventilator Pain med Tube in airway Tube in stomach Infusion pumps

  12. Mechanical Ventilation Positive Pressure P(t) P(t) 5 s 5 s 2 s 5 s time Assist/Control (A/C): Periodic Pressure Waves spontaneous respiration N(f) function Ventilator supplies a given minimum frequency (e.g. 0.2 Hz) f, Hz 0.2

  13. Spontaneous Breathing Trial (SBT) 16 patients Spontaneous Breathing Controlled Ventilation Controlled Ventilation AFTER BEFORE SBT OFF ON P(t) P=const time 30 min 30 min 30 min Periodically Driven System Free Running System Periodically Driven System

  14. BEFORE SBT AFTER

  15. When Theory Fails: Non-Exponential Relaxation BEFORE SBT AFTER

  16. This work was supported by grants from the James S. McDonnell Foundation, DARPA, and the Barnes-Jewish Hospital Foundation.

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