fluctuation-dissipation theorem (fdt) provides a simple analytical relationship between post-stress...
TRANSCRIPT
Fluctuation-Dissipation Theorem (FDT)Provides a Simple Analytical Relationship between
Post-Stress Heart Rate Recovery (HRR) andHeart 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]
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
heartnt heart
nt 1
time (sec)
Electrocardiogram (ECG)
heartn
heartnn ttRR 1
time (msec)
Heart Rate
Hart Rate Variability (HRV) - microscopic fluctuations of HR at rest
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
HRV (SD)
(msec)RR
Reduced HRV as a predictor of mortality
Post-Exercise (Treadmill) Heart Rate Recovery (HRR)BEFORE STRESS AFTER
HeartRate
exponential fit~exp(-t/Toff)
Hart Rate Recovery (HRR) – macroscopic change of HR after exercise
Lu L-Y, Kuo H-K, Lai L-P, Lin J-L, Tseng C-D, Hwang J-J. Inverse correlation between heart rate recovery and metabolic risks in healthy children and adolescents. Diabetes Care 2008;31(5):1015-9.
1
offT
n=9454
n=509n=484
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.
Prolonged HRR as a predictor of mortality
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:
indexHRVHRRToff
1~)(
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.
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
)())(()( 0000 ttBttBtB
IIkIVIIIk ttftfkT
Bftf )()()( 0 FDT:
Fluctuation-Dissipation Theorem (FDT)
IIkIVIIIk ttftfkT
Bftf )()()( 0
22~ fkT f
kTf ~
IVIIfffB 0
IIkk ttftftC )()()(
220 )( fftC
constf IV
00 )( ftffIIII
- Stress Intensity
- “Thermal Energy”
(width of the distribution)
200 fIV kT
Bff
Fluctuation-Dissipation Theorem (FDT)
kfIIrknfnfkC 2)()()( 2
( ) ( )( )ff
f t t f tr t
f
t
tt
ffIVIVIIIk
k
trffftf
0
)()()( 0
]/)(exp[)()( 00 offkIVIVIIIk Tttffftf
)](ln[ tr
tT
ff
off
Patient “Relaxation Time”
II
IIII IV
F, Hz
)(tf)( ttf f
Connection between HRV <f(t)> & HRR
0 2000 4000 6000 80000.0
0.5
1.0
1.5
2.0
2.5
3.0
)(tf
)( ttf
Recovery time after stress-test is related to the correlation coefficient of hart rate fluctuation during
the stress-test
)](ln[ tr
tT
ff
off
2
( ) ( )( )ff
f t t f tr t
f
Poincare Plot (return map)
ventilator
sedativesedative antibiotic
BP medmonitor
Pain med
Tube in stomach
Tube in airway
Infusion pumps
Mechanical Ventilation
P(t)
PositivePressure
Assist/Control (A/C):Periodic Pressure Waves
P(t)
time
5 s 2 s5 s 5 s
0.2 f, Hz
N(f)
function
Ventilator supplies a givenminimum frequency (e.g. 0.2 Hz)
spontaneousrespiration
P=const
OFFP(t)
time
ONSBTBEFORE AFTER
30 min30 min30 min
Periodically Driven System
Periodically Driven System
Free Running System
Spontaneous Breathing Trial (SBT)
Controlled Ventilation Spontaneous Breathing
Controlled Ventilation
16 patients
SBTBEFORE AFTER
SBTBEFORE AFTER
When Theory Fails: Non-Exponential Relaxation
This work was supported by grants from the James S. McDonnell Foundation,
DARPA, and the Barnes-Jewish Hospital Foundation.