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Detrended Fluctuation Analyses of Electrocardiagrams from Ventricular Fibrillation Patients and Cardiac Ti
ssue Simulations
國立東華大學物理系
蕭又新4/29/2006
Outline
Oscillations in nature Non-stationary time series analysis: circle map and
DFA Arrhythmias and spiral waves Statistical signatures of myocardial fibrosis
Damped oscillations
Oscillations and ping pong
Chaotic (or stochastic) oscillations
Cardiac activity and ECG
正常人的心率及 R-R 分佈圖
食用搖頭丸的女性患者
Nonlinear noise-reduction applied to RR intervals
Concept of nonlinear dynamics: circle map analysis
Reference: N. B. Janson et al., Physiological Measurement 22, 565 (2001)
Circle map analysis for a marathon player (5 min ECG recording)
Circle map analysis for ICU patients
Fractal correlation measure : DFAFractal correlation measure : DFA
[2] Detrended Fluctuation Analysis(DFA,QISA) To quantify the fractal-like scaling properties of the R-R interval time series at different temporal scales Scaling exponent represents the slope() of regression line which related log(fluctuation) to log(window size) Low exponent values : magnitude of beat-to-beat HRV is close to magnitude of long-term variability(Anti correlation)
High exponent values : magnitude of long-term variability is substantially higher than beat-to-beat variability(Strong correlation)
Scaling-law exponent(=2-1)1)
- fractal-like signal : = 1 - White noise : = 0.5 (ACor : <0.5, Cor : >0.5) - Brownian motion : = 1.5
DFA algorithm
1. Integrating
: i-th interbeat interval time series
: average interbeat interval
2. Divided into boxes of equal length n
3. In each box of length n, least-squares line fitting
: local trend in each box(order l)
4. Calculating
k
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1) N. Iyengar, C. Peng, R. Morn, A. Goldberger and L. Lipsitz, Age-related alterations in the fractal scaling of cardiac interbeat interval dynamics, Am. J. Physiol. 271, R1078-R1084(1996).2) H. Shono et al., Changes in fractal structure of heart rate variability during a nap in one case, Psychiatry Clin. Neurosci. 55, 175-176(2001)
Correlations in sleep statesCorrelations in sleep states
Long-range correlation (DFA2)
REM sleep.
Decreased correlation
light, deep sleep
1) A. Bunde et. al., Correlated and Uncorrelated regions in HRV fluctuation during sleep, PRL, V85, 3736 (2000)
One night HRV of a healthy subject
Action Potential in a ventricular musclAction Potential in a ventricular muscle fibree fibre
動作電位週期
動作電位週期
舒張區間
舒張區間
APD V.S. DIAPD V.S. DI
Restitution Curve by ExperimentRestitution Curve by Experiment
Restitution Curve in canine endocardial muscle
Koller, Marcus L. et al. Dynamic restitution of action potential duration during electrical alternans and ventricular fibrillation. Am. J. Physiol. 275(Heart Circ. Physiol. 44): H1635-H1642, 1998.
APDAPD 、、 DI and T(CL)DI and T(CL)
TDA
DRA
nn
nn
)(1
Restitution CurveRestitution Curve
Conduction BlockConduction Block
Spatially distributed action potential dynamics in a canine cardiac Purkinje fiber
Jeffrey J. Fox et al. Spatiotemporal Transition to Conduction Block in Canine Ventricle. Circ Res. 2002;90:289-296
Normal Rhythm & Arrhythmias
Normal sinus rhythm
60~100 beats per minute Ectopic rhythms
For example : Ventricular tachycardia(心室頻脈 )
Ventricular fibrillation(心室顫動 )
Ventricular Tachycardia (VT)
Ventricular tachycardia (VT) is a tachydysrhythmia originating from a ventricular ectopic focus, characterized by a rate typically greater than 120 beats per minute and wide QRS complexes.
VT may be monomorphic or polymorphic. Nonsustained VT is defined as a run of tachycardia of less than 30 seconds duration; a longer duration is considered sustained VT.
Referencehttp://www.emedicine.com/
Ventricular Fibrillation (VF)
What is ventricular fibrillation? The heart beats when electrical signals move through it. Ventricular fibrillation is a condition in which the heart's electrical activity becomes disordered. When this happens, the heart's lower chambers contract in a rapid, unsynchronized way. The heart pumps little or no blood.
VT & VF in Electrocardiogram
Reference: Chaos, Solitons and Fractals Vol.13 (2002) 1755.
Normal Rhythm
ventricle cells 2.5 days in culture 8 day old embryo 0.8 ml plating density recorded temp: 36 deg.
C each frame is
approximately 1 cm square
Reference :Optical Mapping Image Database
http://www.cnd.mcgill.ca/bios/bub/imagebase.html
Spiral Waves
ventricle cells 2 days in culture 8 day old embryo recorded temp: 36 deg
C. each frame is approxim
ately 1 cm square
Reference :Optical Mapping Image Database
http://www.cnd.mcgill.ca/bios/bub/imagebase.html
Spiral Waves Breakup
ventricle cells 2 days in culture 8 day old embryo 0.4 ml plating density alphaGA acid 50ul recorded temp: 36 deg C. each frame is approximately
1 cm square
Reference :Optical Mapping Image Database
http://www.cnd.mcgill.ca/bios/bub/imagebase.html
Experimental Results for Multi-armed Spirals in Cardiac Tissue
Reference: PNAS, vol. 101, p15530 (2004).
Cable TheoryCable Theory
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Normal Rhythm & Conduction Block
Simulation results of normal rhythm and conduction block
Spiral Waves Formation and Breakup
Simulated 3D Spirals Based on MRI Images
Statistical Analyses on Human Recordings and Model Results
Model Results
A comparison between experimental and simulated exponents
Effects of obstacles on wave propagation: myocardial fibrosis
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