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

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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

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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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