Download Electrical Activities of a heart

Detrended Fluctuation Analyses of Electrocardiagrams from
Ventricular Fibrillation Patients and Cardiac Tissue Simulations
國立東華大學物理系
蕭又新
4/29/2006
Outline
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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 : 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)
DFA algorithm
 Scaling-law exponent(=2-1)1)
- fractal-like signal :  = 1
- White noise :  = 0.5 (ACor : <0.5, Cor : >0.5)
- Brownian motion : = 1.5
k
1. Integrating
y[k ]   [ B(i )  B ]
i 1
B (i ) : i-th interbeat interval time series
: average interbeat interval
B
2. Divided into boxes of equal length n
3. In each box of length n, least-squares line
fitting
y [k ]
n

: local trend in each box(order l)
4. Calculating
F [ n] 
~
1 N
2
~  ( y[k ]  yn [k ])
N k 1
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, 175176(2001)
Correlations in sleep states
 One night HRV of a healthy subject
 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)
Action Potential in a ventricular
muscle fibre
動
作
電
位
週
期
舒
張
區
間
APD V.S. DI
Restitution 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.
APD、DI and T(CL)
An 1  R( Dn )
An  Dn  T
Restitution Curve
Conduction 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)
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Ventricular Tachycardia (VT)
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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.
Reference
http://www.emedicine.com/
Ventricular Fibrillation (VF)
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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
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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
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ventricle cells
2 days in culture
8 day old embryo
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 Breakup
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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 Theory
 2V
 raxial I m
2
x
I m  I c  I ion ; I c  Cm
dV
dt
1  2V
V
 Cm
 I ion
2
raxial x
t
V
 2V
 I ion / Cm  D 2
t
x
D  1 /(Cm raxial )
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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