Prognostic value of the nonlinear dynamicity measurement of atrial fibrillation waves detected by...
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Prognostic value Prognostic value of of the nonlinear dynamicity the nonlinear dynamicity measurement measurement of of atrial fibrillation atrial fibrillation waves waves detected by GPRS detected by GPRS internet long-term ECG internet long-term ECG monitoring monitoring S. Khoór 1 , J. Nieberl 2 , S., K. Fügedi 1 , E. Kail 2 Szent István Hospital 1 , BION Ltd 2 , Pannon GSM, Budapest, Hungary
Prognostic value of the nonlinear dynamicity measurement of atrial fibrillation waves detected by GPRS internet long- term ECG monitoring S. Khoór 1, J
Prognostic value of the nonlinear dynamicity measurement of
atrial fibrillation waves detected by GPRS internet long- term ECG
monitoring S. Khor 1, J. Nieberl 2, S., K. Fgedi 1, E. Kail 2 Szent
Istvn Hospital 1, BION Ltd 2, Pannon GSM, Budapest, Hungary
Slide 2
Complicate title simple the study 5 min ECG was recorded with
our mobile-internet-ECG (CyberECG) in 68 pts with paroxysmal atrial
fibrillation (t
Slide 3
Patient population
Slide 4
CyberECG: mobile GPRS ECG System
Slide 5
CyberECG: online monitoring
Slide 6
ECG pre-processing ECG pre-processing R-wave detection (smooth
first derivative largest deflection) Signal averaging in all time
windows around the detected R-waves Obtaining the template of the
QRST by averaging the deflections in the corresponding time
Smoothing the template using a MA filter (M=5) The filtered
template was multiplied by a taper function to force the edges of
the template to the baseline. The taper function is given by: h(t i
) 0.5-0.5cos(10t i /T), if 0
Empirical data Math. equations First: represent (phase plot)
Next: calculate
Slide 16
Measurement of Complexity_1: Grassberger-Procaccia Algorithm
(GPA): determining the correlation dimension using the correlation
integral Surrogate data analysis: the experimental time series
competes with its linear stochastic (i.e. linear filtered Gaussian
process) component. The chaos can be correctly identified (certain
stochastic processes with law power- spectra can also produce a
finite correlation dimension which can be erroneously attributed to
low-dimensional chaos)
Slide 17
From correlation integral to correlation dimension Measurement
of Complexity_2: From correlation integral to correlation dimension
C() = lim n 1/n 2 x [ number of pairs i,j whose distance y i - y j
< ] C() = lim n 1/n 2 i,j=1 n ( -y i - y j ) y i = ( x i, x i+r,
x i+2r,. x i+(m-1)r), i=1,2 C() The points on the chaotic attractor
are spatially organized, of the signal from a noisy random process
are not. One measure of this spatial organization is the
correlation integral This correlation function can be written by
the Heaviside function (z), where (z) = 1 for positive z, and 0
otherwise. The vector used in the correlation integral is a point
in the embedded phase space constructed from a single time series
For a limited range of it is found that, the correlation integral
is proportional to some power of . This power is called the
correlation dimension, and is a simple measure of the (possibly
fractal) size of the attractor.
Slide 18
Steps of the Grassberger-Procaccia Algorithm Measurement of
Complexity_3: Steps of the Grassberger-Procaccia Algorithm Original
time-series & Phase plot of time-series (delayed values) are
visualized Correlation Integral (C m (r)) dimension for different
embedding (delayed) dimension (m) is calculated If (C m (r)) shows
scaling (=linear part on double logarithmic scale) the Correlation
Dimension (D) and Correlation entropy (K) are estimated If (C m
(r)) shows no scaling a distance r and an embedding dimension m are
chosen at which the coarse-grained D cg and K cg are estimated
Slide 19
Measurement of Complexity_4: (CI, D, K, D cg, K cg values of
our f-wave data) Correlation Integral (C m (r)) dimension for
different embedding (delayed) dimension (m) is calculated If (C m
(r)) shows scaling (=linear part on double logarithmic scale) the
Correlation Dimension (D) and Correlation entropy (K) are estimated
with coarse- grained D cg and K cg If (C m (r)) shows no scaling a
distance r and an embedding dimension m are chosen at which the
coarse-grained D cg and K cg are estimated
Slide 20
Measurement of Complexity_5: (D cg, K cg values of our f-wave
series data) If (C m (r)) shows scaling (=linear part on double
logarithmic scale) the Correlation Dimension (D) and Correlation
entropy (K) are estimated with coarse-grained D cg and K cg If (C m
(r)) shows no scaling a distance r and an embedding dimension m are
chosen at which the coarse-grained D cg and K cg are estimated
Slide 21
Measurement of Complexity_6: (K cg values of our f-wave series
data) If (C m (r)) shows scaling (=linear part on double
logarithmic scale) the Correlation Dimension (D) and Correlation
entropy (K) are estimated with coarse-grained D cg and K cg If (C m
(r)) shows no scaling a distance r and an embedding dimension m are
chosen at which the coarse-grained D cg and K cg are estimated
Slide 22
Multivariate Discriminant Analysis_1. The input parameters were
chosen from the rectangular space. The amplitude values of CI, CD,
CE at various m were determined with the coarse-grained values
Slide 23
Multivariate Discriminant Analysis_2. The DSC model selects the
best parameters stepwise, the entry or removal based on the
minimalization of the Wilks lambda Three variables remained
finally: x1 = CI mean-value at log r=-1.0 (m 9- 14 ) x2 = CI
mean-value at log r=-0.5 (m 12-17 ) x3 = CD_cg Canonical DSC
functions: Wilks lambda 0.011, chi-square 299.68, significance:
p