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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

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Complicate title simple the study 5 min ECG was recorded with our mobile-internet-ECG (CyberECG) in 68 pts with paroxysmal atrial fibrillation (t

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Patient population

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CyberECG: mobile GPRS ECG System

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CyberECG: online monitoring

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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

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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)

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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.

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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

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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

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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

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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

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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

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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