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S. Khoór 1 , J. Nieberl 2 , S., K. Fügedi 1 , E. Kail 2

Prognostic value of the nonlinear dynamicity measurement of atrial fibrillation waves detected by GPRS internet long-term ECG 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.

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S. Khoór 1 , J. Nieberl 2 , S., K. Fügedi 1 , E. Kail 2

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  1. Prognostic value ofthe nonlinear dynamicity measurement ofatrial fibrillation waves detected by GPRS internet long-term ECG monitoring S. Khoór1, J. Nieberl2, S., K. Fügedi1, E. Kail2 Szent István Hospital1, BION Ltd2 , Pannon GSM, Budapest, Hungary

  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<24 hour) • Nonlinear dynamicity of the f-waves was calculated • 28-day continuous mobile, internet ECG was recorded for monitoring the atrial fibrillation recurrence • Using multivariate discriminant analysis a significant difference of f-wave dynamicity between the two groups (recurrent PAF [Group-A, N=39] or not [Group-B, N=29]) was found.

  3. Patient population

  4. CyberECG:mobile GPRS ECG System

  5. CyberECG:online monitoring

  6. 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(ti) 0.5-0.5cos(10πti/T), if 0<= ti<=0.1 or 0.9T<=ti<=T, • 1, if 0.1T<ti<=0.9T, where T is the length of the template segment • The template was subtracted from the ECG in time windows of length T centered at the detected QRST-waves.

  7. F-waves before calculations

  8. P Grassberger, I Procaccia: Characterization of strange attractors. Phys Rev Lett 50, 346-349, 1983. • “Dissipative dynamical systems which exhibit chaotic behavior often have an attractor in phase space which is strange. • Strange attractors are typically characterized by fractal dimensionality D • Several attempts to compute this number directly from box-counting algorithms, which stem from the definition of this • The definition of the correlation integral is:…”

  9. Dynamic processes_1. • GP: “Dissipativedynamical systemswhich exhibit chaotic behavior often have an attractor in phase space which is strange” • dissipative = non conservative (=energy loosing) • dynamic : stochastic vs. deterministic & linear vs. nonlinear & nonlinear chaotic vs non-chaotic

  10. Dynamic processes_2/a. • GP: “Dissipative dynamical systemswhich exhibit chaotic behavior often have an attractor in phase space which is strange” • phase space m-dimensional space & each point represents all of information at one time (e.g. amplitude, its first derivative, time-interval...). An orbit (or trajectory) built from that points. • attractor • strange

  11. Dynamic processes_2/b. • GP: “Dissipative dynamical systemswhich exhibit chaotic behavior often have an attractor in phase space which is strange” • phase space:(left)m-dimensional space & each point represents all of information at one time (e.g. amplitude, its first derivative, time-interval...). An orbit (or trajectory) built from that points. Poincaré section = 2D plot of the 3D space (first-ordered e.g.: ampl(i) vs. ampl(i+1)) (right)Lorenz phase space • attractor • strange

  12. Dynamic processes_3. • GP: “Dissipative dynamical systemswhich exhibit chaotic behavior often have an attractorin phase space which is strange” • phase space • attractor • strange

  13. Mandelbrot chaotic set(self-similarity, scaling, dimension<>integer) • Deterministic and nonlinear • Shows sudden qualitative changes in its output (bifurcation) • Representation in phase space shows fractal properties (fractal dimensions)

  14. Chaotic nonlinear system • Eq.: X(n+1)=1.0-p*X(n)2+0.3*X(n-1)

  15. Empirical data <> Math. equations • First: represent (phase plot) • Next: calculate

  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)

  17. C(ε) = limn→∞ 1/n2 x [number of pairs i,j whose distance │yi - yj │< ε] C(ε) = limn→∞ 1/n2 i,j=1Σn Θ ( ε -│yi - yj │) yi = ( xi, xi+r, xi+2r,.xi+(m-1)r), i=1,2… C(ε) α εν 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  θ(z), where θ(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 ε it is found that, the correlation integral is proportional to some power of ν. This power is called the correlation dimension , and is a simple measure of the (possibly fractal) size of the attractor. Measurement of Complexity_2:From correlation integral to correlation dimension

  18. Measurement of Complexity_3:Steps of the Grassberger-Procaccia Algorithm • Original time-series & • Phase plot of time-series (delayed values) are visualized • Correlation Integral (Cm(r)) dimension for different embedding (delayed) dimension (m) is calculated • If (Cm(r)) shows scaling (=linear part on double logarithmic scale) the Correlation Dimension (D) and Correlation entropy (K) are estimated • If (Cm(r)) shows no scaling a distance r and an embedding dimension m are chosen at which the coarse-grained Dcg and Kcg are estimated

  19. Measurement of Complexity_4:(CI, D, K, Dcg, Kcg values of our f-wave data) • Correlation Integral (Cm(r)) dimension for different embedding (delayed) dimension (m) is calculated • If (Cm(r)) shows scaling (=linear part on double logarithmic scale) the Correlation Dimension (D) and Correlation entropy (K) are estimated with coarse-grained Dcg and Kcg • If (Cm(r)) shows no scaling a distance r and an embedding dimension m are chosen at which the coarse-grained Dcg and Kcg are estimated

  20. Measurement of Complexity_5:(Dcg, Kcg values of our f-wave series data) • If (Cm(r)) shows scaling (=linear part on double logarithmic scale) the Correlation Dimension (D) and Correlation entropy (K) are estimated with coarse-grained Dcg and Kcg • If (Cm(r)) shows no scaling a distance r and an embedding dimension m are chosen at which the coarse-grained Dcg and Kcg are estimated

  21. Measurement of Complexity_6:(Kcg values of our f-wave series data) • If (Cm(r)) shows scaling (=linear part on double logarithmic scale) the Correlation Dimension (D) and Correlation entropy (K) are estimated with coarse-grained Dcg and Kcg • If (Cm(r)) shows no scaling a distance r and an embedding dimension m are chosen at which the coarse-grained Dcg and Kcgare estimated

  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

  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 (m9-14) • x2 = CI mean-value at log r=-0.5 (m12-17) • x3 = CD_cg • Canonical DSC functions: Wilks’ lambda 0.011, chi-square 299.68, significance: p<0,001 PAFr + PAFr - Group_A=1 Group_B=2

  24. Conclusions: Good News • High resolution measurement of surface (not epicardial) atrial fibrillation wave • More accessibility of quick ECG & delayed calculation in the internet database • Long-term (weeks) & real-time arrhythmia monitoring with mobile ECG • Time series analysis of f-wave & predictability of sinus rhythm maintenance • Powerful method for the predicting of PAF recurrence and it would be help in the managing strategy (surveillance of the individual risk, frequency of ECG monitoring, change of drug therapy etc.) of PAF.

  25. Conclusions: Bad News • By math • Not too simple calculations in Grassberger-Procaccia Algorithm • Backdrawns of GPA – other nonlinear methods • How to handle the noise & other nonstationarities • More exact process separation: stochastic (random) vs. deterministic & deterministic linear vs. nonlinear & deterministic nonlinear chaotic vs. non-chaotic • Need for longer data sample (now: 3*5 min) • By clinical • Best choice of patient population (prediction of the first PAF by other clinical methods, e.g. Computer in Cardiology Challenge 2001) • Effect of drugs (beta-blocker and other antiarrhythmics • Need to larger study • By informatics • Expensive total ECG data transmission – need for more sophisticated compression methods • Expansion & more confident GPRS local communication

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