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

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.

Patient population

CyberECG: mobile GPRS ECG System

CyberECG: online monitoring

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 ) cos(10πt i /T), if 0<= t i <=0.1 or 0.9T<= t i <=T, 1, if 0.1T< t i <=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.

F-waves before calculations

P Grassberger, I Procaccia : Characterization of strange attractors. Phys Rev Lett 50, , “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:…”

Dynamic processes_1. GP: “ Dissipative dynamical systems which 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

Dynamic processes_2/a. GP: “Dissipative dynamical systems which 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

Dynamic processes_2/b. GP: “Dissipative dynamical systems which 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

Dynamic processes_3. GP: “Dissipative dynamical systems which exhibit chaotic behavior often have an attractor in phase space which is strange” phase space attractor strange

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)

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

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

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)

From correlation integral to correlation dimension Measurement of Complexity_2: From correlation integral to correlation dimension C(ε) = lim n→∞ 1/n 2 x [ number of pairs i,j whose distance │y i - y j │< ε] C(ε) = lim n→∞ 1/n 2 i,j=1 Σ n Θ ( ε -│y i - y j │) y i = ( x i, x i+r, x i+2r,. x i+(m-1)r), i=1,2… C(ε) α ε ν 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.

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

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

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

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

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

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 ) x2 = CI mean-value at log r=-0.5 (m ) x3 = CD_cg Canonical DSC functions: Wilks’ lambda 0.011, chi-square , significance: p<0,001 PAF r + PAF r - Group_A=1 Group_B=2

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.

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