Abstract— Detection of atrial fibrillation in HRV signals needs analysis of irregular time series. Standard time domain and spectral method are not sufficient. We applied three new methods of time series analysis – symbolic method, fractal method, and empirical mode decomposition. Our method enables distinguishing atrial fibrillation, atrial flutter, and sinus rhythm, and are helpfull in tracking irregular heart rate activity. Keywords— HRV, RR intervals, sinus rhythm, atrial fibrillation, atrial fluttter, time series analysis, symbolic methods, Higuchi’s fractal dimension, empirical mode decomposition I. INTRODUCTION Typical diagnosis of atrial fibrillation, AF, is based on 12- leads ECG. AF usually narrow QRS complexes and causes irregular RR intervals. The last feature allows the use of heart rate variability, HRV, for the diagnosis of atrial fibrillation and then for assessing the progress of treatment. However, statistical and spectral methods, which are commonly used to analyze the HRV signal can not cope with irregularity of RR series [1], [2]. We propose three new methods of HRV analysis for diagnosis of AF – symbolic method, method based on Higuchi’s fractal dimension, and method applying empirical mode decomposition. The calculations was based on the data from PhysioNet [3] and the data received from G.Varoneckas from Klaipedia Hospital in Lithuania (NHL) (cf. [4]). II. NEW METHOD OF SYMBOLIC ANALYSIS OF HEART RATE VARIABILITY IN ATRIAL FIBRILLATION A. Method The symbolic methods proposed in this work and modified spectral methods are based on the same idea of tracking trends in acceleration and de-acceleration of heart rate. Those trends are non-symmetric [5], [6]. When the rhythm is abnormal asymmetry between these trends is disappearing. Manuscript received August 24, 2011. This work was supported in part by Nalecz IBBE PAS statutory activity 4.4/st/11. M.Pierzchalski, R.A.Stepien. P.Stepien are with the Lab of Biosignal Analysis Fundamentals, Nalecz Institute of Biocybernetics and Biomedical Engineering, Polish Academy of Sciences, Warsaw, Poland, e-mail: mpierzchalski@ibib.waw.pl, step@ibib.waw.pl, stepienp@ibib.waw.pl The time series of RR intervals is encoded into a series of symbols. For the series of RR intervals x(i) we calculate the first range differences and represent them by the symbols from the two-elements set {0,1}: ( ) ( ) [ ] ( ) () [ ] ⎩ ⎨ ⎧ < − + ≥ − + = 0 1 i x if 0 0 1 i x if 1 ) ( i x i x i s , i=1,…,(I - 1) (1) As a result of signal’s encoding we obtain a series of symbols, P, for example [1,1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,0,0,1,1,1,11,1,0,0,0,0,0,0,0] In such a series symbol “0” represents acceleration of the heart rhythm - negative value of the first range difference corresponds to shortening of the successive RR intervals, while symbol “1” represents de-acceleration of the heart rhythm. Symbolic series P contains tuples consisted of identical symbols - mono-sequences. They correspond to periods of heart rate acceleration (these composed of “0”’s) or to periods where heart rhythm de-accelerates or does not change (these composed of “1”’s). By calculating the cardinalities, L, of such mono-sequences in P we obtain a pattern of rhythm changes in the analyzed signal. In our approach we calculate cardinality only of mono- sequences of length two - [00] and [11]. These mono- sequences dominate the distributions of mono-sequences, so called seq-spectra [7], both for atrial fibrillation (Fig. 1.) and for sinus rhythm (Fig. 2.). Due to non-stationarity of the analyzed signals cardinality calculation is done using technique of double windowing. The string of symbols P is divided into windows of chosen length. In order to improve the resolution the consecutive windows are overlapped. Each of these windows is divided into sub windows of two symbols each and cardinalities of tuples [00] and [11] are calculated. This method of calculation allows to take into account the contribution of long mono-sequences to the calculated cardinality. For example, mono-sequence of length 4 is represented by two mono-sequences of length 2, mono-sequence of length 6 by the three mono-sequences of length 2, etc. The cardinality L[00] is the characteristic of acceleration trend in HRV and the cardinality L[11] is the characteristic of de-acceleration (slowing down) trend in HRV. New Nonlinear Methods of Heart Rate Variability Analysis in Diagnostics of Atrial Fibrillation Michal Pierzchalski, Robert A. Stepien, Pawel Stepien INTERNATIONAL JOURNAL OF BIOLOGY AND BIOMEDICAL ENGINEERING Issue 4, Volume 5, 2011 201