November 2014 EPL, 108 (2014) 40005 www.epljournal.org doi: 10.1209/0295-5075/108/40005 Detrended fluctuation analysis of non-stationary cardiac beat-to-beat interval of sick infants Rathinaswamy B. Govindan 1(a) , An N. Massaro 2 , Tareq Al-Shargabi 3 , Nickie Niforatos Andescavage 2 , Taeun Chang 4 , Penny Glass 5 and Adre J. du Plessis 1 1 Division of Fetal and Transitional Medicine, Fetal Medicine Institute, Children’s National Health System 111 Michigan Ave, NW, Washington, DC 20010, USA 2 Division of Neonatology, Children’s National - 111 Michigan Ave, NW, Washington, DC 20010, USA 3 Department of Biomedical Engineering, Virginia Commonwealth University - 401 West Main Street, Richmond, VA 23284, USA 4 Division of Neurology, Children’s National - 111 Michigan Ave, NW, Washington, DC 20010, USA 5 Division of Psychology, Children’s National - 111 Michigan Ave, NW, Washington, DC 20010, USA received 18 May 2014; accepted in final form 2 November 2014 published online 18 November 2014 PACS 05.45.Tp – Time series analysis PACS 87.19.Hh – Cardiac dynamics PACS 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion Abstract –We performed detrended fluctuation analysis (DFA) of cardiac beat-to-beat intervals (RRis) collected from sick newborn infants over 1–4 day periods. We calculated four different metrics from the DFA fluctuation function: the DFA exponents αL (>40 beats up to one-fourth of the record length), αs (15–30 beats), root-mean-square (RMS) fluctuation on a short-time scale (20–50 beats), and RMS fluctuation on a long-time scale (110–150 beats). Except αL, all metrics clearly distinguished two groups of newborn infants (favourable vs. adverse) with well-characterized outcomes. However, the RMS fluctuations distinguished the two groups more consistently over time compared to αS. Furthermore, RMS distinguished the RRi of the two groups earlier compared to the DFA exponent. In all the three measures, the favourable outcome group displayed higher values, indicating a higher magnitude of (auto-)correlation and variability, thus normal physiology, compared to the adverse outcome group. Copyright c  EPLA, 2014 Introduction. – The cardiac beat-to-beat interval (RRi), measured as time between successive R-waves in the cardiogram, provides the opportunity to interrogate the integrity of the autonomic nervous system (ANS) [1]. To date, several methods have been applied to characterize RRi data. Spectral analysis of RRi has been used to quan- tify the sympathetic and parasympathetic components of the ANS [1–5]. Using the modulations caused by respira- tion on the RRi, the spectral analysis can also be used to quantify respiratory sinus arrhythmia (RSA) [6,7]. Time domain quantification of the sympathetic and parasym- pathetic components can be achieved using standard de- viation of the normal-to-normal interval (SDNN) and root mean square of the successive differences (RMSSD) of RRis, respectively. Further, pNNx, the probability that the current interval is greater than x milliseconds from the previous interval, has been used to quantify the (a) E-mail: rgovinda@childrensnational.org parasympathetic component of RRi [1]. Several novel time domain approaches based on the concepts derived from statistical physics [8,9], nonlinear dynamics [10,11] and in- formation theory [12] have been developed to characterize the RRi. Another approach commonly used to characterize RRi is the detrended fluctuation analysis (DFA) [8,13]. In DFA, the trends in RRis are eliminated using polynomial de- trending and the (auto-)correlations in the RRis are reli- ably characterized. Hence, this technique was chosen in this work to quantify the RRis of sick infants receiving hy- pothermia treatment for encephalopathy. Encephalopathy is defined as a clinical syndrome characterized by dis- turbed neurological function (i.e. altered state of con- sciousness, abnormal motor activity, or abnormal central autonomic regulation) and/or seizures [14]. Therapeutic hypothermia in newborns is an established neuroprotec- tive therapy that involves a standardized protocol for ac- tive whole-body cooling to a temperature of 33.5 ◦ C for 40005-p1