Applying fractal analysis to heart rate time series of sheep experiencing pain Solveig M. Stubsjøen a,c, ⁎, Jon Bohlin b , Eystein Skjerve b , Paul S. Valle a,d , Adroaldo J. Zanella a,e a Norwegian School of Veterinary Science, Department of Production Animal Clinical Sciences, P.O. Box 8146 Dep., NO-0033 Oslo, Norway b Norwegian School of Veterinary Science, Department of Food Safety and Infectious Biology, P.O. Box 8146 Dep., NO-0033 Oslo, Norway c Animalia - Norwegian Meat and Poultry Research Centre, P.O. Box 396, Økern, NO-0513 Oslo, Norway d Molde University College, P.O. Box 2110, NO-6402 Molde, Norway e The Norwegian University of Life Sciences, Department of Animal and Aquacultural Sciences, P.O. Box 5003, NO-1432 Aas, Norway abstract article info Article history: Received 24 November 2009 Received in revised form 13 April 2010 Accepted 15 April 2010 Keywords: Detrended fluctuation analysis Heart rate variability Pain Sheep Welfare The objective assessment of pain is difficult in animals and humans alike. Detrended fluctuation analysis (DFA) is a method which extracts “hidden” information from heart rate time series, and may offer a novel way of assessing the subjective experience associated with pain. The aim of this study was to investigate whether any fractal differences could be detected in heart rate time series of sheep due to the infliction of ischaemic pain. Heart rate variability (HRV) was recorded continuously in five ewes during treatment sequences of baseline, intervention and post-intervention for up to 60 min. Heart rate time series were subjected to a DFA, and the median of the scaling coefficients (α) was found to be α = 1.10 for the baseline sequences, 1.01 for the intervention sequences and 1.00 for the post-intervention sequences. The complexity in the regulation of heartbeats decreased between baseline and intervention (p ∼ 0.03) and baseline and post-intervention (p ∼ 0.01), indicating reperfusion pain and nociceptive sensitization in the post- intervention sequence. Random time series based on Gaussian white noise were generated, with similar mean and variance to the HRV sequences. No difference was found between these series (p ∼ 0.28), pointing to a true difference in complexity in the original data. We found no difference in the scaling coefficient α between the different treatments, possibly due to the small sample size or a fear induced sympathetic arousal during test day 1 confounding the results. The decrease in the scaling coefficient α may be due to sympathetic activation and vagal withdrawal. DFA of heart rate time series may be a useful method to evaluate the progressive shift of cardiac regulation toward sympathetic activation and vagal withdrawal produced by pain or negative emotional responses such as fear. © 2010 Elsevier Inc. All rights reserved. 1. Introduction Quantifying the degree of pain experienced by animals is an important component when assessing animal welfare [1]. The objective assessment of pain in sheep is difficult, particularly because overt behavioural responses in this species are limited. Non-invasive, dynamic, real-time measures of sympathovagal activity may offer a novel way of assessing the subjective experience associated with pain. The sheep heart is similar to that of a human in many ways, including dimensions of the chambers, coronary anatomy, and magnitude of hemodynamic variables such as blood pressure, heart rate and cardiac output. Autonomic innervations of the sheep heart are also similar to that of a human [2]. Comparative studies have therefore been performed in sheep [3]. Physiologic systems generate complex fluctuations in their output signals that reflect the underlying dynamics. Three particularly vexing features of physiological time series such as heart rates are non- stationarity, nonlinearity and nonequilibrium phenomena [4]. Heart rate variability (HRV) is measured by determining the constantly changing temporal distance between consecutive heartbeats (R–R intervals), and is an integrative measurement variable that reflects the prevailing balance of vagal and sympathetic tone [5]. It has been suggested that the time series from heart rate recordings contain hidden information, which is not extractable with conventional methods of analysis [6]. Detrended fluctuation analysis (DFA) is a recent approach for extracting such information from physiological time series. The DFA method has been used to detect long-range or long-term correlation in non-stationary time series in various physiological and pathological conditions, including the activation of the autonomic nervous system [7], ventricular fibrillation [8] and dilated cardio- myopathy [9]. The highly irregular behaviour of cardiac interbeat intervals defies conventional analyses that require “well-behaved,” stationary data sets [6]. Time and frequency domain HRV measures attempt to quantify HRV on various time scales. These traditional measures can be complemented by nonlinear HRV measures, which attempt to Physiology & Behavior 101 (2010) 74–80 ⁎ Corresponding author. Animalia, P.O. Box 396, Økern, NO-0513 Oslo, Norway. Tel.: +47 22 59 74 96; fax: +47 22 59 70 83. E-mail address: solveigmarie.stubsjoen@veths.no (S.M. Stubsjøen). 0031-9384/$ – see front matter © 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.physbeh.2010.04.018 Contents lists available at ScienceDirect Physiology & Behavior journal homepage: www.elsevier.com/locate/phb