Applying fractal analysis to heart rate time series of sheep experiencing pain
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 quantify the structure or complexity of the R–R interval time series [10].
Normal heart rate time series have been shown to be fractal-like and self-similar, defined as when a subunit of R–R interval time series resembles the larger time scale. This indicates long-range correlation between R–R intervals, which means that interbeat intervals are partially dependent on the intervals at previous points [11]. Using the DFA method, such correlated, fractal-like behaviour can be measured with the use of a ‘scaling coefficient’ known as α[10]. A scaling coefficient α value of 0.5 (white noise) implies no correlation between the R–R intervals as a result of random heart rate dynamics. A scaling coefficient value of 1.0 (1/f or pink noise) contains both random and highly correlated characteristics in R–R interval time series and indicates fractal heart rate dynamics [11]. The Brownian noise has a value of 1.5 and is the integration of the white noise [10]. A change from pink noise towards more random fluctuations (white noise) with no correlation between interbeat intervals has been shown to be physiologically deleterious, and this breakdown in long-range correlations occur during atrial fibrillation over relatively short time scales [6], [12]. The DFA algorithm quantifies fractal-like correlation properties by calculating the scaling property of the root-mean-square fluctuation of the integrated and detrended time series data [4].
Pain induces systemic responses that affect physiological processes such as heart rate. A decrease in HRV parameters has been found to be associated with the progress of laminitis, a disease that leads to considerable pain in horses [13]. Time domain HRV parameters were also found to be decreased during mild to moderate pain in sheep [14].
The tourniquet pain model has previously been used in sheep, and the administration of the non-steroidal anti-inflammatory drug (NSAID) flunixin meglumine (1 mg/kg) has been found to reduce hyperalgesia in sheep during a noxious ischemic stimulus [15]. Theories on why prolonged tourniquet inflation produces pain have supported the role of C-fibers in the transmission of tourniquet-related pain [16]. It is hypothesized that the pain resulting from tourniquet-related nerve compression and ischaemic pain may involve several changes in peripheral afferent input and in the threshold of spinal dorsal horn neurons [17].
Traditional time series analysis gives little or no information regarding the fractality of the sequence of points studied. Hence, it is difficult to detect underlying structural differences in HRV data using standard time series analysis [12]. Our aim was therefore to investigate whether the DFA method could detect fractal differences in the heart rate time series of sheep when subjected to sustained, mild to moderate pain infliction.
Section snippets
Materials and methods
This study was conducted as part of a larger study which aimed to explore HRV and infrared thermography as non-invasive methods to assess pain in sheep [14].
Results
No association was found between the different treatments and the scaling coefficient α (ANOVA, p ∼ 0.5). Using linear regression, we found differences of the scaling coefficient α between baseline and intervention (p < 0.03) and baseline and post-intervention (p < 0.01). No difference was found between the intervention and post-intervention sequences (p ∼ 0.75). By adding each ewe as a factor, the variance explained of the regression model increased from adjusted R2 = 0.10, p ∼ 0.35 to adjusted R2 = 0.19, p ∼
Discussion
We reported previously that linear parameters of HRV (RMSSD; the root mean square of successive R–R intervals and SDNN; the standard deviation of all interbeat intervals) provided a method sufficiently sensitive to detect the presence of mild to moderate ischaemic pain in sheep [14]. The time domain parameters were found to be decreased during the noxious ischaemic stimulus (S) treatment. Complementary to our previous work [14], in the present study we report that the DFA method was able to
Acknowledgements
The authors wish to thank Eystein Glattre for interesting discussions. The Norwegian Research Council, NORTURA and ‘Fondet for forskningsavgift på landbruksprodukter’ are acknowledged for funding this study.
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