Heart rate variability and stroke

The publication of James Gleick's book ‘Chaos: Making a New Science’ in 1987 brought the terminology of the ‘butterfly effect’ into popular parlance [1]. This esoteric and rather poetic concept refers to the dependence of the response of a system to initial conditions, such that the flapping of the wings of a butterfly in one location can perturb the weather pattern so as to cause a tornado at a distant location. As an illustrative concept, it was developed by the renowned mathematician and meteorologist, Edward Lorenz [2], who showed that simple perturbations with different initial conditions can evolve into different states that are unstable and exhibit a complex and chaotic behavior. These chaotic states are bounded by paths that form attractors, where the specific path is determined by initial conditions, much like the oscillation of a pendulum. However, whereas the damped pendulum attractor is a single point (the lowest point), attractors of nonlinear dynamical systems do not converge to a single dimensional point, but to a different dimension in three-dimensional space – a fractal dimension. Attractors that have a fractal dimension are known as ‘strange attractors’ as originally described by Ruelle [3], and these are typical of complex systems ranging from weather patterns to biological systems. The Lorenz attractor is one such attractor which is frequently used to exemplify a chaotic system and that can be generated from three simple ordinary nonlinear differential equations in a three-dimensional space [1,2]. Self-similarity is the underlying concept in fractals. That is, the morphology is similar at small and large scales. Fractals are inherent in natural systems, they form a fundamental component of chaos [4], and are found in such biological forms, among others, as the spatial branching of vascular beds [5,6], age-related disorganization of arterial elastin [7,8], or in time-related signals of heart rate variability [9]. Recent genetic studies in molecular clocks that are inherent in the origin and maintenance of the heart beat also invoke the fractal concepts of self-similar operation in both small and large time and spatial scales [10,11]. This reinforces the notion that studies of biological and physiological systems that exhibit a broad range of temporal and structural patterns cannot be characterized adequately using linear behavior, and that computational techniques used in the study of complex systems, as exemplified by nonlinear dynamics and chaos, can provide much more powerful approaches to characterizing both normal and diseased states in terms of parameters of complexity [12]. Indeed, there are emerging trends suggesting that disease itself can be understood as loss of complexity [13]. In this issue of the Journal, Graff et al.[14] assess the potential of heart rate variability (HRV) for prediction of outcome of ischemic stroke in short (7 days) and long-term (90 days). Indices of HRV are determined by conventional (linear) measures of time and frequency domain parameters and by methods that characterize the (nonlinear) complex behavior of the time-varying interbeat (RR) interval. The linear methods measure the RR changes around a mean or the magnitude of fluctuations as a function of frequency. Nonlinear methods involve parameters such as heart rate turbulence, fractal dimensions and entropy. In this study, the linear HRV parameters used by Graff et al.[14] are the time domain indices of mean RR interval, standard deviation of all normal-to-normal RR intervals (STD RR), root mean square of differences of adjacent normal-to-normal RR intervals (RMSSD), and the number and the percentage of interval differences of successive normal RR intervals greater than 50 ms (NN50 and pNN50); the frequency domain indices of power spectral density in frequency bands of very low frequency (0–0.04 Hz), low frequency (0.04–0.15 Hz), and high frequency (0.15–0.6 Hz) according to standard protocols [15]. (The conventional high-frequency range is 0.15–0.4 Hz. However, in this study, it was expanded from 0.15 to 0.6 Hz to account for the higher respiratory rates found in the cohort investigated.) The nonlinear parameters computed in the study essentially concentrated on measures of entropy of the time-varying RR signal: approximate entropy (ApEn), sample entropy (SampEn), and fuzzy entropy (FuzzyEn). Detailed description of the computation of these metrics from the time sampled RR signal is given in an appendix in the article. Generally, entropy is used to describe the complexity of the signal, with ApEn, SampEn, and FuzzyEn being modifications to account for real data sequences that are nonstationary, of finite sample length and can contain ectopic beats [16–19]. The concept of entropy emanates from the seminal work of Claude Shannon in 1948 [20] as applied to communication systems and describes the information content of a signal. That is, the higher the complexity, the greater the entropy and so the greater the information contained in the variability of the signal. Thus, it is fitting indeed that this concept be used to quantify the complex cellular and molecular communication involved in the fractal nature of the chaotic system that is at the basis of the intrinsic variability of the normal pattern of heart rate [10,11]. Other nonlinear metrics used in the study include the quantification of the fractal properties of heart rate by scaling components using detrended fluctuation analysis (DFA) and indices of Poincaré plots (SD1 and SD2). Linear and nonlinear metrics were applied to recordings taken from 63 patients (44 men and 19 women) who suffered an ischemic stroke and followed for 90 days. Short-term (7 days) and long-term (90 days) assessment was done using the National Institutes of Health Stroke Scale (NIHSS) and the modified Rankin Scale (mRS). The nature of the stroke scales is such that the NIHSS is used to assess the degree of clinical stroke severity and the mRS is used to assess the degree of disability following stroke [21,22]. In addition to HRV parameters, noninvasive beat-to-beat changes in finger blood pressure and respiratory rate were also measured. Blood pressure variability (BPV) was computed as the SD of the SBP over records of blocks of 512 cardiac cycles [14]. Of the 63 patients, 16 had poor early outcome and 18 had a poor 90-day outcome. In patients with poor early neurological outcome, the nonlinear entropy metrics of ApEn, SampEn, and FuzzyEn were lower than those with a good outcome as quantified by the stroke scales. In contrast, patients with poor 90-day outcome showed higher percentage of high-frequency spectrum and normalized high-frequency power, lower normalized low-frequency power, and lower low-frequency/high-frequency ratio. Low-frequency/high-frequency ratio correlated negatively with scores in NIHSS and mRS at the early (7 days) and late (90 days) assessment. There was no difference in mean RR interval, values of blood pressure as well as BPV between groups with good and poor outcomes. Respiratory frequency was significantly correlated with functional early (7 days) and late (90 days) neurological outcome. The overall conclusion of the study is that poor early (7 days) neurological outcome in patients with ischemic stroke is associated with lower nonlinear entropy-based metrics, whereas late (90 days) outcome can be differentiated by linear parameters of spectral HRV. This suggests that parameters of poor early outcome are associated with reduced complexity, as inherent in reduced information (entropy) contained in the time course of change of heart rate (as quantified by interbeat RR interval). That is, a lower complexity is associated with an elevated disease state and vulnerability to disturbances [13,23]. In addition, a higher respiratory rate in the acute phase was associated with a poor outcome, but indices of BPV showed no association with scores of stroke scales. Whereas the results of the study by Graff et al.[14] have the potential to characterize the complex relationship between measures of HRV and outcome following ischemic stroke, they do not readily facilitate the elucidation of underlying physiological mechanisms. Some aspects of the spectral parameters related to low-frequency and high-frequency power and their association with the sympathovagal balance are generally consistent with previous studies showing an association between baroreflex impairment and poor outcome following ischemic stroke [24]. However, the study contains a number of limitations, some of which are addressed by the authors. The analysis of HRV indices is limited to patients in sinus rhythm, thus excluding many elderly patients who would have both atrial fibrillation and also poor stroke outcome. Recent studies suggest the expansion of the use of parameters of nonlinear dynamics in the elderly to differential modalities of autonomic tone and autonomic modulation [25]. A substantial number of patients in the study (27%) were treated with beta-blocking agents, and these were mainly those with poor stroke outcomes. It is not clear what confounding effects this would have on the overall assessment of HRV and stroke outcome in this specific group of patients, as it is known that beta-blockade is associated with reduced low-frequency/high-frequency ratio of spectral power [26], and so with altered sympathovagal balance. A potential limitation related to variability of blood pressure not addressed by the study is that BPV was determined from continuous finger pressure. BPV as measured did not show any association with stroke outcome. However, it is not known if a similar result would be found if BPV was computed from changes in central aortic systolic pressure, a value of pressure that would be closer to the cerebral circulation than the finger systolic pressure. Importantly, amplification of the pressure pulse from central to peripheral locations is strongly heart rate-dependent [27], hence the changes in SD of peripheral systolic pressure would not be similar to concomitant changes of computed SD of central systolic pressure in the presence of HRV (given that changes in pulse pressure affect systolic pressure much more than diastolic pressure). Pulse amplification has also been shown to be relevant in quantification of indices of baroreflex sensitivity [7,28,29]. Thus, future studies could include pulse wave analysis techniques to enhance the assessment of pressure-related parameters [30]. The study by Graff et al.[14] has shown an intriguing association of nonlinear parameters of variability of heart rate and early poor outcomes of ischemic stroke and linear parameters with late outcomes. The (nonlinear) entropy parameters form part of a complex system characterized by descriptors of dynamic behavior: chaos, strange attractors, fractal dimensions, dependence on initial conditions [1]. If development of pathological conditions is considered to be characterized by the loss of complexity [6,7,9,12,13], the appropriate quantification of metrics of short-term variability in fundamental cardiorespiratory parameters has the potential to open the window to other possible strange attractors that lead towards the disease state through the interaction of fractal dimensional worlds from the genetic scale [10,11] through the continuum of nature in biological systems [4]. ACKNOWLEDGEMENTS Conflicts of interest There are no conflicts of interest.