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Fractal Electrodynamics of the Heartbeat

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... Pink noise is an intersystem phenomenon ubiquitous in biology and physiology. A nonexhaustive list of observations includes heart rate (26,28,29), respiratory rate (30)(31)(32), postural sway (33,34), gait strides (25,35), and relevant for the current study, bimanual coordination (13,15,20,36) and brain dynamics (37)(38)(39)(40)(41). Fascinatingly, pink noise is pervasive in nature, being present in fluctuations of tide and river heights (42), climate (43), and song production in zebra finches (44). Many theoretical explanations have been proposed for the origin and function of pink noise in physiology and behavior (45)(46)(47)(48)(49). ...
... The presence of pink noise in various healthy biological processes has been widely documented (29,39,(65)(66)(67), supporting the idea that faster transitions to an in-phase pattern during pink noise movements indicate a more adaptable system, thus aligning the OMVH. However, the behavioral explanations for Brown, invariant, and white noise signals do not necessarily follow the progression suggested by the OMVH. ...
Article
The seemingly straightforward task of tying one’s shoes requires a sophisticated interplay of joints, muscles, and neural pathways, posing a formidable challenge for researchers studying the intricacies of coordination. A widely accepted framework for measuring coordinated behavior is the Haken–Kelso–Bunz (HKB) model. However, a significant limitation of this model is its lack of accounting for the diverse variability structures inherent in the coordinated systems it frequently models. Variability is a pervasive phenomenon across various biological and physical systems, and it changes in healthy adults, older adults, and pathological populations. Here, we show, both empirically and with simulations, that manipulating the variability in coordinated movements significantly impacts the ability to change coordination patterns—a fundamental feature of the HKB model. Our results demonstrate that synchronized bimanual coordination, mirroring a state of healthy variability, instigates earlier transitions of coordinated movements compared to other variability conditions. This suggests a heightened adaptability when movements possess a healthy variability. We anticipate our study to show the necessity of adapting the HKB model to encompass variability, particularly in predictive applications such as neuroimaging, cognition, skill development, biomechanics, and beyond.
... The fractals demonstrate ability in the representation overall of objects found in the nature, as already attested in [1] Following this idea, one can find the work of Carlin [2] demonstrating the viability of a fractal dimension method in the calculus of fractal dimension of non fractal objects. Works like [1], [2] and others encouraged the development of works describing natural objects by the fractal dimension345. These works experimented a lot of techniques for the extraction of image features based on fractal geometry and more specifically on methods for the calculus of fractal dimension, like Minkowski sausage [6], Fourier [7], etc. Extending the concept of fractal dimension, [8] presents the concept of multiscale fractal dimension, in which the fractal dimension is calculated at different scales of observation, allowing the obtainment of a set of numbers called the descriptors of the analyzed object, allowing for the enrichment of this sort of analysis. ...
... Mandelbrot [1] and other authors [2] [7] observed that many objects found in the nature present characteristics intrinsic to fractals, like the selfsimilarity and advanced levels of complexity. Such observations motivated authors like [4,5,17] to employ the fractal dimension concept as a descriptor for objects of real world, represented in images. Extending this idea, [8] suggested the use of not only the fractal dimension as a unique descriptor but a set of values extracted from the fractal dimension measure process to characterize an image. ...
Article
This work proposes the development and study of a novel technique for the generation of fractal descriptors used in texture analysis. The novel descriptors are obtained from a multiscale transform applied to the Fourier technique of fractal dimension calculus. The power spectrum of the Fourier transform of the image is plotted against the frequency in a log- log scale and a multiscale transform is applied to this curve. The obtained values are taken as the fractal descriptors of the image. The validation of the propose is performed by the use of the descriptors for the classification of a dataset of texture images whose real classes are previously known. The classification precision is compared to other fractal descriptors known in the literature. The results confirm the efficiency of the proposed method.
... Dear Sir: The activation of the ventricular myocardium normally occurs via the cardiac His-Purkinje network. The highly ramified nature of the Purkinje system has led to the proposal that it is a "fractal-like" structure (1) (see also234567). Because the activation of the ventricular myocardium occurs through the Purkinje network, it has been further hypothesized that the activation of the ventricles via the Purkinje fibers leads to fractal (time-scale invariant) depolarization of the ventricles (1) (see also2345). ...
... The highly ramified nature of the Purkinje system has led to the proposal that it is a "fractal-like" structure (1) (see also234567). Because the activation of the ventricular myocardium occurs through the Purkinje network, it has been further hypothesized that the activation of the ventricles via the Purkinje fibers leads to fractal (time-scale invariant) depolarization of the ventricles (1) (see also2345). The wave of activation of the ventricular myocardium is reflected in the QRS complex on the electrocardiogram (ECG). ...
... Furthermore, in a review of the role of autonomic activity in anxiety (including PD and GAD), these researchers limited their discussion to the SNS (Hoehn-Saric and McLeod 1988). This omission is at odds with contemporary models of autonomic cardiovascular control that emphasize the ongoing interplay of both sympathetic and parasympathetic (vagal) activity (e.g., Appel et al 1989; Berne and Levy 1992; Goldberger 1990; Linden 1985; Saul 1990; Stein et al 1994). It appears that parasympathetic influences are particularly important in HR regulation (Berne and Levy 1992; Bronis 1983; Goldberger 1990; Levy 1984, 1990; Saul 1990; Uijtdehaage and Thayer, 1989). ...
... This omission is at odds with contemporary models of autonomic cardiovascular control that emphasize the ongoing interplay of both sympathetic and parasympathetic (vagal) activity (e.g., Appel et al 1989; Berne and Levy 1992; Goldberger 1990; Linden 1985; Saul 1990; Stein et al 1994). It appears that parasympathetic influences are particularly important in HR regulation (Berne and Levy 1992; Bronis 1983; Goldberger 1990; Levy 1984, 1990; Saul 1990; Uijtdehaage and Thayer, 1989). Congruent with the ubiquity of tachycardia in PD (Barlow 1988), recent research has found diminished vagal cardiac control in panickers (Friedman et al 1993; Friedman and Thayer 1993; George et al 1989; Sartory and Olajide 1988; Yeragani et al 1990). ...
Article
Autonomic characteristics of generalized anxiety disorder (GAD) and worry were examined using measures of heart period variability. The cardiorespiratory responses of 34 GAD clients and 32 nonanxious control subjects were recorded during resting baseline, relaxation, and worry periods. Results indicated differences between GAD subjects and controls as well as among baseline, relaxation, and worry periods. GAD clients exhibited shorter cardiac interbeat intervals (IBIs) and lower high frequency spectral power across all task conditions. Relative to baseline and relaxation conditions, worry was associated with (1) shorter IBIs, (2) smaller mean successive differences (MSD) of the cardiac IBIs, and (3) lower high frequency spectral power. These findings suggest that GAD and its cardinal feature (worry), are associated with lower cardiac vagal control. The findings of the present study provide evidence for the utility of further exploration of the role of autonomic nervous system activity in GAD.
... The consequent implication of long-range correlations observed in behavioral time series is rich temporal embeddedness, such that each behavioral event is found to be nested with respect to all proceeding and all future events. In the literature this phenomenon is referred to variously as 1/f noise, 1/f scaling, long-term memory, and fractal process (Eke et al., 2000;Goldberger, 1990;Van Orden, Holden, & Turvey, 2005;West, 2006). In these terms, memory refers to the observation that systems exhibiting longrange correlations give the appearance of keeping a memory of the system's history. ...
Article
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Dexterous action, as conceptualized by Bernstein in his influential ecological analysis of human behavior, is revealed in the ability to flexibly generate behaviors that are adaptively tailored to the demands of the context in which they are embedded. Conceived as complex adaptive behavior, dexterity depends upon the qualities of robustness and degeneracy, and is supported by the functional complexity of the agent-environment system. Using Bernstein's and Gibson's ecological analyses of behavior situated in natural environments as conceptual touchstones, we consider the hypothesis that complex adaptive behavior capitalizes upon general principles of self-organization. Here, we outline a perspective in which the complex interactivity of nervous-system, body, and environment is revealed as an essential resource for adaptive behavior. From this perspective, we consider the implications for interpreting the functionality and dysfunctionality of human behavior. This paper demonstrates that, optimal variability, the topic of this special issue, is a logical consequence of interpreting the functionality of human behavior as complex adaptive behavior.
... Heart rate fluctuations have been recognized as complex dynamical behaviors originating from nonlinear processes [8,10,11,12,13,14,15,16,17]. Nonlinear dy-namic approaches to HRV are used to determine if HRV has features typical of chaos (complexity & fractal-like behavior) [18]. Nonlinear measures study complex interactions of hemodynamic, electrophysiological, and humoral variables and their regulation by the autonomic and central nervous systems, and have been shown to have prognostic value in CHF [8,9,10,11,12,13]. ...
Article
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Patients with chronic heart failure (CHF) exhibit a morning surge in ventricular arrhythmias, but the underlying cause remains unknown. The aim of this study was to determine if heart rate dynamics, autonomic input (assessed by heart rate variability (HRV)) and nonlinear dynamics as well as their abnormal time-of-day-dependent oscillations in a newly developed arrhythmogenic canine heart failure model are associated with a morning surge in ventricular arrhythmias. CHF was induced in dogs by aortic insufficiency & aortic constriction, and assessed by echocardiography. Holter monitoring was performed to study time-of-day-dependent variation in ventricular arrhythmias (PVCs, VT), traditional HRV measures, and nonlinear dynamics (including detrended fluctuations analysis α1 and α2 (DFAα1 & DFAα2), correlation dimension (CD), and Shannon entropy (SE)) at baseline, as well as 240 days (240d) and 720 days (720d) following CHF induction. LV fractional shortening was decreased at both 240d and 720d. Both PVCs and VT increased with CHF duration and showed a morning rise (2.5-fold & 1.8-fold increase at 6 AM-noon vs midnight-6 AM) during CHF. The morning rise in HR at baseline was significantly attenuated by 52% with development of CHF (at both 240d & 720d). Morning rise in the ratio of low frequency to high frequency (LF/HF) HRV at baseline was markedly attenuated with CHF. DFAα1, DFAα2, CD and SE all decreased with CHF by 31, 17, 34 and 7%, respectively. Time-of-day-dependent variations in LF/HF, CD, DFA α1 and SE, observed at baseline, were lost during CHF. Thus in this new arrhythmogenic canine CHF model, attenuated morning HR rise, blunted autonomic oscillation, decreased cardiac chaos and complexity of heart rate, as well as aberrant time-of-day-dependent variations in many of these parameters were associated with a morning surge of ventricular arrhythmias.
... [Tilling and Dvorak, 1993]. [West, 1990; Goldberger, 1990; Goldberger et al., 1988; Suki et al. 1994] ...
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Self-organized systems are often used to describe natural phenomena where power laws and scale invariant geometry are observed. The Piton de la Fournaise volcano shows power-law behavior in many aspects. These include the temporal distribution of eruptions, the frequency-size distributions of induced earthquakes, dikes, fissures, lava flows and interflow periods, all evidence of self-similarity over a finite scale range. We show that the bounds to scale-invariance can be used to derive geomechanical constraints on both the volcano structure and the volcano mechanics. We ascertain that the present magma bodies are multi-lens reservoirs in a quasi-eruptive condition, i.e. a marginally critical state. The scaling organization of dynamic fluid-induced observables on the volcano, such as fluid induced earthquakes, dikes and surface fissures, appears to be controlled by underlying static hierarchical structure (geology) similar to that proposed for fluid circulations in human physiology. The emergence of saturation lengths for the scalable volcanic observable argues for the finite scalability of complex naturally self-organized critical systems, including volcano dynamics.
... A basic feature of a fractal system is scale-invariance, i.e., same features repeat themselves on different measurement scales (Goldberger, 1996). Healthy subjects´erratic fluctuations of sinus rhythm have fractal-like characteristics (Denton et al., 1990;Goldberger, 1990a). ...
Article
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The time-domain measures and power–spectral analysis of heart rate variability (HRV) are classic conventional methods to assess the complex regulatory system between autonomic nervous system and heart rate and are most widely used. There are abundant scientific data about the prognostic significance of the conventional measurements of HRV in patients with various conditions, particularly with myocardial infarction. Some studies have suggested that some newer measures describing non-linear dynamics of heart rate, such as fractal measures, may reveal prognostic information beyond that obtained by the conventional measures of HRV. An ideal risk indicator could specifically predict sudden arrhythmic death as the implantable cardioverter-defibrillator (ICD) therapy can prevent such events. There are numerically more sudden deaths among post-infarction patients with better preserved left ventricular function than in those with severe left ventricular dysfunction. Recent data support the concept that HRV measurements, when analyzed several weeks after acute myocardial infarction, predict life-threatening ventricular tachyarrhythmias in patients with moderately depressed left ventricular function. However, well-designed prospective randomized studies are needed to evaluate whether the ICD therapy based on the assessment of HRV alone or with other risk indicators improves the patients’ prognosis. Several issues, such as the optimal target population, optimal timing of HRV measurements, optimal methods of HRV analysis, and optimal cutpoints for different HRV parameters, need clarification before the HRV analysis can be a widespread clinical tool in risk stratification.
... A theoretical model suggests that chaotic vasomotion dissipates transients more readily than periodic vasomotion, thereby conferring greater stability to microcirculatory perfusion; further, specific modes of chaotic vasomotion may influence flow independently of their amplitude (Parthimos et al. 1996). Interestingly, several situations have been found in physiology where chaotic behaviour represents a 'healthy' system whereas degeneration of chaos to more regular behaviour represents pathology (Goldberger 1990, Tsuda et al. 1992). In our recent theoretical studies, with the help of a phenomenological model, we have shown that irregular (chaotic) nature of vasomotion in skeletal muscle enhances the efficiency of tissue oxygenation compared to regular (periodic) form of vasomotion (Pradhan & Chakravarthy 2007a, Pradhan et al. 2007b. ...
Article
Full-text available
Vasomotion refers to spontaneous oscillation of small vessels observed in many microvascular beds. It is an intrinsic phenomenon unrelated to cardiac rhythm or neural and hormonal regulation. Vasomotion is found to be particularly prominent under conditions of metabolic stress. In spite of a significant existent literature on vasomotion, its physiological and pathophysiological roles are not clear. It is thought that modulation of vasomotion by vasoactive substances released by metabolizing tissue plays a role in ensuring optimal delivery of nutrients to the tissue. Vasomotion rhythms exhibit a great variety of temporal patterns from regular oscillations to chaos. The nature of vasomotion rhythm is believed to be significant to its function, with chaotic vasomotion offering several physiological advantages over regular, periodic vasomotion. In this article, we emphasize that vasomotion is best understood as a network phenomenon. When there is a local metabolic demand in tissue, an ideal vascular response should extend beyond local microvasculature, with coordinated changes over multiple vascular segments. Mechanisms of information transfer over a vessel network have been discussed in the literature. The microvascular system may be regarded as a network of dynamic elements, interacting, either over the vascular anatomical network via gap junctions, or physiologically by exchange of vasoactive substances. Drawing analogies with spatiotemporal patterns in neuronal networks of central nervous system, we ask if properties like synchronization/desynchronization of vasomotors have special significance to microcirculation. Thus the contemporary literature throws up a novel view of microcirculation as a network that exhibits complex, spatiotemporal and informational dynamics.
... THE FRACTAL HYPOTHESIS (1)(2)(3)(4)(5)(6) In the mammalian heart, normal electrical activation starts in the sinus node; it spreads through the atria, and then reaches the atrioventricular node where it suffers a major delay. Once the impulse arrives at the His bundle, it then travels through the multiple branches of the Purkinje network and enters the right and left ventricular muscle. ...
... Fractal dynamics can be considered as a specific form of deterministic chaos and can be explained by a nonlinear rule. Healthy subjects' erratic fluctuations of sinus rhythm have fractal-like characteristics (Denton et al. 1990;Goldberger 1990a). Fractal (1/f ) organization is flexible, and breakdown of this scale invariance (self-similarity) may lead to a more rigid and less adaptable system with either random or highly correlated behaviour of heart rate dynamics. ...
Article
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Heart rate variability (HRV) has been conventionally analysed with time- and frequency-domain methods, which measure the overall magnitude of RR interval fluctuations around its mean value or the magnitude of fluctuations in some predetermined frequencies. Analysis of heart rate dynamics by novel methods, such as heart rate turbulence after ventricular premature beats, deceleration capacity of heart rate and methods based on chaos theory and nonlinear system theory, have gained recent interest. Recent observational studies have suggested that some indices describing nonlinear heart rate dynamics, such as fractal scaling exponents, heart rate turbulence and deceleration capacity, may provide useful prognostic information in various clinical settings and their reproducibility may be better than that of traditional indices. For example, the short-term fractal scaling exponent measured by the detrended fluctuation analysis method has been shown to predict fatal cardiovascular events in various populations. Similarly, heart rate turbulence and deceleration capacity have performed better than traditional HRV measures in predicting mortality in post-infarction patients. Approximate entropy, a nonlinear index of heart rate dynamics, which describes the complexity of RR interval behaviour, has provided information on the vulnerability to atrial fibrillation. There are many other nonlinear indices which also give information on the characteristics of heart rate dynamics, but their clinical usefulness is not as well established. Although the concepts of nonlinear dynamics, fractal mathematics and complexity measures of heart rate behaviour, heart rate turbulence, deceleration capacity in relation to cardiovascular physiology or various cardiovascular events are still far away from clinical medicine, they are a fruitful area for research to expand our knowledge concerning the behaviour of cardiovascular oscillations in normal healthy conditions as well as in disease states.
... The effect of propranolol was more pronounced in the LF band, which reflects that both the sympathetic and the parasympathetic systems mediate low-frequency fluctuations, while parasympathetic activity dominates at higher frequencies. The parallel shift in frequency and time domain indexes and Lyapunov exponent supports a major autonomic influence over non-linear behaviour of heart rate variability, as previously suggested both from a theoretical [S] and an empirical standpoint [6,31]. Parasympathetic activity, however, seems to be a more important determinant than sympathetic activity. ...
Article
To study non-linear complexity or chaotic behaviour of heart rate in short time series and its dependence on autonomic tone. Ten healthy individuals (5 men, mean age 44 years) were investigated at rest, after intravenous injections of propranolol (0.15 mg/kg), followed by atropine (0.03 mg/kg). On another occasion, investigation was made during exercise on a bicycle ergometer at 40% and at 70% of maximal working capacity. Heart rate variability was assessed by: local sensitive dependence on initial conditions as quantitated by the dominant Lyapunov exponent, coefficient of variation of heart rate, power spectral analysis of high- and low-frequency bands and the 1/f-slope of the very-low-frequency band and time domain analysis. The approximate dominant Lyapunov exponent was positive at rest and remained positive during autonomic blockade and during exercise. The exponent decreased significantly with propranolol+atropine and even more so during exercise but did not attain zero. At baseline approximate predictability was lost after about 30 s whereas after autonomic blockade or exercise it was lost after about 60 s. The 1/f-slope remained unaltered around -1. As expected, power in high- and low-frequency bands as well as time domain index decreased significantly with autonomic blockade. The low-frequency band and time domain index were affected by exercise. Heart rate variability of sinus rhythm in healthy individuals has characteristics suggestive of low-dimensional chaos-like determinism which is modulated but not eliminated by inhibition of autonomic tone or by exercise. The dominant Lyapunov exponent characterises heart rate variability independent or the other investigated measures.
... Besides pure oscillatory behaviour, a less specific variability exists which extends over a wide frequency range. In a double logarithmic plot, power density and frequency are in inverse proportion, the l/f [21,38,54]. This is typically found in circulatory variables [42,65]. ...
Article
A number of control mechanisms are comprised within blood pressure regulation, ranging from events on the cellular level up to circulating hormones. Despite their vast number, blood pressure fluctuations occur preferably within a certain range (under physiological conditions). A specific class of dynamic systems has been extensively studied over the past several years: nonlinear coupled systems, which often reveal a characteristic form of motion termed "chaos". The system is restricted to a certain range in phase space, but the motion is never periodic. The attractor the system moves on has a non-integer dimension. What all chaotic systems have in common is their sensitive dependence on initial conditions. The question arises as to whether blood pressure regulation can be explained by such models. Many efforts have been made to characterise heart rate variability and EEG dynamics by parameters of chaos theory (e.g., fractal dimensions and Lyapunov exponents). These method were successfully applied to dynamics observed in single organs, but very few studies have dealt with blood pressure dynamics. This mini-review first gives an overview on the history of blood pressure dynamics and the methods suitable to characterise the dynamics by means of tools derived from the field of nonlinear dynamics. Then applications to systemic blood pressure are discussed. After a short survey on heart rate variability, which is indirectly reflected in blood pressure variability, some dynamic aspects of resistance vessels are given. Intriguingly, systemic blood pressure reveals a change in fractal dimensions and Lyapunov exponents, when the major short-term control mechanism--the arterial baroreflex--is disrupted. Indeed it seems that cardiovascular time series can be described by tools from nonlinear dynamics [66]. These methods allow a novel description of some important aspects of biological systems. Both the linear and the nonlinear tools complement each other and can be useful in characterising the stability and complexity of blood pressure control.
... An estimate of spectral reserve can be obtained by plotting these spectra on double-log axes of power and frequency, and calculating the slope of the regression line fitted to these points (Lipsitz et al., 1990). Steeper slopes correspond to narrow-band spectra, diminished HF power, and less spectral reserve (Goldberger, 1990) 5 . These attributes mark a system that lacks flexibility and adaptability. ...
Article
Autonomic characteristics of panickers, blood phobics, and nonanxious controls were compared with a variety of cardiovascular measures, including spectral analysis of the cardiac inter-beat interval time series (derived from the electrocardiogram). Responses to laboratory stressors (shock avoidance and cold face stress) of 16 participants who reported recent occurrences of frequent severe panic attacks, 15 participants who reported strong somatic reactions and fainting to the sight of blood, and 15 controls, were recorded. Results suggested distinct autonomic patterns among the three groups. Across conditions, panickers displayed the highest heart rates (HR) coupled with the least HR variability, which indicates low levels of cardiac vagal tone. Blood phobics showed more vagally mediated HR variability than panickers, with a significant association between cardiac rate and mean arterial pressure. Controls generally showed the most HR variability and 'spectral reserve' (a quality that indicates flexible responsivity). Results are discussed in the context of traditional models of anxiety and autonomic activity in contrast to contemporary notions of stability and change in biological systems.
... Spectral analysis of heart rate variability (HRV) has been advanced as a non-invasive method of estimating relative piration being the primary rhythmic stimulus, whereas low-frequency power ( 0.15 Hz) comprises both cardiac sympathetic and parasympathetic neural modulation of sino-atrial discharge [1][2][3][4][5][6]. These two harmonic contributions to HRV are superimposed on broadband non-harmonic ' noise ', which occurs primarily in the very-low-frequency range (0.00003-0.1 Hz) [4,7], is fractal in nature [8], and can be quantified by plotting the log of spectral power as a function of the log of frequency (a 1\f β plot). Atropine [9] and vagal withdrawal during exercise [5] increase β, whereas propranolol has no effect on the slope of this relationship [10]. ...
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The concept that spectral analysis of heart rate variability (HRV) can estimate cardiac sympathetic nerve traffic in subjects with both normal and impaired left ventricular systolic function has not been validated against muscle sympathetic nerve activity (MSNA). We used coarse-graining spectral analysis to quantify the harmonic and non-harmonic, or fractal, components of HRV and to determine low-frequency (0.0-0.15 Hz; PL) and high-frequency (0.15-0.5Hz; PH) harmonic power. To test the hypothesis that MSNA and HRV representations of sympathetic nerve activity (PL and PL/PH) increase in parallel in heart failure, we recorded heart rate and MSNA during supine rest in 35 patients (age 52.4+/-2 years; mean+/-S. E.M.), with a mean left ventricular ejection fraction of 22+/-2%, and in 34 age-matched normal subjects. Power density was log10 transformed. Mean MSNA was 52.9+/-2.6 bursts/min in heart failure patients and 34.9+/-1.9 bursts/min in normal subjects (P<0.0001). In normal subjects, but not in heart failure patients, total power (PT) (r=-0.41; P=0.02) and fractal power (PF) (r=-0.36; P=0.04) were inversely related to age. In heart failure patients, total and fractal power were reduced (P<0.009 for both), and were inversely related to MSNA burst frequency (r=-0.55, P=0.001 and r=-0.60, P=0. 0003 respectively). In normal subjects, there was no relationship between MSNA and either PL or PH. In heart failure patients, as anticipated, PH was inversely related to MSNA (r=-0.41; P<0.02). However, PL was also inversely rather than directly related to MSNA (r=0.44 for 1/log10 PL; P<0.01). There was no relationship between other sympathetic (PL/PH) or parasympathetic (PH/PT) indices and MSNA in either heart failure patients or normal subjects. The lack of concordance between these direct and indirect estimates of sympathetic nervous system activity indicates that this component of HRV cannot be used for between-subject comparisons of central sympathetic nervous outflow. It is the absence of low-frequency power that relates most closely to sympathetic activation in heart failure.
... The underlying concept is that harmonic contributions to heart rate variability are superimposed on broadband non-harmonic 'noise'. This occurs primarily in the very low frequency range, from 0·00003 to 0·1 Hz [6] , is fractal in nature [11] , and can be quantified by plotting the log of spectral power as a function of the log of frequency (a 1/f B plot). Since non-harmonic noise can be a confounding influence within the low frequency range, this method provides more precise estimates of the harmonic contributions to low and high frequency power [6,7] . ...
Article
Spectral analysis of heart rate variability has gained popularity as a simple, non-invasive tool for assessing autonomic function in both normal subjects and in patients in a variety of clinical settings. However, the use of this method as a means of estimating the magnitude of cardiac sympathetic activation in individual patients with heart failure has proved disappointing, with a lack of concordance with more direct measures of sympathetic outflow. This review will describe the rationale involved in using sympathetic indices obtained from spectral analysis of heart rate variability to assess cardiac sympathetic outflow in normal subjects and patients with heart failure. The specific limitations and technological concerns that dictate how it may most effectively be used in this patient population will be discussed.
Book
This book is a comprehensive and up-to-date resource on the use of regenerative medicine for the treatment of cardiovascular disease. It provides a much-needed review of the rapid development and evolution of bio-fabrication techniques to engineer cardiovascular tissues as well as their use in clinical settings. The book incorporates recent advances in the biology, biomaterial design, and manufacturing of bioengineered cardiovascular tissue with their clinical applications to bridge the basic sciences to current and future cardiovascular treatment. The book begins with an examination of state-of-the-art cellular, biomaterial, and macromolecular technologies for the repair and regeneration of diseased heart tissue. It discusses advances in nanotechnology and bioengineering of cardiac microtissues using acoustic assembly. Subsequent chapters explore the clinical applications and translational potential of current technologies such as cardiac patch-based treatments, cell-based regenerative therapies, and injectable hydrogels. The book examines how these methodologies are used to treat a variety of cardiovascular diseases including myocardial infarction, congenital heart disease, and ischemic heart injuries. Finally, the volume concludes with a summary of the most prominent challenges and perspectives on the field of cardiovascular tissue engineering and clinical cardiovascular regenerative medicine. Cardiovascular Regenerative Medicine is an essential resource for physicians, residents, fellows, and medical students in cardiology and cardiovascular regeneration as well as clinical and basic researchers in bioengineering, nanomaterial and technology, and cardiovascular biology.
Chapter
Myocardial infarction (MI) is projected to increase globally in the coming decades. The long-term outlook for patients with ischemic heart injury undergoing current treatment modalities is bleak, due to the lack of regenerative capacity of native heart tissue. Tissue engineering and regenerative medicine have developed numerous strategies to repair or replace injured myocardium. One of the most promising strategies to date is the attempt to engineer tissues and cells at the nanoscale by utilizing nanobiomaterials to mimic the native nanoscale structure of the heart. Nanobiomaterials have proliferated enormously in the past few decades and have great potential for creating biomimetic systems that can replace or repair injured myocardium. Tissue engineering scaffolds with precisely controlled nanotopography, electrically conductive nanomaterials with the potential for mimicking conductive pathways in the heart, and numerous nanocarriers for targeted cardiac drug delivery have now been achieved. In this chapter we review the rationale for engineering biological tissues at the nanoscale as well as recent applications in nanofabrication and nanomedicine for cardiac regeneration.
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Estimating the long memory parameter of the fMRI time series enables us to understand the fractal behavior of neural activity of the brain through fMRI time series. However, the existence of white noise and physiological noise compounds which also have fractal properties prevent us from making the estimation precise. As basic strategies to overcome noises, we address how to estimate the long memory parameter in the presence of additive noises, and how to estimate the long memory parameters of linearly combined long memory processes.
Chapter
The nonlinear dynamics of heart action are such as to generate and to support irregular nonrandom variations in the main output parameters of pulse and pressure, in response to external stimulation such as stressors (Pearson 1972; Gregson 2009; Herbert 1995; Mezentseva et al. 2002; Rao and Yeragani 2001; Shiferaw and Karma 2006). These dynamic complexities have serious implications for the analysis and treatment of hypertension, as the probabilities of misdiagnosis of state, dysfunction, and potential morbidity cannot with certainty be based on the linear or Gaussian statistics usually employed in epidemiological and related studies. A Bayesian analysis of decision probabilities is used to point up ambiguities in reported results. There is gradual recognition of this situation, but so far little established linkage between nonlinear dynamical modeling and clinical practice, except perhaps in some recent biomedical physics modeling.
Chapter
The nonlinear dynamics of heart action are such as to generate and to support irregular nonrandom variations in the main output parameters of pulse and pressure, in response to external stimulation such as stressors (Pearson 1972; Gregson 2009; Herbert 1995; Mezentseva et al. 2002; Rao and Yeragani 2001; Shiferaw and Karma 2006). These dynamic complexities have serious implications for the analysis and treatment of hypertension, as the probabilities of misdiagnosis of state, dysfunction, and potential morbidity cannot with certainty be based on the linear or Gaussian statistics usually employed in epidemiological and related studies. A Bayesian analysis of decision probabilities is used to point up ambiguities in reported results. There is gradual recognition of this situation, but so far little established linkage between nonlinear dynamical modeling and clinical practice, except perhaps in some recent biomedical physics modeling.
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Aims The need for a readily available, inexpensive, non-invasive method for improved risk stratification of heart failure (HF) patients is paramount. Prior studies have proposed that distinct fluctuation patterns underlying the variability of physiological signals have unique prognostic value. We tested this hypothesis in an extensively phenotyped cohort of HF patients using EntropyXQT, a novel non-linear measure of cardiac repolarization dynamics. Methods and results In a prospective, multicentre, observational study of 852 patients in sinus rhythm undergoing clinically indicated primary prevention implantable cardioverter-defibrillator (ICD) implantation (2003–10), exposures included demographics, history, physical examination, medications, laboratory results, serum biomarkers, ejection fraction, conventional electrocardiographic (ECG) analyses of heart rate and QT variability, and EntropyXQT. The primary outcome was first ‘appropriate’ ICD shock for ventricular arrhythmias. The secondary outcome was composite events (appropriate ICD shock and all-cause mortality). After exclusions, the cohort (n = 816) had a mean age of 60 ± 13 years, 28% women, 36% African Americans, 56% ischaemic cardiomyopathy, and 29 ± 16% Seattle HF risk score (SHFS) 5-year predicted mortality. Over 45 ± 24 months, there were 134 appropriate shocks and 166 deaths. After adjusting for 30 exposures, the hazard ratios (comparing the 5th to 1st quintile of EntropyXQT) for primary and secondary outcomes were 3.29 (95% CI 1.74–6.21) and 2.28 (1.53–3.41), respectively. Addition of EntropyXQT to a model comprised of the exposures or SHFS significantly increased net reclassification and the ROC curve area. Conclusions EntropyXQT measured during ICD implantation strongly and independently predicts appropriate shock and all-cause mortality over follow-up. EntropyXQT complements conventional risk predictors and has the potential for broad clinical application.
Article
Heart Rate Variability (HRV) reflects the response of the heart to a variety of influences and provides informations about sympathetic and parasympathetic influences affecting the cardiovascular system in the perioperative period. However, because of the complexity of the autonomic control of the cardiovascular system the interpretation of HRV measurements needs caution. The knowledge of the pathophysiology underlying HRV is critical in order to understand the state of the autonomic nervous system and its relevance for patient management. HRV seems to be a useful tool for preoperative cardiovascular risk stratification. Confounding effects of multiple factors influencing HRV in the perioperative setting limit this methodology for example as a depth-of-anaesthesia monitor. Lack of standardization renders the comparison of results of different investigations difficult. Of major concern in this context is the quality of the electro-cardiogram recording when assessing HRV. Because of the ongoing progress in monitoring with regard to acquisition and computer-based analysis of HRV data it seems at least possible to measure HRV routinely in the perioperative setting. However, large prospective and standardized trials are necessary. Depending on the results the clinical relevance of HRV as a relatively simple and noninvasive perioperative monitoring should be reevaluated.
Article
This work proposes the development and study of a novel set of fractal descriptors for texture analysis. These descriptors are obtained by exploring the fractal-like relation among the coefficients and magnitudes of a particular type of wavelet decomposition, to know, the best basis selection. The proposed method is tested in the classification of three sets of textures from the literature: Brodatz, Vistex and USPTex. The method is also applied to a challenging real-world problem, which is the identification of species of plants from the Brazilian flora. The results are compared with other classical and state-of-the-art texture descriptors and demonstrate the efficiency of the proposed technique in this task.
Conference Paper
Life support with a mechanical ventilator is used to manage patients with a variety of lung diseases including acute respiratory distress syndrome (ARDS). Recently, management of ARDS has concentrated on ventilating at lower airway pressure using lower tidal volume. A large international study demonstrated a 22% reduction in mortality with the low tidal volume approach. The potential advantages of adding physiologic noise with fractal characteristics to the respiratory rate and tidal volume as delivered by a mechanical ventilator are discussed. A so-called biologically variable ventilator (BVV), incorporating such noise, has been developed. Here we show that the benefits of noisy ventilation - at lower tidal volumes can be deduced from a simple probabilistic result known as Jensen's Inequality. Using the local convexity of the pressure-volume relationship in the lung we demonstrate that the addition of noise results in higher mean tidal volume or lower mean airway pressure. The consequence is enhanced gas exchange or less stress on the lungs, both clinically desirable. Jensen's Inequality has important considerations in engineering, information theory and thermodynamics. Here is an example of the concept applied to medicine that may have important considerations for the clinical management of critically ill patients. Life support devices, such as mechanical ventilators, are of vital use in critical care units and operating rooms. These devices usually have monotonous output. Improving mechanical ventilators and other life support devices may be as simple as adding noise to their output signals.
Article
Let Xi = F (Xi-1), where F is chaotic on a domain Ω of Rn. If F becomes insensitive, i.e. gives the same response, H, in an open subset of D of Ω, then F engenders locally stable periodic orbits. We discussed the relationship between F, D, H and the periods of these orbits. The idea of local defect might be of use in discussing chaos in health and disease.
Article
Autonomic characteristics of panickers, blood phobics, and nonanxious controls were compared with a variety of cardiovascular measures, including spectral analysis of the cardiac inter-beat interval time series (derived from the electrocardiogram). Responses to laboratory stressors (shock avoidance and cold face stress) of 16 participants who reported recent occurrences of frequent severe panic attacks, 15 participants who reported strong somatic reactions and fainting to the sight of blood, and 15 controls, were recorded. Results suggested distinct autonomic patterns among the three groups. Across conditions, panickers displayed the highest heart rates (HR) coupled with the least HR variability, which indicates low levels of cardiac vagal tone. Blood phobics showed more vagally mediated HR variability than panickers, with a significant association between cardiac rate and mean arterial pressure. Controls generally showed the most HR variability and `spectral reserve' (a quality that indicates flexible responsivity). Results are discussed in the context of traditional models of anxiety and autonomic activity in contrast to contemporary notions of stability and change in biological systems.
Article
Continuous periodogram power spectral analysis of daily incidence of acute myocardial infarction (AMI) reported at a hospital for cardiology in Pune, India for the two-year period June 1992–May 1994 show that the power spectra follow the universal and unique inverse power law form of the statistical normal distribution. The same time inverse power law form for power spectra of space-time fluctuations are also ubiquitous to dynamical systems in nature and have been identified as signatures of self-organized criticality. The unique quantification for self-organized criticality presented in this paper is shown to be intrinsic to quantumlike mechanics governing fractal space-time fluctuation patterns in dynamical systems and suggest a possibly fruitful relation and analogy between different subject such as chaos, diffusion and quantum physics. The results found which mimic those obtained in quantum physics by El Naschie using the concept of Cantorian space ε(∞) suggest that, that tools developed in some of these areas may be used advantageously in the medical field as pioneered by A.T. Winfree [Int. J. Bifurcation and Chaos 7 (3) (1997) 487–526] and A.V. Holden [Chaos, Solitons and Fractals 5 (3/4) (1995) 691–704; Int. J. Bifurcation and Chaos 7 (9) (1997) 2075–2104].
Article
Many new methods of analyzing heart rate (HR) variability have been developed to describe the features in HR behavior that cannot be detected by traditional time- and frequency-domain methods. Some of the new methods, such as analysis of fractal correlation properties and complexity of HR dynamics, have provided clinically useful information in various patient populations. Importantly, some fractal analysis methods are better risk predictors of mortality than traditional HR variability measures, and analysis of complexity of HR dynamics has been shown to predict the spontaneous onset of atrial fibrillation. New analysis methods based on nonlinear dynamics are a promising tool for better understanding of normal and abnormal HR behavior. More work will be needed to establish the clinical applicability of traditional and new analysis methods of HR variability.
Article
Nutritional metabolomics is rapidly maturing to use small-molecule chemical profiling to support integration of diet and nutrition in complex biosystems research. These developments are critical to facilitate transition of nutritional sciences from population-based to individual-based criteria for nutritional research, assessment, and management. This review addresses progress in making these approaches manageable for nutrition research. Important concept developments concerning the exposome, predictive health, and complex pathobiology serve to emphasize the central role of diet and nutrition in integrated biosystems models of health and disease. Improved analytic tools and databases for targeted and nontargeted metabolic profiling, along with bioinformatics, pathway mapping, and computational modeling, are now used for nutrition research on diet, metabolism, microbiome, and health associations. These new developments enable metabolome-wide association studies (MWAS) and provide a foundation for nutritional metabolomics, along with genomics, epigenomics, and health phenotyping, to support the integrated models required for personalized diet and nutrition forecasting.
Conference Paper
Fetal heart rate variability has long been considered an indicator of fetal health, with a decrease in variability associated with the progression of disease. The purpose of this study was to develop an index of fetal health by applying the nonlinear analytic techniques of chaotic systems to measurements of the beat-to-beat intervals of the fetal heart. This study was carried out using Doppler ultrasound data obtained from 30 patients in advanced stages of pregnancy, the fetuses between 36 and 40 weeks of gestation. The index used to determine the degree of variability in the fetal heart, and thus the health of the fetus, was the correlation dimension (CD). This was calculated from the interbeat intervals (IBI) using the method of time delays. Results from the analysis indicated close correlation with the clinical diagnosis, showing healthy fetuses with CDs above 7 and poor outcome (low birthweight) in fetuses with CD below 7
Article
This pilot study has examined the rate of repetitive speech production through use of nonlinear methods. Durational measures were obtained from a normal subject who was required to produce a stimulus word in four speaking conditions: normal, controlled-normal, accelerated, and controlled-accelerated. Phase plots and accumulated time series plots were utilized to display intra-subject variability. Attractors were observed in each of the four phase plots and of particular interest was the direction of their shift for the different speaking conditions. The accumulated time series plots also revealed patterns of intra-subject variability across time. In summary, these two forms of nonlinear representation successfully characterized qualitative changes within, and across, the four speaking conditions. The observed spectral distributions and patterns of variability have implications for differentiating normal from abnormal speaking conditions.
Article
We introduce our recent approach to study autonomic nervous system control of heart rate during exercise by means of heart rate variability (HRV) spectral analysis with special reference to its relationship to ventilatory threshold (Tvent). The rationale for the study was that HRV has been shown to reflect (cardiac) parasympathetic and sympathetic nervous system (PNS and SNS, respectively) activity, together with the underlying complexity of cerebral autonomic system in terms of fractal dimension (DF) of HRV time series. The experimental results showed that PNS was markedly reduced below Tvent, that the rate of change in sympathoadrenal activity indicators (plasma norepinephrine and epinephrine concentrations and SNS indicator) was enhanced above Tvent, and that these changes in PNS and SNS indicators were associated with the appearance of the low-dimensional (low DF) dynamics that might reflect less complex autonomic activity. These findings have been considered with respect to implication for clinical cardiology.
Article
Recently, considerable effort was focused on unifying various aspects of cardiac pathophysiology in terms of nonlinear dynamics, particularly through application of chaos theory and the concept of fractal geometry.1–5 Goldberger et al4–7 have suggested that the specialized cardiac conduction network, the His-Purkinje system, has a fractal geometry. Fractals, first described by Mandelbrot8 and found ubiquitously in nature, are self-similar geometric structures composed of subunits that in turn are composed of smaller subunits in a cascade down to microscopic scales. Each subunit appears as a smaller but otherwise identical version of the super-structure.The normal QRS complex is a broad-band wave-form,9,10 and its power spectrum has been shown to fall with frequency according to the following relation: P(f) = kfβ (1) where k is a positive constant and β is a negative constant.6 This type of frequency dependence is generally referred to as an inverse power law, or more simply, a power law. Goldberger et al6 have provided a theoretical argument suggesting that the power-law nature of the QRS spectrum is a direct consequence of the proposed fractal geometry of the His-Purkinje system. We sought to test this hypothesis by studying the power spectra of QRS complexes from both normally and abnormally conducted beats. During a ventricular premature beat or an exogenously ventricular-paced beat, involvement of the His-Purkinje system in ventricular depolarization is reduced or absent.11 Thus, comparing power spectra for these beat types with spectra for normally conducted beats provides a means for establishing the importance of the conduction system in determining QRS spectral morphology.
Article
Our objective was to determine whether continuous positive airway pressure augments the low heart rate variability of congestive heart failure, a marker of poor prognosis. Nasal continuous positive airway pressure improves ventricular function in selected patients with heart failure. In 21 sessions in 16 men (mean [+/- SE] age 56 +/- 2 years) with New York Heart Association functional class II to IV heart failure, we assessed the effects of 45 min with (n = 14) and without (as a time control, n = 7) nasal continuous positive airway pressure (10 cm of water) on heart rate variability and end-expiratory lung volume. Coarse-graining spectral analysis was used to derive total spectral power (PT), its nonharmonic component (fractal power [PF]) and the low (0.0 to 0.15 Hz [PL]) and high (0.15 to 0.50 Hz [PH]) frequency components of harmonic power. Standard deviation of the RR interval, high frequency power and the PH/PT ratio were used to estimate parasympathetic activity in the time and frequency domains, and the PL/PH ratio was used to estimate cardiac sympathetic activity in the frequency domain. Use of continuous positive airway pressure increased end-expiratory lung volume by 445 +/- 82 ml (p < 0.01) and both time (p < 0.006) and frequency domain indexes of heart rate variability: Total spectral power (p < 0.01), nonharmonic power (p < 0.023) and low (p < 0.04) and high (p < 0.05) frequency components of harmonic power all increased. Time alone had no effect on these variables. By comparison, the PH/PT ratio increased during nasal continuous positive airway pressure (p < 0.004), whereas the PL/PH ratio was unchanged. Breathing rate remained constant in both groups. Short-term application of nasal continuous positive airway pressure increases heart rate variability and time and frequency domain indexes of parasympathetic activity without influencing cardiac sympathetic activity. This increase may occur reflexively, through stimulation of pulmonary mechanoreceptor afferents.
Article
Deterministic chaos is a pattern of fluctuations that may seem to be stochastic (caused by random external forces) but is actually produced, in a determined manner, by the action of nonlinear dynamic processes. The existence of this phenomenon has important implications for pathologists because it means that experimental data with apparently random fluctuations may be caused by a deterministic process. The patterns noted in deterministic chaos are very sensitive to variation in initial conditions, so if chaotic processes do occur in pathology then methods of predicting biological behavior (prognosis) of lesions, such as tumors, will have to be modified. This review shows the properties of deterministic chaos using a simple mathematical model of tumor growth and describes the methods that may be used to analyze experimental data for the presence of such chaos illustrating these with some clinical data. Established applications in medicine are reviewed and antichaotic mechanisms are discussed.
Article
We review a certain number of medical applications of a new non-euclidean geometry: the fractal geometry described by Mandelbrot. Examples come from anatomy, cytology, general physiology and physiopathology. Furthermore, real clinical applications are shown, in particular, in cardiology, neurology, ophtalmology, radiology and other imaging techniques. An easy reading mathematical approach is added. Some of the fractal images will certainly capture your attention and spur your interest for further applications of this new concept.
Article
Beat-to-beat heart rate (HR) and blood pressure (BP) were measured by the Finapres system in 28 healthy subjects and 64 diabetic subjects. Autonomic controls in diabetic subjects were assessed by scoring 5 cardiovascular function tests (high score = abnormal control). The fractal dimension (FD) of HR (or SBP) was estimated as follows: Measuring the curve of 500 successive HRs with a rule of length L, one obtains N times L. The FD is the slope of the regression line of Log(N) versus Log(1/L) for different L. We found a lower FD of HR in diabetic subjects than in healthy subjects (1.35 +/- 0.10/1.44 +/- 0.09, p = 0.0002) and a similar FD of SBP in the 2 groups. In diabetic subjects, the FD of HR was negatively correlated with age (r = -0.27, p = 0.03), duration of diabetes (r = -0.33, p = 0.0078) and score of disautonomy (r = -0.43, p = 0.0007). So, heartbeat is more fractal in healthy status: a low fractal fluctuation is a sign of pathology.
Article
Spectral analysis of heart period variability was used to examine autonomic cardiac control in several tasks used in experimental and clinical assessments of autonomic nervous system function. Cardiovascular measures were recorded in healthy humans during quiet rest, reaction time shock-avoidance, cold face stress, and combined shock-avoidance/cold face stress. Shock-avoidance was characterized by sympathetic beta-adrenergic dominance, as evidenced by (1) shorter heart periods, (2) less high-frequency spectral power, (3) elevated low-frequency power, (4) increased ratios of low- to high-frequency power, and (5) a steep regression line fitted to the log-log plot of the power spectra. Cold face stress yielded (1) longer heart periods, (2) more high-frequency power, (3) decreased low-frequency spectral power, and (4) a flat regression slope, indicating vagal dominance. Quiet rest appeared as mildly vagal, with less total spectral power, and the combination task elicited a mixed vagal-sympathetic pattern. These results are discussed in the context of (1) the autonomic underpinnings of low-frequency power, (2) the autonomic effects of facial cooling, and (3) the utility of spectral analysis of heart period variability during autonomic challenge tasks for basic research and clinical application.
Article
The goal of our study was to determine whether evidence for chaos in heart rate variability (HRV) can be observed when the respiratory input to the autonomic controller of heart rate is forced by the deterministic pattern associated with periodic breathing. We simultaneously recorded, in supine healthy volunteers, RR intervals and breathing volumes for 20 to 30 min (1024 data point series) during three protocols: rest (control), fixed breathing (15 breath/min) and voluntary periodic breathing (3 breaths with 2 s inspiration and 2 s expiration followed by an 8 s breath hold). On both the RR interval and breathing volume series we applied the non-linear prediction method (Sugihara and May algorithm) to the original time series and to distribution-conserved isospectral surrogate data. Our results showed that, in contrast to the control test, during both fixed and voluntary periodic breathing the variability of breathing volumes was clearly deterministic non-chaotic. During all the three protocols, the RR-interval series' non-linear predictability was consistent with one of a chaotic series. However, at rest, no clear difference was observed between the RR-interval series and their surrogates, which means that no clear chaos was observed. During fixed breathing a difference appeared, and this difference seemed clearer during voluntary periodic breathing. We concluded that HRV dynamics were chaotic when respiration was forced with a deterministic non-chaotic pattern and that normal spontaneous respiratory influences might mask the normally chaotic pattern in HRV.
Article
Unlabelled: We examined the different characteristics of heart rate variability (HRV) to define the time course of HRV profile after coronary artery surgery (CAS). Spectral analysis of HRV was performed on a 512-s segment of R-R intervals of the electrocardiogram on the preoperative day and on Postoperative Days 1, 2, 3, 4, 5, 6, 7, 14, 21, and 28. Power spectral area was divided into low (0.04-0.15 Hz; LF)- and high (0.15-0.5 Hz; HF)-frequency components. Fractal slope and sympathovagal slope of 1/f characteristics of HRV were determined in two different frequency ranges (from 0.01 to 0.15 Hz and from 0.01 to 0.5 Hz, respectively). Three recovery profiles of HRV were identified. Early HRV recovery profiles (Postoperative Days 1-6) included reduction in LF, HF, and sympathovagal slope, as well as an increase in fractal slope. Subsequent HRV recovery profiles (Postoperative Days 7-21) revealed reductions in LF, HF, and sympathovagal slope. Fractal slope became normal. Later HRV recovery profiles (Postoperative Day 28) demonstrated that all spectral components of HRV remained reduced, but sympathovagal and fractal slopes became normal. These changes in the HRV profile after CAS suggest significant postoperative alterations in cardiovascular homeostasis with significant but incomplete recovery during the first 28 postoperative days. Implications: Heart rate variability reflects normal neural regulation of cardiac function. This variability remains depressed as long as 28 days after coronary artery bypass surgery, but can recover as early as 1 wk postoperatively. Despite implied loss of normal neural regulation of cardiac function, a specific correlation between depressed heart rate variability and outcomes was not performed.
Article
The mechanism by which heart rate variability (HRV) changes during neonatal illness is not known. One possibility is that reduced HRV is merely a diminished or scaled-down version of normal. Another possibility is that there is a fundamental change in the mechanism underlying HRV, resulting in a change in the ordering of RR intervals. We investigated the nature and extents of order in RR interval time series from 25 Neonatal Intensive Care Unit patients with a spectrum of clinical illness severity and HRV. We measured predictability (deviation of predicted intervals from observed), and regularity (measured as approximate entropy) of RR interval time series showing different degrees of HRV. In RR interval time series where the effects of scaling were removed, we found 1) records showing normal HRV had more order than those showing low HRV; 2) the nature of the order was more like that of a periodic process with frequencies over a large range (time series whose log-log power spectrum had a 1/f distribution) than that of chaotic one (logistic map); and 3) the nature of order did not change greatly as HRV fell. We conclude that neonatal RR interval time series are ordered by periodic processes with frequencies over a large range, and that the extent of order is less during illness when HRV is low.
Article
For more than 100 years, chiropractors have asserted that overall health can be improved through the use of spinal manipulative therapy. The autonomic nervous system is known to control and regulate all involuntary physiologic activities by controlling the activities of the internal organs, glands, and circulation. Recent studies document a potential relationship between the vertebral subluxation complex, autonomic tone, and cardiac function. This discussion reviews how it is possible to use heart rate variability analysis to calculate a quantitative index of autonomic function, which accurately reflects the sympathetic and parasympathetic tone and the sympathovagal balance. The technique of heart rate analysis known as heart rate variability could be extremely useful in assessment of treatment outcomes in clinical chiropractic practice. At present, heart rate variability is in widespread use in the fields of neurology, cardiology, psychology, psychophysiology, obstetrics, anesthesiology, and psychiatry. Further studies in this area may lead to a better understanding of the effects of spinal manipulation on (1) the general health of an individual, (2) an individual's susceptibility to lowered immunity and recuperative capacity, and (3) conditions that lie outside the scope of musculoskeletal therapeutics and are more in line with classical chiropractic concepts. This can also contribute to a better-informed interprofessional cooperation between allopathic and chiropractic health care providers.
Article
The pattern of variation in heart rate on a beat-to-beat basis contains information concerning sympathetic (SNS) and parasympathetic (PNS) contributions to autonomic nervous system (ANS) modulation of heart rate (HR). In the present study, heart period (RR interval) time series data were collected at rest and during 3 different treadmill exercise protocols from 6 Thoroughbred horses. Frequency and spectral power were determined in 3 frequency bands: very low (VLF) 0-< or = 0.01, low (LO) >0.01-< or = 0.07 and high (HI) >0.07-< or = 0.5 cycles/beat. Indicators of sympathetic (SNSI = LO/HI) and parasympathetic (PNSI = HI/TOTAL) activity were calculated. Power in all bands fell progressively with increasing exercise intensity from rest to trot. At the gallop VLF and LO power continued to fall but HI power rose. SNSI rose from rest to walk, then fell with increasing effort and was lowest at the gallop. PNSI fell from rest to walk, then rose and was highest at the gallop. Normalised HI power exceeded combined VLF and LO power at all gaits, with the ratio HI to LO power being lowest at the walk and highest at the gallop. ANS indicators showed considerable inter-horse variation, and varied less consistently than raw power with increasing physical effort. In the horses studied, the relationship between power and HR changed at exercise intensities associated with heart rates above approximately 120-130 beats/min. At this level, humoral and other non-neural mechanisms may become more important than autonomic modulation in influencing heart rate and heart rate variability (HRV). HRV at intense effort may be influenced by respiratory-gait entrainment, energetics of locomotion and work of breathing. HRV analysis in the frequency domain would appear to be of potential value as a noninvasive means of assessing autonomic modulation of heart rate at low exercise intensities, only. The technique may be a sensitive method for assessing exercise response to experimental manipulations and disease states.
Article
Measurement of heart rate variability (HRV) in the perioperative period is not yet part of routine monitoring. Because of a lack of standardization, comparison of results of different investigations is difficult. Caution is needed in interpreting data of HRV measurements because of the complexity of autonomic control of the cardiovascular system. Moreover, confounding effects of multiple factors influencing HRV in the perioperative setting make interpretation of data difficult and limit this methodology, for example, as a depth-of-anaesthesia monitor. HRV reflects the response of the heart to a variety of influences. None of the parameters obtained, however, elucidates directly the mechanism or site of action of an anaesthetic drug. Knowledge of the pathophysiology underlying HRV is critical in order to understand the state of the autonomic nervous system and its relevance for patient management. Nevertheless, previous studies show that HRV can provide information about sympathetic and parasympathetic influences affecting the cardiovascular system in the perioperative period. Thus, HRV seems to be a useful tool for preoperative cardiovascular risk stratification. Of major concern in this context is the quality of the recording of the electrocardiogram when assessing HRV. Because of the ongoing progress in monitoring with regard to acquisition and computer-based analysis of HRV data, it seems at least possible to measure HRV routinely in the perioperative setting. However, the need for standardization requires large prospective and standardized trials. Depending on the results, the clinical relevance of HRV as a relatively simple and non-invasive perioperative monitoring has to be re-evaluated.
Article
Power spectral analysis was used to analyze fluctuations of systolic blood pressure and heart rate. Non-invasive finger plethysmography and electrocardiography were performed in 20 patients with chronic atrial fibrillation and in 10 age-matched healthy subjects with normal sinus rhythm. The impulse train was stored on a personal computer and the power spectrum of R-R interval and systolic blood pressure were obtained by Fourier analysis (0.01-0.03 Hz). The power spectrum (log power vs log frequency) characteristically revealed a linear regression as 1/f beta. The R-R interval spectrum during atrial fibrillation showed a white noise-like flat spectrum when plotted as log power against log frequency, whereas the systolic blood pressure spectrum during atrial fibrillation showed a 1/f noise-like negative slope linear pattern. The spectrum exponent of systolic blood pressure in patients with atrial fibrillation was significantly lower than that in subjects with normal sinus rhythm (2.3 +/- 0.1 vs 1.3 +/- 0.1, p < 0.0001). Systolic blood pressure fluctuation in patients with atrial fibrillation has a fractal component and is more complex than that of healthy subjects with normal sinus rhythm.
Article
Optimizing perioperative mechanical ventilation remains a significant clinical challenge. Experimental models indicate that "noisy" or variable ventilation (VV)--return of physiologic variability to respiratory rate and tidal volume--improves lung function compared with monotonous control mode ventilation (CV). VV was compared with CV in patients undergoing abdominal aortic aneurysmectomy, a patient group known to be at risk of deteriorating lung function perioperatively. After baseline measurements under general anesthesia (CV with a tidal volume of 10 ml/kg and a respiratory rate of 10 breaths/min), patients were randomized to continue CV or switch to VV (computer control of the ventilator at the same minute ventilation but with 376 combinations of respiratory rate and tidal volume). Lung function was measured hourly for the next 6 h during surgery and recovery. Forty-one patients for aneurysmectomy were studied. The characteristics of the patients in the two groups were similar. Repeated-measures analysis of variance (group x time interaction) revealed greater arterial oxygen partial pressure (P = 0.011), lower arterial carbon dioxide partial pressure (P = 0.012), lower dead space ventilation (P = 0.011), increased compliance (P = 0.049), and lower mean peak inspiratory pressure (P = 0.013) with VV. The VV mode of ventilation significantly improved lung function over CV in patients undergoing abdominal aortic aneurysmectomy.
Article
In order to compare the heart rate variability (HRV) and stroke volume variability (SVV), supine electrocardiographic (ECG) and the time series data of left ventricular (LV) volume recordings were taken in 12 healthy adult male volunteers. The low frequency (LF) and high frequency (HF) peaks of HRV and SVV were evaluated quantitatively by power spectral analysis. The fractal dimension (FD) of the time series data was analyzed by the box-counting method. A LF peak around 0.1 Hz and a HF peak around 0.3 Hz were as clearly observed in the SVV spectrum as in the HRV spectrum. The LF/HF ratio in SVV was significantly lower than that in HRV, while the FD was significantly higher in SVV than in HRV. No significant correlation of HF, LF or FD was observed between HRV and SVV. Our results indicate that SVV provides different information about the activity of the autonomic nervous system than HRV.
Article
Full-text available
The healthy heart beats to a rhythm that is ever-changing - but that can become more periodic at the onset of disease. Chaotic dynamics may underlie the formation of many fractallike structures in the body.
Article
Full-text available
Nonlinear dynamics, a branch of the basic sciences that studies complex physical systems, offers novel approaches to long-standing problems of physiological form and function. The nonlinear concept of fractals, introduced and developed over the last decade, provides insights into the organization of complex structures such as the tracheobronchial tree and heart, as well as into the dynamics of healthy physiological variability. Alterations in fractal scaling may underlie a number of pathophysiological disturbances, including sudden cardiac death syndromes. Images FIG. 2 FIG. 4
Article
Fourier analysis of heart rate (HR) may be used to characterize overall HR variability as well as low- and high-frequency components attributable to sympathetic and vagal influences, respectively. We analyzed HR spectral characteristics of 12 healthy young (18-35 years) and 10 healthy old (71-94 years) subjects before and during 60 degrees head-up tilt. Total spectral power in the 0.01-0.40-Hz frequency range and low-frequency (0.06-0.10 Hz) and high-frequency (0.15-0.40 Hz) components of the HR power spectrum were significantly lower in old than in young subjects in supine and upright positions. To characterize and compare overall HR variability in young and old subjects, we computed the regression lines relating the log amplitude to the log frequency of the supine HR spectra (l/fx plots). The regression lines for old subjects were lower and steeper (mean slope, -0.78 [5%, 95% confidence limits (CL), -0.73, -0.83]) than in young (mean slope, -0.67 [CL, -0.62, -0.72]), indicating not only reduced overall spectral amplitude but also relatively greater attenuation of high-frequency HR components in the old subjects. This finding illustrates a novel way to quantify the loss of autonomic influences on HR regulation as a function of age. During postural tilt, HR variability was unchanged in the old subjects. For the entire group of young subjects, total HR variability increased during tilt. Six young subjects developed vasovagal syncope during tilt, enabling us to examine differences in the HR spectra of these subjects while they were asymptomatic before syncope.(ABSTRACT TRUNCATED AT 250 WORDS)
Article
Patients at high risk of sudden cardiac death show evidence of nonlinear heartrate dynamics, including abrupt spectral changes (bifurcations) and sustained low frequency (.01-.04 Hz) oscillations in heartrate.
Article
(1) Nonlinear mechanisms may apply both to the understanding of SA-AV node interactions and to bifurcations leading to certain types of AV block. (2) The fractal His-Purkinje system serves as the structural substrate for the generation of the broadband, inverse power-law spectrum of the stable ventricular depolarization (QRS) waveform. (3) Fractal anatomy is also seen in multiple other systems: pulmonary, hepatobiliary, renal, etc. Fractal morphogenesis may reflect a type of critical phenomenon that results in the generation of these irregular, but self-similar structures. (4) Self-similar (fractal) scaling may underlie the 1/f-like spectra seen in multiple systems (e.g., interbeat interval variability, daily neutrophil fluctuations). This fractal scaling may provide a mechanism for the "constrained randomness" that appears to underlie physiological variability and adaptability. (5) Behavior consistent with subharmonic bifurcations is seen in cardiac electrophysiology (e.g., sick sinus syndrome) and hemodynamic perturbations (e.g., swinging heart phenomenon in pericardial tamponade). (6) Ventricular tachyarrhythmias associated with sudden cardiac death (e.g., torsades de pointes, ventricular fibrillation) appear to reflect relatively periodic, not chaotic (turbulent) processes resulting from disruption of the physiologic fractal depolarization sequence. (7) Spectral analysis of Holter monitor data may help in the detection of patients at high risk for sudden death.
Article
Electrical activation of the ventricles via the His-Purkinje system is represented on the body surface by a waveform with a broad range of frequency components. We speculate that this process is mediated by current flow through a fractal-like conduction network and therefore that the broadband spectrum of the depolarization waveform should be scaled as a power-law distribution. The prediction is confirmed by Fourier analysis of electrocardiographic data from healthy men. This observation suggests a new dynamical link between nonlinear (fractal) structure and nonlinear function in a stable physiologic system.
Article
Nonlinear dynamics has become a major area of research in theoretical physics. One of its central foci of investigation concerns transitions between states of order and apparent randomness (“chaos”).l A paradoxic and important finding in this area is that a variety of mathematical and physical systems become more rather than less organized after being perturbed. Furthermore, this type of new order is often characterized by low-frequency (long-wavelength) oscillations that appear to control (slave) the multiple components of the system.’ The possible implications of this theory for the dynamics of physiologic disturbances remain to be explored. A potentially important interdisciplinary link is suggested by the patients described below with heart failure and Cheyne-Stokes breathing, who showed long (~0.02 Hz) sinusoidal oscillations with congruent periods in cardiac interbeat interval, ventilatory amplitude, and systemic arterial oxygen saturation. This observation is consistent with the hypothesis that perturbation of complex physiologic systems may also lead to their entrainment (slaving) by a dominant long wavelength. The emergence of such periodic order with disease conforms to
Article
Small, high-frequency electrocardiographic signals were recorded from the body surface in 39 patients with and 27 patients without ventricular tachycardia (VT). All patients were in normal sinus rhythm, had a previous myocardial infarction, were not taking antiarrhythmic drugs, and did not have bundle branch block. Bipolar X, Y, Z leads were signal averaged and processed by a bidirectional digital filter that allowed low-amplitude signals to be detected in the terminal QRS complex and ST segment. The high-pass filter frequency was 25 Hz. Patients with VT had a lower amplitude of high-frequency signal in the late QRS complex. In the last 40 msec of the filtered QRS complex, the patients with VT had 14.9 +/- 14.4 microV of high-frequency signal; patients without VT had 73.8 +/- 47.7 microV (p less than 0.0001). Ninety-two percent of the patients with VT had less than 25 microV of high-frequency voltage; only 7% of patients without VT had less than 25 microV (p less than 0.0001). Patients with VT had a longer QRS duration than those without VT, 139 +/- 26 vs 95 +/- 10 msec (p less than 0.0001). The QRS duration was longer than 120 msec in 72% of the patients with VT but in none of the patients without VT (p less than 0.0001). In all patients there was no separate and discrete high-frequency signal in the ST segment. Advanced signal processing of the ECG accurately identified the patients in the study with VT after myocardial infarction.
Conference Paper
A three-dimensional model of the ventricles with a self-similar (fractal) conduction system is introduced to generate high-temporal-resolution QRS signals. The signals are obtained under normal and various damaged conditions. The obtained signals are 60-200 Hz bandpass filtered, and two parameters which have been used as markers for the presence of late potential activity are measured: (1) the filtered QRS duration and (2) the root-mean-square voltage of the last 40 ms. The effects of the ventricular conditions on the two parameters are described. It is demonstrated that the late potential activity can be attributed to a regional reduction in propagation velocity but that this is not a sufficient condition for their detection
Article
It is found that a heartbeat period fluctuation usually has a power spectral density which is inversely proportional to frequency, to which a spike is added at a breathing frequency.
On a mechanism Applications of nonlinear dynamics to clinical Fractals in physiology and medicine Physiology in fractal dimensions The fractal geometry of nature
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Distinctive heart rate dynamics precede cocaine-induced sudden death Chaos and fractals in human physiology
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Distinctive heart rate dynamics precede cocaine‐induced sudden death
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