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All sourcesNASA NTRSDOE OSTI
NASA NTRS1999

Cardiac interbeat interval dynamics from childhood to senescence : comparison of conventional and new measures based on fractals and chaos theory

BACKGROUND: New methods of R-R interval variability based on fractal scaling and nonlinear dynamics ("chaos theory") may give new insights into heart rate dynamics. The aims of this study were to (1) systematically characterize and quantify the effects of aging from early childhood to advanced age on 24-hour heart rate dynamics in healthy subjects; (2) compare age-related changes in conventional time- and frequency-domain measures with changes in newly derived measures based on fractal scaling and complexity (chaos) theory; and (3) further test the hypothesis that there is loss of complexity and altered fractal scaling of heart rate dynamics with advanced age. METHODS AND RESULTS: The relationship between age and cardiac interbeat (R-R) interval dynamics from childhood to senescence was studied in 114 healthy subjects (age range, 1 to 82 years) by measurement of the slope, beta, of the power-law regression line (log power-log frequency) of R-R interval variability (10(-4) to 10(-2) Hz), approximate entropy (ApEn), short-term (alpha(1)) and intermediate-term (alpha(2)) fractal scaling exponents obtained by detrended fluctuation analysis, and traditional time- and frequency-domain measures from 24-hour ECG recordings. Compared with young adults (<40 years old, n=29), children (<15 years old, n=27) showed similar complexity (ApEn) and fractal correlation properties (alpha(1), alpha(2), beta) of R-R interval dynamics despite lower spectral and time-domain measures. Progressive loss of complexity (decreased ApEn, r=-0.69, P<0.001) and alterations of long-term fractal-like heart rate behavior (increased alpha(2), r=0.63, decreased beta, r=-0.60, P<0.001 for both) were observed thereafter from middle age (40 to 60 years, n=29) to old age (>60 years, n=29). CONCLUSIONS: Cardiac interbeat interval dynamics change markedly from childhood to old age in healthy subjects. Children show complexity and fractal correlation properties of R-R interval time series comparable to those of young adults, despite lower overall heart rate variability. Healthy aging is associated with R-R interval dynamics showing higher regularity and altered fractal scaling consistent with a loss of complex variability.

NASA Discipline Cardiopulmonary↗
NASA NTRS1994

Effects of head-down bed rest on complex heart rate variability: Response to LBNP testing

Head-down bed rest is used to model physiological changes during spaceflight. We postulated that bed rest would decrease the degree of complex physiological heart rate variability. We analyzed continuous heart rate data from digitized Holter recordings in eight healthy female volunteers (age 28-34 yr) who underwent a 13-day 6 deg head-down bed rest study with serial lower body negative pressure (LBNP) trials. Heart rate variability was measured on a 4-min data sets using conventional time and frequency domain measures as well as with a new measure of signal 'complexity' (approximate entropy). Data were obtained pre-bed rest (control), during bed rest (day 4 and day 9 or 11), and 2 days post-bed rest (recovery). Tolerance to LBNP was significantly reduced on both bed rest days vs. pre-bed rest. Heart rate variability was assessed at peak LBNP. Heart rate approximate entropy was significantly decreased at day 4 and day 9 or 11, returning toward normal during recovery. Heart rate standard deviation and the ratio of high- to low-power frequency did not change significantly. We conclude that short-term bed rest is associated with a decrease in the complex variability of heart rate during LBNP testing in healthy young adult women. Measurement of heart rate complexity, using a method derived from nonlinear dynamics ('chaos theory'), may provide a sensitive marker of this loss of physiological variability, complementing conventional time and frequency domain statistical measures.

Goldberger, Ary L.↗
NASA NTRS1994

Gender- and age-related differences in heart rate dynamics: are women more complex than men?

OBJECTIVES. This study aimed to quantify the complex dynamics of beat-to-beat sinus rhythm heart rate fluctuations and to determine their differences as a function of gender and age. BACKGROUND. Recently, measures of heart rate variability and the nonlinear "complexity" of heart rate dynamics have been used as indicators of cardiovascular health. Because women have lower cardiovascular risk and greater longevity than men, we postulated that there are important gender-related differences in beat-to-beat heart rate dynamics. METHODS. We analyzed heart rate dynamics during 8-min segments of continuous electrocardiographic recording in healthy young (20 to 39 years old), middle-aged (40 to 64 years old) and elderly (65 to 90 years old) men (n = 40) and women (n = 27) while they performed spontaneous and metronomic (15 breaths/min) breathing. Relatively high (0.15 to 0.40 Hz) and low (0.01 to 0.15 Hz) frequency components of heart rate variability were computed using spectral analysis. The overall "complexity" of each heart rate time series was quantified by its approximate entropy, a measure of regularity derived from nonlinear dynamics ("chaos" theory). RESULTS. Mean heart rate did not differ between the age groups or genders. High frequency heart rate power and the high/low frequency power ratio decreased with age in both men and women (p < 0.05). The high/low frequency power ratio during spontaneous and metronomic breathing was greater in women than men (p < 0.05). Heart rate approximate entropy decreased with age and was higher in women than men (p < 0.05). CONCLUSIONS. High frequency heart rate spectral power (associated with parasympathetic activity) and the overall complexity of heart rate dynamics are higher in women than men. These complementary findings indicate the need to account for gender-as well as age-related differences in heart rate dynamics. Whether these gender differences are related to lower cardiovascular disease risk and greater longevity in women requires further study.

NASA Discipline Cardiopulmonary↗
NASA NTRS1991

Aging and the complexity of cardiovascular dynamics

Biomedical signals often vary in a complex and irregular manner. Analysis of variability in such signals generally does not address directly their complexity, and so may miss potentially useful information. We analyze the complexity of heart rate and beat-to-beat blood pressure using two methods motivated by nonlinear dynamics (chaos theory). A comparison of a group of healthy elderly subjects with healthy young adults indicates that the complexity of cardiovascular dynamics is reduced with aging. This suggests that complexity of variability may be a useful physiological marker.

Non-NASA Center↗
NASA NTRS2002

Dynamical Approach Study of Spurious Numerics in Nonlinear Computations

The last two decades have been an era when computation is ahead of analysis and when very large scale practical computations are increasingly used in poorly understood multiscale complex nonlinear physical problems and non-traditional fields. Ensuring a higher level of confidence in the predictability and reliability (PAR) of these numerical simulations could play a major role in furthering the design, understanding, affordability and safety of our next generation air and space transportation systems, and systems for planetary and atmospheric sciences, and in understanding the evolution and origin of life. The need to guarantee PAR becomes acute when computations offer the ONLY way of solving these types of data limited problems. Employing theory from nonlinear dynamical systems, some building blocks to ensure a higher level of confidence in PAR of numerical simulations have been revealed by the author and world expert collaborators in relevant fields. Five building blocks with supporting numerical examples were discussed. The next step is to utilize knowledge gained by including nonlinear dynamics, bifurcation and chaos theories as an integral part of the numerical process. The third step is to design integrated criteria for reliable and accurate algorithms that cater to the different multiscale nonlinear physics. This includes but is not limited to the construction of appropriate adaptive spatial and temporal discretizations that are suitable for the underlying governing equations. In addition, a multiresolution wavelets approach for adaptive numerical dissipation/filter controls for high speed turbulence, acoustics and combustion simulations will be sought. These steps are corner stones for guarding against spurious numerical solutions that are solutions of the discretized counterparts but are not solutions of the underlying governing equations.

Yee, H. C.↗
NASA NTRS1997

Chaotic Time Series Analysis Method Developed for Stall Precursor Identification in High-Speed Compressors

A new technique for rotating stall precursor identification in high-speed compressors has been developed at the NASA Lewis Research Center. This pseudo correlation integral method uses a mathematical algorithm based on chaos theory to identify nonlinear dynamic changes in the compressor. Through a study of four various configurations of a high-speed compressor stage, a multistage compressor rig, and an axi-centrifugal engine test, this algorithm, using only a single pressure sensor, has consistently predicted the onset of rotating stall.

Source record↗
NASA NTRS1992

Loss of 'complexity' and aging. Potential applications of fractals and chaos theory to senescence

The concept of "complexity," derived from the field of nonlinear dynamics, can be adapted to measure the output of physiologic processes that generate highly variable fluctuations resembling "chaos." We review data suggesting that physiologic aging is associated with a generalized loss of such complexity in the dynamics of healthy organ system function and hypothesize that such loss of complexity leads to an impaired ability to adapt to physiologic stress. This hypothesis is supported by observations showing an age-related loss of complex variability in multiple physiologic processes including cardiovascular control, pulsatile hormone release, and electroencephalographic potentials. If further research supports this hypothesis, measures of complexity based on chaos theory and the related geometric concept of fractals may provide new ways to monitor senescence and test the efficacy of specific interventions to modify the age-related decline in adaptive capacity.

Non-NASA Center↗
NASA NTRS1984

Nonlinear problems in flight dynamics

A comprehensive framework is proposed for the description and analysis of nonlinear problems in flight dynamics. Emphasis is placed on the aerodynamic component as the major source of nonlinearities in the flight dynamic system. Four aerodynamic flows are examined to illustrate the richness and regularity of the flow structures and the nature of the flow structures and the nature of the resulting nonlinear aerodynamic forces and moments. A framework to facilitate the study of the aerodynamic system is proposed having parallel observational and mathematical components. The observational component, structure is described in the language of topology. Changes in flow structure are described via bifurcation theory. Chaos or turbulence is related to the analogous chaotic behavior of nonlinear dynamical systems characterized by the existence of strange attractors having fractal dimensionality. Scales of the flow are considered in the light of ideas from group theory. Several one and two degree of freedom dynamical systems with various mathematical models of the nonlinear aerodynamic forces and moments are examined to illustrate the resulting types of dynamical behavior. The mathematical ideas that proved useful in the description of fluid flows are shown to be similarly useful in the description of flight dynamic behavior.

Chapman, G. T.↗
NASA NTRS1990

An introduction to chaos theory in CFD

The popular subject 'chaos theory' has captured the imagination of a wide variety of scientists and engineers. CFD has always been faced with nonlinear systems and it is natural to assume that nonlinear dynamics will play a role at sometime in such work. This paper will attempt to introduce some of the concepts and analysis procedures associated with nonlinear dynamics theory. In particular, results from computations of an airfoil at high angle of attack which exhibits a sequence of bifurcations for single frequency unsteady shedding through period doublings cascading into low dimensional chaos are used to present and demonstrate various aspects of nonlinear dynamics in CFD.

Pulliam, Thomas H.↗
NASA NTRS1991

Predicting chaos for infinite dimensional dynamical systems: The Kuramoto-Sivashinsky equation, a case study

The results of extensive computations are presented in order to accurately characterize transitions to chaos for the Kuramoto-Sivashinsky equation. In particular, the oscillatory dynamics in a window that supports a complete sequence of period doubling bifurcations preceding chaos is followed. As many as thirteen period doublings are followed and used to compute the Feigenbaum number for the cascade and so enable, for the first time, an accurate numerical evaluation of the theory of universal behavior of nonlinear systems, for an infinite dimensional dynamical system. Furthermore, the dynamics at the threshold of chaos exhibit a fractal behavior which is demonstrated and used to compute a universal scaling factor that enables the self-similar continuation of the solution into a chaotic regime.

Smyrlis, Yiorgos S.↗
NASA NTRS1987

Application of non-linear dynamics to the characterization of cardiac electrical instability

Beat-to-beat alternation in the morphology of the ECG has been previously observed in hearts susceptible to fibrillation. In addition, fibrillation has been characterized by some as a chaotic state. Period doubling phenomena, such as alternation, and the onset of chaos have been connected by non-linear dynamical systems theory. In this paper, we describe the use of a technique from nonlinear dynamics theory, the construction of a first return nap, to assess the susceptibility to fibrillation threshhold in canine experiments.

NASA Discipline Cardiopulmonary↗
NASA NTRS1988

Nonlinear dynamics in cardiac conduction

Electrical conduction in the heart shows many phenomena familiar from nonlinear dynamics. Among these phenomena are multiple basins of attraction, phase locking, and perhaps period-doubling bifurcations and chaos. We describe a simple cellular-automation model of electrical conduction which simulates normal conduction patterns in the heart as well as a wide range of disturbances of heart rhythm. In addition, we review the application of percolation theory to the analysis of the development of complex, self-sustaining conduction patterns.

NASA Discipline Cardiopulmonary↗
NASA NTRS1992

Fractal mechanisms in the electrophysiology of the heart

The mathematical concept of fractals provides insights into complex anatomic branching structures that lack a characteristic (single) length scale, and certain complex physiologic processes, such as heart rate regulation, that lack a single time scale. Heart rate control is perturbed by alterations in neuro-autonomic function in a number of important clinical syndromes, including sudden cardiac death, congestive failure, cocaine intoxication, fetal distress, space sickness and physiologic aging. These conditions are associated with a loss of the normal fractal complexity of interbeat interval dynamics. Such changes, which may not be detectable using conventional statistics, can be quantified using new methods derived from "chaos theory.".

NASA Discipline Cardiopulmonary↗
NASA NTRS1987

Nonlinear dynamics, fractals, cardiac physiology and sudden death

The authors propose a diametrically opposite viewpoint to the generally accepted tendency of equating healthy function with order and disease with chaos. With regard to the question of sudden cardiac death and chaos, it is suggested that certain features of dynamical chaos related to fractal structure and fractal dynamics may be important organizing principles in normal physiology and that certain pathologies, including ventricular fibrillation, represent a class of 'pathological periodicities'. Some laboratory work bearing on the relation of nonlinear analysis to physiological and pathophysiological data is briefly reviewed, with tentative theories and models described in reference to the mechanism of ventricular fibrillation.

Goldberger, Ary L.↗
NASA NTRS1991

Future missions studies: Combining Schatten's solar activity prediction model with a chaotic prediction model

K. Schatten (1991) recently developed a method for combining his prediction model with our chaotic model. The philosophy behind this combined model and his method of combination is explained. Because the Schatten solar prediction model (KS) uses a dynamo to mimic solar dynamics, accurate prediction is limited to long-term solar behavior (10 to 20 years). The Chaotic prediction model (SA) uses the recently developed techniques of nonlinear dynamics to predict solar activity. It can be used to predict activity only up to the horizon. In theory, the chaotic prediction should be several orders of magnitude better than statistical predictions up to that horizon; beyond the horizon, chaotic predictions would theoretically be just as good as statistical predictions. Therefore, chaos theory puts a fundamental limit on predictability.

Ashrafi, S.↗
NASA NTRS1987

Deterministic representation of chaos with application to turbulence

Chaotic motions of nonlinear dynamical systems are decomposed into mean components and fluctuations. The approach is based upon the concept that the fluctuations driven by the instability of the original (unperturbed) motion grow until a new stable state is approached. The Reynolds-type equations written for continuous as well as for finite-degrees-of-freedom dynamical systems are closed by using this stabilization principle. The theory is applied to conservative systems, to strange attractors and to turbulent motions.

Zak, M.↗
NASA NTRS1989

Evanescent radiation, quantum mechanics and the Casimir effect

An attempt to bridge the gap between classical and quantum mechanics and to explain the Casimir effect is presented. The general nature of chaotic motion is discussed from two points of view: the first uses catastrophe theory and strange attractors to describe the deterministic view of this motion; the underlying framework for chaos in these classical dynamic systems is their extreme sensitivity to initial conditions. The second interpretation refers to randomness associated with probabilistic dynamics, as for Brownian motion. The present approach to understanding evanescent radiation and its relation to the Casimir effect corresponds to the first interpretation, whereas stochastic electrodynamics corresponds to the second viewpoint. The nonlinear behavior of the electromagnetic field is also studied. This well-understood behavior is utilized to examine the motions of two orbiting charges and shows a closeness between the classical behavior and the quantum uncertainty principle. The evanescent radiation is used to help explain the Casimir effect.

Schatten, Kenneth H.↗