Application Of Chaos Theory Research Articles

Neurocardiology: Brain Mechanisms Underlying Fatal Cardiac Arrhythmias

Chaos theory may have a widespread application in medicine, from the analysis of protein structure at one end of the spectrum to fetal monitoring and the measurement of aging on the other. This application is especially on firm ground in cardiology, where it is simple and precise for the experimenter, and a primer exists for the clinician. As just presented, the point-correlation-dimension analysis of heartbeat variability is able to characterize the patterns of low-dimensional chaos produced by the heartbeat generator, a mechanism that is a composite of the voltage-dependent, neurotransmitter-dependent, and circulation-dependent ionic conductances that are all located in the myocardium where the heartbeat is formed. Most importantly, this deterministic measure of heartbeat variability is able to predict imminent lethal arrhythmogenesis with an accuracy that the more familiar stochastic measures do not have. This may arise because the PD2 is sensitive to the net degrees of freedom of the heartbeat generator, which, under the influence of the nerves and the coronary circulation, can be shifted so the resulting dynamics cause the initiation of lethal arrhythmogenesis. Application of chaos theory in neurology may be equally fruitful because the deterministic measures can discriminate among neuronal firing patterns, reveal subtle changes in brain waves, and be related to higher cognitive processes. Psychiatry also seems quite likely to benefit more and more from the application because the algorithms can discriminate schizophrenic brain functions from normal ones. Thus it can be expected that future applications will enable observation of biologic processes all along the brain-heart axis by which lethal ventricular fibrillation is regulated and perhaps even caused by its determination of the heartbeat dynamics. The subfield of neurocardiology has come a long way since it was first positively identified as an important research area. It took a lot of experiments to show how lethal cardiac arrhythmogenesis is involved with cerebral activities delivered over autonomic pathways. Although we do not yet fully understand the causal mechanism of lethal arrhythmogenesis, we may be getting close. It will become increasingly imperative for the clinical neurologist, along with the cardiologist, to understand the importance of neurocardiology in medical therapy and for the neurologist, along with the cardiologist and psychiatrist, to understand its importance in preventive treatments.

Is the power spectrum of the QRS complex related to a fractal His-Purkinje system?

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 al 4–7 have suggested that the specialized cardiac conduction network, the His-Purkinje system, has a fractal geometry. Fractals, first described by Mandelbrot 8 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) = kf β (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 al 6 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.

Application of chaos theory to biology and medicine.

The application of "chaos theory" to the physical and chemical sciences has resolved some long-standing problems, such as how to calculate a turbulent event in fluid dynamics or how to quantify the pathway of a molecule during Brownian motion. Biology and medicine also have unresolved problems, such as how to predict the occurrence of lethal arrhythmias or epileptic seizures. The quantification of a chaotic system, such as the nervous system, can occur by calculating the correlation dimension (D2) of a sample of the data that the system generates. For biological systems, the point correlation dimension (PD2) has an advantage in that it does not presume stationarity of the data, as the D2 algorithm must, and thus can track the transient non-stationarities that occur when the systems changes state. Such non-stationarities arise during normal functioning (e.g., during an event-related potential) or in pathology (e.g., in epilepsy or cardiac arrhythmogenesis). When stochastic analyses, such as the standard deviation or power spectrum, are performed on the same data they often have a reduced sensitivity and specificity compared to the dimensional measures. For example, a reduced standard deviation of heartbeat intervals can predict increased mortality in a group of cardiac subjects, each of which has a reduced standard deviation, but it cannot specify which individuals will or will not manifest lethal arrhythmogenesis; in contrast, the PD2 of the very same data can specify which patients will manifest sudden death. The explanation for the greater sensitivity and specificity of the dimensional measures is that they are deterministic, and thus are more accurate in quantifying the time-series. This accuracy appears to be significant in detecting pathology in biological systems, and thus the use of deterministic measures may lead to breakthroughs in the diagnosis and treatment of some medical disorders.

Cyclone Track Prediction over the North Indian Ocean

Abstract With the application of chaos theory, the attractor dimension for the system of tropical cyclones over the North Indian Ocean is estimated. The dimension of the attractor is found to be between 5 and 6. On the basis of the low dimension of the attractor, a simple multivariate regression prediction formula is suggested in which only the previous six 6-h positions of the cyclone are used as predictors. Regression coefficients reveal that the cyclones over the North Indian Ocean behave in such a way that the meridional acceleration changes sign during a 24-h period, but the zonal acceleration retains its sign during this period.

Continuous-time models of chaos in economics

In this paper, we shall discuss some applications of chaos theory to the study of continuous-time economic dynamic models, i.e., models represented by systems of ordinary differential equations. Two such applications will be considered. The first, discussed in Part I of the paper, is a continuous-time generalization of a class of non-linear, one-dimensional maps which encompasses the majority of existing economic models of chaotic dynamics. The second, discussed in Part II, is a model of inventory cycles of Keynesian inspiration, represented by a system of three differential equations, including a single ‘one-humped’ non-linearity. Two points will be given particular emphasis, namely: in Part I, the relationship between discrete- and continuous-time representation of economic phenomena; in both Parts I and II, the combined role of lags and non-linearity in generating chaotic output.

Chaos Theory and Microeconomics: An Application to Model Specification and Hedonic Estimation

This paper is the first to apply the theory of deterministic chaos to a microeconomic problem. Previous applications of chaos theory to time-series data, while successful in uncovering nonlinearities, have not provided guidelines for resolving uncovered misspecification problems. In contrast, the authors show that a modified test statistic from chaos theory is an extremely valuable tool in microeconomic model specification because it shows when excluded information is correlated with included information. This test, applied to hedonic estimation of marginal housing prices, is able to distinguish among alternative regression specifications and assists in discovering a parsimonious specification devoid of nonlinear effects. Copyright 1991 by MIT Press.

Applications of chaos theory to the molecular biology of aging

New developments in the field of chaos theory can help us describe in detail many hitherto unexplained natural phenomena. Some of the developments of this theory can be applied to molecular gerontology to complement existing techniques used in this field. Thus, there is the potential of better description, quantification, and manipulation of some aging mechanisms.

Chaos from PWM Electrohydraulic Servo

The phenomenon of CHAOS for discret models control systems is discussed. A PWM electrohidraulic servo Is studied. This nonlinear servo control has Its fixed point determined, it has its stability regions delimited as a function of its parameters. We use Marotto's theorem to show the sufficient conditions to exist CHAOS. We make use of a digital simulation with nonlinear programming techniques to show these conditions and to observe the dynamic behavior of the system. The main results are the possibilité of application of CHAOS theory to to discret models control systems, description of the behavior of such systems in unstable regions and the identification and prevision of CHAOS.

The Potential Importance of Boundaries of Fluvial Ecosystems

Boundaries separating adjacent resource patches are dynamic components of the aquatic landscape. This article addresses some fundamental questions about boundary structure and function in lotic ecosystems. We give examples of longitudinal and lateral boundaries associated with stream systems, demonstrate the application of chaos theory to understanding the inherent variability of boundary properties, and compare characteristics of boundaries in an arctic-tropical transect. We conclude that studies of resource patches, their boundaries, and the nature of exchange with adjacent patches will improve our perspective of drainage basin dynamics over a range of temporal and spatial scales.