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PubMed2006

Nonlinear dynamics and self-organization of rotary molecular motor ensembles.

The coupled nonlinear dynamics of rotary motor ensembles and an embedding fluid medium are simulated on the basis of Navier-Stokes equations. The model description considers space-dependent rotation of motors and a spatially inhomogeneous motor distribution as well as spatial fluctuations in molecular properties. The mutual influence of motor rotations and fluid dynamics as well as spatial inhomogeneities of their molecular properties are self-consistently included. Space-time simulations visualize the complex interplay between the fluid dynamics and motor rotation and show that the dynamic coupling to the environment via the velocity field as well as the spatial inhomogeneity and distribution of rotors determines the overall behavior of the motor complex. Depending on the initial molecular distribution, rotation frequency, and fluid dynamics a spatial self-organization or a chaotic behavior may arise.

Computer Simulation↗
PubMed1989

A dynamic nonlinear lumped parameter model for skeletal muscle circulation.

A dynamic nonlinear lumped parameter model of the circulation of skeletal muscle for constant vasoactive state is presented. This model consists of four compartments that represent the large arteries, the arterioles, the capillaries and venules, and the veins, respectively. The first compartment consists of a linear compliance (C1) and resistance (R1). The third compartment possesses no compliance and is represented by a linear resistance (R3). The second and fourth compartments each consist of a nonlinear pressure-volume relation, resulting in a pressure dependent compliance (C2, C4, respectively) and nonlinear resistance (R2, R4, respectively). The eleven model parameters were collected in a complementary way: they were partly obtained from a priori knowledge including information at the microscopic level, and partly determined by means of an estimation algorithm. Estimated values of the compliances (in cm3.kPa-1.100 g-1, 1 kPa = 7.5 mmHg) and resistances (in kPa.s.cm-3.100 g) at an (arterial) inflow pressure of 10 kPa and a (venous) outflow pressure of 0 kPa were: C1: 0.014; R1: 6.6; C2: 0.565; R2: 84.6; R3: 37.9; C4: 1.044; R4: 24.5. The model (with the nonlinear pressure-volume relations) is able to predict the static and dynamic instantaneous (i.e., for constant vasomotor tone) pressure-flow relation and the instantaneous zero flow pressure intercept. These phenomena are therefore not necessarily the result of the rheological properties of blood. The secondary or delayed dilatation upon a positive inflow pressure step (or negative step in venous pressure) is predicted by the model implying that delayed dilatation is not necessarily related to changes in vasomotor tone. Venous outflow delay, upon a positive inflow pressure step (starting from zero flow), is also predicted by the model.

Algorithms↗
PubMed2003

[Nonlinear dynamic analysis of heart rate variability in patients with diabetic autonomic neuropathy].

OBJECTIVE: To explore earlier detection methods for diabetic autonomic neuropathy (DAN) by heart rate variability (HRV) analysis. METHODS: Thirty-four diabetic patients (including 22 with explicit clinical DAN symptoms) were randomly selected for this study from the in-patient department of endocrinology. On the basis of Virtual Instrumental WorkBench- LabVIEW and using several nonlinear dynamic analysis measures, including Allan factor, lyapunov exponent, approximate entropy, fractal dimension, complexity, wavelet-transform standard deviation and nonlinear energy operator, the analysis of the HRV in these diabetic patients was performed in comparison with normal subjects. RESULTS: The nonlinear indices of both DAN patients and patients without obvious DAN were significantly different from those of the normal subjects, especially in terms of Lyapunov exponent, approximate entropy, and nonlinear energy operator. CONCLUSION: Nonlinear dynamic methods of HRV analysis can provide assistance in assessing the status and impairment of the autonomic system, and can be used to efficiently detect diabetic neuropathy in early stages.

Autonomic Nervous System Diseases↗
PubMed1997

Towards a biomolecular computer. Information processing capabilities of biomolecular nonlinear dynamic media.

The information processing capabilities of biomolecular excitable media based on nonlinear dynamic mechanisms are discussed. Given even the simplest medium geometry, dynamics and information processing features inherent in biomolecular excitable media proves to be diverse and sophisticated. For the case of pseudo two-dimensional versions these media can be described in terms of neural networks having lateral connections. The main responses of shunting on-center off-surround feedback neural networks and pseudo two-dimensional excitable systems to the external excitations are surprisingly similar. The excitable media are capable of short-time memory, of contour enhancement and quenching or amplifying small features depending on medium state. The analogies discussed reaffirm specific neural net characteristics of excitable media and give the opportunity to estimate more accurate excitable medium characteristics.

Computers↗
PubMed1996

Nonlinear dynamics and quantitative EEG analysis.

Quantitative, computerized electroencephalogram (EEG) analysis appears to be based on a phenomenological approach to EEG interpretation, and is primarily rooted in linear systems theory. A fundamentally different approach to computerized EEG analysis, however, is making its way into the laboratories. The basic idea, inspired by recent advances in the area of nonlinear dynamics and chaos theory, is to view an EEG as the output of a deterministic system of relatively simple complexity, but containing nonlinearities. This suggests that studying the geometrical dynamics of EEGs, and the development of neurophysiologically realistic models of EEG generation may produce more successful automated EEG analysis techniques than the classical, stochastic methods. A review of the fundamentals of chaos theory is provided. Evidence supporting the nonlinear dynamics paradigm to EEG interpretation is presented, and the kind of new information that can be extracted from the EEG is discussed. A case is made that a nonlinear dynamic systems viewpoint to EEG generation will profoundly affect the way EEG interpretation is currently done.

Brain↗
PubMed1995

Improved analysis of heart rate variability by methods of nonlinear dynamics.

The traditional analysis of heart rate variability (HRV) in the time and frequency domains seems to be an independent predictive marker for sudden cardiac death. Because the usual applied methods of HRV analysis describe only linear or strong periodic phenomena, the authors have developed new methods of HRV analysis based on nonlinear dynamics. In that way, parameters are extracted that quantify more complex processes and their complicated relationships. These methods are symbolic dynamics that describes the beat-to-beat dynamics and renormalized entropy that compares the complexity of power spectra on a normalized energy level. In an initial investigation, the HRV of 35 healthy subjects and 39 cardiac patients have been analyzed. Using discriminant functions, the authors found an optimal (100%) differentiation between the group of healthy subjects (even using only an age-matched subgroup of 12 subjects) and that of patients after myocardial infarction with a high electrical risk (Lown 4b). Applying this discriminant function to a group of patients with low electrical risk, four patients show the same behavior indicative of a high risk score, which might be a sign for a hidden high risk, two patients show healthy behavior, and the remaining patients show a separate pattern. The use of new methods of nonlinear dynamics in combination with parameters of the time and frequency domains in HRV offers possibilities for improved classification of HRV behavior. It is suggested that this could lead to a more detailed classification of individual high risk.

Adult↗
PubMed2001

Nonlinear dynamics of heart rate variability in cocaine-exposed neonates during sleep.

The aim of this study was to determine the effects of prenatal cocaine exposure (PCE) on the dynamics of heart rate variability in full-term neonates during sleep. R-R interval (RRI) time series from 9 infants with PCE and 12 controls during periods of stable quiet sleep and active sleep were analyzed using autoregressive modeling and nonlinear dynamics. There were no differences between the two groups in spectral power distribution, approximate entropy, correlation dimension, and nonlinear predictability. However, application of surrogate data analysis to these measures revealed a significant degree of nonlinear RRI dynamics in all subjects. A parametric model, consisting of a nonlinear delayed-feedback system with stochastic noise as the perturbing input, was employed to estimate the relative contributions of linear and nonlinear deterministic dynamics in the data. Both infant groups showed similar proportional contributions in linear, nonlinear, and stochastic dynamics. However, approximate entropy, correlation dimension, and nonlinear prediction error were all decreased in active versus quiet sleep; in addition, the parametric model revealed a doubling of the linear component and a halving of the nonlinear contribution to overall heart rate variability. Spectral analysis indicated a shift in relative power toward lower frequencies. We conclude that 1) RRI dynamics in infants with PCE and normal controls are similar; and 2) in both groups, sympathetic dominance during active sleep produces primarily periodic low-frequency oscillations in RRI, whereas in quiet sleep vagal modulation leads to RRI fluctuations that are broadband and dynamically more complex.

Cocaine↗
PubMed2004

Nonlinear dynamics of incommensurate surface layers.

We describe analytically the nonlinear dynamics of the incommensurate surface layer ("self-modulated" system) with a spatially periodical structure. In the framework of the Frenkel-Kontorova model the nonlinear excitations of the periodic soliton lattice, such as moving additional kinks and gap solitons, are investigated.

Journal Article↗
PubMed1999

Nonlinear dynamics of a DNA chain affected by endogenous AC fields.

In this paper we investigate the nonlinear dynamics of a DNA chain in the presence of endogenous AC fields (EACF) generated by the living cell itself. The dynamics of the DNA chain is described in the framework of the nonlinear breather mode. The transition of breather localized modes into open states, affected by AC fields is calculated by using Kubo's formalism for the linear response of the system.

DNA↗
PubMed2003

Nonlinear dynamics indicates aging affects variability during gait.

OBJECTIVE: To investigate the nature of variability present in time series generated from gait parameters of two different age groups via a nonlinear analysis. DESIGN: Measures of nonlinear dynamics were used to compare kinematic parameters between elderly and young females. BACKGROUND: Aging may lead to changes in motor variability during walking, which may explain the large incidence of falls in the elderly. METHODS: Twenty females, 10 younger (20-37 yr) and 10 older (71-79 yr) walked on a treadmill for 30 consecutive gait cycles. Time series from selected kinematic parameters of the right lower extremity were analyzed using nonlinear dynamics. The largest Lyapunov exponent and the correlation dimension of all time series, and the largest Lyapunov exponent of the original time series surrogated were calculated. Standard deviations and coefficient of variations were also calculated for selected discrete points from each gait cycle. Independent t-tests were used for statistical comparisons. RESULTS: The Lyapunov exponents were found to be significantly different from their surrogate counterparts. This indicates that the fluctuations observed in the time series may reflect deterministic processes by the neuromuscular system. The elderly exhibited significantly larger Lyapunov exponents and correlation dimensions for all parameters evaluated indicating local instability. The linear measures indicated that the elderly demonstrated significantly higher variability. CONCLUSIONS: The nonlinear analysis revealed that fluctuations in the time series of certain gait parameters are not random but display a deterministic behavior. This behavior may degrade with physiologic aging resulting in local instability. RELEVANCE: Elderly show increased local instability or inability to compensate to the natural stride-to-stride variations present during locomotion. We hypothesized that this may be the one of the reasons for the increases in falling due to aging. Future efforts should attempt to evaluate this hypothesis by making comparisons to pathological subjects (i.e. elderly fallers), and examine the sensitivity and specificity of the nonlinear methods used in this study to aid clinical assessment.

Adult↗
PubMed2003

Application of a new method of nonlinear dynamical system identification to biochemical problems.

The system identification method for a variety of nonlinear dynamic models is elaborated. The problem of identification of an original nonlinear model presented as a system of ordinary differential equations in the Cauchy explicit form with a polynomial right part reduces to the solution of the system of linear equations for the constants of the dynamical model. In other words, to construct an integral model of the complex system (phenomenon), it is enough to collect some data array characterizing the time-course of dynamical parameters of the system. Collection of such a data array has always been a problem. However difficulties emerging are, as a rule, not principal and may be overcome almost without exception. The potentialities of the method under discussion are demonstrated by the example of the test problem of multiparametric nonlinear oscillator identification. The identification method proposed may be applied to the study of different biological systems and in particular the enzyme kinetics of complex biochemical reactions.

Enzymes↗
PubMed1988

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.

Animals↗
PubMed2007

Process and meaning: nonlinear dynamics and psychology in visual art.

Creating and viewing visual art are both nonlinear experiences. Creating a work of art is an irreversible process involving increasing levels of complexity and unpredictable events. Viewing art is also creative with collective responses forming autopoietic structures that shape cultural history. Artists work largely from the chaos of the unconscious and visual art contains elements of chaos. Works of art by the author are discussed in reference to nonlinear dynamics. "Travelogues" demonstrates continued emerging interpretations and a deterministic chaos. "Advice to the Imperfect" signifies the resolution of paradox in the nonlinear tension of opposites. "Quanah" shows the nonlinear tension of opposites as an ongoing personal evolution. "The Mother of All Things" depicts seemingly separate phenomena arising from undifferentiated chaos. "Memories" refers to emotional fixations as limit cycles. "Compassionate Heart," "Wind on the Lake," and "Le Mal du Pays" are a series of works in fractal format focusing on the archetype of the mother and child. "Sameness, Depth of Mystery" addresses the illusion of hierarchy and the dynamics of symbols. In "Chasadim" the origin of worlds and the regeneration of individuals emerge through chaos. References to chaos in visual art mirror the nonlinear complexity of life.

Art↗
PubMed2002

Impact of regulatory proteins on the nonlinear dynamics of DNA.

In this paper we examine the nonlinear dynamics of a DNA chain whose exciton modes are affected by regulatory proteins that may become bound to the DNA chain by hydrogen bonds. The dynamics of the DNA chain is described by the Peyrard-Bishop model. Since this model gives rise to large-amplitude broad oscillations of base pairs, we consider the impact of attached regulatory proteins on the so-called breathers or bubbles. Assuming that an ideal gas of bubbles may exist in the DNA chain at physiological temperatures we adopt a statistical approach to calculate the average size of base-pair stretching under the prevailing conditions.

Adenine↗
PubMed2002

Study of features based on nonlinear dynamical modeling in ECG arrhythmia detection and classification.

We present a study of the nonlinear dynamics of electrocardiogram (ECG) signals for arrhythmia characterization. The correlation dimension and largest Lyapunov exponent are used to model the chaotic nature of five different classes of ECG signals. The model parameters are evaluated for a large number of real ECG signals within each class and the results are reported. The presented algorithms allow automatic calculation of the features. The statistical analysis of the calculated features indicates that they differ significantly between normal heart rhythm and the different arrhythmia types and, hence, can be rather useful in ECG arrhythmia detection. On the other hand, the results indicate that the discrimination between different arrhythmia types is difficult using such features. The results of this work are supported by statistical analysis that provides a clear outline for the potential uses and limitations of these features.

Algorithms↗
PubMed2006

Electrodermal arousal between participants in a conversation: nonlinear dynamics and linkage effects.

Physiological linkages between two people in conversation were investigated from a nonlinear dynamical systems theory perspective. Thirty-seven pairs of college students engaged in a 20-minute discussion while connected to electrodes that measured their electrodermal response (ED). Greater incidents of linkage were detected through the nonlinear regression analysis compared to linear models. The nonlinear models were exponential structures that determined positive Lyapunov exponents (and thus the presence of chaos) for 73 out of 74 participants. Results support the use of nonlinear models for interpersonal linkage effects of this type. For each participant, Social Sensitivity from the Social Skills Inventory was correlated with the nonlinear model R(2) coefficient, but not with the size of the Lyapunov exponent. The latter results supported the conclusion that empathy acted as a moderator of the nonlinear process that underlies changes in ED levels over time.

Adult↗
PubMed2002

Nonlinear dynamics of the left ventricle.

The cnoidal method is applied to solve the set of nonlinear dynamic equations of the left ventricle. By using the theta-function representation of the solutions and a genetic algorithm, the ventricular motion can be described as a linear superposition of cnoidal pulses and additional terms, which include nonlinear interactions among them.

Algorithms↗