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PubMed1995

Characteristic nonlinearities of the 3/s ictal electroencephalogram identified by nonlinear autoregressive analysis.

We describe a method for the characterization of electroencephalographic (EEG) signals based on a model which features nonlinear feedback. The characteristic EEG 'fingerprints' obtained through this approach display the time-course of nonlinear interactions, rather than aspects susceptible to standard spectral analysis. Fingerprints of seizure discharges in six patients (five with typical absence seizures, one with complex partial seizures) revealed significant nonlinear interactions. The timing and pattern of these interactions correlated closely with the seizure type. Nonlinear autoregressive (NLAR) analysis is compared with other nonlinear dynamical measures that have been applied to the EEG.

Electroencephalography↗

PubMed2001

Stochastic noise interferes coherently with a model biological clock and produces specific dynamic behaviour.

The influence of noise is unavoidable in all living systems. Its impact on a model of a biological clock, normally running in regular oscillating modes, is examined. It is shown that in a specific system in which endogenous rhythmicity is produced by a beat oscillator acting on a feedback coupled metabolic pool system, noise can act coherently to produce unexpected dynamic behaviour, running from regular over pseudo-regular to irregular time-structures. If the biological system consists of a set of identical weakly coupled cells, stochasticity may lead to phase decoupling producing irregular spatio-temporal patterns. Synchronization via phase resetting can be achieved by external short-time temperature pulses. Explicit results are obtained for the well-studied circadian photosynthesis oscillations in plants performing crassulacean acid metabolism. Because of the generic structure of the underlying nonlinear dynamics they can, however, be regarded as a general property of the influence of noise on nonlinear excitable systems with fixed points occuring close to limit cycles.

Biological Clocks↗

PubMed2002

Identification of determinism in noisy neuronal systems.

Most neuronal ensembles are nonlinear excitable systems. Thus it is becoming common to apply principles derived from nonlinear dynamics to characterize neuronal systems. One important characterization is whether such systems contain deterministic behavior or are purely stochastic. Unfortunately, many methods used to make this distinction do not perform well when both determinism and high-amplitude noise are present which is often the case in physiological systems. Therefore, we propose two novel techniques for identifying determinism in experimental systems. The first, called short-time expansion analysis, examines the expansion rate of small groups of points in state space. The second, called state point forcing, derives from the technique of chaos control. The system state is forced onto a fixed point, and the subsequent behavior is analyzed. This technique can be used to verify the presence of fixed points (or unstable periodic orbits) and to assess stationarity. If these are present, it implies that the system contains determinism. We demonstrate the use and possible limitations of these two techniques in two systems: the Hénon map, a classic example of a chaotic system, and spontaneous epileptiform bursting in the rat hippocampal slice. Identifying the presence of determinism in a physiological system assists in the understanding of the system's dynamics and provides a mechanism for manipulating this behavior.

Action Potentials↗

PubMed1997

Linear and nonlinear ARMA model parameter estimation using an artificial neural network.

This paper addresses parametric system identification of linear and nonlinear dynamic systems by analysis of the input and output signals. Specifically, we investigate the relationship between estimation of the system using a feedforward neural network model and estimation of the system by use of linear and nonlinear autoregressive moving-average (ARMA) models. By utilizing a neural network model incorporating a polynomial activation function, we show the equivalence of the artificial neural network to the linear and nonlinear ARMA models. We compare the parameterization of the estimated system using the neural network and ARMA approaches by utilizing data generated by means of computer simulations. Specifically, we show that the parameters of a simulated ARMA system can be obtained from the neural network analysis of the simulated data or by conventional least squares ARMA analysis. The feasibility of applying neural networks with polynomial activation functions to the analysis of experimental data is explored by application to measurements of heart rate (HR) and instantaneous lung volume (ILV) fluctuations.

Computer Simulation↗

PubMed1994

Kinetic theory of living pattern.

The self-organization whereby developing organisms generate the patterns and spatial relationships of their parts has not been explained on any generally accepted theoretical basis. There is a wide gulf between physical scientists and experimental biologists in their expectations of the kind of theory that is best to pursue. Physical scientists incline towards the power of nonlinear dynamics to generate pattern and are trying evangelistically to interest biologists in this approach.

Animals↗

PubMed2005

Nonlinear characteristics of heart rate time series: influence of three recumbent positions in patients with mild or severe coronary artery disease.

The aim of this study was to investigate the nonlinear characteristics of heart rate variability (HRV) for three recumbent positions: the supine, left lateral and right lateral decubitus positions. Recently, using a linear analyses method (for time and frequency domains), the effect of the right lateral decubitus position on vagal modulation has been found to increase parasympathetic activity and decrease sympathetic modulation. Little is known about the nonlinear dynamics of HRV for the three recumbent positions. Therefore, we studied the correlation dimension (CD), the largest Lyapunov exponent (LLE), the sample entropy (SampEn), the approximate entropy (ApEn) and the exponent alpha of the 1/falpha power spectrum as nonlinear characteristics of HRV. In response to the right lateral decubitus position, the CD, LLE, SampEn and ApEn increased significantly in both coronary artery disease (CAD) and control groups. In the linear analyses, the normalized high-frequency power (nHF) increased in the right lateral decubitus position. The CD, LLE, ApEn and SampEn correlated positively to the nHF. The alpha exponent did not correlate to either linear measure or CD, but correlated negatively to LLE, ApEn and SampEn. Among the three recumbent positions, it was found that the right lateral decubitus position can increase the complexity of the human physiological system and the vagal modulation of the cardiac autonomic nervous system the most.

Algorithms↗

PubMed1999

A model for human skin impedance during surface functional neuromuscular stimulation.

A new mathematical model for the bulk electrical impedance of human skin is presented. In particular this model describes the impedance of skin during surface functional neuromuscular stimulation (FNS) with square stimulation pulses. Experimental data are presented that illustrate the nonlinear dynamic properties of human skin during current and voltage controlled stimulation. Model predictions are compared to experimental data, measured under both constant voltage and constant current transcutaneous stimulation. It is found that this model captures a variety of nonlinear time-varying effects observed in the skin impedance when stimulating with either protocol. This model may be used as part of large neuromusculoskeletal models or in the more accurate modeling of transcutaneous FNS, which is currently the most common clinical implementation of FNS.

Electric Impedance↗

PubMed1999

Finite strain elastodynamics of intracranial saccular aneurysms.

Various investigators suggest that intracranial saccular aneurysms are dynamically unstable, that they resonate in response to pulsatile blood flow. This hypothesis is based on linearized analyses or experiments on rubber "models", however, and there is a need for a more critical examination. Toward this end, we (a) derive a new nonlinear equation of motion for a pulsating spherical aneurysm that is surrounded by cerebral spinal fluid and whose behavior is described by a Fung-type pseudostrain-energy function that fits data on human lesions, and (b) use methods of nonlinear dynamics to examine the stability of such lesions against perturbations to both in vivo and in vitro conditions. The numerical results suggest that this sub-class of lesions is dynamically stable. Moreover, with the exception of transients associated with initial perturbations, inertial effects appear to be insignificant for fundamental forcing frequencies less than 10 Hz and hence for typical physiologic and laboratory conditions. We submit, therefore, that further study of the mechanics of saccular aneurysms should be focused on quasi-static stress analyses that investigate the roles of lesion geometry and material properties, including growth and remodeling.

Algorithms↗

PubMed2001

Decreased chaos and increased nonlinearity of heart rate time series in patients with panic disorder.

In this study, we investigated measures of nonlinear dynamics and chaos of heart rate time series in 30 normal control subjects and 36 age-matched patients with panic disorder in supine and standing postures. We obtained minimum embedding dimension (MED), largest Lyapunov exponent (LLE) and measures of nonlinearity (NL) of heart rate time series. MED quantifies system's complexity, LLE predictability and NL, deviation from linear processes. There was a significant increase in complexity (p < 0.00001), an increase in predictability (decreased chaos) (p < 0.00001) and an increase in nonlinearity (Snet GS) (p = 0.00001), especially in supine posture in patients with panic disorder. Increased NL score in supine posture may be due to a relative increase in cardiac sympathetic activity and an overall decrease in LLE may indicate an impaired cardiac autonomic flexibility in these patients due possibly to a decrease in cardiac vagal activity. These findings may further explain the reported higher incidence of cardiovascular mortality in patients with anxiety disorders.

Adult↗

PubMed2000

Determinants of ventilatory instability and variability.

This paper reviews the major mechanisms that can give rise to various forms of variability in the ventilatory pattern. First, an elevated controller gain, coupled with the presence of delays and response lags in the chemoreflex loops, can lead to instability in feedback control and give rise to periodic breathing. This form of ventilatory stability can be assessed quantitatively by employing the concept of 'loop gain'. Several different methods of estimating loop gain from steady state or dynamic respiratory measurements are discussed. An inherently stable respiratory control system can also exhibit periodic behavior due to the influence of primary fluctuations in sleep-wake state and other physiological variables, such as cardiac output and cerebral blood flow. Self-sustained, irregular ventilatory fluctuations may be generated by nonlinear dynamic interactions between various components of the respiratory control system, such as the lung vagal afferents and the respiratory pattern generator, or through the propagation of stochastic disturbances around the chemoreflex loops.

Algorithms↗

PubMed2005

Nonlinear multivariate analysis of neurophysiological signals.

Multivariate time series analysis is extensively used in neurophysiology with the aim of studying the relationship between simultaneously recorded signals. Recently, advances on information theory and nonlinear dynamical systems theory have allowed the study of various types of synchronization from time series. In this work, we first describe the multivariate linear methods most commonly used in neurophysiology and show that they can be extended to assess the existence of nonlinear interdependence between signals. We then review the concepts of entropy and mutual information followed by a detailed description of nonlinear methods based on the concepts of phase synchronization, generalized synchronization and event synchronization. In all cases, we show how to apply these methods to study different kinds of neurophysiological data. Finally, we illustrate the use of multivariate surrogate data test for the assessment of the strength (strong or weak) and the type (linear or nonlinear) of interdependence between neurophysiological signals.

Action Potentials↗

PubMed2003

Seizure prediction using scalp electroencephalogram.

Using a measure of nonlinear dynamical changes we term marginal predictability, we report evidence of robust changes in this parameter on scalp EEG in a cohort of patients with medically refractory mesiobasal temporal lobe epilepsy (MBTLE). In the baseline (interictal) state there are distinct differences in this nonlinear measure between epileptic and neurologically normal subjects. At baseline, in patients with MBTLE there are differences in these measures between electrodes adjacent to the ictal onset zone and more remotely placed electrodes. The character of these differences evolves over a period of approximately 30 min before a seizure. We discuss and integrate our findings with two emerging concepts in epileptology, first, the concept of a preictal or transition phase rather than an abrupt movement from interictal to ictal activity, and second, the notion of an epileptic neural network with changes in areas of brain remote from what has traditionally been considered the ictal onset zone influencing "ictogenesis."

Adolescent↗

PubMed1998

Dynamics of effortful touch and interlimb coordination.

In biological movement systems, the level of muscular-articular links is responsible for assembling highly reliable, stable, and reproducible coordination patterns involving very many joints and muscles. Research shows that the important perceptual capabilities of this level arise from the bulk sensitivity of muscles and tendons, so-called effortful or dynamic touch, to the quantities of rotational dynamics that remain invariant (such as the inertia tensor) over variations in rotational forces and motions. The power laws characterizing this sensitivity point to underlying fractal (self-similar) processes. Other research shows that the hallmark ability of this level to produce repetitive interlimb coordinations can be addressed through a dynamics of coordination in which equations express the time-evolution of collective neuromuscular states. This research also suggests that the assembled rhythms exploit the unique blend of stability and variability characteristic of low-dimensional chaotic motion on strange attractors. In overview, research into the capabilities of the level of muscular-articular links highlights the importance of applying classical and modern (nonlinear) dynamics to understanding the assembly and perceptual control of biological movements.

Extremities↗

PubMed2000

Nonlinear measures of heart rate time series: influence of posture and controlled breathing.

In this study, we investigated measures of nonlinear dynamics and chaos theory in regards to heart rate variability in 27 normal control subjects in supine and standing postures, and 14 subjects in spontaneous and controlled breathing conditions. We examined minimum embedding dimension (MED), largest Lyapunov exponent (LLE) and measures of nonlinearity (NL) of heart rate time series. MED quantifies the system's complexity, LLE predictability and NL, a measure of deviation from linear processes. There was a significant decrease in complexity (P < 0.00001), a decrease in predictability (P < 0.00001) and an increase in nonlinearity (P = 0.00001) during the change from supine to standing posture. Decrease in MED, and increases in NL score and LLE in standing posture appear to be partly due to an increase in sympathetic activity of the autonomous nervous system in standing posture. An improvement in predictability during controlled breathing appears to be due to the introduction of a periodic component.

Adult↗

PubMed2006

Dynamic modeling and torque estimation of FES-assisted arm-free standing for paraplegics.

This paper presents an application of recent findings in the field of redundant robotic systems' control, toward investigating the feasibility of functional electrical stimulation (FES) assisted arm-free standing for paraplegics. Twelve degrees-of-freedom (DOF) forward and inverse dynamic models of quiet standing have been developed. These models were used to investigate the minimum number of DOF that would need to be actuated in order to generate stable quiet standing in paraplegics despite internal and external disturbances. The results presented herein suggest that the proposed nonlinear dynamic model could achieve guaranteed asymptotic stability with only six active DOF, assuming that the remaining six DOF are passive, i.e., there is no active or passive torques applied to those DOF. The stability analyses were performed using a proportional and derivative (PD) controller coupled with gravity compensation. The results of this analysis suggest that if only six particular DOF are actively controlled in a paraplegic subject, this individual should be able to achieve stable quiet standing despite disturbances. This result has both clinical and system-design implications for the development of a device that will facilitate FES-assisted arm-free quiet standing. The clinical implication is, if a paraplegic patient can exert voluntary control over specified six DOF in the lower limbs, that patient, after intensive physiotherapy, will have the potential to perform quiet standing unassisted. The system-design implication is that FES-assisted arm-free standing for paraplegics is theoretically plausible if one would actively control only six out of 12 DOF in the lower limbs. The proposed solution does not require the locking of joints in the lower limbs (commonly applied in the field) or voluntary control of the upper body to compensate for the internal and external disturbances. Another important finding of this study is the existence of six different combinations of six active DOF able to facilitate stable quiet standing. This dynamic redundancy of the biological bipedal stance allows the selection of an ideal subset of six DOF in designing a neuroprosthesis for standing. This further implies that a considerably less complex FES system than previously anticipated needs to be developed for FES-assisted standing.

Algorithms↗

PubMed2005

Aging and nonlinear heart rate control in a healthy population.

In recent years more studies are using nonlinear dynamics to describe cardiovascular control. Because of the large dispersion of physiological data, it is important to have large studies with both male and female participants to establish a range of physiological healthy values. This study investigated the effect of gender and age on nonlinear indexes. Nonlinear scaling properties were studied by using 1/f slope (where f is frequency), fractal dimension, and detrended fluctuation analysis short- and long-term correlations (DFAalpha(1) and DFAalpha(2), respectively). Nonlinear complexity was described with correlation dimension (CD), Lyapunov exponent (LE), and approximate entropy (ApEn). The population consisted of 135 women and 141 men (age, 18-71 yr). Twenty-four hour ECG recordings were obtained by using Holter monitoring. The recordings were split into daytime (8 AM-9 PM) and nighttime (11 PM-6 AM). A day-night variation was present in all nonlinear heart rate variability (HRV) indexes, except for the CD in the female population. During the night the percentage of CD values of surrogate data files differing from the CD value of the original data increased. All nonlinear indexes were significantly correlated with age. Deeper analysis per age category of 10 yr showed a stabilization in the age decline of the fractal dimension and ApEn at the age of > or =40 yr. The vagal pathways seemed to be more involved in the generation of nonlinear fluctuations. Higher nonlinear behavior was evident during the night. No clear difference between men and women was found in the nonlinear indexes. Nonlinear indexes decline with age. This can be related to the concept of decreasing autonomic modulation with advancing age.

Adult↗

PubMed2006

Nonlinear modelling of double and triple period pitch breaks in vocal fold vibration.

This paper reports a study on short-time subharmonic pitch breaks in vocal fold vibration, which are found to be a common feature of the human voice in spoken language. The observed pitch breaks correspond to a change in periodicity of the electrolaryngograph (Lx) signal. This paper presents a nonlinear dynamical system capable of producing time-series with subharmonic pitch breaks. The resulting time-series resemble closely Lx recordings of natural speech. The system is developed on the basis of a second order linear system, which is extended with a third dimension and nonlinear coupling terms. It is suggested that improved knowledge about pitch breaks could be used in future speech synthesis systems in order to improve the naturalness of the perceived output.

Female↗

PubMed2005

[Nonlinear analysis of epileptic multichannel EEG].

OBJECTIVE: To study the difference between the nonlinear eigenvalue of epileptic patients and normal subjects for accurate identification of epileptic EEG signal. METHODS: Multivariable phase space reconstruction technique was employed to analyze the EEG of epileptic patients for estimating the correlation dimension(D(2)), which was one of the most often used parameters in quantitative discretion of complicated nonlinear dynamics system. RESULT AND CONCLUSION: The correlation dimension is an important eigenvalue for epileptic EEG identification.

Electroencephalography↗