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In regard to the controls and schizophrenia EEGs, we have got alpha rhythm from three points of view and verified the nonlinearity of the three kinds of rhythms. The results show that neither normal EEG alpha nor patients EEG alpha have the typical nonlinear characteristics. Therefore, we could not blindly use the theories of nonlinear dynamics to analyze the rhythm of brain wave.
In this work, recent advances in the field of nonlinear dynamics (NLD) were applied to fMRI data to examine the spatio-temporal properties of BOLD resting state fluctuations. Five human subjects were imaged during resting state (visual fixation) at 3T using single-shot gradient echo planar imaging (EPI). Respiration and cardiac signals were concurrently recorded for retrospectively removing fluctuations due to these physiologic activities. Patterns of singularity in the complex plane (PSC) and Lempel-Ziv complexity (LZ) were used to study the deterministic nonlinearity in resting state fMRI data. The results show that there is greater nonlinearity (higher PSC) and determinism (lower LZ) in gray matter compared to white matter and CSF. In addition, the removal of respiratory and cardiac pulsations decreases the nonlinearity and determinism but does not alter the relative difference between gray matter and white matter. Therefore, our results demonstrate that determinism and nonlinearity in the fMRI data are tissue-specific, suggesting that they reflect native physiologic and metabolic fluctuations and are not a result of physiologic artifacts due to respiration and cardiac pulsation.
PURPOSE OF REVIEW: The review considers problems in critical illness and critical care in the context of complex systems science. Normal physiology is characterized by nonlinear dynamics, and it appears that the pathophysiology of critical illness alters those dynamics. RECENT FINDINGS: Recent evidence confirms and extends the observation that the rich variability that characterizes normal physiology "decomplexifies" with critical illness. Experimental data in animals and now in humans suggests that physiologic support that mimics normal variability may reduce the severity and/or duration of the illness. SUMMARY: Physiologic dynamics in health and in critical illness appear to reflect complex, interconnected systems biology. Alterations in illness and during recovery may provide important clues to the underlying structure of the system. With knowledge of the structure, therapy could be better focused toward supporting both function and dynamics, offering hope for improved outcomes.
Our aim was to compare the results of the analysis of postprandial duodenojejunal motor patterns provided by a conventional computer-aided analysis with those provided by the new nonlinear mathematical method borrowed from 'chaos theory for determining how nonlinear analysis can improve fed motor pattern analysis and detect organization of postprandial contractions. Ten patients who had been explored for an idiopathic gastroparesis, and 20 healthy volunteers underwent duodenojejunal manometric recording for 3 h after a 750 kcal meal. Computer-aided analysis on each half-hour of the postprandial recording period calculated the number of waves (NW) and the area under the curve (AUC). Pressure signals were concurrently described by phase portraits obtained by plotting each pressure value at time t with the pressure value at time t + 1 s. The shape and amplitude of phase portraits were visually analysed and the relative area covered (RAC) by the phase portraits was calculated. With conventional analysis, NW and AUC were maximal during the first post-meal hour then decreased with time both in healthy volunteers and gastroparetic patients. With this analysis, the only difference between patients and controls was a lower NW (P < 0.02) in patients, observed only in the duodenum. Phase portraits analysis demonstrated lower RAC, a different distribution of RAC and more regular phase portraits in patients than in controls. Phase portraits outlined the heterogeneity of the patient group contrasting with the homogeneity of the control group when no subgroup was demonstrated by conventional analysis. We therefore conclude that the study of post prandial duodenojejunal motor behaviour could be improved by nonlinear dynamic analysis.
The electroencephalogram (EEG) is a multiscaled signal consisting of several time-series components each with different dominant frequency ranges and different origins. Nonlinear measures of the EEG reflect the complexity of the overall EEG, but not of each component in it. The aim of this study is to examine effect of the sound and light (SL) stimulation on the complexity of each component of the EEG. We used independent component analysis to obtain independent components of the EEG. The first positive Lyapunov exponent (L1) was estimated as a nonlinear measure of complexity. Twelve subjects were administered photic and auditory stimuli with a frequency of 10 Hz, which corresponded to the alpha frequency of the EEG, by a sound and light entrainment device. We compared the L1 values of the EEGs and their independent components between baseline and after the SL stimulation. We detected that the L1 values of the EEG decreased after the SL stimulation in all channels except C3 and F4, indicating that the complexity of the EEG decreased. We showed that alpha components increased in proportion but decreased in complexity after the SL stimulation. The beta independent components were found to decrease in proportion and complexity. These results suggest that decreased complexity of the EEG after the SL stimulation may be principally caused by decreased complexity and increased proportion of the alpha independent components. We showed also that theta components increased in complexity after the SL stimulation. We propose that nonlinear dynamical analysis combined with independent component analysis may be helpful in understanding the temporal characteristics of the EEG, which cannot be detected by conventional linear or nonlinear methods.
The electroencephalogram, as a probe of scalp-recorded electrical activity arising from the human cortex, provides useful information because of its temporal and spatial organization. Recent developments in nonlinear dynamics suggest that an object can be constructed in an n-dimensional space out of a temporal sequence of data such as an EEG signal and that its organization is characterized by the dimensionality of the object (in this case, human brain activity). We have carried out an analysis of a set of alpha coma EEG patterns in comparison to the awake alpha EEG patterns of normal volunteers and patients. Alpha coma recorded from a single channel is visually indistinguishable from normal resting alpha due to its similar frequency spectrum (a broad-band spectrum with 1/f characteristics). Our results show that alpha coma dimensionality, however, differs from that of normal alpha in that it has a greater variability over different temporal segments of EEG. Single channel recordings in 7 patients with alpha coma were differentiable from those of 10 subjects with "normal" EEGs. Through dynamic analysis of the EEG, novel methods of signal extraction from EEG may become evident and applicable to clinical practice.
Recent research suggests that traditional biomechanical models of postural stability do not fully characterise the nonlinear properties of postural control. In sports medicine, this limitation is manifest in the postural steadiness assessment approach, which may not be sufficient for detecting the presence of subtle physiological change after injury. The limitation is especially relevant given that return-to-play decisions are being made based on assessment results. This update first reviews the theoretical foundation and limitations of the traditional postural stability paradigm. It then offers, using the clinical example of athletes recovering from cerebral concussion, an alternative theoretical proposition for measuring changes in postural control by applying a nonlinear dynamic measure known as 'approximate entropy'. Approximate entropy shows promise as a valuable means of detecting previously unrecognised, subtle physiological changes after concussion. It is recommended as an important supplemental assessment tool for determining an athlete's readiness to resume competitive activity.
Several metrics from nonlinear dynamics and statistical mechanics have been characterized on computer-generated number series with various signal-to-noise ratios, demonstrating their individual reliability as a function of sample size and their relationships to each other. The root mean square (RMS) evaluates amplitude, and the power spectral density (PSD) provides a visual display of the frequency spectrum; both measures have very high reliability even for an N as low as 50. The Fractal Dimension (D) is shown to converge rapidly and also to be reliable when N is as low as 50. These three measures (RMS, PSD, and D) have been applied to the complex kinetics of tyrosine hydroxylase time courses (50-point curves) at various BH4 concentrations (near physiological, but far from equilibrium levels). Recently developed measures of spectral entropy and the Liapunov Exponent, -lambda are also characterized.
We study optical control of the nonlinear dynamics generated by an ordinary polarized light at a small angle of incidence in a nematic liquid crystal film. Recent experiments have demonstrated the possibility of modifying the molecular reorientation dynamics by the addition of a weak incoherent beam orthogonally polarized to the pump beam. We present a theoretical model for the director dynamics and we demonstrate the possibility to tune the complexity of the dynamics (optical tuning) using the weak beam intensity as a control parameter. The generation of new dynamical regimes, not observed in the single beam geometry, is also predicted. Finally, interpretation of optical tuning effects is discussed on the basis of an effective model.
The nonlinear dynamics of an inviscid magnetohydrodynamic system in a low-beta plasma is investigated through a simplified model obtained by a Galerkin projection. We show that a single Fourier mode dominates over the whole energy spectrum, a self-organization mechanism of turbulence being responsible for this nonlinear effect. Our results are in agreement with observations of an analogous phenomenon, say, the emergence of a quasi-single-helicity state both in numerical simulations and real experiments in reversed field pinch laboratory plasmas.
Intracranial saccular aneurysms have been clinically observed to emit a transient sound, a bruit, on each heartbeat. The mechanism causing the bruits has been a matter of contention. A qualitative analysis of the nonlinear dynamical properties of the Shah-Humphrey model for periodic pressure forcing of a thin-necked saccular aneurysm, using the Fung nonlinear constitutive model for the aneurysm material, shows that a small blood pressure jump on each beat, whether the pressure is weakly aperiodic or periodic, induces transients in the radial deformation response of the aneurysmal wall on each heartbeat. These transient vibrations, which have a component with frequency near the natural frequency of the system but are not resonant phenomena and which decay rapidly to a limit cycle during each distinct forcing pressure cycle, can generate the bruits.
The nonlinear mechanical dynamics of glycerinated insect fibrillar flight muscle are investigated. The most striking nonlinearity reported previously, which often resulted in oscillatory work being limited to frequencies below those of natural flight, disappears if 5 mM or more orthophosphate is added to the experimental solutions. We show that two further asymmetric nonlinearities, which remain even though phosphate is present, are predicted by cross-bridge theory if one takes account of the expected distortion of attached cross-bridges as filament sliding becomes appreciable. Adenosine triphosphate and adenosine diphosphate have opponent effects upon the mechanical rate constants, suggesting a scheme for the sequential ordering of the events comprising the cross-bridge cycle.
With Bayesian modeling and adaptive control of drug dosage regimens, serum and peripheral drug concentrations can be predicted in clinical situations using linear pharmacokinetic compartmental models (PK). Recently, several pathophysiologic and pharmacodynamic nonlinear models (PD) have been developed. The present report illustrates both their utility and limits for the computation of effects in clinical situations in the setting of actual routine and acute patient care. Patients who received therapy with aminoglycosides or/and vancomycin were selected. For each patient, after estimation of individual pharmacokinetic parameters, the computed outputs of the linear compartmental pharmacokinetic model were used as inputs for 2 different a priori nonlinear dynamic models: 1) the EFFECT modeling program, using a Hill model, and 2) the BACTCIDE program, which is a combination of a simple growth model for the organism and a Hill effect model considering both the microorganism, the antibiotic, and the patient's minimal inhibitory concentration (MIC). The programs (1) and (2) can use as inputs the computed concentrations from any of three compartments: central, peripheral, or a spherical diffusion compartment to compute drug diffusion into endocardial vegetations or abscesses. The EFFECT program can be used alone for the evaluation of drug effects. The BACTCIDE program illustrates differences in activity between concentration-dependent and time-dependent antibiotics. Such nonlinear programs are very sensitive to the MIC values.
The 1992 magnitude 7.3 Landers earthquake triggered an exceptional number of additional earthquakes within California and as far north as Yellowstone and Montana. Since this observation, other large earthquakes have been shown to induce dynamic triggering at remote distances--for example, after the 1999 magnitude 7.1 Hector Mine and the 2002 magnitude 7.9 Denali earthquakes--and in the near-field as aftershocks. The physical origin of dynamic triggering, however, remains one of the least understood aspects of earthquake nucleation. The dynamic strain amplitudes from a large earthquake are exceedingly small once the waves have propagated more than several fault radii. For example, a strain wave amplitude of 10(-6) and wavelength 1 m corresponds to a displacement amplitude of about 10(-7) m. Here we show that the dynamic, elastic-nonlinear behaviour of fault gouge perturbed by a seismic wave may trigger earthquakes, even with such small strains. We base our hypothesis on recent laboratory dynamic experiments conducted in granular media, a fault gouge surrogate. From these we infer that, if the fault is weak, seismic waves cause the fault core modulus to decrease abruptly and weaken further. If the fault is already near failure, this process could therefore induce fault slip.
Fly photoreceptor cells were stimulated with steps of light over a wide intensity range. First- and second-order Volterra kernels were then computed from sequences of combined step responses. Diagonal values of the second-order Volterra kernels were much greater than the off-diagonal values, and the diagonal values were roughly proportional to the corresponding first-order kernels, suggesting that the response could be approximated by a static nonlinearity followed by a dynamic linear component (Hammerstein model). The amplitudes of the second-order kernels were much smaller in light-adapted than in dark-adapted photoreceptors. Hammerstein models constructed from the step input/output measurements gave reasonable approximations to the actual photoreceptor responses, with light-adapted responses being relatively better fitted. However, Hammerstein models could not account for several features of the photoreceptor behavior, including the dependence of the step response shape on step amplitude. A model containing an additional static nonlinearity after the dynamic linear component gave significantly better fits to the data. These results indicate that blowfly photoreceptors have a strong early gain control nonlinearity acting before the processes that create the characteristic time course of the response, in addition to the nonlinearities caused by membrane conductances.
We study the initial instability of flat sand surface and further nonlinear dynamics of wind ripples. The proposed continuous model of ripple formation allowed us to simulate the development of a typical asymmetric ripple shape and the evolution of a sand ripple pattern. We suggest that this evolution occurs via ripple merger preceded by several soliton-like interaction of ripples.
A comprehensive set of results from 2-click suppression experiments on otoacoustic emissions (OAEs) have been presented by Kapadia and Lutman [Kapadia, S., Lutman, M.E., 2000a. Nonlinear temporal interactions in click-evoked otoacoustic emissions. I. Assumed model and polarity-symmetry. Hear. Res. 146, 89-100]. They found that the degree of suppression of an OAE evoked by a test click varied systematically with the timing and the level of a suppressor click, being greatest for suppressor clicks occurring some time before the test click, particularly at lower levels of suppression. Kapadia and Lutman also showed that although the general shape of the graph of suppression against suppressor click timing could be predicted by a static power law model, this did not predict the asymmetry with respect to the timing of the suppressor click. A generalised automatic gain control (AGC) is presented as a simple example of a dynamic nonlinear system. Its steady state nonlinear behaviour, as quantified by its level curve, and its dynamic behaviour, as quantified by its transient response, can be independently set by the feedback gain law and detector time constant, respectively. The previously reported suppression results, with the asymmetry in the timing, are found to be predicted better by such an AGC having a level curve with a slope of about 0.5 dB/dB, and a detector time constant of about twice the period at the characteristic frequency. Although this gives adequate predictions for high suppression levels, it under predicts the suppression and the asymmetry for lower levels. Further research is required to establish whether simple peripheral feedback models can explain OAE suppression of this type.
The nonlinear dynamical response of classical spins governed by the stochastic Landau-Lifshitz equation is found to be large and very sensitive to the damping in the medium-to-weak damping regime. This result is interpreted in terms of a cooperation, induced by the driving field, between the precession of the spin and its thermoactivation over the potential barrier. The large damping dependence (absent in the linear response) can be used to determine the evasive damping coefficient in superparamagnets, so clarifying the nature of the spin-environment interaction in these systems.