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Results for “nonlinear analyses”

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At least 19 recordsLinked to original sources

PubMed2005

Nonlinear analyses of heart rate variability in normal and growth-restricted fetuses.

BACKGROUND: Many studies on the physiology of the cardiovascular system reported that nonlinear chaotic dynamics may govern the generation of the heart rate signal. OBJECTIVE: To examine whether the heart rate dynamics of an intrauterine growth restricted (IUGR) fetus is different from a healthy normal fetus by nonlinear methods of time series analysis. DESIGN OF THE STUDY: One hundred nineteen fetal heart rate (FHR) recordings from healthy normal fetuses, and 69 recordings from IUGR fetuses were analyzed. Nonlinear analyses included attractor reconstruction, calculation of the largest Lyapunov exponents using the Wolf algorithm, and estimation of correlation dimension. The largest Lyapunov exponents from normal fetuses were checked by means of surrogate-data test. RESULTS: Abnormal FHR patterns of IUGR fetuses such as decreased variability and repetitive late decelerations presented a remarkably different structure in the reconstructed attractor. Surrogate data suggest that the FHR of healthy normal fetuses has unique nonlinear characteristics. The largest Lyapunov exponents were positive for all of 119 healthy normal fetuses, indicating that the FHR control system is sensitive to initial conditions. The values of IUGR fetuses were significantly lower than those of normal subjects. In normal fetuses, significant changes of correlation dimension according to gestational age were observed. In IUGR fetuses, however, such changes were not found. CONCLUSIONS: The heart rate dynamics of IUGR fetuses is less chaotic than that of normal fetuses. Decreased system complexity suggested by correlation dimension may limit the IUGR fetuses' ability to maintain cardiovascular integrity, and therefore, to adapt to the variety of internal and external cardiovascular stresses.

Female↗

PubMed1998

The spike trains of inhibited pacemaker neurons seen through the magnifying glass of nonlinear analyses.

This communication describes the new information that may be obtained by applying nonlinear analytical techniques to neurobiological time-series. Specifically, we consider the sequence of interspike intervals Ti (the "timing") of trains recorded from synaptically inhibited crayfish pacemaker neurons. As reported earlier, different postsynaptic spike train forms (sets of timings with shared properties) are generated by varying the average rate and/or pattern (implying interval dispersions and sequences) of presynaptic spike trains. When the presynaptic train is Poisson (independent exponentially distributed intervals), the form is "Poisson-driven" (unperturbed and lengthened intervals succeed each other irregularly). When presynaptic trains are pacemaker (intervals practically equal), forms are either "p:q locked" (intervals repeat periodically), "intermittent" (mostly almost locked but disrupted irregularly), "phase walk throughs" (intermittencies with briefer regular portions), or "messy" (difficult to predict or describe succinctly). Messy trains are either "erratic" (some intervals natural and others lengthened irregularly) or "stammerings" (intervals are integral multiples of presynaptic intervals). The individual spike train forms were analysed using attractor reconstruction methods based on the lagged coordinates provided by successive intervals from the time-series Ti. Numerous models were evaluated in terms of their predictive performance by a trial-and-error procedure: the most successful model was taken as best reflecting the true nature of the system's attractor. Each form was characterized in terms of its dimensionality, nonlinearity and predictability. (1) The dimensionality of the underlying dynamical attractor was estimated by the minimum number of variables (coordinates Ti) required to model acceptably the system's dynamics, i.e. by the system's degrees of freedom. Each model tested was based on a different number of Ti; the smallest number whose predictions were judged successful provided the best integer approximation of the attractor's true dimension (not necessarily an integer). Dimensionalities from three to five provided acceptable fits. (2) The degree of nonlinearity was estimated by: (i) comparing the correlations between experimental results and data from linear and nonlinear models, and (ii) tuning model nonlinearity via a distance-weighting function and identifying the either local or global neighborhood size. Lockings were compatible with linear models and stammerings were marginal; nonlinear models were best for Poisson-driven, intermittent and erratic forms. (3) Finally, prediction accuracy was plotted against increasingly long sequences of intervals forecast: the accuracies for Poisson-driven, locked and stammering forms were invariant, revealing irregularities due to uncorrelated noise, but those of intermittent and messy erratic forms decayed rapidly, indicating an underlying deterministic process. The excellent reconstructions possible for messy erratic and for some intermittent forms are especially significant because of their relatively low dimensionality (around 4), high degree of nonlinearity and prediction decay with time. This is characteristic of chaotic systems, and provides evidence that nonlinear couplings between relatively few variables are the major source of the apparent complexity seen in these cases. This demonstration of different dimensions, degrees of nonlinearity and predictabilities provides rigorous support for the categorization of different synaptically driven discharge forms proposed earlier on the basis of more heuristic criteria. This has significant implications. (1) It demonstrates that heterogeneous postsynaptic forms can indeed be induced by manipulating a few presynaptic variables. (2) Each presynaptic timing induces a form with characteristic dimensionality, thus breaking up the preparation into subsystems such that the physical variables in each operate as one

Action Potentials↗

PubMed2005

Sometimes higher heart rate variability is not better heart rate variability: results of graphical and nonlinear analyses.

OBJECTIVE: To determine the prevalence and effect on traditional heart rate variability (HRV) indices of abnormal HRV patterns in the elderly. METHODS: Hourly Poincaré plots and plots of spectral HRV from normal-to-normal interbeat intervals and hourly nonlinear HRV values were examined in a subset of 290 consecutive participants in the Cardiovascular Health Study. Only subjects in normal sinus rhythm with > or = 18 hours of usable data were included. Eligible subjects were 71 +/- 5 years. During 7 years of follow-up, 21.7% had died. Hours were scored as normal (0), borderline (0.5), or abnormal (1) from a combination of plot appearance and HRV. Summed scores were normalized to 100% to create an abnormality score (ABN). Short-term HRV versus each 5th percentile of ABN was plotted and a cutpoint for markedly increased HRV identified. The t-tests compared HRV for subjects above and below this cutpoint. Cox regression evaluated the association of ABN and mortality. RESULTS: Of 5,815 eligible hourly plots, 64.4% were normal, 14.5% borderline, and 21.1% abnormal. HR, SDNN, SDNNIDX, ln VLF and LF power, and power law slope did not differ by the cutpoint for increased short-term HRV, while SDANN and ln ULF power were significantly lower for those above the cutpoint. However, many HRV indices including LF/HF ratio and normalized LF and HF power were significantly different between groups (P < 0.001). Increased ABN was significantly associated with mortality (P = 0.019). Despite similar values for many HRV indices, being in the group above the cutpoint was significantly associated with mortality (P = 0.04). CONCLUSIONS: Abnormal HR patterns that elevate many HRV indices are prevalent among the elderly and associated with higher risk of mortality. Consideration of abnormal HRV may improve HRV-based risk stratification.

Aged↗

PubMed2003

Linear and nonlinear analyses of pulsatile blood flow in a cylindrical tube.

A non-Newtonian shear-thinning constitutive relation is proposed to study pulsatile flow of whole blood in a cylindrical tube. The constitutive relation, which satisfies the principle of material frame indifference, is derived from viscometric data obtained from whole blood over a range of hematocrits. Assuming axisymmetric flow in a rigid cylindrical tube of constant diameter, a second-order, nonlinear partial differential equation governing the axial velocity component is obtained. Imposing a periodic pressure gradient, the governing equation was solved numerically using finite difference methods over a range of Stokes values and hematocrits. For a forcing frequency of 1 Hz, results are presented over tube diameters ranging between 0.1 and 2 cm and over hematocrits ranging between 10 and 80%. For a given hematocrit, velocity profiles predicted for the non-Newtonian model under sinusoidal forcing reveal attenuated volume flow rate and enhanced vorticity transport over the tube cross-section relative to a Newtonian fluid having a viscosity corresponding to the high shear-rate limit. For moderate to high Stokes numbers, consistent with flow in large arteries, our results revealed a viscosity distribution that was nearly time invariant. An analytic solution was obtained for a fluid having arbitrarily prescribed radially varying, temporally invariant viscosity and density distributions under arbitrary periodic pressure forcing. Close agreement was observed between our numerical and analytical results when the imposed viscosity distribution was chosen to approximate the time-averaged viscosity distribution predicted by the shear-thinning non-Newtonian model. For St > or approximately= 100, the disparity between our results and those of a Newtonian fluid of constant viscosity grows with a decreasing ratio of the DC to AC components of the pressure-gradient amplitude below 50%. In particular, for any purely oscillatory pressure-gradient (vanishing DC component), the Womersley solution is a particularly poor predictor of the amplitude and phase of wall shear rate for over half of the flow cycle. Under such circumstances, the analytical models presented here provide a simple and accurate means of estimating instantaneous wall shear rate, knowing only the pressure gradient and hematocrit.

Blood Flow Velocity↗

PubMed1998

Should we adjust for covariates in nonlinear regression analyses of randomized trials?

The analyses of the primary objectives of randomized clinical trials often are not adjusted for covariates, except possibly for stratification variables. For analyses with linear models, adjustment is a precision issue only. We review the literature regarding logistic and Cox (proportional hazards) regression models. For these nonlinear analyses, omitting covariates from the analysis of randomized trials leads to a loss of efficiency as well as a change in the treatment effect being estimated. We recommend that the primary analyses adjust for important prognostic covariates in order to come as close as possible to the clinically most relevant subject-specific measure of treatment effect. Additional benefits would be an increase in efficiency of tests for no treatment effect and improved external validity. The latter is particularly relevant to meta-analyses.

Bias↗

PubMedDate not supplied

Geometrical nonlinear stability analyses of cable-truss domes.

The nonlinear finite element method is used to analyze the geometrical nonlinear stability of cable-truss domes with different cable distributions. The results indicate that the critical load increases evidently when cables, especially diagonal cables, are distributed in the structure. The critical loads of the structure at different rise-span ratios are also discussed in this paper. It was shown that the effect of the tensional cable is more evident at small rise-span ratio. The buckling of the structure is characterized by a global collapse at small rise-span ratio; that the torsional buckling of the radial truss occurs at big rise-span ratio; and that at proper rise-span ratio, the global collapse and the lateral buckling of the truss occur nearly simultaneously.

Computer Simulation↗

PubMed2005

Perturbation and nonlinear dynamic analyses of voices from patients with unilateral laryngeal paralysis.

This study used perturbation methods (eg, jitter and shimmer) and nonlinear dynamic methods (eg, phase space reconstruction and correlation dimension) to analyze sustained voices generated by normal subjects and patients with unilateral laryngeal paralysis. We found that normal and pathological voices had low-dimensional dynamic characteristics. For nearly periodic voices, jitter and shimmer values of pathological voices from patients with unilateral laryngeal paralysis were significantly different from normal voices. For nearly periodic and aperiodic voices, the correlation dimensions of pathological voices were statistically higher than normal voices. Receiver operating characteristic analysis was used to evaluate the diagnostic performances of jitter, shimmer, and correlation dimension. High sensitivity and specificity of these three acoustic analyses in distinguishing unilateral laryngeal paralysis patients from normal subjects were found. We concluded that combining traditional perturbation analysis and nonlinear dynamic analysis might provide efficient descriptions of pathological voices and represent a valuable tool for clinical diagnosis of laryngeal paralysis.

Adolescent↗

PubMed1979

Multiple linear and nonlinear regression analyses of factors causing calving difficulty.

Calving difficulty (CD) was analyzed as the dependent variable from observations on 592 first-calf, 2-year-old heifers that were either Angus X Hereford (AH), Charolais X AH or Simmental X AH. Independent variables were birth weight (BW), pelvic area (PA), BW.(33), PA.(5), cow weight (CW), cow condition score (CS) and sex of calf (S). CD was analyzed as score (1 = no difficulty through 4 = extreme difficulty) CD-I, % CD (1 vs 2 + 3 + 4 , CD-II) or % high CD (1 + 2 vs 3 + 4 , CD-III). R(2) values from CD-II and CD-III multiple correlation (R) analyses were consistently lower (.10 to .13) than from the CD-I analysis. When only BW and PA were included in the model, R(2) values for CD-I were .36, .39 and .39 for the linear, quadratic and cubic analyses, respectively. When BW, PA, CW, CS and S were included in the model, the R(2) values for CD-I were .40 and .42 for the linear and quadratic analyses (cubic effects were not tested). In the linear analysis with BW.(33) and PA.(5), the R(2) for CD-I was .36. In all analyses, the order of importance of the factors studied was BW and PA, with a much lower contribution from CW and S. CS did not account for a significant increase in R(2) in any analysis. CD remained below 50% whenever the PA BW ratio exceeded 8.4. This ratio is a convenient practical method to relate PA and BW to CD. Conclusions are that the linear effects of BW and PA account for the majority of the identified variation in CD (R(2)) and that small increases in R(2) can be obtained by adding CW, CS and S to the model and/or by expanding the model to include quadratic effects.

Journal Article↗

PubMed1993

Cross-correlation analyses of nonlinear systems with spatiotemporal inputs.

Methods are presented for analyzing the low-order stimulus-response cross-correlation functions (or kernels) of visual neurons studied with spatiotemporal white noise. In particular, formulas are derived that relate the low-order kernels of a cell to its responses to single-drifting, double-drifting, and counterphase gratings. The harmonic response terms contributed by the low-order kernels include a mean response term, first- and second-harmonic terms, and sum- and difference-harmonic terms. Using the formulas in this paper, one can obtain kernel-based predictions for the spatiotemporal-frequency tuning of each harmonic. These kernel-based predictions can then be compared with harmonic tuning data obtained in experiments with real grating stimuli. The methods are illustrated using data recorded from one simple and one complex cell from the primary visual cortex of the monkey. The approach of transforming low-order kernels into predicted harmonic tuning functions provides a useful data reduction technique as well as providing insight into the interpretation of kernels.

Animals↗

PubMed2003

Signal nonlinearity in fMRI: a comparison between BOLD and MION.

In this paper, we introduce a methodology for comparing the nonlinearities present in sets of time series using four different nonlinearity measures, one of which, the "delay vector variance" method, is a novel approach to the characterization of a time series. It is then applied to examine the difference in nonlinearity between functional magnetic resonance imaging (fMRI) signals that have been recorded using different contrast agents. Recently, an exogenous contrast agent, monocrystalline iron oxide particle (MION), has been introduced for fMRI, which has been shown to increase the functional sensitivity compared with the traditional blood oxygen level dependent (BOLD) technique. The resulting fMRI signals are influenced by cerebral blood volume, whereas the more traditionally recorded BOLD signals are influenced not only by cerebral blood volume, but also by the cerebral blood flow and the metabolic rate of oxygen. The proposed methodology is applied to address the question whether this difference in the number of physiological variables is reflected in a difference in the degree of nonlinearity. We therefore analyze two sets of fMRI signals, one from a BOLD and the other from a MION monkey study with similar experimental designs. In the neuroimaging context, the proposed nonlinearity analyses are different from those described in the literature, since no a priori model is assumed: rather than pinpointing the source(s) of nonlinearity, nonparametric analyses are performed on BOLD and MION fMRI signals. Furthermore, we introduce a strategy for analyzing a population of fMRI signals, rather than focusing the analysis on one signal, as is traditionally done in the domain of nonlinear signal processing. Our results show that, overall, the BOLD signals are more nonlinear in nature than the MION ones, which is in agreement with current hypotheses.

Animals↗

PubMed2006

Linear and nonlinear methods for analyses of cardiovascular variability in bipolar disorders.

OBJECTIVES: Heart rate variability (HRV), blood pressure variability (BPV), and the assessment of baroreflex sensitivity are widely accepted methods for analyzing and characterizing cardiovascular regulation and for an enhanced risk evaluation in different diseases. As a result of the complexity of the investigated regulatory systems, univariate analyses do not often provide a convenient description of pathological changes in the cardiovascular regulation. Therefore, the application of a multivariate approach is preferable. METHODS: We present principal methods of time-domain, frequency-domain, and nonlinear analyses of HRV, BPV as well as methods for coupling and interaction analyses. RESULTS: Changes in autonomic nervous system (ANS) tone are known to accompany various mental disorders. Depressive patients frequently complain of symptoms of ANS dysfunction, such as dry mouth, diarrhea, and insomnia. These clinical observations propose the assumption of altered autonomic dysfunction in these patients. In contrast to these clinical assumptions, inconsistent results have been found in studies of HRV in depressive patients. This work therefore covers a brief review of the literature in respect to bipolar disorder and the rationale to study autonomic changes in such a psychiatric disease. CONCLUSIONS: Prospective studies of cardiovascular changes in mania and depression are needed to evaluate a psychopathological state in connection with cardiovascular changes and cardiac morbidity and mortality. These studies should consider BPV, coupling and interaction analyses, the application of nonlinear methods, and a multivariate approach in addition to the traditional analysis of HRV.

Autonomic Nervous System↗

PubMed1995

Nonlinear regression using spreadsheets.

Pharmacologists are often required to analyse nonlinear experimental effects by fitting the data to defined theoretical models. This may require a specialized computer program capable of performing nonlinear regression analysis, which can prove costly given the variety of pharmacological research. Here, Wayne Bowen and Jeff Jerman describe a generic method of performing nonlinear regression using spreadsheet applications, and demonstrate how this approach can be used to create automated systems of data analysis.

Algorithms↗

PubMed2001

Nonlinear dynamic analysis of the EEG in patients with Alzheimer's disease and vascular dementia.

To assess nonlinear EEG activity in patients with Alzheimer's disease (AD) and vascular dementia (VaD), the authors estimated the correlation dimension (D2) and the first positive Lyapunov exponent (L1) of the EEGs in both patients and age-matched healthy control subjects. EEGs were recorded in 15 electrodes from 12 AD patients, 12 VaD patients, and 14 healthy subjects. The AD patients had significantly lower D2 values than the normal control subjects, (P < H > 0.05), except at the F7 and the O1 electrodes, and the VaD patients, except at the C3 and the C4 electrodes. The VaD patients had relatively increased values of D2 and L1 compared with the AD patients, and rather higher values of D2 than the normal control subjects at the F7, F4, F8, Fp2, O1, and O2 electrodes. The L1 values of the EEGs were also lower for the AD patients than for the normal control subjects, except in the O1 and the O2 channels, and for the VaD patients at all electrodes. The L1 values were higher for the VaD patients than for the normal control subjects (F3, F4, F8, O1, and O2). In addition, the authors detected that the VaD patients had an uneven distribution of D2 values over the regions than the AD patients and the normal control subjects, although the statistics do not confirm this. By contrast, AD patients had uniformly lower D2 values in most regions, indicating that AD patients have less complex temporal characteristics of the EEG in entire regions. These nonlinear analyses of the EEG may be helpful in understanding the nonlinear EEG activity in AD and VaD.

Aged↗

PubMed2004

Decreased nonlinear complexity and chaos during sleep in first episode schizophrenia: a preliminary report.

Schizophrenia is characterized by disturbed sleep architecture. It has been thought that sleep abnormalities may underlie information processing deficits associated with this disorder. Nonlinear analyses of sleep data can provide valuable information on sleep characteristics that may be relevant to the functions of sleep. This study examined the predictability and nonlinear complexity of sleep EEG time series in two EEG channels (C4 and F4) using measures of nonlinearity, such as symbolic dynamics and the largest Lyapunov exponent (LLE) in schizophrenia. A series of antipsychotic naive patients with first episode of schizophrenia or schizoaffective disorder and age-matched healthy controls were studied during awake period, stage 1/2, slow wave sleep (stage 3/4) and rapid eye movement (REM) sleep. Nonlinearity scores were significantly lower during awake stage in patients compared to controls suggesting that there may be a diminished interplay between various parameters for the genesis of waking EEG. Symbolic dynamics and LLE were significantly lower in patients during REM compared to healthy controls, suggesting decreased nonlinear complexity of the EEG time series and diminished chaos in schizophrenia. Decreased nonlinear complexity was also correlated with neurocognitive deficits as assessed by the Wisconsin card sorting test. Diminished complexity of EEG time series during awake and REM sleep in patients with schizophrenia may underlie the impaired ability to process information in psychotic disorders such as schizophrenia.

Adult↗

PubMed1996

Nonlinear control of heart rate variability in human infants.

Nonlinear analyses of infant heart rhythms reveal a marked rise in the complexity of the electrocardiogram with maturation. We find that normal mature infants (gestation greater than or equal to 35 weeks) have complex and distinctly nonlinear heart rhythms (consistent with recent reports for healthy adults) but that such nonlinearity is lacking in preterm infants (gestation > or = to 27 weeks) where parasympathetic-sympathetic interaction and function are presumed to be less well developed. Our study further shows that infants with clinical brain death and those treated with atropine exhibit a similar lack of nonlinear feedback control. These three lines of evidence support the hypothesis championed by Goldberger et al. [Goldberger, A.L., Rigney, D.R. & West, B.J. (1990) Sci. Am. 262, 43-49] that autonomic nervous system control underlies the nonlinearity and possible chaos of normal heart rhythms. This report demonstrates the acquisition of nonlinear heart rate dynamics and possible chaos in developing human infants and its loss in brain death and with the administration of atropine. It parallels earlier work documenting changes in the variability of heart rhythms in each of these cases and suggests that nonlinearity may provide additional power in characterizing physiological states.

Atropine↗

PubMed2001

Analysis of sensory coding with complex stimuli.

Most high-level sensory neurons have complex, nonlinear response properties; a comprehensive characterization of these properties remains a formidable challenge. Recent studies using complex sensory stimuli combined with linear and nonlinear analyses have provided new insights into the neuronal response properties in various sensory circuits.

Acoustic Stimulation↗

PubMed2000

Detecting nonlinearity in psychological data: techniques and applications.

Modern graphical and computational techniques for detecting nonlinearity in psychological data sets are presented. These procedures allow researchers to determine the information complexity of temporal data, using physiological and psychological measurements, and to provide evidence for chaos in time series contaminated by measurement noise. Problems with noise reduction and appropriate experimental control, using surrogate time series, are discussed, and applications of the technology are illustrated, using response time, handwriting, and typing data sets. In an experimental application of appropriate nonlinear analysis procedures, the results of a time series prediction experiment confirm that some subjects are sensitive to chaos. In contrast to previous attempts demonstrating sensitivity to chaos, the experiment reported here employs surrogate series to control for linear stochastic aspects of the stimulus sequences, such as autocorrelation. Recommendations for the selection of appropriate software for performing nonlinear analyses are presented, including a comprehensive list of World-Wide Web sites offering such software.

Behavioral Sciences↗

PubMed2005

Morphology changes in the evolution of liquid two-layer films.

We consider a thin film consisting of two layers of immiscible liquids on a solid horizontal (heated) substrate. Both the free liquid-liquid and the liquid-gas interface of such a bilayer liquid film may be unstable due to effective molecular interactions relevant for ultrathin layers below 100-nm thickness, or due to temperature-gradient-caused Marangoni flows in the heated case. Using a long-wave approximation, we derive coupled evolution equations for the interface profiles for the general nonisothermal situation allowing for slip at the substrate. Linear and nonlinear analyses of the short- and long-time film evolution are performed for isothermal ultrathin layers, taking into account destabilizing long-range and stabilizing short-range molecular interactions. It is shown that the initial instability can be of a varicose, zigzag, or mixed type. However, in the nonlinear stage of the evolution the mode type, and therefore the pattern morphology, can change via switching between two different branches of stationary solutions or via coarsening along a single branch.

Journal Article↗