Posture as a chaotic system and an application to the Parkinson’s disease (original) (raw)
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Considerations on the application of the chaos paradigm to describe the postural sway
Chaos, Solitons & Fractals, 2006
Time-series of statokinesigram (SKG) of healthy subjects and parkinsonians are investigated and compared. This is done by employing the chaos paradigm in order to obtain the main characteristics of the SKG. The interpretation of our findings is twofold: when a proper Theiler window is not used we find a virtual invariance of the chaos parameters when healthy subjects and parkinsonians are compared but a discrepancy of our values (correlation dimension equals to 1.4) with those found in previous works; when a proper Theiler window is used (more) appropriately, the SKGs do not show a convergence of the fractal dimension estimates; therefore nothing can be said in terms of chaoticity of system.
Investigation of brain dynamics in Parkinson's disease by methods derived from nonlinear dynamics
Experimental Brain Research, 2001
EEGs were recorded from patients in early stages of Parkinson's disease (17 patients, 9 females) and healthy controls (12 subjects, 8 females) during rest and during execution/imagining of a complex motor task. The prediction that Parkinson's disease patients compared to controls would show more complex brain dynamics during performance of a complex motor task and imagination of the movements was confirmed by methods derived from nonlinear dynamics. In the resting state, analysis of correlation dimension of EEG time series revealed only slight topographical differences between the groups. During performance of a complex motor task, however, data from Parkinson's disease patients showed higher dimensionality than data from controls, indicating more complex EEG time series. The same difference was found when subjects did not perform any motor movements but imagined the complex movements they had just performed. The data are consistent with the hypothesis that the disturbances in Parkinson's disease result in the recruitment of superfluous cortical networks due to failed inhibition of alternative motor programs in the striatum and thus increase the complexity of cortical representation in motor conditions.
IMF-based chaotic characterization of AP and ML visually-driven postural responses
Human Vision and Electronic Imaging XVIII, 2013
The objective was to analyze visually driven postural responses and characterize any non-linear behaviour. We recorded physiological responses for two adults, 260 trials each. The subjects maintained quite stance while fixating for four seconds within an immersive room, EON Icube, where the reference to the visual stimuli, i.e., the virtual platform, randomly oscillated in Gaussian orientation 90 0 and 270 0 for antero-posterior (AP), and, 0 0 and 180 0 for medio-lateral (ML) at three different frequencies (0.125, 0.25, and 0.5 Hz). We accomplished stationary derivatives of posture time series by taking the intrinsic mode functions (IMFs). The phase space plot of IMF shows evidence of the existence of non-linear attractors in both ML and AP. Correlation integral slope with increasing embedding dimension is similar to random white noise for ML, and similar to non-linear chaotic series for AP. Next, recurrence plots indicate the existence of more non-linearity for AP than that for ML. The patterns of the dots after 200 th time stamp (near onset) appears to be aperodic in AP. At higher temporal windows, AP entropy tends more toward chaotic series, than that of ML. There are stronger non-linear components in AP than that in ML regardless of the speed conditions. Downloaded From: http://proceedings.spiedigitallibrary.org/ on 01/22/2015 Terms of Use: http://spiedl.org/terms Proc. of SPIE Vol. 8651 86511F-2 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 01/22/2015 Terms of Use: http://spiedl.org/terms Proc. of SPIE Vol. 8651 86511F-3 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 01/22/2015 Terms of Use: http://spiedl.org/terms Proc. of SPIE Vol. 8651 86511F-4 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 01/22/2015 Terms of Use: http://spiedl.org/terms • Calculate the value of the discriminating statistics M on the recorded time series Proc. of SPIE Vol. 8651 86511F-5 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 01/22/2015 Terms of Use: http://spiedl.org/terms
On the Calculation of Chaotic Features for Nonlinear Time Series
Recent developments in the theory of nonlinear dynamics have paved the way for analyzing signals generated from nonlinear biological systems. This study is aimed at investigating the application of nonlinear analysis in differentiating between patients and healthy persons, as well as in investigating the relation between ergodicity and stationarity in the dynamics of the heart. The nonlinear analysis in this work includes attractor reconstruction, estimation of the correlation dimension, calculation of the largest Lyapunov exponent, the approximate entropy, the sample entropy, and a Poincaré plot. Four groups of electrical cardiograph (ECG) signals have been investigated. Our results, obtained from clinical data, confirm the previous studies; this allows one to distinguish between a healthy group and a group of patients with more confidence than the standard methods for heart rate time series. Furthermore we extended our understanding of heart dynamics using entropies and a Poincaré plot along with the correlation dimension and the largest Lyapunov exponent. We have also obtained the results that stationarity and ergodicity are related to each other in heart dynamics.
Modeling the gait of normal and Parkinsonian persons for improving the diagnosis
Neuroscience Letters, 2012
In this study, we present a model for the gait of normal and Parkinson's disease (PD) persons. Gait is semiperiodic and has fractal properties. Sine circle map (SCM) relation has a sinusoidal term and can show chaotic behaviour. Therefore, we used SCM as a basis for our model structure. Moreover, some similarities exist between the parameters of this relation and basal ganglia (BG) structure. This relation can explain the complex behaviours and the complex structure of BG. The presented model can simulate the BG behaviour globally. A model parameter, ˝, has a key role in the model response. We showed that when i s between 0.6 and 0.8, the model simulates the behaviour of normal persons; the amounts greater or less than this range correspond to PD persons. Our statistical tests show that there is a significant difference between the ˝ of normal and PD patients. We conclude that ˝ can be introduced as a parameter to distinguish normal and PD persons. Additionally, our results showed that Spearman correlation between the ˝ and the severity of PD is 0.586. This parameter may be a good index of PD severity.
Comparison of the Nature of Chaos in Experimental [EEG] Data and Theoretical [ANN] Data
AIP Conference Proceedings, 2003
Comparison of the Nature of Chaos in Experimental [EEG] Data and Theoretical [ANN] Data | Browse -AIP Conference Proceedings In this paper, nonlinear dynamical tools like largest Lyapunov exponents (LE), fractal dimension, correlation dimension, pointwise correlation dimension will be employed to analyze electroencephalogram [EEG] data and determine the nature of chaos. Results of similar calculations from some earlier works will be produced for comparison with present results. Also, a brief report on difference of opinion among coworkers regarding tools to characterize chaos will be reported; particularly applicability of LE will be reviewed. The issue of nonlinearity present in experimental time series will be addressed by using surrogate data technique. We have extracted another data set which represented chaotic state of the system considered in our earlier work of mathematical modeling of artificial neural network. By comparing the values of measures employed to the two datasets, it can be concluded that EEG represents high dimensional chaos, whereas the experimental data due to its deterministic nature, is of low dimension. Also results give the evidence that LE exponent is applicable for low dimensional chaotic system while for experimental data, due to their stochasticity and presence of noise• LE is not a reliable tool to characterize chaos.
A Chaotic Study on Tremor Behavior of Parkinsonian Patients under Deep Brain Stimulation
2010
Abstract—Deep Brain Stimulation or DBS is a surgical treatment for Parkinson's Disease with three stimulation parameters: frequency, pulse width, and voltage. The parameters should be selected appropriately to achieve more treatment. This selection now, performs clinically. The aim of this research was to study chaotic behavior of recorded tremor of patients under DBS in order to present a quantitative method to recognize stimulation optimum voltage.
Non-Linear Dynamics in Parkinsonism
Frontiers in Neurology, 2013
Over the last 30 years, the functions (and dysfunctions) of the sensory-motor circuitry have been mostly conceptualized using linear modelizations which have resulted in two main models: the "rate hypothesis" and the "oscillatory hypothesis." In these two models, the basal ganglia data stream is envisaged as a random temporal combination of independent simple patterns issued from its probability distribution of interval interspikes or its spectrum of frequencies respectively. More recently, non-linear analyses have been introduced in the modelization of motor circuitry activities, and they have provided evidences that complex temporal organizations exist in basal ganglia neuronal activities. Regarding movement disorders, these complex temporal organizations in the basal ganglia data stream differ between conditions (i.e., parkinsonism, dyskinesia, healthy control) and are responsive to treatments (i.e., l-DOPA, deep brain stimulation). A body of evidence has reported that basal ganglia neuronal entropy (a marker for complexity/irregularity in time series) is higher in hypokinetic state. In line with these findings, an entropy-based model has been recently formulated to introduce basal ganglia entropy as a marker for the alteration of motor processing and a factor of motor inhibition. Importantly, non-linear features have also been identified as a marker of condition and/or treatment effects in brain global signals (EEG), muscular activities (EMG), or kinetic of motor symptoms (tremor, gait) of patients with movement disorders. It is therefore warranted that the non-linear dynamics of motor circuitry will contribute to a better understanding of the neuronal dysfunctions underlying the spectrum of parkinsonian motor symptoms including tremor, rigidity, and hypokinesia.
Some Aspects of Chaotic Time Series Analysis
2001
We address two aspects in chaotic time series analysis, namely the definition of embedding parameters and the largest Lyapunov exponent. It is necessary for performing state space reconstruction and identification of chaotic behavior. For the first aspect, we examine the mutual information for determination of time delay and false nearest neighbors method for choosing appropriate embedding dimension. For the second aspect we suggest neural network approach, which is characterized by simplicity and accuracy.
Statistics in Biopharmaceutical Research, 2018
The article provides a quantitative assessment of the complexity of random time series via the tool of-complexity. The methods is then applied to quantify differences in balance dynamics between Parkinsonian and non-Parkinsonian subjects via the time-dependent data obtained by acceleration measurements for the subjects asked to maintain standing postural balance on hard and soft surfaces. Finally, a comparison of the above novel method with the more classical correlational, and spectral methodologies is carried out. Although all three techniques provide clear separation between the Parkinsonian subjects and controls, it is the complexity analysis of the acceleration signals that separates the two categories most efficiently.