Determining embedding dimension for phase-space reconstruction using a geometrical construction

COMPREHENSIVE ANALYSIS OF NORMAL AND DIABETIC HEART RATE SIGNALS: A REVIEW

A large section of the world's population is affected by diabetes mellitus (DM), commonly referred to as "diabetes." Every year, the number of cases of DM is increasing. Diabetes has a strong genetic basis, hence it is very difficult to cure, but can be controlled with medications to prevent subsequent organ damage. Therefore, early diagnosis of diabetes is very important. In this paper, we examine how diabetes affects cardiac health, which is reflected through heart rate variability (HRV), as observed in electrocardiography (ECG) signals. Such signals provide clues for both the presence and severity of diabetes as well as diabetes-induced cardiac impairments. Heart rate (HR) is a non-linear and non-stationary signal. Thus, extracting useful information from HRV signals is a difficult task. We review several sophisticated signal processing and information extraction methods in order to establish measurable relationships between the presence and the extent of diabetes as well as the changes in the HRV signals. Furthermore, we discuss a typical range of values for several statistical, geometric, time domain, frequency domain, time–frequency, and non-linear features for HR signals from 15 normal and 15 diabetic subjects. We found that non-linear analysis is the most suitable approach to capture and analyze the subtle changes in HRV signals caused by diabetes.

Order Patterns Networks (ORPAN)-a method to estimate time-evolving functional connectivity from multivariate time series

Complex networks provide an excellent framework for studying the function of the human brain activity. Yet estimating functional networks from measured signals is not trivial, especially if the data is non-stationary and noisy as it is often the case with physiological recordings. In this article we propose a method that uses the local rank structure of the data to define functional links in terms of identical rank structures. The method yields temporal sequences of networks which permits to trace the evolution of the functional connectivity during the time course of the observation. We demonstrate the potentials of this approach with model data as well as with experimental data from an electrophysiological study on language processing.

Nonlinear analysis of heart rate variability to assess the reaction of ewe fetuses undergoing fetal cardiac surgery

Fetal cardiac surgery (FCS) represents a challenging issue for the in utero treatment of congenital heart defects. However, FCS has still not gained the sufficient reliability for clinical practice due to an incompletely elucidated fetal stress response. For example, blood sampling can contribute to its onset, leading to fetoplacental unit dysfunction, one of the main causes of failure of the surgical procedure. In order to address this issue, the role of the autonomic control system during an experimental procedure of cardiac bypass on ewe fetuses was investigated by means of recurrence quantification analysis (RQA), a well-recognized method for the analysis of nonlinear systems. RQA was applied to time series extracted from fetal arterial pressure recordings before and after the cardiac bypass established by means of an extracorporeal circuit, including an axial blood pump, and taking advantage of the capability of the placenta to work as a natural oxygenator. Statistically significant correlations were found among RQA-based metrics and fetal blood gas data, suggesting the possibility to infer the clinical status of the fetus starting from its hemodynamic signals.This study shows the relevance of RQA as a complementary tool for the monitoring of the fetal status during cardiac bypass.

Recurrence quantification of fractal structures

By definition, fractal structures possess recurrent patterns. At different levels repeating patterns can be visualized at higher magnifications. The purpose of this chapter is threefold. First, general characteristics of dynamical systems are addressed from a theoretical mathematical perspective. Second, qualitative and quantitative recurrence analyses are reviewed in brief, but the reader is directed to other sources for explicit details. Third, example mathematical systems that generate strange attractors are explicitly defined, giving the reader the ability to reproduce the rich dynamics of continuous chaotic flows or discrete chaotic iterations. The challenge is then posited for the reader to study for themselves the recurrent structuring of these different dynamics. With a firm appreciation of the power of recurrence analysis, the reader will be prepared to turn their sights on real-world systems (physiological, psychological, mechanical, etc.).

Non-Linear Time Analysis to Estimate Gait Stability Using Wearable Gyroscopes Network

Gait stability is very important in assessing human locomotion. Maximum Lyapunov exponent (λ*) has been widely reported to be closely related to the ability of the human locomotor system in maintaining walking balance. Most literature reports have, however, utilized optical motion capture systems, electrogoniometers and accelerometers to determine λ*. This paper introduces the use of wearable wireless gyroscopes for estimating gait stability. An experimental study was conducted to validate the efficacy of this approach. Its outcome was consistent and comparable to results obtained from conventional approaches.

Bursting as a source of non-linear determinism in the firing patterns of nigral dopamine neurons

Nigral dopamine (DA) neurons in vivo exhibit complex firing patterns consisting of tonic single-spikes and phasic bursts that encode information for certain types of reward-related learning and behavior. Non-linear dynamical analysis has previously demonstrated the presence of a non-linear deterministic structure in complex firing patterns of DA neurons, yet the origin of this non-linear determinism remains unknown. In this study, we hypothesized that bursting activity is the primary source of non-linear determinism in the firing patterns of DA neurons. To test this hypothesis, we investigated the dimension complexity of inter-spike interval data recorded in vivo from bursting and non-bursting DA neurons in the chloral hydrate-anesthetized rat substantia nigra. We found that bursting DA neurons exhibited non-linear determinism in their firing patterns, whereas non-bursting DA neurons showed truly stochastic firing patterns. Determinism was also detected in the isolated burst and inter-burst interval data extracted from firing patterns of bursting neurons. Moreover, less bursting DA neurons in halothane-anesthetized rats exhibited higher dimensional spiking dynamics than do more bursting DA neurons in chloral hydrate-anesthetized rats. These results strongly indicate that bursting activity is the main source of low-dimensional, non-linear determinism in the firing patterns of DA neurons. This finding furthermore suggests that bursts are the likely carriers of meaningful information in the firing activities of DA neurons.

An interaction-dominant perspective on reading fluency and dyslexia

The background noise of response times is often overlooked in scientific inquiries of cognitive performances. However, it is becoming widely acknowledged in psychology, medicine, physiology, physics, and beyond that temporal patterns of variability constitute a rich source of information. Here, we introduce two complexity measures (1/f scaling and recurrence quantification analysis) that employ background noise as metrics of reading fluency. These measures gauge the extent of interdependence across, rather than within, cognitive components. In this study, we investigated dyslexic and non-dyslexic word-naming performance in beginning readers and observed that these complexity metrics differentiate reliably between dyslexic and average response times and correlate strongly with the severity of the reading impairment. The direction of change in the introduced metrics suggests that developmental dyslexia resides from dynamical instabilities in the coordination among the many components necessary to read, which could explain why dyslexic readers score below average on so many distinct tasks and modalities.

Nonlinear analysis of electroencephalogram at rest and during cognitive tasks in patients with schizophrenia

BACKGROUND

In spite of the large number of studies on schizophrenia, a full understanding of its core pathology still eludes us. The application of the nonlinear theory of electroencephalography (EEG) analysis provides an interesting tool to differentiate between physiologic conditions (e.g., resting state and mathematical task) and normal and pathologic brain activities. The aim of the present study was to investigate nonlinear EEG activity in patients with schizophrenia.

METHODS

We recorded 19-lead EEGs in patients with stable schizophrenia and healthy controls under 4 different conditions: eyes closed, eyes open, forward counting and backward counting. A nonlinear measure of complexity was calculated by means of correlation dimension (D2).

RESULTS

We included 17 patients and 17 controls in our analysis. Comparing the 2 populations, we observed greater D2 values in the patient group. In controls, increased D2 values were observed during active states (eyes open and the 2 cognitive tasks) compared with baseline conditions. This increase of brain complexity, which can be interpreted as an increase of information processing and integration, was not preserved in the patient population.

LIMITATIONS

Patients with schizophrenia were taking antipsychotic medications, so the presence of medication effects cannot be excluded.

CONCLUSION

Our results suggest that patients with schizophrenia present changes in brain activity compared with healthy controls, and this pathologic alteration can be successfully studied with nonlinear EEG analysis.

Route to chaos for combustion instability in ducted laminar premixed flames

Complex thermoacoustic oscillations are observed experimentally in a simple laboratory combustor that burns lean premixed fuel-air mixture, as a result of nonlinear interaction between the acoustic field and the combustion processes. The application of nonlinear time series analysis, particularly techniques based on phase space reconstruction from acquired pressure data, reveals rich dynamical behavior and the existence of several complex states. A route to chaos for thermoacoustic instability is established experimentally for the first time. We show that, as the location of the heat source is gradually varied, self-excited periodic thermoacoustic oscillations undergo transition to chaos via the Ruelle-Takens scenario.

Unbiased entropy estimates in stress: a parameter study

This study proposes a method for obtaining a stable working point that enables the unbiased estimates of the approximate entropy and the sample entropy. Pattern length, normalized threshold, time delay and tines series length are levels of freedom that are considered. Pulse interval signals used for the experiment are recorded from laboratory animals with different likelihood of developing cardiovascular disease--normal and borderline hypertensive rats--exposed to the acute and to the chronic stress. It is shown that the threshold level is the major source of the instability, and that the generally accepted and widely used methods for a threshold choice may lead to an incorrect psychological interpretation. A method for the threshold level correction is proposed.

Chaotic time series prediction based on a novel robust echo state network

In this paper, a robust recurrent neural network is presented in a Bayesian framework based on echo state mechanisms. Since the new model is capable of handling outliers in the training data set, it is termed as a robust echo state network (RESN). The RESN inherits the basic idea of ESN learning in a Bayesian framework, but replaces the commonly used Gaussian distribution with a Laplace one, which is more robust to outliers, as the likelihood function of the model output. Moreover, the training of the RESN is facilitated by employing a bound optimization algorithm, based on which, a proper surrogate function is derived and the Laplace likelihood function is approximated by a Gaussian one, while remaining robust to outliers. It leads to an efficient method for estimating model parameters, which can be solved by using a Bayesian evidence procedure in a fully autonomous way. Experimental results show that the proposed method is robust in the presence of outliers and is superior to existing methods.

Chaos in ocular aberration dynamics of the human eye

Since the characterization of the eye's monochromatic aberration fluctuations in 2001, the power spectrum has remained the most widely used method for analyzing their dynamics. However, the power spectrum does not capture the complexities of the fluctuations. We measured the monochromatic aberration dynamics of six subjects using a Shack-Hartmann sensor sampling at 21 Hz. We characterized the dynamics using techniques from chaos theory. We found that the attractor embedding dimension for all aberrations, for all subjects, was equal to three. The embedding lag averaged across aberrations and subjects was 0.31 ± 0.07 s. The Lyapunov exponent of the rms wavefront error was positive for each subject, with an average value of 0.44 ± 0.15 µm/s. This indicates that the aberration dynamics are chaotic. Implications for future modeling are discussed.

Dynamical analysis in real time: detecting perturbations to team communication

Dynamical systems methods characterise patterns of change over time. Typically, such methods are applied only after data collection is complete. However, brief disturbances - perturbations - can occur as a process unfolds and can result in undesirable outcomes if not acted on. The application of dynamics in real time would be useful for detecting these sudden changes. Real-time analysis was accomplished by updating dynamical estimates simultaneously across different window sizes. We calculated the largest Lyapunov exponent, a measure of dynamical stability, to detect a perturbation to team communication in a simulated uninhabited air vehicle (UAV) reconnaissance mission. The perturbation consisted of information demands from a confederate that occurred unexpectedly during performance of a UAV mission. We demonstrate the use of real-time methods in detecting that perturbation as it occurred. In application, this technique would have enabled real-time intervention. Extensions of the real-time dynamical method to other domains of psychological inquiry are discussed.

PRACTITIONER SUMMARY

A real-time dynamical analysis method that was developed to detect unexpected perturbations in team communication is described. The use of the method is demonstrated on perturbed communication from a three-person uninhabited air vehicle command-and-control team. The generalisability of the method is considered with respect to physiological and motor coordination dynamics.

Evaluation of muscle fatigue of wheelchair basketball players with spinal cord injury using recurrence quantification analysis of surface EMG

Wheelchair basketball is the most popular exercise activity among individuals with spinal cord injury (SCI). The purpose of this study was to investigate muscular endurance and fatigue in wheelchair basketball athletes with SCI using surface electromyography (SEMG) and maximal torque values. SEMG characteristics of 10 wheelchair basketball players (WBP) were compared to 13 able-bodied basketball players and 12 sedentary able-bodied subjects. Participants performed sustained isometric elbow flexion at 50% maximal voluntary contraction until exhaustion. Elbow flexion torque and SEMG signals were recorded from three elbow flexor muscles: biceps brachii longus, biceps brachii brevis and brachioradialis. SEMG signals were clustered into 0.5-s epochs with 50% overlap. Root mean square (RMS) and median frequency (MDF) of SEMG signals were calculated for each muscle and epoch as traditional fatigue monitoring. Recurrence quantification analysis was used to extract the percentage of determinism (%DET) of SEMG signals. The slope of the %DET for basketball players and WBP showed slower increase with time than the sedentary able-bodied control group for three different elbow flexor muscles, while no difference was observed for the slope of the %DET between basketball and WBP. This result indicated that the athletes are less fatigable during the task effort than the nonathletes. Normalized MDF slope decay exhibited similar results between the groups as %DET, while the slope of the normalized RMS failed to show any significant differences among the groups (p > 0.05). MDF and %DET could be useful for the evaluation of muscle fatigue in wheelchair basketball training. No conclusions about special training for WBP could be determined.

Hemispheric asymmetry in non-linear interdependence of EEG in post-traumatic stress disorder

AIM

While volumetric and metabolic imaging on post-traumatic stress disorder (PTSD) patients has been intensively performed, few studies using electroencephalograms (EEG) have been done as yet. The aim of the present study was to investigate abnormalities in functional connectivity of cortical networks in PTSD.

METHODS

Non-linear interdependence (NI), a measure of bidirectional, non-linear information transmission between two time series, was used. Resting EEG were recorded for 18 PTSD patients and 18 sex-matched healthy subjects on 16 channels with their eyes closed.

RESULTS

The NI patterns in PTSD patients were hemisphere asymmetric: an increase in NI in the fronto-parieto-temporal regions of the left hemisphere (F7, F3, T3, C3, T5 and P3) and a decrease in the fronto-parieto-occipital regions of the right hemisphere (F4, C4, P4 and O2). The non-linearity of NI in EEG, estimated from the surrogate data method, exhibited an increase in the PTSD patients as compared with that of healthy subjects, particularly in the left hemispheric cortex.

CONCLUSION

Abnormal functional connectivity in PTSD can be assessed using NI, a measure of multi-channel EEG.

Complex dynamics of semantic memory access in reading

Understanding a word in context relies on a cascade of perceptual and conceptual processes, starting with modality-specific input decoding, and leading to the unification of the word's meaning into a discourse model. One critical cognitive event, turning a sensory stimulus into a meaningful linguistic sign, is the access of a semantic representation from memory. Little is known about the changes that activating a word's meaning brings about in cortical dynamics. We recorded the electroencephalogram (EEG) while participants read sentences that could contain a contextually unexpected word, such as 'cold' in 'In July it is very cold outside'. We reconstructed trajectories in phase space from single-trial EEG time series, and we applied three nonlinear measures of predictability and complexity to each side of the semantic access boundary, estimated as the onset time of the N400 effect evoked by critical words. Relative to controls, unexpected words were associated with larger prediction errors preceding the onset of the N400. Accessing the meaning of such words produced a phase transition to lower entropy states, in which cortical processing becomes more predictable and more regular. Our study sheds new light on the dynamics of information flow through interfaces between sensory and memory systems during language processing.

Statistical evaluation of recurrence quantification analysis applied on single trial evoked potential studies

OBJECTIVE

We evaluated the potential of recurrence quantification analysis (RQA) to improve the analysis of trial-by-trial-variability in event-related potentials (ERPs) experiments.

METHODS

We use an acoustic oddball paradigm to compare the efficiency of RQA with a linear amplitude based analysis of single trial ERPs with regard to the power to distinguish responses to different tone types. We further probed the robustness of both analyses towards structured noise induced by parallel magnetic resonance imaging (MRI).

RESULTS

RQA provided robust discrimination of responses to different tone types, even when EEG data were contaminated by structured noise. Yet, its power to discriminate responses to different tone types was not significantly superior to a linear amplitude analysis. RQA measures were only moderately correlated with EEG amplitudes, suggesting that RQA may extract additional information from single trial responses not detected by amplitude evaluation.

CONCLUSIONS

RQA allows quantifying signal characteristics of single trial ERPs measured with and without noise induced by parallel MRI. RQA power to discriminate responses to different tone types was similar to linear amplitude based analysis.

SIGNIFICANCE

RQA has the potential to detect differences of signal features in response to a standard oddball paradigm and provide additional trial-by-trial information compared to classical amplitude based analysis.

TIME SERIES ANALYSIS IN RECONSTRUCTED STATE SPACES

Concepts for the analysis of observed scalar time series data in reconstructed vector valued phase spaces are reviewed. Originally exclusively designed for data from deterministic chaotic systems, phase space methods were recently extended to usage for nonlinear stochastic and for nonstationary processes.

Multiscale analysis of biological data by scale-dependent lyapunov exponent

Physiological signals often are highly non-stationary (i.e., mean and variance change with time) and multiscaled (i.e., dependent on the spatial or temporal interval lengths). They may exhibit different behaviors, such as non-linearity, sensitive dependence on small disturbances, long memory, and extreme variations. Such data have been accumulating in all areas of health sciences and rapid analysis can serve quality testing, physician assessment, and patient diagnosis. To support patient care, it is very desirable to characterize the different signal behaviors on a wide range of scales simultaneously. The Scale-Dependent Lyapunov Exponent (SDLE) is capable of such a fundamental task. In particular, SDLE can readily characterize all known types of signal data, including deterministic chaos, noisy chaos, random 1/f(α) processes, stochastic limit cycles, among others. SDLE also has some unique capabilities that are not shared by other methods, such as detecting fractal structures from non-stationary data and detecting intermittent chaos. In this article, we describe SDLE in such a way that it can be readily understood and implemented by non-mathematically oriented researchers, develop a SDLE-based consistent, unifying theory for the multiscale analysis, and demonstrate the power of SDLE on analysis of heart-rate variability (HRV) data to detect congestive heart failure and analysis of electroencephalography (EEG) data to detect seizures.

EFFECTS OF MOBILE PHONE RADIATION ON CARDIAC HEALTH

Mobile phones (MPs) progressed from a tool of the privileged few to a gadget for the masses. However, the physical effects, which enable wireless information transmission, did not change; MP technology still relies on pulsed high-frequency electromagnetic (EM) fields. Therefore, the health risks, associated with EM fields, remain. Studies that investigated these health risks have reported dizziness, numbness in the thigh, and heaviness in the chest. This study investigates neurological effects that are caused by EM fields radiated from MPs. The heart rate variability (HRV) can be used as a measure for these neurological effects, because the automated nervous system modulates the HRV. We measured the HRV of 14 healthy male volunteers. We used the following nonlinear parameters to quantify the MP radiation effects on HRV: approximate entropy (ApEn), capacity dimension (CaD), correlation dimension (CD), fractal dimension (FD), Hurst exponent (H), and the largest Lyapunov exponent (LLE). The results indicate that there is a measurable difference in the parameter values when the MP is kept close to the chest and when it is kept close to the head. However, these differences are very small and statistical analysis showed that they have no clinical significance. Furthermore, the result analysis does not show a consistent trend, which indicates that there is no underlying pathological effect.

Data-driven modeling based on volterra series for multidimensional blast furnace system

The multidimensional blast furnace system is one of the most complex industrial systems and, as such, there are still many unsolved theoretical and experimental difficulties, such as silicon prediction and blast furnace automation. For this reason, this paper is concerned with developing data-driven models based on the Volterra series for this complex system. Three kinds of different low-order Volterra filters are designed to predict the hot metal silicon content collected from a pint-sized blast furnace, in which a sliding window technique is used to update the filter kernels timely. The predictive results indicate that the linear Volterra predictor can describe the evolvement of the studied silicon sequence effectively with the high percentage of hitting the target, very low root mean square error and satisfactory confidence level about the reliability of the future prediction. These advantages and the low computational complexity reveal that the sliding-window linear Volterra filter is full of potential for multidimensional blast furnace system. Also, the lack of the constructed Volterra models is analyzed and the possible direction of future investigation is pointed out.

AUTOMATIC IDENTIFICATION OF EPILEPTIC EEG SIGNALS USING NONLINEAR PARAMETERS

Epilepsy is a brain disorder causing people to have recurring seizures. Electroencephalogram (EEG) is the electrical activity of the brain signals that can be used to diagnose the epilepsy. The EEG signal is highly nonlinear and nonstationary in nature and may contain indicators of current disease, or warnings about impending diseases. The chaotic measures like correlation dimension (CD), Hurst exponent (H), and approximate entropy (ApEn) can be used to characterize the signal. These features extracted can be used for automatic diagnosis of seizure onsets which would help the patients to take appropriate precautions. These nonlinear features have been reported to be a promising approach to differentiate among normal, pre-ictal (background), and epileptic EEG signals. In this work, these features were used to train both Gaussian mixture model (GMM) and support vector machine (SVM) classifiers. The performance of the two classifiers were evaluated using the receiver operating characteristics (ROC) curves. Our results show that the GMM classifier performed better with average classification efficiency of 95%, sensitivity and specificity of 92.22% and 100%, respectively.

EQUIVALENCE BETWEEN "FEELING THE PULSE" ON THE HUMAN WRIST AND THE PULSE PRESSURE WAVE AT FINGERTIP

Feeling the pulse on the wrist is the regular diagnostic method in traditional Chinese medicine. However it is natural to ask whether there is any difference between feeling the pulse on the wrist or at any other part of the body: such as the fingertips at which it is easily measured by electronic devices. We employ a series of neural networks to model blood pressure propagation from the wrist to the fingertip. In order to avoid the problem of over-fitting we apply information theoretic criterion to determine the optimal model in these networks and then apply surrogate data method to the residuals in this model. We demonstrate the application of this method to recordings of human pulse in six subjects. Our result indicates that there is no significant difference between pulse waveform measure on the lateral arterial artery (wrist) and at the fingertip.

RECURRENCE-BASED ESTIMATION OF TIME-DISTORTION FUNCTIONS FOR ERP WAVEFORM RECONSTRUCTION

We introduce an approach to compensate for temporal distortions of repeated measurements in event-related potential research. The algorithm uses a combination of methods from nonlinear time-series analysis and is based on the construction of pairwise registration functions from cross-recurrence plots of the phase-space representations of ERP signals. The globally optimal multiple-alignment path is approximated by hierarchical cluster analysis, i.e. by iteratively combining pairs of trials according to similarity. By the inclusion of context information in form of externally acquired time markers (e.g. reaction time) into a regularization scheme, the extracted warping functions can be guided near paths that are implied by the experimental procedure. All parameters occurring in the algorithm can be optimized based on the properties of the data and there is a broad regime of parameter configurations where the algorithm produces good results. Simulations on artificial data and the analysis of ERPs from a psychophysical study demonstrate the robustness and applicability of the algorithm.

DETERMINISTIC CHAOS IN SOUNDS OF ASIAN CICADAS

We analyze the sound recording of the Southeast Asian cicada Tosena depicta with methods of nonlinear time series analysis. First, we reconstruct the phase space from the sound recording and test it against determinism and stationarity. After positively establishing determinism and stationarity in the series, we calculate the maximal Lyapunov exponent. We find that the latter is positive, from which we conclude that the sound recording possesses clear markers of deterministic chaos. We discuss that methods of nonlinear time series analysis can yield instructive insights and foster the understanding of acoustic and vibrational communication among insects, as well as provide vital clues regarding the origin and functionality of their sound production mechanisms. Furthermore, such studies can serve as means to distinguish different insect genera or even species either from each other or under various environmental influences.

Predicting the spontaneous termination of atrial fibrillation based on Poincare section in the electrocardiogram phase space

Atrial fibrillation (AF) is a commonly encountered cardiac arrhythmia. Predicting the conditions under which AF terminates spontaneously is an important task that would bring great benefit to both patients and clinicians. In this study, a new method was proposed to predict spontaneous AF termination by employing the points of section (POS) coordinates along a Poincare section in the electrocardiogram (ECG) phase space.

The AF Termination Database provided by PhysioNet for the Computers in Cardiology Challenge 2004 was applied in the present study. It includes one training dataset and two testing datasets, A and B. The present investigation was initiated by producing a two-dimensional reconstructed phase space (RPS) of the ECG. Then, a Poincare line was drawn in a direction that included the maximum point distribution in the RPS and also passed through the origin of the RPS coordinate system. Afterward, the coordinates of the RPS trajectory intersections with this Poincare line were extracted to capture the local behavior related to the arrhythmia under investigation. The POS corresponding to atrial activity were selected with regard to the fact that similar ECG morphologies such as P waves, which are corresponding to atrial activity, distribute in a specific region of the RPS. Thirteen features were extracted from the selected intersection points to quantify their distributions. To select the best feature subset, a genetic algorithm (GA), in combination with a support vector machine (SVM), was applied to the training dataset. Based on the selected features and trained SVM, the performance of the proposed method was evaluated using the testing datasets.

The results showed that 86.67% of dataset A and 80% of dataset B were correctly classified. This classification accuracy is in the same range as or higher than that of recent studies in this area. These results show that the proposed method, in which no complicated QRST cancelation algorithm was used, has the potential to predict AF termination.

Synchronous chaos and broad band gamma rhythm in a minimal multi-layer model of primary visual cortex

Visually induced neuronal activity in V1 displays a marked gamma-band component which is modulated by stimulus properties. It has been argued that synchronized oscillations contribute to these gamma-band activity. However, analysis of Local Field Potentials (LFPs) across different experiments reveals considerable diversity in the degree of oscillatory behavior of this induced activity. Contrast-dependent power enhancements can indeed occur over a broad band in the gamma frequency range and spectral peaks may not arise at all. Furthermore, even when oscillations are observed, they undergo temporal decorrelation over very few cycles. This is not easily accounted for in previous network modeling of gamma oscillations. We argue here that interactions between cortical layers can be responsible for this fast decorrelation. We study a model of a V1 hypercolumn, embedding a simplified description of the multi-layered structure of the cortex. When the stimulus contrast is low, the induced activity is only weakly synchronous and the network resonates transiently without developing collective oscillations. When the contrast is high, on the other hand, the induced activity undergoes synchronous oscillations with an irregular spatiotemporal structure expressing a synchronous chaotic state. As a consequence the population activity undergoes fast temporal decorrelation, with concomitant rapid damping of the oscillations in LFPs autocorrelograms and peak broadening in LFPs power spectra. We show that the strength of the inter-layer coupling crucially affects this spatiotemporal structure. We predict that layer VI inactivation should induce global changes in the spectral properties of induced LFPs, reflecting their slower temporal decorrelation in the absence of inter-layer feedback. Finally, we argue that the mechanism underlying the emergence of synchronous chaos in our model is in fact very general. It stems from the fact that gamma oscillations induced by local delayed inhibition tend to develop chaos when coupled by sufficiently strong excitation.

Visual stimulation elicits neuronal responses in visual cortex. When the contrast of the used stimuli increases, the power of this induced activity is boosted over a broad frequency range (30–100 Hz), called the “gamma band.” It would be tempting to hypothesize that this phenomenon is due to the emergence of oscillations in which many neurons fire collectively in a rhythmic way. However, previous models trying to explain contrast-related power enhancements using synchronous oscillations failed to reproduce the observed spectra because they originated unrealistically sharp spectral peaks. The aim of our study is to reconcile synchronous oscillations with broad-band power spectra. We argue here that, thanks to the interaction between neuronal populations at different depths in the cortical tissue, the induced oscillatory responses are synchronous, but, at the same time, chaotic. The chaotic nature of the dynamics makes it possible to have broad-band power spectra together with synchrony. Our modeling study allows us formulating qualitative experimental predictions that provide a potential test for our theory. We predict that if the interactions between cortical layers are suppressed, for instance by inactivating neurons in deep layers, the induced responses might become more regular and narrow isolated peaks might develop in their power spectra.

New insights into anterior cruciate ligament deficiency and reconstruction through the assessment of knee kinematic variability in terms of nonlinear dynamics

PURPOSE

Injuries to the anterior cruciate ligament (ACL) occur frequently, particularly in young adult athletes, and represent the majority of the lesions of knee ligaments. Recent investigations suggest that the assessment of kinematic variability using measures of nonlinear dynamics can provide with important insights with respect to physiological and pathological states. The purpose of the present article was to critically review and synthesize the literature addressing ACL deficiency and reconstruction from a nonlinear dynamics standpoint.

METHODS

A literature search was carried out in the main medical databases for studies published between 1990 and 2010.

RESULTS

Seven studies investigated knee kinematic variability in ACL patients. Results provided support for the theory of "optimal movement variability". Practically, loss below optimal variability is associated with a more rigid and very repeatable movement pattern, as observed in the ACL-deficient knee. This is a state of low complexity and high predictability. On the other hand, increase beyond optimal variability is associated with a noisy and irregular movement pattern, as found in the ACL-reconstructed knee, regardless of which type of graft is used. This is a state of low complexity and low predictability. In both cases, the loss of optimal variability and the associated high complexity lead to an incapacity to respond appropriately to the environmental demands, thus providing an explanation for vulnerability to pathological changes following injury.

CONCLUSION

Subtle fluctuations that appear in knee kinematic patterns provide invaluable insight into the health of the neuromuscular function after ACL rupture and reconstruction. It is thus critical to explore them in longitudinal studies and utilize nonlinear measures as an important component of post-reconstruction medical assessment.

LEVEL OF EVIDENCE

II.

Global modeling of complex data series using the term-ranking approach and its application to voice synthesis

A term-ranking approach is proposed to globally model the underlying dynamics of a chaotic series. The basic idea of this approach is to rank candidate bases before they are used to construct the global model. The ranked bases are involved in the global model one by one in a sequence from high to low until the best model is found. Simulations show that the model obtained by the term-ranking approach has a much longer prediction time, but fewer coefficients, than the widely used standard model. The proposed approach is also successfully applied to coding and synthesis of chaoslike voice data, showing promise for its use with truly noisy experimental data.

Optimal reconstruction of dynamical systems: a noise amplification approach

In this work we propose an objective function to guide the search for a state space reconstruction of a dynamical system from a time series of measurements. These statistics can be evaluated on any reconstructed attractor, thereby allowing a direct comparison among different approaches: (uniform or nonuniform) delay vectors, PCA, Legendre coordinates, etc. It can also be used to select the most appropriate parameters of a reconstruction strategy. In the case of delay coordinates this translates into finding the optimal delay time and embedding dimension from the absolute minimum of the advocated cost function. Its definition is based on theoretical arguments on noise amplification, the complexity of the reconstructed attractor, and a direct measure of local stretch which constitutes an irrelevance measure. The proposed method is demonstrated on synthetic and experimental time series.

Learning a stick-balancing task involves task-specific coupling between posture and hand displacements

Theories of motor learning argue that the acquisition of novel motor skills requires a task-specific organization of sensory and motor subsystems. We examined task-specific coupling between motor subsystems as subjects learned a novel stick-balancing task. We focused on learning-induced changes in finger movements and body sway and investigated the effect of practice on their coupling. Eight subjects practiced balancing a cylindrical wooden stick for 30 min a day during a 20 day learning period. Finger movements and center of pressure trajectories were recorded in every fifth practice session (4 in total) using a ten camera VICON motion capture system interfaced with two force platforms. Motor learning was quantified using average balancing trial lengths, which increased with practice and confirmed that subjects learned the task. Nonlinear time series and phase space reconstruction methods were subsequently used to investigate changes in the spatiotemporal properties of finger movements, body sway and their progressive coupling. Systematic increases in subsystem coupling were observed despite reduced autocorrelation and differences in the temporal properties of center of pressure and finger trajectories. The average duration of these coupled trajectories increased systematically across the learning period. In short, the abrupt transition between coupled and decoupled subsystem dynamics suggested that stick balancing is regulated by a hierarchical control mechanism that switches from collective to independent control of the finger and center of pressure. In addition to traditional measures of motor performance, dynamical analyses revealed changes in motor subsystem organization that occurred when subjects learned a novel stick-balancing task.

A single bout of resistance exercise does not affect nonlinear dynamics of lower extremity kinematics during treadmill walking

Peripheral fatigue has been known to result in altered force output and muscle recruitment patterns by the CNS. These changes may affect lower extremity movement during gait, and such behavior may present implications for the interpretation of nonlinear analysis of gait in situations where a subject might become fatigued. The purpose of this study was to examine the effects of a single bout of resistance training on lower extremity movement during treadmill walking in healthy subjects. Fifteen recreationally active subjects performed two 10min trials of treadmill walking at their preferred speed while knee and ankle kinematics of their right limb were recorded via optical motion capture. Between walking trials, subjects performed a series of lower extremity resistance exercises designed to induce moderate muscular fatigue. Detrended fluctuation analysis of stride length and stride time revealed that statistical persistence was unaffected by moderate muscle fatigue. Estimates of finite-time maximal Lyapunov exponents for ankle angle, knee angle, and vertical ankle movement over the short (0-1 stride) and long (4-10 strides) term were also unaffected by a single bout of resistance training. These results suggest that control of locomotion in healthy individuals, as measured by the nonlinear dynamics of lower extremity movement used here, is relatively robust to moderate muscle fatigue. Additional work with greater levels of fatigue will be necessary to fully characterize the effects of muscular fatigue on gait.

Extracting biomarkers of autism from MEG resting-state functional connectivity networks

The present study is a preliminary attempt to use graph theory for deriving distinct features of resting-state functional networks in young adults with autism spectrum disorder (ASD). Networks modeled neuromagnetic signal interactions between sensors using three alternative interdependence measures: (a) a non-linear measure of generalized synchronization (robust interdependence measure [RIM]), (b) mutual information (MI), and (c) partial directed coherence (PDC). To summarize the information contained in each network model we employed well-established global graph measures (average strength, assortativity, clustering, and efficiency) as well as graph measures (average strength of edges) tailored to specific hypotheses concerning the spatial distribution of abnormalities in connectivity among individuals with ASD. Graph measures then served as features in leave-one-out classification analyses contrasting control and ASD participants. We found that combinations of regionally constrained graph measures, derived from RIM, performed best, discriminating between the two groups with 93.75% accuracy. Network visualization revealed that ASD participants displayed significantly reduced interdependence strength, both within bilateral frontal and temporal sensors, as well as between temporal sensors and the remaining recording sites, in agreement with previous studies of functional connectivity in this disorder.