A. M. Albano

Dynamics of brain electrical activity

SummaryIn addition to providing important theoretical insights into chaotic deterministic systems, dynamical systems theory has provided techniques for analyzing experimental data. These methods have been applied to a variety of physical and chemical systems. More recently, biological applications have become important. In this paper, we report applications of one of these techniques, estimation of a signals correlation dimension, to the characterization of human electroencephalographic (EEG) signals and event-related brain potentials (ERPs). These calculations demonstrate that the magnitude of the technical difficulties encountered when attempting to estimate dimensions from noisy biological signals are substantial. However, these results also suggest that this procedure can provide a partial characterization of changes in cerebral electrical activity associated with changes in cognitive behavior that complements classical analytic procedures.

Experimental Studies of Chaotic Neural Behavior: Cellular Activity and Electroencephalographic Signals

Deterministic systems can display a form of highly irregular, quasirandom behavior called chaos. Even though the observed behavior is very complex, the systems which generate it can be very simple. Thus, in at least some instances, irregular biological systems may obey a simple, potentially discoverable, deterministic dynamical law. These systems can undergo reversible transitions to and from chaotic dynamics in response to small changes in parameter values. As a long term goal, this form of analysis may suggest more effective responses to disordered behavior in physiological control systems.

Traumatic Brain Injury Detection Using Electrophysiological Methods

Measuring neuronal activity with electrophysiological methods may be useful in detecting neurological dysfunctions, such as mild traumatic brain injury (mTBI). This approach may be particularly valuable for rapid detection in at-risk populations including military service members and athletes. Electrophysiological methods, such as quantitative electroencephalography (qEEG) and recording event-related potentials (ERPs) may be promising; however, the field is nascent and significant controversy exists on the efficacy and accuracy of the approaches as diagnostic tools. For example, the specific measures derived from an electroencephalogram (EEG) that are most suitable as markers of dysfunction have not been clearly established. A study was conducted to summarize and evaluate the statistical rigor of evidence on the overall utility of qEEG as an mTBI detection tool. The analysis evaluated qEEG measures/parameters that may be most suitable as fieldable diagnostic tools, identified other types of EEG measures and analysis methods of promise, recommended specific measures and analysis methods for further development as mTBI detection tools, identified research gaps in the field, and recommended future research and development thrust areas. The qEEG study group formed the following conclusions: (1) Individual qEEG measures provide limited diagnostic utility for mTBI. However, many measures can be important features of qEEG discriminant functions, which do show significant promise as mTBI detection tools. (2) ERPs offer utility in mTBI detection. In fact, evidence indicates that ERPs can identify abnormalities in cases where EEGs alone are non-disclosing. (3) The standard mathematical procedures used in the characterization of mTBI EEGs should be expanded to incorporate newer methods of analysis including non-linear dynamical analysis, complexity measures, analysis of causal interactions, graph theory, and information dynamics. (4) Reports of high specificity in qEEG evaluations of TBI must be interpreted with care. High specificities have been reported in carefully constructed clinical studies in which healthy controls were compared against a carefully selected TBI population. The published literature indicates, however, that similar abnormalities in qEEG measures are observed in other neuropsychiatric disorders. While it may be possible to distinguish a clinical patient from a healthy control participant with this technology, these measures are unlikely to discriminate between, for example, major depressive disorder, bipolar disorder, or TBI. The specificities observed in these clinical studies may well be lost in real world clinical practice. (5) The absence of specificity does not preclude clinical utility. The possibility of use as a longitudinal measure of treatment response remains. However, efficacy as a longitudinal clinical measure does require acceptable test–retest reliability. To date, very few test–retest reliability studies have been published with qEEG data obtained from TBI patients or from healthy controls. This is a particular concern because high variability is a known characteristic of the injured central nervous system.

Detecting noise in a time series.

A numerical algorithm is presented for estimating whether, and roughly to what extent, a time series is noise corrupted. Using phase-randomized surrogates constructed from the original signal, metrics are defined which can be used to quantify the noise level. A saturation occurs in these metrics at signal to noise ratios (SNRs) of around 0 dB and below, and also at around 20 dB and above. In between these two regions there is a monotonic transition in the value of the metrics from one region to the other corresponding to changes in the SNR. (c) 1997 American Institute of Physics.

SURROGATE DATA PATHOLOGIES AND THE FALSE-POSITIVE REJECTION OF THE NULL HYPOTHESIS

It is shown that inappropriately constructed random phase surrogates can give false-positive rejections of the surrogate null hypothesis. Specifically, the procedure erroneously indicated the presence of deterministic, nonlinear structure in a time series that was constructed by linearly filtering normally distributed random numbers. It is shown that the erroneous identification was due to numerical errors in the estimation of the signals Fourier transform. In the example examined here, the introduction of data windowing into the algorithm eliminated the false-positive rejection of the null hypothesis. Additional guidelines for the use of surrogates are considered, and the results of a comparison test of random phase surrogates, Gaussian scaled surrogates and iterative surrogates are presented.

Complexity and Chaos

Turbulence was one of the key phenomena that motivated the resurgence of interest in nonlinear dynamical systems. It was, after all, investigations into the mechanisms for turbulence that led Ruelle and Takens to invent the term “strange attractor” in 1971. The turbulence that is described by strange attractors is “turbulence in time” (Schuster, 1988) -- deterministic chaos, or temporal chaos in current terminology. In the past decade, a vocabulary for the quantitative characterization of temporal chaos has been developed, and has been used to describe and analyze an incredible variety of phenomena in practically all fields of science and engineering. The dimensions of strange attractors, and the entropies and Lyapunov exponents describing motions on them, have been used to analyze heartbeats and brain waves, chemical reactions, lasers, the economy, x-ray emissions of stars, flames, and fluid flow ...

Low-dimensional chaotic attractors for an unstable, inhomogeneously broadened, single-mode laser

Quantitative characterization of the intensity pulsations from an inhomogeneously broadened laser confirm that observed irregular pulsing has its origins in deterministic chaos corresponding to motion on a strange attractor of low fractal dimensionality. The pointwise information dimension and the Grassberger-Procaccia K2 (estimators from below of the fractal dimensionality of the attractor and the Kolmogorov entropy, respectively) have been determined for digitized time series from parameter regions identified qualitatively by power spectra as representing periodic, period-doubled, quasi-periodic, and chaotic behavior. Some amount of chaos seems present for almost all operating conditions.

Vasomotion becomes less random as diabetes progresses in monkeys

Please cite this paper as: Tigno, Hansen, Nawang, Shamekh, and Albano (2011). Vasomotion Becomes Less Random as Diabetes Progresses in Monkeys. Microcirculation 18(6), 429–439.

Optimization of Embedding Parameters for Prediction of Seizure Onset with Mutual Information

Normal neurological function is characterized by a high volume of information transferred between different parts of the central nervous system. An imperfect, but nonetheless useful, assessment of this spatially distributed transfer process can be obtained by examining multichannel EEG records that are measured with an array of scalp electrodes. A nonlinear quantitative measure of the transfer can be obtained by calculating the pairwise mutual information of each electrode pair. The average mutual information of two time series is the amount of information of one that can be predicted by measuring the other. As suggested in our previous work, a reduction in information transfer, as estimated by this metric, can occur prior to clinically discernible seizure onset. In the case of the focal seizure examined here, this reduction first occurred in the area of the brain that was subsequently shown to contain the epileptogenic focus. Thus, the calculation contains two clinically valuable elements: a prediction of seizure onset and a preliminary localization of the epileptogenic focus. We predict that in the case of seizures that are generalized at onset, the initiation of a seizure will be preceded by a near-simultaneous reduction in cross-channel average mutual information for several electrode pairs.

Patient Characterization Protocols for Psychophysiological Studies of Traumatic Brain Injury and Post-TBI Psychiatric Disorders

Psychophysiological investigations of traumatic brain injury (TBI) are being conducted for several reasons, including the objective of learning more about the underlying physiological mechanisms of the pathological processes that can be initiated by a head injury. Additional goals include the development of objective physiologically based measures that can be used to monitor the response to treatment and to identify minimally symptomatic individuals who are at risk of delayed-onset neuropsychiatric disorders following injury. Research programs studying TBI search for relationships between psychophysiological measures, particularly ERP (event-related potential) component properties (e.g., timing, amplitude, scalp distribution), and a participant’s clinical condition. Moreover, the complex relationships between brain injury and psychiatric disorders are receiving increased research attention, and ERP technologies are making contributions to this effort. This review has two objectives supporting such research efforts. The first is to review evidence indicating that TBI is a significant risk factor for post-injury neuropsychiatric disorders. The second objective is to introduce ERP researchers who are not familiar with neuropsychiatric assessment to the instruments that are available for characterizing TBI, post-concussion syndrome, and psychiatric disorders. Specific recommendations within this very large literature are made. We have proceeded on the assumption that, as is typically the case in an ERP laboratory, the investigators are not clinically qualified and that they will not have access to participant medical records.