Effect of data length on time delay and embedding dimension for calculating the Lyapunov exponent in walking.

The Lyapunov exponent (LyE) is a trending measure for characterizing gait stability. Previous studies have shown that data length has an effect on the resultant LyE, but the origin of why it changes is unknown. This study investigates if data length affects the choice of time delay and embedding dimension when reconstructing the phase space, which is a requirement for calculating the LyE. The effect of three different preprocessing methods on reconstructing the gait attractor was also investigated. Lumbar accelerometer data were collected from 10 healthy subjects walking on a treadmill at their preferred walking speed for 30 min. Our results show that time delay was not sensitive to the amount of data used during calculation. However, the embedding dimension had a minimum data requirement of 200 or 300 gait cycles, depending on the preprocessing method used, to determine the steady-state value of the embedding dimension. This study also found that preprocessing the data using a fixed number of strides or a fixed number of data points had significantly different values for time delay compared to a time series that used a fixed number of normalized gait cycles, which have a fixed number of data points per stride. Thus, comparing LyE values should match the method of calculation using either a fixed number of strides or a fixed number of data points.

Feasibility of Commercially Marketed Health Devices for Potential Clinical Application.

Concerns have been raised regarding the lack of validation on consumer-marketed health-monitoring devices. An investigation to characterize current health monitoring devices was carried out in the laboratory using widely accepted clinical and industry criteria. In total, 16 unique devices were examined. These devices were assessed according to their sensing modalities: step count, blood pressure, body temperature, electrocardiogram, blood oxygen saturation, and respiratory rate. Devices were tested at rest and immediately following exercise. Our results revealed that only four devices meet target requirements for accuracy. The AliveCor, a portable ECG monitor, accurately detected the heart rate for 87% of all recordings. To meet the target criterion for accuracy, the heart rate must be within ± 5 beats/minute or 10% of the standard measurement, whichever is lower. The Withings Pulse Ox, the Tinké, and the Santamedical SM-110 measured blood oxygen saturation with 2.1, 2.6, and 1.4 root-mean-square (rms) error, respectively. For blood oxygen saturation, the device should demonstrate rms error of < 3%. However, the Withings Pulse Ox and the Tinké failed to meet the accuracy criteria for their alternative biosensing capabilities: step count and respiratory rate, respectively. We conclude that the use of consumer-marketed health-monitoring devices for clinical or medical purposes should be undertaken with caution, especially in the absence of FDA or comparable clearance.

Toward a Label-Free Electrochemical Impedance Immunosensor Design for Quantifying Cortisol in Tears.

Cortisol is a viable biomarker for monitoring physiological, occupational, and emotional stress and is normally present in tear fluid at approximately 40 nM, or higher as a result of stress. We present characterization and quantification of cortisol via several electrochemical methods versus the standard enzyme-linked immunosorbent assay, commonly known as ELISA. We also present a prototyped design of a disposable test strip and handheld sensor based on label-free electrochemical impedance spectroscopy to quantify cortisol levels in tear fluid within approximately 90 seconds. Electrochemical characterization of the cortisol molecule was conducted using cyclic voltammetry, amperometric i-t, and square wave voltammetry. Lower limits of detection for these techniques were not sufficient to quantify cortisol and phycological tear ranges: 0.1 M, 0.23 M, and 193 M for cyclic voltammetry, amperometric i-t, and square wave voltammetry, respectively. However, electrochemical impedance spectroscopy (EIS) was to be the best mode of cortisol quantification and comparison to ELISA technique (detection range of ~ 138 pM - 552 nM). The initial EIS biosensor obtained a lower limit of detection of 59.76 nM with an approximate 10% relative standard deviation. The cortisol assay and tear collection prototype presented here offer a highly reproducible and ultra-low level of detection with a label-free and rapid response.

Basins of attraction in human balance.

Falls are a recognized risk factor for unintentional injuries among older adults, accounting for a large proportion of fractures, emergency department visits, and urgent hospitalizations. Human balance and gait research traditionally uses linear or qualitative tests to assess and describe human motion; however, human motion is neither a simple nor a linear process. The objective of this research is to identify and to learn more about what factors affect balance using nonlinear dynamical techniques, such as basin boundaries. Human balance data was collected using dual force plates for leans using only ankle movements as well as for unrestricted leans. Algorithms to describe the basin boundary were created and compared based on how well each method encloses the experimental data points as well as captures the differences between the two leaning conditions.

A chimeric path to neuronal synchronization.

Synchronization of neuronal activity is associated with neurological disorders such as epilepsy. This process of neuronal synchronization is not fully understood. To further our understanding, we have experimentally studied the progression of this synchronization from normal neuronal firing to full synchronization. We implemented nine FitzHugh-Nagumo neurons (a simplified Hodgkin-Huxley model) via discrete electronics. For different coupling parameters (synaptic strengths), the neurons in the ring were either unsynchronized or completely synchronized when locally coupled in a ring. When a single long-range connection (nonlocal coupling) was introduced, an intermediate state known as a chimera appeared. The results indicate that (1) epilepsy is likely not only a dynamical disease but also a topological disease, strongly tied to the connectivity of the underlying network of neurons, and (2) the synchronization process in epilepsy may not be an "all or none" phenomenon, but can pass through an intermediate stage (chimera).

Chaos computing in terms of periodic orbits.

The complex dynamics of chaotic systems can perform computations. The parameters and/or the initial conditions of a dynamical system are the data inputs and the resulting system state is the output of the computation. By controlling how inputs are mapped to outputs, a specific function can be performed. Previously no clear connection has been drawn between the structure of the dynamics and the computation. In this paper we demonstrate how chaos computation can be explained, modeled, and even predicted in terms of the dynamics of the underlying chaotic system, specifically the periodic orbit structure of the system. Knowing the dynamical equations of the system, we compute the system's periodic orbits as well as its stability in terms of its eigenvalues, thereby demonstrating how, how well, and what the chaotic system can compute.

Stochastic amplification of calcium-activated potassium currents in Ca2+ microdomains.

Small conductance (SK) calcium-activated potassium channels are found in many tissues throughout the body and open in response to elevations in intracellular calcium. In hippocampal neurons, SK channels are spatially co-localized with L-Type calcium channels. Due to the restriction of calcium transients into microdomains, only a limited number of L-Type Ca(2+) channels can activate SK and, thus, stochastic gating becomes relevant. Using a stochastic model with calcium microdomains, we predict that intracellular Ca(2+) fluctuations resulting from Ca(2+) channel gating can increase SK2 subthreshold activity by 1-2 orders of magnitude. This effectively reduces the value of the Hill coefficient. To explain the underlying mechanism, we show how short, high-amplitude calcium pulses associated with stochastic gating of calcium channels are much more effective at activating SK2 channels than the steady calcium signal produced by a deterministic simulation. This stochastic amplification results from two factors: first, a supralinear rise in the SK2 channel's steady-state activation curve at low calcium levels and, second, a momentary reduction in the channel's time constant during the calcium pulse, causing the channel to approach its steady-state activation value much faster than it decays. Stochastic amplification can potentially explain subthreshold SK2 activation in unified models of both sub- and suprathreshold regimes. Furthermore, we expect it to be a general phenomenon relevant to many proteins that are activated nonlinearly by stochastic ligand release.

Unstable periodic orbits and noise in chaos computing.

Different methods to utilize the rich library of patterns and behaviors of a chaotic system have been proposed for doing computation or communication. Since a chaotic system is intrinsically unstable and its nearby orbits diverge exponentially from each other, special attention needs to be paid to the robustness against noise of chaos-based approaches to computation. In this paper unstable periodic orbits, which form the skeleton of any chaotic system, are employed to build a model for the chaotic system to measure the sensitivity of each orbit to noise, and to select the orbits whose symbolic representations are relatively robust against the existence of noise. Furthermore, since unstable periodic orbits are extractable from time series, periodic orbit-based models can be extracted from time series too. Chaos computing can be and has been implemented on different platforms, including biological systems. In biology noise is always present; as a result having a clear model for the effects of noise on any given biological implementation has profound importance. Also, since in biology it is hard to obtain exact dynamical equations of the system under study, the time series techniques we introduce here are of critical importance.

Chaogates: morphing logic gates that exploit dynamical patterns.

Chaotic systems can yield a wide variety of patterns. Here we use this feature to generate all possible fundamental logic gate functions. This forms the basis of the design of a dynamical computing device, a chaogate, that can be rapidly morphed to become any desired logic gate. Here we review the basic concepts underlying this and present an extension of the formalism to include asymmetric logic functions.

Non-parametric early seizure detection in an animal model of temporal lobe epilepsy.

The performance of five non-parametric, univariate seizure detection schemes (embedding delay, Hurst scale, wavelet scale, nonlinear autocorrelation and variance energy) were evaluated as a function of the sampling rate of EEG recordings, the electrode types used for EEG acquisition, and the spatial location of the EEG electrodes in order to determine the applicability of the measures in real-time closed-loop seizure intervention. The criteria chosen for evaluating the performance were high statistical robustness (as determined through the sensitivity and the specificity of a given measure in detecting a seizure) and the lag in seizure detection with respect to the seizure onset time (as determined by visual inspection of the EEG signal by a trained epileptologist). An optimality index was designed to evaluate the overall performance of each measure. For the EEG data recorded with microwire electrode array at a sampling rate of 12 kHz, the wavelet scale measure exhibited better overall performance in terms of its ability to detect a seizure with high optimality index value and high statistics in terms of sensitivity and specificity.

Using recurrence quantification analysis determinism for noise removal in cardiac optical mapping.

Selecting signal processing parameters in optical imaging by utilizing the change in Determinism, a measure introduced in Recurrence Quantification Analysis, provides a novel method using the change in residual noise Determinism for improving noise quantification and removal across signals exhibiting disparate underlying tissue pathologies. The method illustrates an improved process for selecting filtering parameters and how using measured signal-to-noise ratio alone can lead to improper parameter selection.

A method for visualization of ventricular fibrillation: Design of a cooled fiberoptically coupled image intensified CCD data acquisition system incorporating wavelet shrinkage based adaptive filtering.

The measurement of cardiac transmembrane potential changes with voltage sensitive dyes is in increasing use. Detection of these very small fluorescent alterations using large multiplexed arrays, such as charge coupled device (CCD) cameras at high sampling rates, has proven challenging and usually requires significant averaging to improve the signal-to-noise ratio. To minimize the damage of living tissue stained with voltage sensitive dyes, excitation photon exposure must be limited, with the inevitable consequence of diminishing the fluorescence that is generated. State-of-the-art high frame rate CCD cameras have read noise levels in the 5-10 e(-) rms range, which is at least two orders of magnitude above that required to detect voltage sensitive dye alterations at individual pixels corresponding to 1 mm(2) heart regions illuminated with levels of 100 mW/cm(2) at frame rates approaching 1000 frames/sec. Image intensification is thus required prior to photon quantification. We report here the development of such a data acquisition system using commercially available hardware. Additionally, in the past ten years, a mathematical theory of multiresolution has been developed, and new building blocks called wavelets, allow a signal to be observed at different resolutions. Wavelet analysis also makes possible a new method of extricating signals from noise. We have incorporated spatially adaptive filters based on wavelet denoising of individual pixels to significantly reduce the multiple noise sources present in the acquired data. (c) 1998 American Institute of Physics.

Stochastic resonance in mammalian neuronal networks.

We present stochastic resonance observed in the dynamics of neuronal networks from mammalian brain. Both sinusoidal signals and random noise were superimposed into an applied electric field. As the amplitude of the noise component was increased, an optimization (increase then decrease) in the signal-to-noise ratio of the network response to the sinusoidal signal was observed. The relationship between the measures used to characterize the dynamics is discussed. Finally, a computational model of these neuronal networks that includes the neuronal interactions with the electric field is presented to illustrate the physics behind the essential features of the experiment. (c) 1998 American Institute of Physics.

Maintenance of chaos in a computational model of a thermal pulse combustor.

The dynamics of a thermal pulse combustor model are examined. It is found that, as a parameter related to the fuel flow rate is varied, the combustor will undergo a transition from periodic pulsing to chaotic pulsing to a chaotic transient leading to flameout. Results from the numerical model are compared to those obtained from a laboratory-scale thermal pulse combustor. Finally the technique of maintenance (or anticontrol) of chaos is successfully applied to the model, with the result that the operation of the combustor can be continued well into the flameout regime. (c) 1997 American Institute of Physics.

Control and synchronization of chaos in high dimensional systems: Review of some recent results.

Controlling chaos and synchronization of chaos have evolved for a number of years as essentially two separate areas of research. Only recently it has been realized that both subjects share a common root in control theory. In addition, as limitations of low dimensional chaotic systems in modeling real world phenomena become increasingly apparent, investigations into the control and synchronization of high dimensional chaotic systems are beginning to attract more interest. We review some recent advances in control and synchronization of chaos in high dimensional systems. Efforts will be made to stress the common origins of the two subjects. (c) 1997 American Institute of Physics.