Connectivity and Neuronal Synchrony during Seizures.

There is uncertainty regarding when and which groups of neurons fire synchronously during seizures. While several studies found heterogeneous firing during seizures, others suggested synchronous neuronal firing in the seizure core. We tested whether neuronal activity during seizures is orderly in the direction of the excitatory neuronal connections in the circuit.

Partial synchronization of relaxation oscillators with repulsive coupling in autocatalytic integrate-and-fire model and electrochemical experiments.

Experiments and supporting theoretical analysis are presented to describe the synchronization patterns that can be observed with a population of globally coupled electrochemical oscillators close to a homoclinic, saddle-loop bifurcation, where the coupling is repulsive in the electrode potential. While attractive coupling generates phase clusters and desynchronized states, repulsive coupling results in synchronized oscillations. The experiments are interpreted with a phenomenological model that captures the waveform of the oscillations (exponential increase) followed by a refractory period.

Synchronization of action potentials during low-magnesium-induced bursting.

The relationship between mono- and polysynaptic strength and action potential synchronization was explored using a reduced external Mg(2+) model. Single and dual whole cell patch-clamp recordings were performed in hippocampal cultures in three concentrations of external Mg(2+). In decreased Mg(2+) medium, the individual cells transitioned to spontaneous bursting behavior.

Clustering in globally coupled oscillators near a Hopf bifurcation: theory and experiments.

A theoretical analysis is presented to show the general occurrence of phase clusters in weakly, globally coupled oscillators close to a Hopf bifurcation. Through a reductive perturbation method, we derive the amplitude equation with a higher-order correction term valid near a Hopf bifurcation point. This amplitude equation allows us to calculate analytically the phase coupling function from given limit-cycle oscillator models.

Clustering in delay-coupled smooth and relaxational chemical oscillators.

We investigate cluster synchronization in networks of nonlinear systems with time-delayed coupling. Using a generic model for a system close to the Hopf bifurcation, we predict the order of appearance of different cluster states and their corresponding common frequencies depending upon coupling delay. We may tune the delay time in order to ensure the existence and stability of a specific cluster state.

Predictive monitoring for respiratory decompensation leading to urgent unplanned intubation in the neonatal intensive care unit.

Background: Infants admitted to the neonatal intensive care unit (NICU), and especially those born with very low birth weight (VLBW; <1,500 g), are at risk for respiratory decompensation requiring endotracheal intubation and mechanical ventilation. Intubation and mechanical ventilation are associated with increased morbidity, particularly in urgent unplanned cases.

Methods: We tested the hypothesis that the systemic response associated with respiratory decompensation can be detected from physiological monitoring and that statistical models of bedside monitoring data can identify infants at increased risk of urgent unplanned intubation.

Engineering the synchronization of neuron action potentials using global time-delayed feedback stimulation.

We experimentally demonstrate the use of continuous, time-delayed, feedback stimulation for controlling the synchronization of neuron action potentials. Phase-based models were experimentally constructed from a single synaptically isolated cultured hippocampal neuron. These models were used to determine the stimulation parameters necessary to produce the desired synchronization behavior in the action potentials of a pair of neurons coupled through a global time-delayed interaction.

Reconstruction of two-dimensional phase dynamics from experiments on coupled oscillators.

Phase models are a powerful method to quantify the coupled dynamics of nonlinear oscillators from measured data. We use two phase modeling methods to quantify the dynamics of pairs of coupled electrochemical oscillators, based on the phases of the two oscillators independently and the phase difference, respectively. We discuss the benefits of the two-dimensional approach relative to the one-dimensional approach using phase difference.

Breath-by-breath analysis of cardiorespiratory interaction for quantifying developmental maturity in premature infants.

In healthy neonates, connections between the heart and lungs through brain stem chemosensory pathways and the autonomic nervous system result in cardiorespiratory synchronization. This interdependence between cardiac and respiratory dynamics can be difficult to measure because of intermittent signal quality in intensive care settings and variability of heart and breathing rates. We employed a phase-based measure suggested by Schäfer and coworkers (Schäfer C, Rosenblum MG, Kurths J, Abel HH.

Synchronization engineering: tuning the phase relationship between dissimilar oscillators using nonlinear feedback.

A mild, nonlinear, time-delayed feedback signal was applied to two heterogeneous oscillators in order to synchronize their frequencies with an arbitrary and controllable phase difference. The feedback was designed using phase models constructed from experimental measurements of the intrinsic dynamical properties of the oscillators. The feedback signal produced an interaction function that corresponds to the desired collective behaviour.

A Framework for Engineering the Collective Behavior of Complex Rhythmic Systems.

We have developed an engineering framework which utilizes experiment-based phase models to tune complex dynamic structures to desired states; weak, non-destructive signals are employed to alter interactions among nonlinear rhythmic elements. In this manuscript we present an integrated overview and discussion of our recent studies in this area. Experiments on electrochemical reactions were conducted using multi-electrode arrays to demonstrate the use of mild model-engineered feedback to achieve a desirable system response.

Synchronization engineering: theoretical framework and application to dynamical clustering.

A method for engineering the global behavior of populations of rhythmic elements is presented. The framework, which is based on phase models, allows a nonlinear time-delayed global feedback signal to be constructed which produces an interaction function corresponding to the desired behavior of the system. It is shown theoretically and confirmed in numerical simulations that a polynomial, delayed feedback is a versatile tool to tune synchronization patterns.

Resonance clustering in globally coupled electrochemical oscillators with external forcing.

Experiments are carried out with a globally coupled, externally forced population of limit-cycle electrochemical oscillators with an approximately unimodal distribution of heterogeneities. Global coupling induces mutually entrained (at frequency omega1) states; periodic forcing produces forced-entrained (omegaF) states. As a result of the interaction of mutual and forced entrainment, resonant cluster states occur with equal spacing of frequencies that have discretized frequencies following a resonance rule omegan congruent with nomega1-(n-1)omegaF.

Inferring phase equations from multivariate time series.

An approach is presented for extracting phase equations from multivariate time series data recorded from a network of weakly coupled limit cycle oscillators. Our aim is to estimate important properties of the phase equations including natural frequencies and interaction functions between the oscillators. Our approach requires the measurement of an experimental observable of the oscillators; in contrast with previous methods it does not require measurements in isolated single or two-oscillator setups.

Characterization of synchronization in interacting groups of oscillators: application to seizures.

We investigate the emergence of synchronization in two groups of oscillators; one group acts as a synchronization source, and the other as the target. Based on phase model simulations, we construct a synchrony index (SI): a combination of intra- and intergroup synchronies. The SI characterizes the extent of induced synchrony in the population.

Engineering complex dynamical structures: sequential patterns and desynchronization.

We used phase models to describe and tune complex dynamic structures to desired states; weak, nondestructive signals are used to alter interactions among nonlinear rhythmic elements. Experiments on electrochemical reactions on electrode arrays were used to demonstrate the power of mild model-engineered feedback to achieve a desired response. Applications are made to the generation of sequentially visited dynamic cluster patterns similar to reproducible sequences seen in biological systems and to the design of a nonlinear antipacemaker for the destruction of pathological synchronization of a population of interacting oscillators.

Cooperative stochastic behavior in the onset of localized corrosion.

Stochastic temporal and spatiotemporal models of metastable pitting on a metal surface are presented. A stochastic reaction-diffusion model accounts for the effects of local changes in concentration, potential drop, and oxide film damage on the nucleation of subsequent events. The cooperative interactions among events can lead to the formation of clusters of metastable pits and to an explosive growth in the total number of pits.

Electrochemical bursting oscillations on a high-dimensional slow subsystem.

Experiments are carried out with a chemical burster, the electrodissolution of iron in sulfuric acid solution. The system exhibits bursting oscillations in which fast periodic spiking is superimposed on chaotic, slow oscillations. Regularization of the slow dynamics, i.

Predicting mutual entrainment of oscillators with experiment-based phase models.

We show that mutual entrainment in interacting oscillators can be characterized using phase models that are developed from direct experiments with a single oscillator. The models are used to predict order-disorder transitions in populations and the dependence of order on system parameters; the description is verified in independent experiments in sets of chemical oscillators. The experiment-based model properly describes in-phase and antiphase mutual entrainment with positive and negative interactions in small sets as well as dynamical clustering in populations of oscillators.

Desynchronization of coupled electrochemical oscillators with pulse stimulations.

Various stimulation desynchronization techniques are explored in a laboratory experiment on electrochemical oscillators, a system that exhibits transient dynamics, heterogeneities, and inherent noise. Stimulation with a short, single pulse applied at a vulnerable phase can effectively desynchronize a cluster. A double pulse method, that can be applied at any phase, can be improved either by adding an extra weak pulse between the original two pulses or by adding noise to the first pulse.

Synchronization of non-phase-coherent chaotic electrochemical oscillations.

Experiments on phase and generalized synchronization of two coupled, nonidentical chaotic electrochemical oscillations are presented. We adapt measures of characterizing synchronization of a non-phase-coherent chaotic behavior and compare its properties and physicochemical mechanism to those of a phase-coherent behavior. Phase synchronization sets in along with the onset of generalized synchronization for the non-phase-coherent oscillations in contrast to phase-coherent oscillations in which the phase synchronization usually occurs at a weaker coupling strength.

Noise-aided synchronization of coupled chaotic electrochemical oscillators.

We report experimental and numerical results on noise-enhanced synchronization of two coupled chaotic oscillators. Enhanced synchronization is achieved through superimposing small-amplitude Gaussian noise on a common system parameter of the two chaotic oscillators. A resonancelike behavior is found: at an optimum level of noise, maximum synchronization is attained.

Beneficial effects of intraventricularly administered BMP-7 following a striatal 6-hydroxydopamine lesion.

The present study was undertaken to investigate the effects of bone morphogenetic protein-7 (BMP-7), also named osteogenic protein-1 (OP-1), on the progression of a striatal 6-hydroxydopamine (6-OHDA) lesion. BMP-7, a member of the transforming growth factor-beta (TGF-beta) superfamily of proteins, has been shown to have protective effects in other animal models of neuronal damage. In this study, male Fischer 344 rats received striatal 6-OHDA lesions followed 1 week later by an intraventricular dose of BMP-7.

Amplitude death through a Hopf bifurcation in coupled electrochemical oscillators: experiments and simulations.

Amplitude death was observed in experiments with two coupled periodic electrochemical oscillators without time delay. Simulation results confirmed that the observed amplitude death was obtained via a Hopf bifurcation. The two oscillators must have a minimum discrepancy and both be near their individual Hopf bifurcations for amplitude death to occur.