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. There are strong excitatory connections laterally within the septotemporally organized lamella and inhibitory trans-lamellar connections in the hippocampus, which allow testing of the connectivity hypothesis. We further tested whether epileptogenesis enhances synchrony and antiseizure drug administration disrupts it. We recorded local field potentials from CA1 pyramidal neurons using a small microelectrode array and kindled rats by a rapid, recurrent hippocampal stimulation protocol. We compared cross-correlation, theta phase synchronization, entropy, and event synchronization. These analyses revealed that the firing pattern was correlated along the lamellar, but not the septotemporal, axis during evoked seizures. During kindling, neuronal synchrony increased along the lamellar axis, while synchrony along the septotemporal axis remained relatively low. Additionally, the theta phase distribution demonstrated that CA1 pyramidal cell firing became preferential for theta oscillation negative peak as kindling progressed in the lamellar direction but not in the trans-lamellar direction. Last, event synchronization demonstrated that neuronal firings along the lamellar axis were more synchronized than those along the septotemporal axis. There was a marked decrease in synchronization and phase preference after treatment with phenytoin and levetiracetam. The synchrony structure of CA1 pyramidal neurons during seizures and epileptogenesis depends on anatomic connectivity and plasticity.SIGNIFICANCE STATEMENT We could improve the efficacy of brain stimulation to treat seizures by understanding the structure of synchrony. Electrical stimulation may disrupt seizures by desynchronizing neurons, but there is an uncertainty on which groups of neurons fire synchronously or chaotically during seizures. Here, we demonstrate that neurons linked by excitatory connections fire synchronously during seizures, and this synchrony is modulated by epileptogenesis and antiseizure drugs. Closed-loop brain stimulation carefully targeted to disrupt synchrony may improve the treatment of seizures.

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. The globally coupled autocatalytic integrate-and-fire model predicts the development of partially synchronized states that occur through attracting heteroclinic cycles between out-of-phase two-cluster states. Similar behavior can be expected in many other systems where the oscillations occur close to a saddle-loop bifurcation, e.g., with Morris-Lecar neurons.

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. In lowered Mg(2+) media the larger excitatory synaptic events were observed more frequently and fewer transmission failures occurred, suggesting strengthened synaptic transmission. The event synchronization was calculated for the neural action potentials of the cell pairs, and it increased in media where Mg(2+) concentration was lowered. Analysis of surrogate data where bursting was present, but no direct or indirect connections existed between the neurons, showed minimal action potential synchronization. This suggests the synchronization of action potentials is a product of the strengthening synaptic connections within neuronal networks.

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. Moreover, using the phase coupling function, the stability of phase clusters can be analyzed. We demonstrate our theory with the Brusselator model. Experiments are carried out to confirm the presence of phase clusters close to Hopf bifurcations with electrochemical oscillators.

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. We studied 287 VLBW infants consecutively admitted to our NICU and found 96 events in 51 patients, excluding intubations occurring within 12 h of a previous extubation. RESULTS: In order of importance in a multivariable statistical model, we found that the characteristics of reduced O(2) saturation, especially as heart rate was falling; increased heart rate correlation with respiratory rate; and the amount of apnea were all significant independent predictors. The predictive model, validated internally by bootstrap, had a receiver-operating characteristic area of 0.84 ± 0.04. CONCLUSION: We propose that predictive monitoring in the NICU for urgent unplanned intubation may improve outcomes by allowing clinicians to intervene noninvasively before intubation is required.

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. We qualitatively and quantitatively confirm these results in experiments with chemical oscillators. The experiments also exhibit strongly nonlinear relaxation oscillations as we increase the voltage, i.e., go further away from the Hopf bifurcation. In this regime, we find secondary cluster states with delay-dependent phase lags. These cluster states appear in addition to primary states with delay-independent phase lags observed near the Hopf bifurcation. Extending the theory on Hopf normal-form oscillators, we are able to account for realistic interaction functions, yielding good agreement with experimental findings.

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. Nature 392: 239-240, 1998) to obtain a breath-by-breath analysis of cardiorespiratory interaction. This measure of cardiorespiratory interaction does not distinguish between cardiac control of respiration associated with cardioventilatory coupling and respiratory influences on the heart rate associated with respiratory sinus arrhythmia. We calculated, in sliding 4-min windows, the probability density of heartbeats as a function of the concurrent phase of the respiratory cycle. Probability density functions whose Shannon entropy had a <0.1% chance of occurring from random numbers were classified as exhibiting interaction. In this way, we analyzed 18 infant-years of data from 1,202 patients in the Neonatal Intensive Care Unit at University of Virginia. We found evidence of interaction in 3.3 patient-years of data (18%). Cardiorespiratory interaction increased several-fold with postnatal development, but, surprisingly, the rate of increase was not affected by gestational age at birth. We find evidence for moderate correspondence between this measure of cardiorespiratory interaction and cardioventilatory coupling and no evidence for respiratory sinus arrhythmia, leading to the need for further investigation of the underlying mechanism. Such continuous measures of physiological interaction may serve to gauge developmental maturity in neonatal intensive care patients and prove useful in decisions about incipient illness and about hospital discharge.

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. We quantify the dependence of the coupling functions on the coupling magnitude and coupling time delay. We show differences in synchronization predictions of the two models using a toy model. We show that the two-dimensional approach reveals behavior not detected by the one-dimensional model in a driven experimental oscillator. This approach is broadly applicable to quantify interactions between nonlinear oscillators, especially where intrinsic oscillator sensitivity and coupling evolve with time.

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. Measurements made using a dynamic clamp system confirm the generation of the synchronized states predicted by the experimentally constructed phase model. This model was then utilized to extrapolate the feedback stimulation parameters necessary to disrupt the action potential synchronization of a large population of globally interacting neurons.

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. The synchronized phase difference between the elements can be tuned to any value on the interval 0 and 2pi by shifting the phase of the interaction function using the feedback delay. Numerical simulations were conducted and experiments carried out with electrochemical oscillators.

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. Application is made to the tuning of phase difference between two oscillators, generation of sequentially-visited dynamic cluster patterns, engineering dynamically differentiated cluster states, and to the design of a nonlinear anti-pacemaker for the destruction of synchronization of a population of interacting oscillators.

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. Dynamical states consisting of one to four clusters were engineered to demonstrate the application of synchronization engineering in an experimental electrochemical system.

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. Resonance clustering requires an optimal, intermediate global coupling strength; at weak coupling the clusters have smaller sizes and do not strictly follow the resonance rule, while at strong coupling the population behaves similar to a single, giant oscillator.

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. We demonstrate the usefulness of the measure in a test case of mesial temporal lobe epilepsy: the SI can be readily calculated from standard electroencephalographic measurements. We show that the synchrony index has a statistically significant increased value for the ictal periods and that the epileptic focus can be located by identifying the most synchronous pairs of electrodes during the initial part of ictal period of the seizure. We also show that it is possible in this pilot case to differentiate clinical and subclinical seizures based on the dynamical features of the synchronization. The synchronization index was found to be a useful quantity for the characterization of "pathological hypersynchronization" within a well-characterized patient with mesial temporal lobe epilepsy and thus has potential medical value in seizure detection, localizing ability, and association with later surgical outcome.

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. This noninvasive technique can be advantageous in biological systems, where extraction of few oscillators may be a difficult task. The method is most efficient when data are taken from the nonsynchronized regime. Applicability to experimental systems is demonstrated by using a network of electrochemical oscillators; the obtained phase model is utilized to predict the synchronization diagram of the system.

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. Recent progress in the studies of such phenomena is reviewed. New results based on a mean-field analysis of the model and numerical simulations on critical nucleation effects are reported.

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.e., transition from chaotic to periodic bursting oscillations, is investigated through changes in the experimental parameters (circuit potential, external resistance, and electrode diameter). These transitions are accompanied by changes in the fast dynamics; a 'Hopf-Hopf' spiking is transformed to 'homoclinic-Hopf' spiking. The periodic bursting is destroyed through a period lengthening process in which the fast spiking region extends to a large fraction of the slow oscillatory cycle until there is no clear distinction between the fast and slow oscillations. Finally, it is shown that the time-scales of the fast spiking and, to a lesser extent, of the slow oscillations (or the occurrence of fast spiking) can be controlled with periodic perturbation of an experimental parameter, the circuit potential.

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.