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.

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.

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.

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.

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.

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.

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.

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. No significant effect of BMP-7 treatment on spontaneous locomotor activity was observed, however BMP-7 significantly increased the density of tyrosine hydroxylase (TH) immunoreactivity (TH-ir) in the substantia nigra (SN) pars compacta, in the lesioned hemisphere [31.7+/-5.2 (optical density (O.D.) arbitrary units) control vs. 50.2+/-4.3 O.D. BMP-7-treated; p<0.05]. Interestingly, BMP-7 significantly increased TH-ir in the SN of the non-lesioned hemisphere (pars reticulata: 14.8+/-1.19 O.D. control vs. 36+/-2.6 O.D. BMP-7-treated, p<0.05; pars compacta: 29.0+/-4.9 O.D. control vs. 64.4+/-6.9 O.D. BMP-7-treated, p<0.001). A significant increase in DA concentration in the contralateral, non-lesioned hemisphere was also noted (113.2 ng/g control vs. 198.2 ng/g BMP-7-treated, p<0.01). In contrast to other intraventricularly administered neurotrophic factors, BMP-7 was not associated with an increase in the sensitivity to pain. These results suggest that BMP-7 is able to act as a dopaminotrophic agent without unwanted side effects and as such may be a useful pharmacological tool in the treatment of Parkinson's disease in humans.

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. Phase drift (coexisting with unstable asymmetric phase-locked solutions), amplitude death, and in-phase synchronization were observed in both the experiments and simulations as coupling strength was increased. In addition, the simulations showed that a stable asymmetric phase-locked solution exists between the phase drift and amplitude death regions.

Rapid convergence of time-averaged frequency in phase synchronized systems.

Numerical and experimental evidences are presented to show that many phase synchronized systems of nonidentical chaotic oscillators, where the chaotic state is reached through a period-doubling cascade, show rapid convergence of the time-averaged frequency. The speed of convergence toward the natural frequency scales as the inverse of the measurement period. The results also suggest an explanation for why such chaotic oscillators can be phase synchronized.

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. The simulations show that the resonance behavior occurs with both identical and nonidentical oscillators. Noncommon (asymmetric and independent) noise does not enhance synchronization; common noise seems to enhance synchronization.

Experiments on coherence resonance: noisy precursors to Hopf bifurcations.

Experimental and numerical evidence of coherence resonance in an electrochemical system is reported. External noise with a Gaussian distribution is superimposed on the system when the anodic current is exhibiting stationary (fixed point) dynamics below a supercritical Hopf bifurcation. The amplitude of the added stochastic perturbations is increased monotonically and the induced oscillatory behavior is analyzed. It is observed, both in experiments and in simulations, that the regularity of the noise induced current oscillations reaches a maximum value for an optimum noise level. This is indicative of coherence resonance and can be explained with a mechanism based on noisy precursors to a Hopf bifurcation.

Populations of coupled electrochemical oscillators.

Experiments were carried out on arrays of chaotic electrochemical oscillators to which global coupling, periodic forcing, and feedback were applied. The global coupling converts a very weakly coupled set of chaotic oscillators to a synchronized state with sufficiently large values of coupling strength; at intermediate values both intermittent and stable chaotic cluster states occur. Cluster formation and synchronization were also obtained by applying feedback and forcing to a moderately coupled base state. The three cases differ, however, in other details. The feedback and forcing also produce periodic cluster states and more than two clusters. Configurations of two (chaotic) clusters and two, three, or four (periodic) clusters were observed. (c) 2002 American Institute of Physics.

Evolution of spatiotemporal patterns during the electrodissolution of metals: Experiments and simulations.

Spatiotemporal patterns including accelerating fronts, rotating waves, and homogeneous oscillations evolve during the electrodissolution of metals like cobalt and iron that exhibit passivity under potentiostatic control. The nature of the patterns is determined by long-range (nonlocal) coupling through the electric field which in turn is influenced by the geometry of the electrochemical cell, the applied potential, and the conductivity of the electrolyte. A two-variable model in a three-dimensional geometry is presented which is able to simulate the essential features of the experimental system.(c) 2002 American Institute of Physics.

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.

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.