Model-based analysis and forecast of sleep-wake regulatory dynamics: Tools and applications to data.

Extensive clinical and experimental evidence links sleep-wake regulation and state of vigilance (SOV) to neurological disorders including schizophrenia and epilepsy. To understand the bidirectional coupling between disease severity and sleep disturbances, we need to investigate the underlying neurophysiological interactions of the sleep-wake regulatory system (SWRS) in normal and pathological brains. We utilized unscented Kalman filter based data assimilation (DA) and physiologically based mathematical models of a sleep-wake regulatory network synchronized with experimental measurements to reconstruct and predict the state of SWRS in chronically implanted animals. Critical to applying this technique to real biological systems is the need to estimate the underlying model parameters. We have developed an estimation method capable of simultaneously fitting and tracking multiple model parameters to optimize the reconstructed system state. We add to this fixed-lag smoothing to improve reconstruction of random input to the system and those that have a delayed effect on the observed dynamics. To demonstrate application of our DA framework, we have experimentally recorded brain activity from freely behaving rodents and classified discrete SOV continuously for many-day long recordings. These discretized observations were then used as the "noisy observables" in the implemented framework to estimate time-dependent model parameters and then to forecast future state and state transitions from out-of-sample recordings.

Seizure modulation with applied electric fields in chronically implanted animals.

Low Frequency (<<100Hz) applied electric fields have been shown to modulate neuronal activity both In Vitro and in acute whole animal studies. We have been working to apply this technology for seizure control in chronically implanted animals. We have developed electronics for simultaneously recording neural activity while stimulating with low frequency fields. We have observed transient entrainment of spike and wave activity during spontaneous seizures with open loop sinusoidal stimulation with frequencies between 9-15 Hz. This is the first demonstration of low frequency field modulation of neural activity in chronically implanted mammalian brain.

Adaptive electric field control of epileptic seizures.

We describe a novel method of adaptively controlling epileptic seizure-like events in hippocampal brain slices using electric fields. Extracellular neuronal activity is continuously recorded during field application through differential extracellular recording techniques, and the applied electric field strength is continuously updated using a computer-controlled proportional feedback algorithm. This approach appears capable of sustained amelioration of seizure events in this preparation when used with negative feedback. Seizures can be induced or enhanced by using fields of opposite polarity through positive feedback. In negative feedback mode, such findings may offer a novel technology for seizure control. In positive feedback mode, adaptively applied electric fields may offer a more physiological means of neural modulation for prosthetic purposes than previously possible.

From generalized synchrony to topological decoherence: emergent sets in coupled chaotic systems.

We consider the evolution of the unstable periodic orbit structure of coupled chaotic systems. This involves the creation of a complicated set outside of the synchronization manifold (the emergent set). We quantitatively identify a critical transition point in its development (the decoherence transition). For asymmetric systems we also describe a migration of unstable periodic orbits that is of central importance in understanding these systems. Our framework provides an experimentally measurable transition, even in situations where previously described bifurcation structures are inapplicable.

Periodic orbits: a new language for neuronal dynamics.

A new nonlinear dynamical analysis is applied to complex behavior from neuronal systems. The conceptual foundation of this analysis is the abstraction of observed neuronal activities into a dynamical landscape characterized by a hierarchy of "unstable periodic orbits" (UPOs). UPOs are rigorously identified in data sets representative of three different levels of organization in mammalian brain. An analysis based on UPOs affords a novel alternative method of decoding, predicting, and controlling these neuronal systems.

Electric field suppression of epileptiform activity in hippocampal slices.

1. The effects of relatively small external DC electric fields on synchronous activity in CA1 and CA3 from transverse and longitudinal type hippocampal slices were studied. 2. To record neuronal activity during significant field changes, differential DC amplification was employed with a reference electrode aligned along an isopotential with the recording electrode. 3. Suppression of epileptiform activity was observed in 31 of 33 slices independent of region studied and type of slice but was highly dependent on field orientation with respect to the apical dendritic-somatic axis. 4. Modulation of neuronal activity in these experiments was readily observed at field strengths < or = 5-10 mV/mm. Suppression was seen with the field oriented (positive to negative potential) from the soma to the apical dentrites. 5. In vivo application of these results may be feasible.