In a spontaneously bursting neuronal network in vitro, chaos can be demonstrated by the presence of unstable fixed-point behaviour. Chaos control techniques can increase the periodicity of such neuronal population bursting behaviour. Periodic pacing is also effective in entraining such systems, although in a qualitatively different fashion. Using a strategy of anticontrol such systems can be made less periodic. These techniques may be applicable to in vivo epileptic foci.

Epilepsy has been historically seen as a functional brain disorder associated with excessive synchronization of large neuronal populations leading to a hypersynchronous state. Recent evidence showed that epileptiform phenomena, particularly seizures, result from complex interactions between neuronal networks characterized by heterogeneity of neuronal firing and dynamical evolution of synchronization. Desynchronization is often observed preceding seizures or during their early stages; in contrast, high levels of synchronization observed towards the end of seizures may facilitate termination. In this review we discuss cellular and network mechanisms responsible for such complex changes in synchronization. Recent work has identified cell-type-specific inhibitory and excitatory interactions, the dichotomy between neuronal firing and the non-local measurement of local field potentials distant to that firing, and the reflection of the neuronal dark matter problem in non-firing neurons active in seizures. These recent advances have challenged long-established views and are leading to a more rigorous and realistic understanding of the pathophysiology of epilepsy.

Cerebrospinal fluid shunt failure, predominantly from shunt obstruction and infection, remains a persistent problem in pediatric hydrocephalus. Two new valve designs did not significantly affect shunt failure rates.

In these companion papers, we study how the interrelated dynamics of sodium and potassium affect the excitability of neurons, the occurrence of seizures, and the stability of persistent states of activity. In this first paper, we construct a mathematical model consisting of a single conductance-based neuron together with intra-and extracellular ion concentration dynamics. We formulate a reduction of this model that permits a detailed bifurcation analysis, and show that the reduced model is a reasonable approximation of the full model. We find that competition between intrinsic neuronal currents, sodium-potassium pumps, glia, and diffusion can produce very slow and large-amplitude oscillations in ion concentrations similar to what is seen physiologically in seizures. Using the reduced model, we identify the dynamical mechanisms that give rise to these phenomena. These models reveal several experimentally testable predictions. Our work emphasizes the critical role of ion concentration homeostasis in the proper functioning of neurons, and points to important fundamental processes that may underlie pathological states such as epilepsy.