Widespread neuronal chaos induced by slow oscillating currents.

This paper investigates the origin and onset of chaos in a mathematical model of an individual neuron, arising from the intricate interaction between 3D fast and 2D slow dynamics governing its intrinsic currents. Central to the chaotic dynamics are multiple homoclinic connections and bifurcations of saddle equilibria and periodic orbits. This neural model reveals a rich array of codimension-2 bifurcations, including Shilnikov-Hopf, Belyakov, Bautin, and Bogdanov-Takens points, which play a pivotal role in organizing the complex bifurcation structure of the parameter space.

Weak coupling of neurons enables very high-frequency and ultra-fast oscillations through the interplay of synchronized phase shifts.

Recently, in the past decade, high-frequency oscillations (HFOs), very high-frequency oscillations (VHFOs), and ultra-fast oscillations (UFOs) were reported in epileptic patients with drug-resistant epilepsy. However, to this day, the physiological origin of these events has yet to be understood. Our study establishes a mathematical framework based on bifurcation theory for investigating the occurrence of VHFOs and UFOs in depth EEG signals of patients with focal epilepsy, focusing on the potential role of reduced connection strength between neurons in an epileptic focus.

An in silico and in vitro human neuronal network model reveals cellular mechanisms beyond Na1.1 underlying Dravet syndrome.

Human induced pluripotent stem cell (hiPSC)-derived neuronal networks on multi-electrode arrays (MEAs) provide a unique phenotyping tool to study neurological disorders. However, it is difficult to infer cellular mechanisms underlying these phenotypes. Computational modeling can utilize the rich dataset generated by MEAs, and advance understanding of disease mechanisms.

Glial Chloride Homeostasis Under Transient Ischemic Stress.

High water permeabilities permit rapid adjustments of glial volume upon changes in external and internal osmolarity, and pathologically altered intracellular chloride concentrations ([Cl]) and glial cell swelling are often assumed to represent early events in ischemia, infections, or traumatic brain injury. Experimental data for glial [Cl] are lacking for most brain regions, under normal as well as under pathological conditions. We measured [Cl] in hippocampal and neocortical astrocytes and in hippocampal radial glia-like (RGL) cells in acute murine brain slices using fluorescence lifetime imaging microscopy with the chloride-sensitive dye MQAE at room temperature.

On the Role of Arkypallidal and Prototypical Neurons for Phase Transitions in the External Pallidum.

The external pallidum (globus pallidus pars externa [GPe]) plays a central role for basal ganglia functions and dynamics and, consequently, has been included in most computational studies of the basal ganglia. These studies considered the GPe as a homogeneous neural population. However, experimental studies have shown that the GPe contains at least two distinct cell types (prototypical and arkypallidal cells).

Bistability and Stabilization of Human Visual Perception under Ambiguous Stimulation.

We discuss a computational model that describes stabilization of percept choices under intermittent viewing of an ambiguous visual stimulus at long stimulus intervals. Let T_off and T_on be the time that the stimulus is off and on, respectively. The behavior was studied by direct numerical simulation in a grid of (T_off, T_on) values in a 2007 paper of Noest, van Ee, Nijs, and van Wezel.

Ion dynamics at the energy-deprived tripartite synapse.

The anatomical and functional organization of neurons and astrocytes at 'tripartite synapses' is essential for reliable neurotransmission, which critically depends on ATP. In low energy conditions, synaptic transmission fails, accompanied by a breakdown of ion gradients, changes in membrane potentials and cell swelling. The resulting cellular damage and cell death are causal to the often devastating consequences of an ischemic stroke.

Pathological responses to single-pulse electrical stimuli in epilepsy: The role of feedforward inhibition.

Delineation of epileptogenic cortex in focal epilepsy patients may profit from single-pulse electrical stimulation during intracranial EEG recordings. Single-pulse electrical stimulation evokes early and delayed responses. Early responses represent connectivity.

A Comparison of Evoked and Non-evoked Functional Networks.

The growing interest in brain networks to study the brain's function in cognition and diseases has produced an increase in methods to extract these networks. Typically, each method yields a different network. Therefore, one may ask what the resulting networks represent.

Evoked directional network characteristics of epileptogenic tissue derived from single pulse electrical stimulation.

We investigated effective networks constructed from single pulse electrical stimulation (SPES) in epilepsy patients who underwent intracranial electrocorticography. Using graph analysis, we compared network characteristics of tissue within and outside the epileptogenic area. In 21 patients with subdural electrode grids (1 cm interelectrode distance), we constructed a binary, directional network derived from SPES early responses (<100 ms).

Phenomenological network models: Lessons for epilepsy surgery.

The current opinion in epilepsy surgery is that successful surgery is about removing pathological cortex in the anatomic sense. This contrasts with recent developments in epilepsy research, where epilepsy is seen as a network disease. Computational models offer a framework to investigate the influence of networks, as well as local tissue properties, and to explore alternative resection strategies.

Estimation and Identifiability of Model Parameters in Human Nociceptive Processing Using Yes-No Detection Responses to Electrocutaneous Stimulation.

Healthy or pathological states of nociceptive subsystems determine different stimulus-response relations measured from quantitative sensory testing. In turn, stimulus-response measurements may be used to assess these states. In a recently developed computational model, six model parameters characterize activation of nerve endings and spinal neurons.

Dependence of Nociceptive Detection Thresholds on Physiological Parameters and Capsaicin-Induced Neuroplasticity: A Computational Study.

Physiological properties of peripheral and central nociceptive subsystems can be altered over time due to medical interventions. The effective change for the whole nociceptive system can be reflected in changes of psychophysical characteristics, e.g.

Computational modeling of Adelta-fiber-mediated nociceptive detection of electrocutaneous stimulation.

Sensitization is an example of malfunctioning of the nociceptive pathway in either the peripheral or central nervous system. Using quantitative sensory testing, one can only infer sensitization, but not determine the defective subsystem. The states of the subsystems may be characterized using computational modeling together with experimental data.

Modeling focal epileptic activity in the Wilson-cowan model with depolarization block.

Unlabelled: Measurements of neuronal signals during human seizure activity and evoked epileptic activity in experimental models suggest that, in these pathological states, the individual nerve cells experience an activity driven depolarization block, i.e. they saturate.

Exploiting pallidal plasticity for stimulation in Parkinson's disease.

Objective: Continuous application of high-frequency deep brain stimulation (DBS) often effectively reduces motor symptoms of Parkinson's disease patients. While there is a growing need for more effective and less traumatic stimulation, the exact mechanism of DBS is still unknown. Here, we present a methodology to exploit the plasticity of GABAergic synapses inside the external globus pallidus (GPe) for the optimization of DBS.

Phase-locking of epileptic spikes to ongoing delta oscillations in non-convulsive status epilepticus.

The EEG of patients in non-convulsive status epilepticus (NCSE) often displays delta oscillations or generalized spike-wave discharges. In some patients, these delta oscillations coexist with intermittent epileptic spikes. In this study we verify the prediction of a computational model of the thalamo-cortical system that these spikes are phase-locked to the delta oscillations.

Tracking of nociceptive thresholds using adaptive psychophysical methods.

Psychophysical thresholds reflect the state of the underlying nociceptive mechanisms. For example, noxious events can activate endogenous analgesic mechanisms that increase the nociceptive threshold. Therefore, tracking thresholds over time facilitates the investigation of the dynamics of these underlying mechanisms.

Travelling waves in a neural field model with refractoriness.

At one level of abstraction neural tissue can be regarded as a medium for turning local synaptic activity into output signals that propagate over large distances via axons to generate further synaptic activity that can cause reverberant activity in networks that possess a mixture of excitatory and inhibitory connections. This output is often taken to be a firing rate, and the mathematical form for the evolution equation of activity depends upon a spatial convolution of this rate with a fixed anatomical connectivity pattern. Such formulations often neglect the metabolic processes that would ultimately limit synaptic activity.

Analysis of stability and bifurcations of fixed points and periodic solutions of a lumped model of neocortex with two delays.

A lumped model of neural activity in neocortex is studied to identify regions of multi-stability of both steady states and periodic solutions. Presence of both steady states and periodic solutions is considered to correspond with epileptogenesis. The model, which consists of two delay differential equations with two fixed time lags is mainly studied for its dependency on varying connection strength between populations.

Comparing epileptiform behavior of mesoscale detailed models and population models of neocortex.

Two models of the neocortex are developed to study normal and pathologic neuronal activity. One model contains a detailed description of a neocortical microcolumn represented by 656 neurons, including superficial and deep pyramidal cells, four types of inhibitory neurons, and realistic synaptic contacts. Simulations show that neurons of a given type exhibit similar, synchronized behavior in this detailed model.

Frequency-selectivity of a thalamocortical relay neuron during Parkinson's disease and deep brain stimulation: a computational study.

In this computational study, we investigated (i) the functional importance of correlated basal ganglia (BG) activity associated with Parkinson's disease (PD) motor symptoms by analysing the effects of globus pallidus internum (GPi) bursting frequency and synchrony on a thalamocortical (TC) relay neuron, which received GABAergic projections from this nucleus; (ii) the effects of subthalamic nucleus (STN) deep brain stimulation (DBS) on the response of the TC relay neuron to synchronized GPi oscillations; and (iii) the functional basis of the inverse relationship that has been reported between DBS frequency and stimulus amplitude, required to alleviate PD motor symptoms [A. L. Benabid et al.