Towards a computational model for stimulation of the Pedunculopontine nucleus

The pedunculopontine nucleus (PPN) has recently been suggested as a new therapeutic target for deep brain stimulation (DBS) in patients suffering from Parkinson's disease, particularly those with severe gait and postural impairment [1]. Stimulation at this site is typically delivered at low frequencies in contrast to the high frequency stimulation required for therapeutic benefit in the subthalamic nucleus (STN) [1]. Despite real therapeutic successes, the fundamental physiological mechanisms underlying the effect of DBS are still not understood. A hypothesis is that DBS masks the pathological synchronized firing patterns of the basal ganglia that characterize the Parkinsonian state with a regularized firing pattern. It remains unclear why stimulation of PPN should be applied with low frequency in contrast to the high frequency stimulation of STN. To get a better understanding of PPN stimulation we construct a computational model for the PPN Type I neurons in a network

Synchronization of the parkinsonian globus pallidus by gap junctions

We introduce pallidal gap junctional coupling as a possible mechanism for synchronization of the GPe after dopamine depletion. In a confocal imaging study, we show the presence of the neural gap junction protein Cx36 in the human GPe, including a possible remodeling process in PD patients. Dopamine has been shown to down-regulate the conductance of gap junctions in different regions of the brain [2,3], making dopamine depletion a possible candidate for increased influence of gap junctional coupling in PD

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. This observation is captured by a population model that describes the activity of large neuronal populations with two differential equations with two delays. Both models appear to have similar sensitivity to variations of total network excitation. Analysis of the population model reveals the presence of multistability, which was also observed in various simulations of the detailed model

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

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. We examined the effect of such a saturation in the Wilson–Cowan formalism by adapting the nonlinear activation function; we substituted the commonly applied sigmoid for a Gaussian function. We discuss experimental recordings during a seizure that support this substitution. Next we perform a bifurcation analysis on the Wilson–Cowan model with a Gaussian activation function. The main effect is an additional stable equilibrium with high excitatory and low inhibitory activity. Analysis of coupled local networks then shows that such high activity can stay localized or spread. Specifically, in a spatial continuum we show a wavefront with inhibition leading followed by excitatory activity. We relate our model simulations to observations of spreading activity during seizures

On analysis of inputs triggering large nonlinear neural responses: Slow-fast dynamics in the Wendling neural mass model

Many applications in neuroscience, such as electrical and magnetic stimulation, can be modelled as short transient input to non-linear dynamical systems. In excitable systems, small input yields more or less linear responses, while for increasing stimulation strength large non-linear responses may show up suddenly. A challenging task is to determine the transition between the two different response types. In this work we consider such a transition between normal and pathological responses in a model of coupled Wendling neural masses as we encountered in a previous study. First, the different timescales of inhibition in this model allow a slow-fast analysis. This reveals two different dynamical regimes for the systems’ response. Second, the two response types are separated by a high-dimensional stable manifold of a saddle slow manifold. Large pathological responses appear if the fast subsystem escapes from this manifold to another attractor. The typical fast oscillations seen during the pathological responses are explained by the bifurcation diagram of the fast subsystem. Under normal conditions these oscillations are suppressed by slow inhibition. External stimulation temporarily releases the fast subsystem from this slow inhibition. The critical response can be formulated as a boundary value problem with one free parameter and can be used to study the dependency of the transition between the two response types upon the system parameters

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. Equilibria are identified, and using linear stability analysis, all transitions are determined under which both trivial and non-trivial fixed points lose stability. Periodic solutions arising at some of these bifurcations are numerically studied with a two-parameter bifurcation analysis

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. We subsequently describe the physiological mechanism underlying this observation as suggested by the model. It is suggested that the spikes reflect inhibitory stochastic fluctuations in the input to thalamo-cortical relay neurons and phase-locking is a consequence of differential excitability of relay neurons over the delta cycle. Further analysis shows that the observed phase-locking can be regarded as a stochastic precursor of generalized spike-wave discharges. This study thus provides an explanation of intermittent spikes during delta oscillations in NCSE and might be generalized to other encephathologies in which delta activity can be observed

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. The severity of ischemic damage depends on the age and the brain region in which a stroke occurs, but the reasons for this differential vulnerability are far from understood. In the present study, we address this question by developing a comprehensive biophysical model of a glutamatergic synapse to identify key determinants of synaptic failure during energy deprivation. Our model is based on fundamental biophysical principles, includes dynamics of the most relevant ions, i.e., Na+, K+, Ca2+, Cl− and glutamate, and is calibrated with experimental data. It confirms the critical role of the Na+/K+-ATPase in maintaining ion gradients, membrane potentials and cell volumes. Our simulations demonstrate that the system exhibits two stable states, one physiological and one pathological. During energy deprivation, the physiological state may disappear, forcing a transit to the pathological state, which can be reverted when blocking voltage-gated Na+ and K+ channels. Our model predicts that the transition to the pathological state is favoured if the extracellular space fraction is small. A reduction in the extracellular space volume fraction, as, e.g. observed with ageing, will thus promote the brain’s susceptibility to ischemic damage. Our work provides new insights into the brain’s ability to recover from energy deprivation, with translational relevance for diagnosis and treatment of ischemic strokes