Extracellular stimulation window explained by a geometry-based model of the neuron-electrode contact

Extracellular stimulation of single cultured neurons which are completely sealing a microelectrode is usually performed using anodic or biphasic currents of at least 200 nA. However, recently obtained experimental data demonstrate the possibility to stimulate a neuron using cathodic current pulses with less amplitude. Also, a stimulation window is observed. These findings can be explained by a finite-element model which permits geometry-based electrical representation of the neuron-electrode interface and can be used to explore the required conditions for extracellular stimulation in detail. Modulation of the voltage sensitive channels in the sealing part of the membrane appears to be the key to successful cathodic stimulation. Furthermore, the upper limit of the stimulation window can be explained as a normal consequence of the neuronal membrane electrophysiology

Modeled channel distributions explain extracellular recordings from cultured neurons sealed to microelectrodes

Amplitudes and shapes of extracellular recordings from single neurons cultured on a substrate embedded microelectrode depend not only on the volume conducting properties of the neuron-electrode interface, but might also depend on the distribution of voltage-sensitive channels over the neuronal membrane. In this paper, finite-element modeling is used to quantify the effect of these channel distributions on the neuron-electrode contact. Slight accumulation or depletion of voltage-sensitive channels in the sealing membrane of the neuron results in various shapes and amplitudes of simulated extracellular recordings. However, estimation of channel-specific accumulation factors from extracellular recordings can be obstructed by co-occuring ion currents and defect sealing. Experimental data from cultured neuron-electrode interfaces suggest depletion of sodium channels and accumulation of potassium channels

Changes within bursts during learning in dissociated neural networks

We have studied the effect of imprinting a new stimulus-response (SR) relationship into a neuronal network cultured on a multi electrode array (MEA). We have used the Conditional Repetitive Stimulation (CRS) algorithm introduced by Shahaf et al in 2004. In this algorithm focal electrical stimulation is delivered at a low rate (≪1 Hz) and is withdrawn when a desired response is observed. We confirmed that CRS could train the network to strengthen an initially weak SR relationship. With the acquisition of a new SR relationship, we studied its effect on network activity. Specifically, spontaneously occurring network bursts measured before, during and after training were analyzed. The total firing rate within bursts was estimated with a temporal resolution of milliseconds (burst profiles). We have shown earlier that these profiles change shape on a time base of several hours during spontaneous development. We show that the rate of change of the profiles during training (i.e. CRS) was higher than when no stimulation was applied

Geometry-based finite-element modeling of the electrical contact between a cultured neuron and a microelectrode

The electrical contact between a substrate embedded microelectrode and a cultured neuron depends on the geometry of the neuron-electrode interface. Interpretation and improvement of these contacts requires proper modeling of all coupling mechanisms. In literature, it is common practice to model the neuron-electrode contact using lumped circuits in which large simplifications are made in the representation of the interface geometry. In this paper, the finite-element method is used to model the neuron-electrode interface, which permits numerical solutions for a variety of interface geometries. The simulation results offer detailed spatial and temporal information about the combined electrical behavior of extracellular volume, electrode-electrolyte interface and neuronal membrane

Generic Trace Semantics via Coinduction

Trace semantics has been defined for various kinds of state-based systems, notably with different forms of branching such as non-determinism vs. probability. In this paper we claim to identify one underlying mathematical structure behind these "trace semantics," namely coinduction in a Kleisli category. This claim is based on our technical result that, under a suitably order-enriched setting, a final coalgebra in a Kleisli category is given by an initial algebra in the category Sets. Formerly the theory of coalgebras has been employed mostly in Sets where coinduction yields a finer process semantics of bisimilarity. Therefore this paper extends the application field of coalgebras, providing a new instance of the principle "process semantics via coinduction."Comment: To appear in Logical Methods in Computer Science. 36 page

Coalgebra, concurrency and control

Coalgebra is used to generalize notions and techniques from concurrency theory, in order to apply them to problems concerning the supervisory control of discrete event systems. The main ingredients of this approach are the characterization of controllability in terms of (a variant of) the notion of bisimulation, and the observation that the fa

Elements of generalized ultrametric domain theory

Generalized ultrametric spaces are a common generalization of preorders and ordinary ultra-metric spaces, as was observed by Lawvere (1973). Guided by his enriched-categorical view on (ultra)metric spaces, we generalize the standard notions of Cau