1,721,007 research outputs found
The Hindmarsh-Rose neuron model: Bifurcation analysis and piecewise-linear approximations
No full textThis paper provides a global picture of the bifurcation scenario of the Hindmarsh-Rose model. A combination between simulations and numerical continuations is used to unfold the complex bifurcation structure. The bifurcation analysis is carried out by varying two bifurcation parameters and evidence is given that the structure that is found is universal and appears for all combinations of bifurcation parameters. The information about the organizing principles and bifurcation diagrams are then used to compare the dynamics of the model with that of a piecewise-linear approximation, customized for circuit implementation. A good match between the dynamical behaviors of the models is found. These results can be used both to design a circuit implementation of the Hindmarsh-Rose model mimicking the diversity of neural response and as guidelines to predict the behavior of the model as well as its circuit implementation as a function of parameters. (C) 2008 American Institute of Physics
A method based on a genetic algorithm to find PWL approximations of multivariate nonlinear functions
No full textIn this paper we present a systematic approach to find piecewise-linear approximations of multivariate continuous nonlinear functions, by ensuring a good trade-off between approximation accuracy and model complexity. The proposed (suboptimal) method is based on genetic programming and takes into account the circuit constraints concerning the lower bounds for the size of each domain region (called simplex) where a given nonlinear function is approximated linearly. As a benchmark example, we approximate the well-known Hodgkin- Huxley neuron model
A parameter-dependent approximation of the Hindmarsh-Rose neuron model suitable for analog circuit implementation
No full textA parameter-dependent approximation of the Hindmarsh-Rose neuron model suitable for analog circuit implementation
No full textPWL approximation of the Hindmarsh-Rose neuron model in view of its circuit implementation
No full textSimulation of stochastic electromagnetic transients in EMTP: A bug turned into a feature
No full textThis paper proposes a systematic approach to simulating stochastic electromagnetic transients in emtp, through the reliable numerical solution of stochastic differential equations. Actually, numerical integration schemes for stochastic differential equations (sdes) are not available in emtp. It is shown how to set up the Semi-Implicit Backward Euler scheme specific for stochastic differential equations. The implemented interaction strategy between the engine for the solution of electrical circuits and the engine for the Transient Analysis of Control Systems of emtp is exploited. This is a bolt from the blue feature of this simulator that makes it the only one on the shelf able to handle stochastic differential equations. Exploiting this unveiled capability, some basic and tutorial case studies are presented. They pave the way for the simulation of more complex circuits and systems that go beyond the scope of this work. Simulation files are provided as supplementary material and they are available on GitHub
Experimental bifurcation diagram of a circuit-implemented neuron model
No full textAn experimental bifurcation diagram of a circuit implementing an approximation of the Hindmarsh-Rose (HR) neuron model is presented. Measured asymptotic time series of circuit voltages are automatically classified through an ad hoc algorithm. The resulting two-dimensional experimental bifurcation diagram evidences a good match with respect to the numerical results available for both the approximated and original HR model. Moreover, the experimentally obtained current-frequency curve is very similar to that of the original model. The obtained results are both a proof of concept of a quite general method developed in the last few years for the approximation and implementation of nonlinear dynamical systems and a first step towards the realisation in silica of HR neuron networks with tunable parameters. (C) 2010 Elsevier B.V. All rights reserved
Dynamical response properties of neocortical neurons to conductance-driven time-varying inputs
Full text linkEnsembles of cortical neurons can track fast-varying inputs and relay them in their spike trains, far beyond the cut-off imposed by membrane passive electrical properties and mean firing rates. Initially explored in silico and later demonstrated experimentally, investigating how neurons respond to sinusoidally modulated stimuli provides a deeper insight into spike initiation mechanisms and information processing than conventional F–I curve methodologies. Besides net membrane currents, physiological synaptic inputs can also induce a stimulus-dependent modulation of the total membrane conductance, which is not reproduced by standard current-clamp protocols. Here, we investigated whether rat cortical neurons can track fast temporal modulations over a noisy conductance background. We also determined input–output transfer properties over a range of conditions, including: distinct presynaptic activation rates, postsynaptic firing rates and variability and type of temporal modulations. We found a very broad signal transfer bandwidth across all conditions, similar large cut-off frequencies and power-law attenuations of fast-varying inputs. At slow and intermediate input modulations, the response gain decreased for increasing output mean firing rates. The gain also decreased significantly for increasing intensities of background synaptic activity, thus generalising earlier studies on F-I curves. We also found a direct correlation between the action potentials' onset rapidness and the neuronal bandwidth. Our novel results extend previous investigations of dynamical response properties to non-stationary and conductance-driven conditions, and provide computational neuroscientists with a novel set of observations that models must capture when aiming to replicate cortical cellular excitability.SCOPUS: ar.jinfo:eu-repo/semantics/publishe
Real-time electrophysiology : using closed-loop protocols to probe neuronal dynamics and beyond
No full textAbstract: Experimental neuroscience is witnessing an increased interest in the development and application of novel and often complex, closed-loop protocols, where the stimulus applied depends in real-time on the response of the system. Recent applications range from the implementation of virtual reality systems for studying motor responses both in mice(1) and in zebrafish(2), to control of seizures following cortical stroke using optogenetics(3). A key advantage of closed-loop techniques resides in the capability of probing higher dimensional properties that are not directly accessible or that depend on multiple variables, such as neuronal excitability(4) and reliability, while at the same time maximizing the experimental throughput. In this contribution and in the context of cellular electrophysiology, we describe how to apply a variety of closed-loop protocols to the study of the response properties of pyramidal cortical neurons, recorded intracellularly with the patch clamp technique in acute brain slices from the somatosensory cortex of juvenile rats. As no commercially available or open source software provides all the features required for efficiently performing the experiments described here, a new software toolbox called LCG(5) was developed, whose modular structure maximizes reuse of computer code and facilitates the implementation of novel experimental paradigms. Stimulation waveforms are specified using a compact metadescription and full experimental protocols are described in text-based configuration files. Additionally, LCG has a command-line interface that is suited for repetition of trials and automation of experimental protocols
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