The derivation of continuum limits of neuronal networks with gap-junction couplings

We consider an idealized network, formed by N neurons individually described by the FitzHugh-Nagumo equations and connected by electrical synapses. The limit for N to infinity of the resulting discrete model is thoroughly investigated, with the aim of identifying a model for a continuum of neurons having an equivalent behaviour. Two strategies for passing to the limit are analysed: i) a more conventional approach, based on a fixed nearest-neighbour connection topology accompanied by a suitable scaling of the diffusion coefficients; ii) a new approach, in which the number of connections to any given neuron varies with N according to a precise law, which simultaneously guarantees the non-triviality of the limit and the locality of neuronal interactions. Both approaches yield in the limit a pde-based model, in which the distribution of action potential obeys a nonlinear reaction-convection-diffusion equation; convection accounts for the possible lack of symmetry in the connection topology. Several convergence issues are discussed, both theoretically and numerically

The complexity of dynamics in small neural circuits

Mean-field theory is a powerful tool for studying large neural networks. However, when the system is composed of a few neurons, macroscopic differences between the mean-field approximation and the real behavior of the network can arise. Here we introduce a study of the dynamics of a small firing-rate network with excitatory and inhibitory populations, in terms of local and global bifurcations of the neural activity. Our approach is analytically tractable in many respects, and sheds new light on the finite-size effects of the system. In particular, we focus on the formation of multiple branching solutions of the neural equations through spontaneous symmetry-breaking, since this phenomenon increases considerably the complexity of the dynamical behavior of the network. For these reasons, branching points may reveal important mechanisms through which neurons interact and process information, which are not accounted for by the mean-field approximation.Comment: 34 pages, 11 figures. Supplementary materials added, colors of figures 8 and 9 fixed, results unchange

"Multispecies" models to describe large neuronal networks

Today modeling large neural network is a topic more relevant than ever. In particular, the set up of computer simulations describing complex networks with a huge number of nodes is a formidable challenge. The intrinsic difficulties concerning the prohibitive computational costs may be handled to some extent by exploiting what we call ``multispecies'' models. From a mathematical perspective this issue consists in formalizing the PDE-based continuum models which describe the high-density populations inside the network and studying interactions between them and the ODE-based discrete models for each neuron belonging to the low-density populations. In particular, we exploit such an approach to describe the Golgi-Granular cell loop network in the Cerebellum. Each single cell is described by means of the FitzHugh-Nagumo model and both electrical and chemical (excitatory and inhibitory) synapses are taken into account. Several simulations describing interesting phenomena as synchronization and travelling waves have been done. Biological aspects have also been examined in order to provide our work with scientific completeness

A hybrid model for the computationally-efficient simulation of the cerebellar granular layer

The aim of the present paper is to efficiently describe the membrane potential dynamics of neural populations formed by species having a high density difference in specific brain areas. We propose a hybrid model whose main ingredients are a conductance-based model (ODE system) and its continuous counterpart (PDE system) obtained through a limit process in which the number of neurons confined in a bounded region of the brain tissue is sent to infinity. Specifically, in the discrete model, each cell is described by a set of time-dependent variables, whereas in the continuum model, cells are grouped into populations that are described by a set of continuous variables.Communications between populations, which translate into interactions among the discrete and the continuous models, are the essence of the hybrid model we present here. The cerebellum and cerebellum-like structures show in their granular layer a large difference in the relative density of neuronal species making them a natural testing ground for our hybrid model. By reconstructing the ensemble activity of the cerebellar granular layer network and by comparing our results to a more realistic computational network, we demonstrate that our description of the network activity, even though it is not biophysically detailed, is still capable of reproducing salient features of neural network dynamics. Our modeling approach yields a significant computational cost reduction by increasing the simulation speed at least $270$ times. The hybrid model reproduces interesting dynamics such as local microcircuit synchronization, traveling waves, center-surround and time-windowing

Nanostructures in hydrogen peroxide sensing

In recent years, several devices have been developed for the direct measurement of hydrogen peroxide (H2O2 ), a key compound in biological processes and an important chemical reagent in industrial applications. Classical enzymatic biosensors for H2O2 have been recently outclassed by electrochemical sensors that take advantage of material properties in the nano range. Electrodes with metal nanoparticles (NPs) such as Pt, Au, Pd and Ag have been widely used, often in combination with organic and inorganic molecules to improve the sensing capabilities. In this review, we present an overview of nanomaterials, molecules, polymers, and transduction methods used in the optimization of electrochemical sensors for H2O2 sensing. The different devices are compared on the basis of the sensitivity values, the limit of detection (LOD) and the linear range of application reported in the literature. The review aims to provide an overview of the advantages associated with different nanostructures to assess which one best suits a target application.Fil: Trujillo, Ricardo Matias. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tucumán. Instituto Superior de Investigaciones Biológicas. Universidad Nacional de Tucumán. Instituto Superior de Investigaciones Biológicas; Argentina. Universidad Nacional de Tucumán. Facultad de Ciencias Exactas y Tecnología. Departamento de Bioingeniería. Laboratorio de Medios e Interfases; ArgentinaFil: Barraza, Daniela Estefanía. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tucumán. Instituto Superior de Investigaciones Biológicas. Universidad Nacional de Tucumán. Instituto Superior de Investigaciones Biológicas; Argentina. Universidad Nacional de Tucumán. Facultad de Ciencias Exactas y Tecnología. Departamento de Bioingeniería. Laboratorio de Medios e Interfases; ArgentinaFil: Zamora, Martín Lucas. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tucumán. Instituto Superior de Investigaciones Biológicas. Universidad Nacional de Tucumán. Instituto Superior de Investigaciones Biológicas; Argentina. Universidad Nacional de Tucumán. Facultad de Ciencias Exactas y Tecnología. Departamento de Bioingeniería. Laboratorio de Medios e Interfases; ArgentinaFil: Cattani Scholz, Anna. Universitat Technical Zu Munich; AlemaniaFil: Madrid, Rossana Elena. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tucumán. Instituto Superior de Investigaciones Biológicas. Universidad Nacional de Tucumán. Instituto Superior de Investigaciones Biológicas; Argentina. Universidad Nacional de Tucumán. Facultad de Ciencias Exactas y Tecnología. Departamento de Bioingeniería. Laboratorio de Medios e Interfases; Argentin

Computer-based cognitive rehabilitation: the CoRe system

This work aims at providing a tool for supporting cognitive rehabilitation. This is a wide field, that includes a variety of diseases and related clinical pictures; for this reason the need arises to have a tool available that overcomes the difficulties entailed by what currently is the most common approach, that is, the so-called pen and paper rehabilitation. Methods: We first organized a big number of stimuli in an ontology that represents concepts, attributes and a set of relationships among concepts. Stimuli may be words, sounds, 2D and 3D images. Then, we developed an engine that automatically generates exercises by exploiting that ontology. The design of exercises has been carried on in synergy with neuropsychologists and speech therapists. Solutions have been devised aimed at personalizing the exercises according to both patients’ preferences and performance. Results: Exercises addressed to rehabilitation of executive functions and aphasia-related diseases have been implemented. The system has been tested on both healthy volunteers (n 1/4 38) and patients (n 1/4 9), obtaining a favourable rating and suggestions for improvements. Conclusions: We created a tool able to automate the execution of cognitive rehabilitation tasks. We hope the variety and personalization of exercises will allow to increase compliance, particularly from elderly people, usually neither familiar with technology nor particularly willing to rely on it. The next step involves the creation of a telerehabilitation tool, to allow therapy sessions to be undergone from home, thus guaranteeing continuity of care and advantages in terms of time and costs for the patients and the National Healthcare System (NHS).Postprint (published version