No description available.

The study of neurons is of fundamental importance in biology and medicine. Neurons are the most basic unit of information processing in the nervous system of humans and all other vertebrates and in complex invertebrates. In addition, networks of neurons (the human brain) are the most sophisticated computational devices known, and the study of neurons individually and working in concert is seen as a step toward understanding consciousness and cognition. In the 1950's Hodgkin and Huxley developed a system of nonlinear ordinary differential equations to describe the behavior of a neuron found in the squid. Equations of this form have since been used to model the behavior of a multitude of neurons across a broad spectrum of species. Hodgkin-Huxley type neuron models helped lay the foundation for computational neuroscience, and they remain widely used in the study of neuron behavior almost sixty years after their development. Hodgkin-Huxley type models accept a set of parameters as input and generate data describing the electrical activity of the neuron as a function of time. We develop inversion algorithms to predict a set of input parameter values from the voltage trace data generated by the model. We test our algorithm on data from the Hodgkin-Huxley equations, and we extend the algorithm to solve the inverse problem associated with a more complex Hodgkin-Huxley type model for a lobster stomatogastric neuron. We find strong empirical evidence that the algorithms produce parameter values that generate a good fit to the target voltage trace, and we prove that under certain conditions the inversion algorithm for the Hodgkin-Huxley equations converges to a perfect match. To our knowledge this is the first parameter optimization procedure for which convergence has been shown theoretically. Understanding the relationship between the parameters of a neuron model and its output has implications for designing effective neuron models and for explaining the mechanisms by which neurons regulate their behavior. Inversion algorithms for Hodgkin-Huxley type neuron models are an important theoretical and practical step toward understanding the relationship between model parameters and model behavior, and toward the larger problem of inferring neuronal parameters from behavior observed experimentally.

Abstract Visual world is naturally correlated both spatially and temporally. The correlations are used in vision to enhance performance of neurons. For gaining maximal neural performance of the visual neurons, the experiments, from stimulus to the analysis, should be designed to take advantage of the correlations. In this thesis methods for generating and analyzing natural stimuli were examined by using computations and algorithms. For analyzing responses to natural stimuli in visual neurons, a method with only a few assumptions was developed for estimating information rate in long responses. The novel method gave a good agreement with Shannon information rate with linear system and Gaussian input but was able to handle also nonlinear processing and non-Gaussian data. Secondly, a computer controlled 3D virtual environment with a spherical screen was developed, with a large visual field. The image of the world was projected to the screen with a DLP projector, giving good enough temporal performance for insect vision research. A track-ball was used in closed loop experiments. Thirdly, properties of single photon (“bump”) information transfer at various light levels were investigated in cockroach photoreceptor with a coarse computational model. At dim light (< 10 ph/s), where single bump responses were visible, shot noise was dominant. At higher light levels latency distribution of the bump decreased the information rate, but amplitude distribution of bump did not have an effect. Fourthly, the contribution of K⁺ channels to information rate and energy consumption was investigated by creating a database of computation models with varying channel compositions. The information rate has a maximum as a function of mean conductance, which was a sum of the average K⁺ conductance and the leak conductance. This maximum was fine-tuned by the K⁺ channel composition, which had high so-called novel contribution and relatively low amount of other conductances.

No description available.

The aim of the research is to provide a computationally efficient neural network model for the study of deep brain stimulation efficacy in the treatment of Parkinson's disease. An Izhikevich neuron model was used to accomplish this task and four classes of neurons were modeled. The parameters of each class were estimated using a genetic algorithm with a fitness function based on spike frequency as a function of input current. After computing the optimal parameters the neurons were interconnected to form the network model. The estimated parameters were capable of replicating the normal firing characteristics for each type of neuron, but failed to replicate richer spiking characteristics such as post-inhibitory bursting and tonic firing. Without these characteristics, the network was unable to produce biologically feasible results. Findings indicate the Izhikevich model relies heavily on manual tuning and must be trained under an extensive set of conditions to allow for the majority of spiking characteristics to be learned. The use of the Izhikevich model in a network simulation will always be limited to the characteristics trained on a single neuron. When connected to the network the neuron may be exposed to a variety of unlearned conditions and therefore may not be capable of replicating biologically realistic behavior. / Electrical and Computer Engineering

In this thesis, we introduce several closely related stochastic models which generalize the deterministic Hodgkin-Huxley formalism to an SDE framework. We provide analytical results on the existence and uniqueness of solutions as well as the exact formulas for the moments of a simplified model, with simplifications motivated by the experiments performed by Hodgkin and Huxley in their seminal paper.For more complicated models, we provide an approach for the approximation and simulation of solutions to the corresponding SDEs, and show several realizations of the sample paths and moments of these simulations to verify qualitative behavior in this case. All code for the project is written in the Julia language and can be obtained upon request by the reader.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2018-11-12T14:27:26Z No. of bitstreams: 1 raffaelbechararameh.pdf: 1503042 bytes, checksum: 87e66fa77937ca9a85aac3231b27ac84 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-11-23T13:13:22Z (GMT) No. of bitstreams: 1 raffaelbechararameh.pdf: 1503042 bytes, checksum: 87e66fa77937ca9a85aac3231b27ac84 (MD5) / Made available in DSpace on 2018-11-23T13:13:22Z (GMT). No. of bitstreams: 1 raffaelbechararameh.pdf: 1503042 bytes, checksum: 87e66fa77937ca9a85aac3231b27ac84 (MD5) Previous issue date: 2018-08-31 / Para representar diferentes fenômenos e sistemas modelos matemáticos são largamente utilizados. Muitos deles são fundamentados em sistemas de equações diferenciais ordinárias (EDOs), isto é, baseiam-se em conjuntos de igualdades que envolvem variáveis dependentes, suas derivadas de primeira ordem e a variável independente. Neste trabalho, estudamos a modelagem da geração do potencial de ação em células excitáveis, como os neurônios. Existem dois modelos tradicionais e pioneiros que se destacam nessa área: Hodgkin-Huxley e FitzHugh-Nagumo. O objetivo desta dissertação é avaliar a possibilidade de modelar a geração do potencial de ação via uma única equação diferencial com atraso. Equações diferenciais com atraso são importantes por sua capacidade em reproduzir uma grande diversidade de fenômenos. Porém, seu uso na modelagem do potencial de ação de células excitáveis é ainda incipiente. Nesta dissertação, o método usado para alcançar este objetivo se baseou no desenvolvimento, inicialmente, de uma equação integro-diferencial que aproxima o sistema de EDOs. Em seguida, desenvolvemos uma aproximação para as integrais que usa termos tanto no instante atual quanto em instante anteriores, i.e., atrasados no tempo. Dessa forma, mostramos que é possível aproximar cada um dos sistemas de EDOS dos modelos de Hodgkin-Huxley e FitzHugh-Nagumo por uma única equação diferencial com atraso. Por fim, estes novos modelos são comparados com os originais, e são apontadas direções para a continuidade desta pesquisa. / To represent different phenomena and systems mathematical models are widely used. Many of them are based on systems of ordinary differential equations (ODEs), that is, they are based on sets of equalities involving dependent variables, their derivatives of first order and the independent variable. In this work, we study the modeling of action potential generation in excitable cells, such as neurons. There are two traditional and pioneering models that stand out in this area: Hodgkin-Huxley and FitzHugh-Nagumo. The objective of this dissertation is to evaluate the possibility of modeling the generation of the action potential via a single differential equation with delay. Differential equations with delay are important because of their capacity to reproduce a great diversity of phenomena. However, its use in modeling the action potential of excitable cells is still incipient. In this dissertation, the method used to achieve this goal was based on the development, initially, of an integral-differential equation that approximates the ODE system. Next, we develop an approximation for integrals that uses terms at both the current instant and the previous instant, i.e., time delayed. Thus, we show that it is possible to approximate each of the ODEs systems of the Hodgkin-Huxley and FitzHugh-Nagumo models by a single differential equation with delay. Finally, these new models are compared with the original ones, and directions are indicated for future works.

Made available in DSpace on 2017-07-21T19:25:53Z (GMT). No. of bitstreams: 1 Rafael R Borges.pdf: 2438169 bytes, checksum: 7ddddb02731c3c29cfcf61b843e0f82d (MD5) Previous issue date: 2016-05-11 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this thesis, it was investigated the influence of synaptic plasticity in the dynamics of neuronal networks. Specifically, we analyzed the effect on creation and suppression of synchronization spikes in networks composed of neurons with excitatory and inhibitory synapses. The spike timing-dependent plasticity (STDP) changes the strength of existing synapses in the neuronal network. To simulate the dynamics of each neuron, we considered the Hodgkin and Huxley model (HH), that is able to provide the main features of the temporal evolution of the membrane potential of each cell. The Kuramoto order parameter was utilized as synchronization diagnostic. First of all, we have studied the dynamics spikes in neuronal networks on a global and random topology with excitatory synapses with plasticity (STDP). It was observed that the STDP improves synchronization in a sufficiently dense neuronal networks. However, this effect is maximized by the insertion of an external perturbation of moderate intensity. Further, the system behavior was analyzed using the combination of inhibitory and excitatory synapses, both with spike timing-dependent plasticity. Our results indicated that the network becomes desynchronized when the intensity of inhibitory synapses is increased. Nevertheless, for small intensities of these synapses there was an increase in the values of the order parameter when the system with STDP was perturbed. / Nesta tese foi investigada a influência dos modelos de plasticidade sináptica na dinâmica de redes neuronais. Especificamente, foi analisado o efeito da plasticidade na criação e supressão da sincronização ao de disparos em redes compostas por neurônios com sinapses excitatórias e inibitórias. O modelo de plasticidade sináptica dependente do tempo entre disparos (do inglês: Spike-timing-dependent plasticity: STDP), modifica a intensidade das sinapses existentes na rede neuronal. Para simular a dinâmica de cada neurônio foi utilizado o modelo de Hodgkin e Huxley (HH), que ´e capaz de fornecer as principais características da evolução ao temporal do potencial de membrana de cada célula. Como diagnóstico de sincronização foi utilizado o parâmetro de ordem de Kuramoto. Primeiramente foi investigada a dinâmica de disparos em redes neuronais com topologia global e aleatória com sinapses excitatórias com plasticidade (STDP). Observou-se que a STDP contribui para a sincronização ao do sistema em redes neuronais suficientemente densas. No entanto, este efeito é maximizado com a inserção de uma perturbação o externa de intensidade moderada. Na sequência, foi analisado o comportamento do sistema com a combinação de sinapses excitatórias e inibitórias, ambas com STDP. Os resultados indicaram que a rede torna-se não sincronizada com o aumento da intensidade das sinapses inibitórias. Entretanto, para pequenas intensidades destas sinapses, observou-se um acréscimo nos valores do parâmetro de ordem quando o sistema com STDP foi perturbado.

Ce sujet de recherche a pour principaux objectifs la réalisation d'une bibliothèque de fonctions électroniques analogiques intégrées réalisant les opérations mathématiques présentes dans les modèles des canaux ioniques des neurones et l'évaluation des éléments de cette même bibliothèque. Ce travail se poursuit par la conception d'un système démonstrateur basé sur un circuit intégré analogique neuromimétique utilisant la bibliothèque d'opérateurs pour que ce même circuit intégré puisse être utilisé dans de nouvelles expériences mettant en oeuvre la technique hybride. En fonction des performances du circuit, il a été aussi étudié la faisabilité de son utilisation pour le développement d'un outil d'extraction des paramètres d'une cellule nerveuse, voire même d'un mini-réseau composé de moins d'une dizaine de neurones, par la technique d'optimisation.

The purpose of this thesis work is to model the gate control theory, which explains the modulation of pain signals, with a motivation of finding new possible targets for pain treatment and to find novel control algorithms that can be used in engineering practice. The difference of the current study from the previous modeling trials is that morphologies of neurons that constitute gate control system are also included in the model by which structure-function relationship can be observed. Model of an excitable neuron is constructed and the response of the model for different perturbations are investigated. The simulation results of the excitable cell model is obtained and when compared with the experimental findings obtained by using crayfish, it is found that they are in good agreement. Model encodes stimulation intensity information as firing frequency and also it can add sub-threshold inputs and fire action potentials as real neurons. Moreover, model is able to predict depolarization block. Absolute refractory period of the single cell model is found as 3.7 ms. The developed model, produces no action potentials when the sodium channels are blocked by tetrodotoxin. Also, frequency and amplitudes of generated action potentials increase when the reversal potential of Na is increased. In addition, propagation of signals along myelinated and unmyelinated fibers is simulated and input current intensity-frequency relationships for both type of fibers are constructed. Myelinated fiber starts to conduct when current input is about 400 pA whereas this minimum threshold value for unmyelinated fiber is around 1100 pA. Propagation velocity in the 1 cm long unmyelinated fiber is found as 0.43 m/s whereas velocity along myelinated fiber with the same length is found to be 64.35 m/s. Developed synapse model exhibits the summation and tetanization properties of real synapses while simulating the time dependency of neurotransmitter concentration in the synaptic cleft. Morphometric analysis of neurons that constitute gate control system are done in order to find electrophysiological properties according to dimensions of the neurons. All of the individual parts of the gate control system are connected and the whole system is simulated. For different connection configurations, results of the simulations predict the observed phenomena for the suppression of pain. If the myelinated fiber is dissected, the projection neuron generates action potentials that would convey to brain and elicit pain. However, if the unmyelinated fiber is dissected, projection neuron remains silent. In this study all of the simulations are preformed using Simulink.