Publicación: Modelos de disparo neuronal
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2018-10-09
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Universidad Nacional de Educación a Distancia (España). Facultad de Ciencias
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En este trabajo se van a estudiar y comparar los modelos más importantes de disparo neuronal basados en ecuaciones diferenciales no lineales, empezando por el modelo de Hodgkin–Huxley, original y precursor de todos ellos, y siguiendo con los modelos de Morris-Lecar, Fitzhugh-Nagumo, Hindmarsh-Rose e Izhikevich, como un intento de simplificar el original. Para ello se hará un estudio eléctrico de la neurona como sistema excitable, lo que permitirá, posteriormente, comprender los diferentes parámetros que van a formar parte de las distintas ecuaciones. A continuación se estudiará el modelo matemático de Hodgkin-Huxley y su potencial de acción (o disparo neuronal), lo cual dará una base para describir cada uno de los restantes modelos y, finalmente, para la obtención de resultados, se simularán las ecuaciones de los distintos modelos analizando la evolución del potencial en el tiempo y/o en el espacio de fases, lo cual permitirá descubrir el avance que supone cada uno de ellos respecto a sus predecesores.
In this paper we will study and compare the most important models of neuronal firing based on nonlinear differential equations, starting with the Hodgkin-Huxley model, original and precursor of all of them, and following with Morris-Lecar, Fitzhugh-Nagumo, Hindmarsh-Rose and Izhikevich models, as an attempt to simplify the original. To do this, an electrical study of the neuron as an excitable system will be done, which will allow, later, to understand the different parameters that will be part of the different equations. Next, the Hodgkin-Huxley mathematical model and its action potential (or neuronal firing) will be studied, which will provide a basis for describing each of the remaining models and, finally, for obtaining results, the equations of the different models will be simulated analyzing the evolution of the potential in time and/or in the phase portrait, which will allow to discover the progress that each of them represents with respect to their predecessors.
In this paper we will study and compare the most important models of neuronal firing based on nonlinear differential equations, starting with the Hodgkin-Huxley model, original and precursor of all of them, and following with Morris-Lecar, Fitzhugh-Nagumo, Hindmarsh-Rose and Izhikevich models, as an attempt to simplify the original. To do this, an electrical study of the neuron as an excitable system will be done, which will allow, later, to understand the different parameters that will be part of the different equations. Next, the Hodgkin-Huxley mathematical model and its action potential (or neuronal firing) will be studied, which will provide a basis for describing each of the remaining models and, finally, for obtaining results, the equations of the different models will be simulated analyzing the evolution of the potential in time and/or in the phase portrait, which will allow to discover the progress that each of them represents with respect to their predecessors.
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Facultades y escuelas::Facultad de Ciencias
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Física Fundamental