A Study For Simulation Models Of The Electrical Activities Of The Nerve In Brain

The dynamical simulation of the electrical activities of the nerve in brain is one of subjects in the computational neuroscience. The synchronous oscillation and propagation and the forward problem of the nerval activities are the main contents of the dissertation. The numerical method of electrical field and circuit and nonlinear and complexity of automation are the main means utilized in the subject. It is the helpful to understand the complex activities and explain some mechanism, for example, epileptic seizure, because the synchrony of excitable neurons and propagation are the important characters. Three parts of work are done in the subject:First: The synchrony of the abnormal oscillation.At first, a model of a pair of excitable neurons coupled via gap junction is built by Chay model, the effect of the strength of gap junction on the synchronous oscillation is studied; then, the synchronous oscillations of a 2-D network are also studied; at last, the Lyapunov exponent and phase portrait are utilized in the analysis of nonlinear, the approximate entropy is utilized to measure the complexity. Three results are received: (1) The population of neurons can synchronize when the strength of gap junction is large enough and the process is chaotic and complex; (2) The nonlinear and complexity of the seriously disorder oscillation are larger than that of slightly disorder oscillation in a 2-D network; (3) The nonlinear and complexity of the oscillations with strong strength of gap junction are larger than that of that with weak strength of gap junction.Second: The effect of the propagation of the abnormal oscillations on other abnormal oscillations and action potentials.From the ion channel, a 2-D partly differential equation (PDE) in the temporal region is built to study the gap junctional effect of the propagation of the abnormal oscillation, implicit scheme of finite differential and numerical method of nonlinear ordinary differential equation are utilized to solve the PDE, and the nonlinear of the propagation is analyzed by the Lyapunov exponent and phase portraits, the complexity is measured by the approximate entropy.At first, the effect of the propagation of the seriously abnormal oscillation on the slightly abnormal oscillation is studied with the different strength of gap junction. The results are indicated that only the strength of gap junction is large enough, can the abnormal oscillation propagate to synchronize the other neurons around and the process is chaotic and complex; the nonlinear and complexity of the oscillations with strong strength of gap junction are larger than that of oscillation with weak strength of gap junction.Then, the effect of the propagation of the seriously abnormal oscillation on the action potential of normal neuron is studied with the different strength of gap junction. The results are indicated that when the strength of gap junction is large, the abnormal oscillation can propagate to cause the action potential to oscillate. The dynamical process of the action potential changes to be chaotic from the stable state, and, the complexity is increased. But, the ability of producing the new oscillation is limited with the dynamical process and the new oscillations are made by the abnormal oscillation.Third: The forward problem of the nerve activities by the dipole of the abnormal oscillation.Some simulation waves are obtained based on the 2-D and 3-D models, for example, the sharp wave with negative phase, polyspike and slow waves, and the sharp wave with two phases. It is found that the amplitude of the spikes with negative phase is lowered and the interval of spikes is longed with the increase of the permeability of Ca2+ ion in a neuron.