Network Simulation Of The Neurological Dysfunction

Neurons are the elementary structure and function units of nervous system, the signal in the nervous system is transmitted by firing activity of neurons. Spiral waves of the disinhibited mammalian neocortex have positive effects on electrical signal transmission. Studies have found that the interference of external stimulations will have effects on electrical signal transmission of the nervous system, such as noise, changing of external current and ironic conductance and so on. Hence, it is important and meaningful for signal transmission in the nervous system by researching and analyzing and reasonable controlling these external stimulations. It also offers some theoretical references to the medical research. The main results are included as follows:1. The results of firing activity of neurons as follows(1) The resonant circuit of resistive-capacitive-inductive-shunted Josephson junction is used to simulate behavior of neuronal discharges. Based on tracking control theory, the controller contains gain coefficients was constructed to control the resonant circuit of Josephson junction to synchronize the chaotic Hindmarsh-Rose system, and the single controller was approached analytically. The results confirmed that the controller with appropriate gain coefficients was effective to reach complete synchronization, phase synchronization of Josephson junction and neurons, respectively. As a result, the electric activities of neurons could be simulated by using Josephson junction model completely.(2) To simulate neurons response to external stimuli by constructing a cyclic neuron network. The results confirm that the firing activity of the resting state neurons will be waked up by changing ionic conductance to stimulate the part neurons of cyclic network. Coupling strength affects the response speed of the neural network to external stimuli. The explain of acupuncture and moxibustion of traditional Chinese medical science may use this theory as reference.2. The experimential evidences confirmed that spiral waves were observed in the disinhibited mammalian neocortex and Spiral waves of the disinhibited mammalian neocortex have positive effects on electrical signal transmission. The scheme of ceullar networks is used to simulate the formation and evolution of spiral wave in the neocortical slices. The regular networks of neurons are constructed in the two-dimensional space, the dynamical properties of thermosensitive neurons is described by temperature factor, and the effect of membrane temperature on the evolution of spiral wave is investigated in detail. A statistical factor of synchronization is defined to measure the critical condition inducing phase transition of spiral wave (death or breakup) by the factor of temperature of membrane. It is confirmed that spiral wave is removed and the whole networks become homogeneous and synchronous completely when the membrane temperature exceeds certain threshold; breakup of spiral wave is induced in the presence of weak channel noise being considered. Furthermore, it suggested that the mechanism of temporary heat stupor could be due to the blocking of spiral wave propagation in some functional domain.