Dynamics Analysis And Synchronization Control Of Neurons Under External Electrical Field

Mental disease is a kind of diseases harmful to human health seriously. It is showed that these diseases are caused mainly by the abnormal firing and encoding of neurons and neural network. For example, Parkinson’s Disease is corresponding to the abnormal synchronization of neurons in basal ganglia. These diseases are generally treated by medical therapies and physical therapies. Deep Brain Stimulation (DBS) has become a basic physical method and been widely applied. DBS would change the states of the neural network, but its mechanism remains uncertain. At present, DBS is modulated manually, and its therapy effects, energy efficiency and parameters adjustment are not satisfied. Therefore, it is necessary to utilize closed-loop control methods to optimize its power efficiency, tune its parameters and enhance its therapeutic outcome. To study firing patterns, features and synchronization control of neurons and neural network are helpful to reveal the principle and extend the ability of DBS, and have potential prospects in investigating the mechanism and the therapy effects of DBS.Firstly, this thesis analyzes the progress of neuron model and its firing patterns, also the applications of DBS in the treatment of mental diseases. The minimum neuron firing model under external electrical field is established. The influences of different frequencies and amplitudes of the external electrical field on the firing patterns are studied based on this model, and the relationships between the external stimulus and firing patterns are obtained. The results show that the frequency and amplitude have significant effects on the firing patterns.Secondly, a simplified model is established to analyze neural firing sensitivity under external electrical field, the relationships between the firing patterns and alternative signals with different frequencies, amplitudes and noises are analyzed, that shows that neurons are sensitive and certain adaptive to amplitudes, frequencies and noises.Then, the influence of high frequency signals with different amplitudes and phases on neural dynamics is analyzed. It is found that there exists an optimal high-frequency amplitude that makes the neuron faithfully response to the external low frequency input. The responses of coupled neurons with chemical synapses and electrical synapses to the external low frequency input are also studied, which proves that the information transferred by chemical synapses is more efficient than electrical synapses when being stimulated locally.Finally, the nonlinear control theory is introduced for the synchronization and desynchronization control of neural network to realize the closed-loop control of DBS. The adaptive internal model control method is proposed to achieve chaotic synchronization of the neural network with expected performance. Next, the artificial neural network is adopted to approximate the HH model, and H? is hired to restrain the approximation error and external interference, thus the synchronization control of HH model is realized. Then, the synchronization control of HH model with random noise of ion channel is also achieved through fuzzy adaptive control algorithm. Furthermore the adaptive neural network H? control is proposed to realize synchronization control of ML neural network. The desynchronization of a synchronous neural network simulated by ML models is also realized using the proposed methods mentioned above, and the closed-loop DBS is simulated successfully. The simulation results prove the effectiveness of the proposed control algorithm.This thesis’s results will provide theoretical foundation for DBS treating mental illness, and hopeful to be applied to clinical DBS closed-loop control.