Phase Resetting In Neuronal Information Processing And Control Of Neuronal Synchronization

The prominent functions of the brain are to encode, process, store, and transmit information in the nervous system. Therefore, the principal problem confronted in neuronal information processing is how to encode neuronal information; in other words, how to represent neuronal information in the brain. Based on the biophysical property of neuronal activity, there is a unified encoding pattern in terms of neuronal pulse in biological nervous systems. There is insufficient for neuronal encoding in terms of spiking of individual neuron. Neuronal population coding is a general pattern for neuronal information processing. In particular, synchronous oscillation of neuronal firing in a neuronal population is a candidate mechanism for neuronal information processing. Neuronal synchronization is the foundation for representing neuronal information. Therefore, the study of synchronous oscillations of neuronal population is a crucial issue for neuronal information processing,Along with an abundance of neurophysiology and a rapid development of advanced computing technology, since the early nineties, the investigations of computing models of large-scale neuronal population have been of great interest in mathematics, nonlinear science, physics, computer science, computing neuroscience, and theoretic neuroscience. A mathematic model describing collective behavior of large-scale neuronal population is significant for simulating activity of neuronal population. On the basis of synchronous oscillations of neuronal population, it is considered as an effective and simple candidate strategy to model a neuron as a limit cycle oscillator. Moreover, background noise in the nervous system is ubiquitous. Therefore, the theory about stochastic nonlinear phase resetting dynamics provides a theoretic frame for neuronal information processing.The nervous system is characterized by the plasticity of configuration and function, which adapt brain to the change of surrounding inter or outer nervous system. Synaptic joint is an important location of information transformation from one neuron to another neuron as well as a crucial position of neural plasticity. Synaptic efficacy is modified by the variability of active-dependent coupling strength among neurons. The variability of coupling strength consequentially influences dynamics of neuronal population. On the other hand, for real biological networks, we can not understand neuronal coding and neuronal information processing without taking into account synaptic dynamics. So, we first investigate the stochastic evolution models of large-scale neuronal population activity in spontaneous activity, where synaptic dynamics is considered, and introduce an average number density describing the collective behavior of a neuronal population as a neuronal coding pattern. Numerical simulation indicates that the synchronized activity of neural population enhances the coupling among neural oscillators, and the neural coding is dominated by the coupling configuration in the absence of external stimulus. In the weaker noise, the alteration of the coupling strength shows the slow learning process; in the stronger noise, the coupling strength displays transient process, which is dominated by the noise. Numerical simulation also indicates that different coupling levels represent the different effects of learning. In the lower level, the gradual learning process occurs. In the higher level, the learning process becomes very rapid.Nervous circuits in the brain receive natural sensory stimuli constantly. Synchronization or desynchronization of oscillatory activity in neuronal networks, induced by various sensory stimuli, associates with the neural information processing. Oscillatory synchronization in a neuronal population is one of important mechanisms integrating neuronal information. Therefore, in this study, we proposed a mathematical model describing associative dynamics about phase and coupling strength in the presence of external stimulation. Numerical simulations indicate that the phase synchrony in a neuronal population induced by external simulation can be dominated by the stimulation intensity and the stimulation modality. Stimulation with stronger intensity or higher harmonic can alter the configuration of synchronous cluster state of neuronal networks, so that improve the capability of neuronal response to stimulation and enhance the coupling among neurons. For the combined stimuli with different harmonics, these stimuli don't influence neural coding separately, but a nonlinear interaction occurs between them, in other words, there is a competitive and also cooperative relation between deferent modalities of stimulation.In general, a neuron is in the state of two activities: firing state or resting state. The information embodied in amplitude must be introduced in a neuronal model in order to represent two states mentioned above. Hence, two variables, phase and amplitude, describe the state of a neuronal oscillator. The phase of a neuronal oscillator describes the timing of neuronal firing; the amplitude represents the pulse intensity of neuronal firing. Besides, there are a large number of special coupling structures, such as presynaptic inhibition,presynaptic facility and lateral inhibition, etc. These complicated synaptic configurations can change the amplitude of neuronal spiking. Based on above considerations, we investigate the model of population of neuronal oscillators, where the amplitude dynamics is introduced. Numerical simulations show that low-frequency spontaneous rhythmic activity in a neuronal population associates with the variability of amplitude; in the presence of a stronger stimulation, the rhythmic activity in a neuronal population is a threshold behavior, viz. the rhythmic activity is steady when the amplitude changes under the threshold, whereas bursting rhythmic activity emerges when the amplitude reaches the threshold. Our investigations indicate that the rhythmic activity in nervous system associates not only with the amplitude dynamics but also with the property of external stimulation.Synchronous firing in nervous system is ubiquitous phenomena. Oscillatory synchronization of neuronal firing has always been referred as a principal mechanism for neuronal information processing. Synchronization occurs in neuronal population composed of deferent neurons in order to effectively process neuronal information. This synchronization is very useful for effective information transmission. However, egregious synchronized firing in a large-scale neuronal population induces abnormal neuronal activity, such as Parkinson's disease or epilepsy. Therefore, in order to effectively process neuronal information and avoid immoderate or abnormal synchronized firing, it is very important to control or suppress synchronized neuronal activity for neuronal information processing or the research in physical therapy of Parkinson's disease.Oscillatory synchronization is a phenomenon widely observed in visual cortex and hippocampus. Although the underlying neuronal mechanisms remain elusive, more investigations indicate that inhibitory connections play an important role inγrhythmic oscillation (30～100Hz). However, as yet, model study in collective behavior of a neuronal population with excitatory and inhibitory connection is lacking. Taking into account the property of synaptic coupling in real biological nervous system, we proposed a stochastic phase model of neuronal population with excitatory and inhibitory connection. We investigated the synchronized firing patterns of neuronal population using Fokker-Planck approach. Our study indicates that without inhibitory connection, the firing pattern of neuronal population is low-frequency and regular; whereas the firing pattern of neuronal population with inhibitory connection delays stochastic oscillation. This result also shows that inhibitory connection among neurons can subserve an adequate basis for stochastic oscillation. This result is in agreement with experimental research.These synchronized neurons can induce a abnormal rhythmic activity, which is believed to play a crucial role in the emergence of pathological rhythmic brain activity in Parkinson's disease, essential tremor, and epilepsy. Hence, the development of control techniques that would be used to effectively suppress the neural synchrony is an important clinical problem. Based on our model studies, we proposed a control technique with time delay feedback stimulation, which can be used to effectively suppress the synchronized firing in a neuronal population. This result can be applied to devise an electrophysiological stimulation for therapy of Parkinson's disease, essential tremor, and epilepsy.