Analysis Of Compartmental Model Neurons And Basal Ganglia Circuits

Computational neuroscience,also known as the theory of neural science,is from the point of view information processing characteristics of the nervous system structure to s-tudy the brain function,and focuses on physical biological models of real neurons and ner-vous system and their physiology and dynamics behavior.Therefore,constructing circuit models which can capture the essential characteristics of biological systems plays a key role in understanding the function of the nervous system.This thesis mainly investigates neurons and neural circuits associated with basal ganglia and presents dynamical analysis and numerical simulations of a single-compartment model of the dopaminergic neuron,a multi-compartment model of the medium spiny neuron and cortico-basal-thalamic circuit models.The main contributions of this dissertation are as follows:In Chapter 1,we mainly introduce the theoretical basis of the Hodgkin-Huxley model and Rall cable model,and give the dendritic biophysical mechanisms.The Hodgkin-Huxley model is proposed based on a large number of experiments and is a classical model that describes how action potentials in neurons are initiated and propagated using mathematics methods.The Rall model is a classic example that describes how electric current in dendritic trees is propagating.Firstly,we provide detail derivation process of these two classic models.Then we present a brief introduction to compartmental model and dendritic detection.Finally,the main content of this paper is proposed.In Chapter 2,we consider the dimensionality reduction of a high dimensional neu-ronal model and analyze the dynamical properties of the reduced system.Firstly,for the original thirteen dimensional model,using the correlation between variables,we reduce its dimensionality and obtain a simplified three-dimensional system.Then we discuss the changing characteristics of the number of spikes within a burst by simultaneously varying two parameters.Finally we study the codimension 2 bifurcation in the reduced system and present the bifurcation behavior near the Bogdanov-Takens bifurcation.In Chapter 3,we research a multi-compartmental model of medium spiny neurons and mainly discuss the influence of the exogenous factor and endogenous factor on the dynamical properties of the neuron.Firstly,based on medium spiny neuron model of biological anatomy,we obtain various firing patterns by comparing the responses of the medium spiny neuron under direct current,alternating current and square wave stimuli,and the results show that the change of alternating current have a huge influence on the firing rhythm of this neuron.Then,we discuss the impact of three different ions conductance or permeability(sodium,potassium and calcium)on the firing properties of medium spiny neuron.Finally,by removing part of dendrites which simulates the death and degradation of them,the difference between soma firing in the healthy neuron and incomplete neuron is gained.These results reveal both the endogenic factor and extrinsic factor have an effect on the firing rhythm of the medium spiny neuron.We firstly simulate and analyze the role of dendritic structure in the detection soma firing.In Chapter 4,we study the dynamic mechanism of the cortico-basal-thalamic circuit.The first part is to introduce components,circuit connections and deep brain stimulation of the basal ganglia.The second part is to simulate high-frequency electrical stimulation of different targets to treat Parkinson's disease.To simulate high frequency stimulation to the different targets in Parkinson's disease,a cortico-basal-thalamic circuit model is constructed based on the biological-anatomical structure and utilization of neuron models based on conductance.Taking three different nucleus regions as targets,we simulate and analyze the diversity of different stimulus durations and periods,along with stimulus ef-ficacy,for the three targets.Then,by adopting different stimulus magnitudes that acted on the three targets,a comparative analysis of the effects of different stimulus magnitudes and targets for the treatment of Parkinson's disease is performed.To identify the optimal target,different effects of the two major pathways on the thalamus are calculated.The calculation results show that the cortico-basal-thalamic circuit is reliable,and through this model,high frequency stimulation of the three targets can improve the pathological thalamic rhythmicity.It is shown that the direct pathway excites the thalamus,while the indirect pathway plays a regulatory role in the thalamus.The third part mainly studies the signal transduction mechanism in a cortico-basal-thalamic circuit.The same theoretical basis is used to construct another cortico-basal-thalamic circuit model and the neural circuit presents different firing patterns.We discuss the impact on down-stream neurons in the network with acting on the different internal and external factors.Firstly,we consider mutual promotion and inhibition of downstream subthalamic nucleus and globus pallidus neurons and the discharge characteristics of the thalamic neuron by changing excitatory synaptic connection strength.Secondly,we introduce the correlation of signal transduction in downstream neurons by changing inhibitory synaptic connection strength.Then,we explore the discharge characteristics of downstream neurons in the circuit with different external stimuli applied to the subthalamic nucleus.By contrast,fi-nally we discuss the discharge characteristics of the efferent neuron under hyperpolarizing current stimulation on the globus pallidus internus.