Study on the Complex Neuron Model’s Reduction and Its Dynamic Characteristics

Abstract

In the paper, based on the theory of neurodynamics, the nine-dimensional one-compartment complex model of CA1 pyramid neuron developed by David Golomb [J. Neurophysiol., 96 (2006), 1912-1926 is reduced, and the two-dimensional reduced neuron model is obtained for the first time. According to the definition of the minimal model, the nine-dimensional complex dynamic model has first be reduced to the minimal models. Then the minimal model is reduced into the two-dimensional model by the model reduction theory of neurodynamics and the polynomial regression algorithm. Finally, dynamic characteristics of the twodimensional reduced neuron model are analyzed and discussed in detail by the neurodynamic analysis methods. When the stimulation current gradually increases from zero, the two-dimensional reduced neuron model undergoes the saddle-node bifurcation. It is equivalent to a bistable integrator and has the common dynamic properties of the integrator such as definite threshold value and class 2 neural excitability. The investigation provides a simple and convenient method to investigate deeply the high-dimensional complex neuron model's dynamic characteristics and functions by the neurodynamic theory. Moreover, it is helpful to know the dynamic characteristics of the hippocampal neuron.

Study on dynamic characteristics’ change of hippocampal neuron reduced models caused by the Alzheimer’s disease

“…Based on the electrophysiological experimental data under the pathology condition of AD [15], we can only modify suitably parameters' values of the normal I Na + I Kdr minimal neuron model [17], and get the I Na + I Kdr minimal neuron model under the AD pathology condition.…”

“…The AD I Na + I Kdr minimal neuron model has the same form as the normal I Na + I Kdr minimal neuron model described by formula (1), which has been discussed in reference [17].…”

“…In the following, we reduce the AD minimal neuron model described by formula (1) into the two-dimension reduced neuron model by the model reduction theory and the polynomial regression algorithm [17]. Then, we analyze and discuss comparatively the two-dimension reduced neuron model's dynamic changing characteristics before and after effect of AD.…”

“…But this model is still a nine-dimension complex ordinary differential equation set, which is very inconvenient to analyze and discuss deeply specified dynamic characteristics or given parameters' effect of the neuron model. In recent years, reduction work of the nine-dimension one-compartment complex model of CA1 pyramid neuron is done by He and Peng [8] and Peng et al [16,17]. They have reduced the nine-dimension complex neuron model to minimal models and the two-dimension reduced model, and analyzed comparatively dynamic characteristics of the original model and reduced models [17].…”

“…In this paper, we take the reduced models of CA1 pyramid neuron [17] as the object. Based on the electrophysiological experimental data under the AD pathology condition, we build the reduced neuron models under the AD pathology condition by modifying suitably parameters' values, and discuss comparatively neuron models' dynamic characteristics' change before and after effect of AD.…”