Fractal Behavior And Control Of Calcium In Nerve Cells

The phenomena of complex and irregular are common in nature. The traditional Euclidean geometry can not solve this kind of the problems. The initial research object of fractal is to describe and reveal the inherent rules of this kind of complex geometry, that is an object or act which may be complex and irregular which has the characteristics of self similar or scale-free. Therefore, fractal is a description of nature language. As a matter of fact, fractal theory is not only a description method, but also a means to explore the essence of things. Fractal set has fractal dimension, which is an important index to describe the fractal complexity. With the development of fractal theory, fractal has been applied in many research fields, such as mathematics, biology, physics, chemistry, economics and geology etc.Diffusion limited aggregation (DLA) fractal model is to solve the problem of the growth and aggregation that is far from equilibrium. This model is often applied to the condensation of atmospheric dust, discharge phenomenon, bacterial colonies, cancer cell proliferation, and the pollution of harmful algae, etc. At present, the method is usually laboratory combined with computer simulation, by changing the relevant parameters and conditions, but rarely by quantitative analysis and explore the object of growth pattern and influence factor. At the same time, the change of calcium concentration usually used experimental tracking detection and probability analysis in nerve cell, but seldom use the fractal model to carry out quantitative analysis. This paper is focused on the diffusion of calcium in the nerve cell, which is similar to the characteristics of diffusion limited aggregation (DLA) growth model. For the first time, we have analyzed the growth model of calcium ion diffusion and growth rate changing trend by using DLA. The main contents are as follows:(1) The concentration distribution and the growth rate of the diffusion of calcium ion in nerve cells were affected by the external stimulation and many kinds of interference factors. We first discuss the control of the growth of calcium ions in a specific region when the interference term is an arbitrary general function. By changing the interference parameters to effectively control the calcium ion diffusion range and regional.(2) Secondly, we discuss the effect of different external disturbance on the diffusion rate changing trend of calcium ions. Using partial differential equations, we analyze the effects of different disturbances on the growth rate of calcium ions, which becomes slow, constant, or zero, In addition, the validity of the conclusion was illustrated by simulation.In theory, we can use DLA growth model to analyze and control of calcium ions in nerve cells in fractal growth. That is to say, we can use the quantitative relationship between the concentration diffusion and diffusion rate change tendency and the outside interference to control in the dendrites in diffusion region and range, to reached the purpose that is control of calcium ion diffusion by controlling the external interference function parameters. The concentration of calcium ions is related to the secretion of neurotransmitters, and the secretion of neurotransmitter affects the nerve conduction. Therefore, this method has a new idea for the control of calcium in nerve cells, and it has a positive significance for the future research on the nervous system disease treatment and brain computer interface research.