In the paper, the mathematical model describing the generation of action potential and propagation of an impulse in the neuron's filaments on the basis of the analysis of parametric electriс circuits with distributed parameters and the mathematical model of synaptic interneuron connections are proposed.
Developed models allow taking into account the influence of such factors as geometric, physical and chemical parameters of the neuron's filaments and the presence of different neurotransmitters in chemical synapses on transmitting a neural impulse. Further, such models can be used for investigating the conditions of neuron firing at spatial and time integration of input signals, as well as for the simulation of neuromuscular junctions.
- A. Hodgkin and A. Huxley “A quantitative description of membrane current and its application to conduction and excitation in nerve”, Journal of Physiology, vol. 117, pp. 500–544, 1952.
https://doi.org/10.1113/jphysiol.1952.sp004764 - I. Tasaki, Physiology and Electrochemistry of Nerve Fibers. Cambridge, MA, USA: Academic Press, 1982.
- P. Kostiuk, V. Zyma, V. Mahura et al., Biophysics. Kyiv, Ukraine: Oberegy, 2001. (Ukrainian)
- V. Horyachko, Kh. Drohomyretska, and M. Kotsyuba, “Mathematical model of action potential propogation in neuron axon”, in Proc. VI International Workshop Computational Problems of Electrical Engineering, pp. 137-138, Zakopane, Poland, September 1–4, 2004.
- V. Horyachko, “Mathematical model of the neural impulse propagation in the neuron”, Teoretychna elektrotekhnika, Issue 58, pp. 20-26, Lviv, Ukraine, 2005. (Ukrainian)
- E.N. Marieb, Essentials of Human Anatomy and Physiology, 10th ed. San Francisco, CA, USA: Benjamin Cummings, 2012.