title: ÐÐ¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ñ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð½ÐµÐ¹ÑÐ¾Ð½Ð° Ð¿Ð¾ ÐºÑÐ¸ÑÐµÑÐ¸Ñ ÑÐ¾Ð¾ÑÐ²ÐµÑÑÑÐ²Ð¸Ñ ÑÐ°ÑÑÐ¾ÑÐ½Ð¾-ÑÐ¾ÐºÐ¾Ð²Ð¾Ð¹ Ñ Ð°ÑÐ°ÐºÑÐµÑÐ¸ÑÑÐ¸ÐºÐ¸ ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐ°Ð»ÑÐ½ÑÐ¼ Ð´Ð°Ð½Ð½ÑÐ¼
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Optimization of the mathematical model of a neuron according to the criterion of compliance of the frequency-current characteristic with experimental data
Creators: name: Ð¢Ð¸ÑÐ¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°, ÐÐºÐ°ÑÐµÑÐ¸Ð½Ð°
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2022
Subjects: Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
ÑÐ°ÑÑÐ¾ÑÐ½Ð¾-ÑÐ¾ÐºÐ¾Ð²Ð°Ñ Ñ Ð°ÑÐ°ÐºÑÐµÑÐ¸ÑÑÐ¸ÐºÐ°
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Ð¿Ð¾ÑÐµÐ½ÑÐ¸Ð°Ð» Ð´ÐµÐ¹ÑÑÐ²Ð¸Ñ
Ð¾Ð±Ð»Ð°ÑÑÑ Ð³ÐµÐ½ÐµÑÐ°ÑÐ¸Ð¸ ÑÐ¿Ð°Ð¹ÐºÐ¾Ð²
mathematical modeling
frequency-current characteristic
neuron
action potential
spike generation area

description: Ð¢ÐµÐ¼Ð° Ð²ÑÐ¿ÑÑÐºÐ½Ð¾Ð¹ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÑ: Â«ÐÐ¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ñ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð½ÐµÐ¹ÑÐ¾Ð½Ð° Ð¿Ð¾ ÐºÑÐ¸ÑÐµÑÐ¸Ñ ÑÐ¾Ð¾ÑÐ²ÐµÑÑÑÐ²Ð¸Ñ ÑÐ°ÑÑÐ¾ÑÐ½Ð¾-ÑÐ¾ÐºÐ¾Ð²Ð¾Ð¹ ÑÐ°ÑÐ°ÐºÑÐµÑÐ¸ÑÑÐ¸ÐºÐ¸ ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐ°Ð»ÑÐ½ÑÐ¼ Ð´Ð°Ð½Ð½ÑÐ¼Â».Â  ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð¸Ñ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸, ÐºÐ¾ÑÐ¾ÑÐ°Ñ ÑÐ¾ÑÐ¾ÑÐ¾ Ð¾Ð¿Ð¸ÑÑÐ²Ð°ÐµÑ ÑÐ»ÐµÐºÑÑÐ¸ÑÐµÑÐºÑÑ Ð°ÐºÑÐ¸Ð²Ð½Ð¾ÑÑÑ ÑÐµÐ°Ð»ÑÐ½ÑÑ Ð½ÐµÐ¹ÑÐ¾Ð½Ð¾Ð² Ð² ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐ°Ñ. ÐÐ¾Ð´ÐµÐ»Ñ Ð½ÐµÐ¹ÑÐ¾Ð½Ð° Ð±ÑÐ»Ð° ÑÐ¾Ð·Ð´Ð°Ð½Ð° Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ñ NEURONÂ 7.8 Ð½Ð° Ð²Ð½ÑÑÑÐµÐ½Ð½ÐµÐ¼ ÑÐ·ÑÐºÐµ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ hoc. Ð ÑÐ¾Ð´Ðµ ÑÐ°Ð±Ð¾ÑÑ Ð±ÑÐ»Ð¸ Ð¿Ð¾Ð»ÑÑÐµÐ½Ñ Ð³ÑÐ°ÑÐ¸ÐºÐ¸ Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÐ¸ ÑÐ°ÑÑÐ¾ÑÑ Ð¾Ñ ÑÐ¾ÐºÐ° Ð¸ Ð´Ð¾Ð±Ð°Ð²Ð»ÐµÐ½Ð½Ð¾Ð¹ Ð¿ÑÐ¾Ð²Ð¾Ð´Ð¸Ð¼Ð¾ÑÑÐ¸, Ð¿Ð¾ÑÐµÐ½ÑÐ¸Ð°Ð»Ð° Ð¾Ñ Ð²ÑÐµÐ¼ÐµÐ½Ð¸ Ð¸ ÑÐ°ÑÑÐ¾ÑÐ½Ð¾-ÑÐ¾ÐºÐ¾Ð²Ð°Ñ ÑÐ°ÑÐ°ÐºÑÐµÑÐ¸ÑÑÐ¸ÐºÐ° Ð½ÐµÐ¹ÑÐ¾Ð½Ð° Ð¿ÑÐ¸ Ð²Ð°ÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ð¸ Ð¿ÑÐ¾Ð²Ð¾Ð´Ð¸Ð¼Ð¾ÑÑÐ¸ Ð½Ð°ÑÑÐ¸ÐµÐ²ÑÑ Ð¸ ÐºÐ°Ð»Ð¸ÐµÐ²ÑÑ ÐºÐ°Ð½Ð°Ð»Ð¾Ð², ÐºÐ¾Ð½ÑÐµÐ½ÑÑÐ°ÑÐ¸Ð¸ Ð¸Ð¾Ð½Ð¾Ð² Ð²Ð½ÑÑÑÐ¸ Ð¸ ÑÐ½Ð°ÑÑÐ¶Ð¸ ÐºÐ»ÐµÑÐºÐ¸, ÑÐµÐ¼Ð¿ÐµÑÐ°ÑÑÑÑ, Ð¿ÑÐ¾Ð²Ð¾Ð´Ð¸Ð¼Ð¾ÑÑÐ¸ ÑÑÐµÑÐºÐ¸. Ð¡ÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ Ð³ÑÐ°ÑÐ¸ÐºÐ¾Ð², Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÑ Ð² MATLAB Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² ÑÐ°Ð±Ð¾ÑÑ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ñ Â NEURONÂ  Ñ ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐ°Ð»ÑÐ½ÑÐ¼Ð¸ Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÑÐ¼Ð¸ Ð¿Ð¾Ð·Ð²Ð¾Ð»Ð¸Ð»Ð¸ Ð²ÑÐ´ÐµÐ»Ð¸ÑÑ Ð´Ð²Ðµ Ð½Ð°Ð¸Ð±Ð¾Ð»ÐµÐµ ÑÐµÐ°Ð»Ð¸ÑÑÐ¸ÑÐ½ÑÐµ Ð¼Ð¾Ð´ÐµÐ»Ð¸. Ð¢Ð°ÐºÐ¸Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð¿Ð¾Ð·Ð²Ð¾Ð»ÑÑÑ ÑÐµÑÑÐ¸ÑÐ¾Ð²Ð°ÑÑ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÐµ Ð³Ð¸Ð¿Ð¾ÑÐµÐ·Ñ Ð¸ Ð´ÐµÐ»Ð°ÑÑ Ð¿ÑÐµÐ´ÑÐºÐ°Ð·Ð°Ð½Ð¸Ñ Ð¾ÑÐ½Ð¾ÑÐ¸ÑÐµÐ»ÑÐ½Ð¾ ÑÐ°Ð±Ð¾ÑÑ ÑÐ¾Ð¹ Ð¸Ð»Ð¸ Ð¸Ð½Ð¾Ð¹ ÑÐ¸ÑÑÐµÐ¼Ñ. Ð­ÑÐ¾ Ð¼Ð¾Ð¶ÐµÑ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°ÑÑÑÑ, Ð½Ð°Ð¿ÑÐ¸Ð¼ÐµÑ, Ð´Ð»Ñ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ ÑÐ¿Ð¸Ð»ÐµÐ¿ÑÐ¸Ð¸ Ð¸ ÑÐµÑÐµÐ¿Ð½Ð¾-Ð¼Ð¾Ð·Ð³Ð¾Ð²ÑÑ ÑÑÐ°Ð²Ð¼, Ð° ÑÐ°Ðº Ð¶Ðµ ÑÐµÐ¾ÑÐµÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð¿Ð¾Ð´Ð±Ð¾ÑÐ° ÑÐ¾Ð¾ÑÐ²ÐµÑÑÑÐ²ÑÑÑÐµÐ³Ð¾ Ð»ÐµÑÐµÐ½Ð¸Ñ. ÐÑÐ±ÑÐ°Ð½Ð½Ð°Ñ Ð¸ÑÑÐ¾Ð´Ñ Ð¸Ð· ÐºÑÐ¸ÑÐµÑÐ¸ÐµÐ² Ð½Ð°Ð¸Ð»ÑÑÑÐµÐ³Ð¾ ÑÐ¾Ð¾ÑÐ²ÐµÑÑÑÐ²Ð¸Ñ, Ð¼Ð¾Ð´ÐµÐ»Ñ Ð¼Ð¾Ð¶ÐµÑ Ð´Ð¾Ð²Ð¾Ð»ÑÐ½Ð¾ ÑÐ¾ÑÐ¾ÑÐ¾ Ð¾Ð¿Ð¸ÑÑÐ²Ð°ÑÑ ÑÐ°ÐºÐ¸Ðµ ÑÐ°ÑÐ°ÐºÑÐµÑÐ¸ÑÑÐ¸ÐºÐ¸ Ð½ÐµÐ¹ÑÐ¾Ð½Ð°, ÐºÐ°Ðº ÑÐ°ÑÑÐ¾ÑÐ° Ð³ÐµÐ½ÐµÑÐ°ÑÐ¸Ð¸ Ð¿Ð¾ÑÐµÐ½ÑÐ¸Ð°Ð»Ð¾Ð² Ð´ÐµÐ¹ÑÑÐ²Ð¸Ñ Ð¸ Ð¾Ð±Ð»Ð°ÑÑÑ Ð²Ð¾Ð·Ð±ÑÐ¶Ð´ÐµÐ½Ð¸Ñ Ð½ÐµÐ¹ÑÐ¾Ð½Ð°, Ð° ÑÐ°Ðº Ð¶Ðµ Ð¼Ð¸Ð½Ð¸Ð¼ÑÐ¼ Ð¸ Ð¼Ð°ÐºÑÐ¸Ð¼ÑÐ¼ Ð¿Ð¾ÑÐµÐ½ÑÐ¸Ð°Ð»Ð° Ð´ÐµÐ¹ÑÑÐ²Ð¸Ñ, ÐµÐ³Ð¾ Ð°Ð¼Ð¿Ð»Ð¸ÑÑÐ´Ñ, Ð¾Ð´Ð½Ð°ÐºÐ¾ ÑÐ¾ÑÐ¼Ð° Ð¿Ð¾ÑÐµÐ½ÑÐ¸Ð°Ð»Ð° Ð´ÐµÐ¹ÑÑÐ²Ð¸Ñ Ð¼Ð¾Ð¶ÐµÑ Ð·Ð°Ð¼ÐµÑÐ½Ð¾ Ð¾ÑÐ»Ð¸ÑÐ°ÑÑÑÑ Ð¾Ñ ÑÐµÐ°Ð»ÑÐ½Ð¾Ð¹.
description: The subject of the graduate qualification work is âOptimization of the mathematical model of a neuron according to the criterion of compliance of the frequency-current characteristic with experimental dataâ.Â  The given work is devoted to the construction of Â a mathematical model that describes well the electrical activity of real neurons in experiments. The neuron model was created using the NEURON 7.8 program in the hoc internal programming language. In the course of the work, graphs of the dependence of frequency on current and added conductivity, potential on time, and the frequency-current characteristic of the neuron were obtained by varying the conductivity of sodium and potassium channels, the concentration of ions inside and outside the cell, temperature, and leakage conductivity. Comparison of the graphs obtained in MATLAB based on the results of the NEURON program with the experimental ones made it possible to identify the two most realistic models. Such models allow testing of various hypotheses and making predictions about the operation of a particular system. This can be used, for example, for the study of epilepsy and traumatic brain injury, as well as the theoretical selection of appropriate treatment. Selected as the best fit, the model can quite well describe such characteristics of the neuron as the frequency of generation of action potentials and the region of excitation of the neuron, as well as the minimum and maximum of the action potential, its amplitude, however, the form of the action potential may be significantly different from the real one.