Title | Mathematical modeling of the influence of invasive electric fields on the neural networks' dynamics in Parkinson's disease |
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Authors | M. A. Kutyrkina^{1}, T. F. Mamedova^{1}^{1}National Research Mordovia State University |

Annotation | This work is devoted to studying the effect of invasive electrical stimulation of deep brain structures on the dynamics of neural networks in Parkinson's disease. The work uses the Hodgkin-Huxley mathematical model to simulate the activity of neurons under the action of electric fields. The study takes into account stimulation parameters such as the conductance of potassium and sodium channels, as well as electric field parameters, including dielectric constant, medium conductivity and electric field strength. Simulation results allow us to understand the interaction between electrical stimulation and neural activity in the brain, as well as to predict the impact of various stimulation parameters on the dynamics of natural neural networks. |

Keywords | Hodgkin-Huxley model, invasive electrical stimulation, Parkinson's disease, membrane potential |

Citation | Kutyrkina M. A., Mamedova T. F. ''Mathematical modeling of the influence of invasive electric fields on the neural networks' dynamics in Parkinson's disease'' [Electronic resource]. Proceedings of the XVI International scientific conference "Differential equations and their applications in mathematical modeling". (Saransk, July 17-20, 2023). Saransk: SVMO Publ, 2023. - pp. 116-120. Available at: https://conf.svmo.ru/files/2023/papers/paper17.pdf. - Date of access: 02.12.2023. |

**© SVMO, National Research Mordovia State University, 2023**

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