Mathematical Models of Brain Neural Networks

2025/2026

Учебный год

ENG

Обучение ведется на английском языке

6

Кредиты

Кто читает:

Кафедра фундаментальной математики (Факультет информатики, математики и компьютерных наук (Нижний Новгород))

Статус:

Курс обязательный

Когда читается:

1-й курс, 3, 4 модуль

Course Syllabus

Abstract

The discipline covers modern approaches to modeling neural systems of the brain, including computational neuroscience. Key topics include: the Hodgkin-Huxley model, resting potential, formalism of stroboscopic particles and variables, action potential, simplified neuron models, and their response to external signals. Synaptic connections, gap junctions, chemical synapse models, synaptic plasticity, short-term frequency-dependent plasticity, and STDP models are also discussed. The architecture of neural networks and their synaptic connections is studied.

Learning Objectives

• The objective of this course is to provide students with probabilistic and statistical methods to analyze data in the field of biology

Expected Learning Outcomes

• Know basic notions and definitions in computational neuroscience, its connections with other sciences.
• Possess skills for choosing appropriate computational neuroscience methods for psychological research.
• Know the basic ionic mechanisms of neuronal electrophysiology. Know basis of the neuronal model construction.
• Ability to apply computational and mathematical methods to solve problems in computational neuroscience.
• Students will be able to construct and interpret ordinary differential equation (ODE) models that capture the key dynamics of IP₃-dependent calcium oscillations in astrocytes
• Students will be able to evaluate how astrocytic calcium signals propagate through gap junctions and influence neighboring cells by implementing a coupled multicellular model
• Students will be able to design and implement closed-loop control strategies for simulated underwater animates that replicate the propulsive dynamics of aquatic animals, such as fish and cetaceans.
• Students will be able to develop and test hybrid control architectures that combine central pattern generators (CPGs) with sensory feedback to enable adaptive locomotion in changing flow environments for both simulated and physical swimming robots.

Course Contents

• Introduction. Modern approaches to modeling brain neural systems.
• Hodgkin-Huxley Equations
• Mathematical Models of Synaptic Transmission
• Mathematical Modelling of Calcium Sugnalling in Astrocytes
• Simulated Animates and Bionic Robots

Assessment Elements

• Mathematical Modelling of Neuron Membrane Potential
• Simulation of self-oscillations in astro-glia cells of brain
• Biomoprhic robotics

Interim Assessment

• 2025/2026 4th module
  0.35 * Simulation of self-oscillations in astro-glia cells of brain + 0.3 * Biomoprhic robotics + 0.35 * Mathematical Modelling of Neuron Membrane Potential

Bibliography

Recommended Core Bibliography

• 9780262277327 - Koch, Christof; Segev, Idan - Methods in Neuronal Modeling : From Ions to Networks - 1998 - MIT Press - https://search.ebscohost.com/login.aspx?direct=true&db=nlebk&AN=49321 - nlebk - 49321
• Atlas of human brain connections, Catani, M., 2015
• Computational Cognitive Neuroscience - CCBY4_019 - O'Reilly, Munakata, Hazy & Frank - 2022 - Open Educational Resources: libretexts.org - https://ibooks.ru/products/390536 - 390536 - iBOOKS
• Computational neuroscience, by W. Chaovalitwongse, P. M. Pardalos, P. Xanthopoulos, 369 p., , 2010
• Dehaene, S., Sergent, C., & Changeux, J.-P. (2003). A neuronal network model linking subjective reports and objective physiological data during conscious perception. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.9E60F42A
• Neuronal dynamics : from single neurons to networks and models of cognition, , 2015
• Neuroscience : exploring the brain, Bear, M. F., 2007
• Neuroscience, , 2012
• Rhythmas of the brain, Buzsaki, G., 2011

Recommended Additional Bibliography

• Mark Bear, Barry Connors, & Michael A. Paradiso. (2020). Neuroscience: Exploring the Brain, Enhanced Edition: Vol. Enhanced fourth edition. Jones & Bartlett Learning.
• White, J. S. (2008). Neuroscience (Vol. 2nd ed). New York: McGraw-Hill Professional. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=223742

Authors

• Bagaev Andrei Vladimirovich
• Stankevich Nataliia Vladimirovna