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Related Experiment Video

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Computational Modeling of Retinal Neurons for Visual Prosthesis Research - Fundamental Approaches

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Published on: June 21, 2022

Linked Gauss-Diffusion processes for modeling a finite-size neuronal network.

M F Carfora¹, E Pirozzi²

¹Istituto per le Applicazioni del Calcolo "Mauro Picone", Consiglio Nazionale delle Ricerche, via Pietro Castellino 111, 80131 Napoli, Italy.

|August 7, 2017

Summary

This summary is machine-generated.

This study models neuronal firing activity using a Leaky Integrate-and-Fire (LIF) model with stochastic linkages. Researchers developed a method to estimate neuron firing probability densities in interacting neural networks.

Keywords:

First passage time Simulation Stochastic differential equations Synaptic current-based linkages

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Area of Science:

Computational Neuroscience
Mathematical Biology
Network Dynamics

Background:

Neuronal firing activity is complex and influenced by network interactions.
Stochastic processes play a crucial role in subthreshold neuronal dynamics.
Accurate modeling of coupled neurons is essential for understanding brain function.

Purpose of the Study:

To model the firing activity of neurons in a feed-forward network using a Leaky Integrate-and-Fire (LIF) model.
To develop a method for estimating firing probability densities in interacting neuronal networks.
To analyze the impact of stochastic current-based linkages on neuronal voltage dynamics.

Main Methods:

Utilized a Leaky Integrate-and-Fire (LIF) model with stochastic current-based linkages.
Applied Linked Gauss-Diffusion processes to describe neuronal voltage dynamics.
Employed an iterated integral equation-based approach for numerical evaluation of first passage time densities.
Incorporated asymptotic approximations for simplifying calculations and extending the model to larger networks.

Main Results:

Developed a method to estimate firing probability densities for neurons in a (2x2) feed-forward network.
Demonstrated that stochastic interactions introduce random jumps in neuronal membrane voltage.
Validated numerical firing estimates by comparing them with simulation-based histograms.
Provided an extension of the model for (N×N)-size networks.

Conclusions:

The proposed Linked Gauss-Diffusion process effectively models neuronal firing in networks with stochastic linkages.
The iterated integral equation approach provides accurate numerical estimates of firing probabilities.
The study offers a framework for analyzing complex neuronal dynamics in interconnected systems.
The findings contribute to a deeper understanding of neural information processing.