On the return process with refractoriness for a non-homogeneous Ornstein-Uhlenbeck neuronal model

Area of Science:

• Computational Neuroscience
• Mathematical Biology
• Stochastic Processes

Background:

• Neuron membrane potential dynamics are crucial for understanding neural computation.
• Existing models often simplify synaptic input and refractory period effects.
• A more comprehensive model is needed to capture realistic neuronal firing patterns.

Purpose of the Study:

• To develop a novel mathematical model for single neuron membrane potential activity.
• To incorporate time-dependent synaptic potentials and random refractoriness.
• To analyze the statistical properties of neuronal firing.

Main Methods:

• Utilized an Ornstein-Uhlenbeck diffusion process to model membrane potential.
• Constructed a non-homogeneous Ornstein-Uhlenbeck return process with jumps.
• Introduced random refractoriness and performed asymptotic analysis.
• Assumed exponential distribution for firing time for analytical tractability.

Main Results:

• The developed model accurately describes membrane potential with time-dependent drift and jumps.
• Asymptotic analysis provided insights into firing rate and interspike interval distributions.
• Numerical evaluations quantified the influence of model parameters on neuronal activity.

Conclusions:

• The proposed model offers a more realistic representation of single neuron dynamics.
• The mathematical framework allows for quantitative predictions of neuronal firing behavior.
• This approach can be valuable for studying neural network function and disorders.