The effect of a random initial value in neural first-passage-time models.

Area of Science:

• Computational Neuroscience
• Mathematical Biology
• Neural Modeling

Background:

• Stochastic integrate-and-fire neural models are crucial for understanding neuronal dynamics.
• Investigating the influence of random initial values is essential for model accuracy.
• Previous models often assumed deterministic initial conditions.

Purpose of the Study:

• To analyze the impact of random initial values on three stochastic neural models.
• To compare different initial value distributions and their effects on model outputs.
• To explore the relationships between various neural models and their robustness.

Main Methods:

• Examined three approximations of Stein's model: leaky integrator, Wiener process, and Ornstein-Uhlenbeck process.
• Investigated discrete, uniform, and truncated normal distributions for initial values.
• Analyzed parameter estimation procedures and first-passage-time distributions.

Main Results:

• Random initial values affect interspike interval distributions in the leaky integrator model.
• The coefficient of variation exceeds 1 for the Ornstein-Uhlenbeck process with a truncated normal initial distribution.
• First-passage-time distributions approach exponential as threshold increases.
• Effects are most pronounced at high firing rates.

Conclusions:

• Random initial values are a critical factor in stochastic neural modeling, particularly at high firing rates.
• The choice of initial value distribution impacts model predictions for interspike intervals and firing statistics.
• Model assumptions and verification methods require careful consideration in light of initial value effects.