A qualitative comparison of some diffusion models for neural activity via stochastic ordering

Area of Science:

• Computational Neuroscience
• Mathematical Biology
• Neuronal Dynamics

Background:

• Diffusion processes model neuronal subthreshold membrane potential and interspike intervals as first-passage-time problems.
• The Ornstein-Uhlenbeck model is a common baseline, but more complex models are biologically suggested.
• Previous comparisons relied on limited numerical simulations without general parameter sensitivity analysis.

Purpose of the Study:

• To qualitatively compare interspike interval distributions from different diffusion models using stochastic ordering.
• To analyze the role and impact of model parameters on neuronal firing patterns.
• To assess the differences between Ornstein-Uhlenbeck, Feller, and double reversal potential models.

Main Methods:

• Application of stochastic ordering to compare interspike interval distributions.
• Qualitative analysis of model parameter roles, extending numerical simulation findings.
• Comparison of specific diffusion models: Ornstein-Uhlenbeck, Feller, and a double reversal potential model.

Main Results:

• For highly excited neurons, reversal potential models show minimal difference from the Ornstein-Uhlenbeck model.
• Increased neuronal inhibition leads to more pronounced differences in interspike interval distributions across models.
• When mean trajectories are matched, the Feller model yields shorter intervals than Ornstein-Uhlenbeck but longer than the double reversal potential model.

Conclusions:

• Stochastic ordering provides a robust method for comparing neuronal firing models beyond specific numerical examples.
• Neuronal inhibition is a critical factor influencing the divergence of interspike interval distributions among different diffusion models.
• The choice of diffusion model significantly impacts predicted interspike intervals, particularly under conditions of increased inhibition.