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Parameter estimation for a leaky integrate-and-fire neuronal model from ISI data.

Paul Mullowney¹, Satish Iyengar

¹Tech-X Corporation, 5621 Arapahoe Avenue, Suite A, Boulder, CO 80303, USA. paulm@txcorp.com

Journal of Computational Neuroscience

|July 31, 2007

Summary

This study presents a new method for estimating neuron model parameters using interspike intervals. The approach efficiently computes maximum likelihood estimates for Ornstein-Uhlenbeck process models.

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Area of Science:

Computational Neuroscience
Mathematical Biology
Statistical Physics

Background:

The Ornstein-Uhlenbeck process models neuronal spontaneous activity.
Neuronal firing is modeled as the process reaching a threshold.
Tractable probability distribution functions for first-passage times are lacking.

Purpose of the Study:

To develop methods for estimating Ornstein-Uhlenbeck process parameters from interspike interval data.
To compute maximum likelihood estimates and confidence regions for identifiable model parameters.
To compare the data requirements for two-parameter versus three-parameter estimation.

Main Methods:

Utilizing interspike intervals as the sole data source.
Numerically inverting Laplace transforms to obtain parameter estimates.

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Calculating maximum likelihood estimates and confidence regions for model parameters.

Main Results:

An algorithm for computing maximum likelihood estimates and confidence regions for three identifiable parameters was developed.
The three-parameter estimation algorithm requires significantly more data than the two-parameter algorithm for comparable resolution.
The computational methods offer an efficient alternative to existing techniques for leaky integrate-and-fire models.

Conclusions:

The developed computational methods provide an efficient approach for parameter inference in Ornstein-Uhlenbeck neuronal models.
The methods can serve as a template for parameter inference in more complex neuronal models.
Accurate parameter estimation is crucial for understanding neuronal dynamics and network function.