Efficient and accurate time-stepping schemes for integrate-and-fire neuronal networks

Area of Science:

• Computational neuroscience
• Numerical analysis
• Neuronal network simulation

Background:

• Simulating neuronal networks accurately requires precise handling of membrane potential resets after spikes.
• Existing methods can introduce numerical errors, limiting simulation fidelity and efficiency.

Purpose of the Study:

• To analytically verify the order of a modified time-stepping method for neuronal simulations.
• To develop efficient, higher-order algorithms for handling resets in neuronal network models.
• To introduce a modified fourth-order scheme for improved accuracy and computational cost.

Main Methods:

• Analytical derivation of the order of accuracy for modified time-stepping schemes.
• Development of a modified fourth-order Runge-Kutta scheme incorporating spike time interpolation and recalibration.
• Simulation of conductance-based integrate-and-fire neuronal networks with all-to-all coupling.

Main Results:

• The modified time-stepping scheme is analytically shown to be second-order.
• A novel modified fourth-order scheme achieves six-digit accuracy with a time-step of 0.5 x 10(-3) seconds.
• This fourth-order scheme offers comparable accuracy to first- and second-order methods but with significantly larger time-steps.

Conclusions:

• The developed fourth-order scheme provides a substantial improvement in accuracy and efficiency for neuronal network simulations.
• The method overcomes limitations of existing numerical approaches for handling spike-induced potential resets.
• Achieving high-order accuracy is computationally feasible, even with standard neuronal network models.