Event-Driven Simulation of Integrate-and-Fire Neurons with Exponential Synaptic Conductances

It has become widely accepted that in neurons, spike timing is important. Simulating realistic spiking neuron models requires efficient numerical methods, but standard integration schemes need small time steps in order to obtain an acceptable accuracy, which has led several authors to introduce interpolation techniques. In other methods, the membrane potential is calculated only at the times of incoming spikes, but it is generally believed that only the standard leaky integrator with instantaneous depolarizations can be simulated with an event-driven method. We show that an integrate-and-fire model with exponential synaptic conductances can be simulated this way, by expressing the solutions of the differential equation with the help of an incomplete gamma function. Using precalculated tables, the resulting algorithm is both fast and extremely precise. (127 words)