On the evaluation of firing densities for periodically driven neuron models

The leaky integrate-and-fire model for neuronal spiking events driven by a periodic stimulus is studied by using the Fokker–Planck formulation. To this purpose, an essential use is made of the asymptotic behavior of the first-passage-time probability density function of a time homogeneous diffusion process through an asymptotically periodic threshold. Numerical comparisons with some recently published results derived by a different approach are performed. Use of a new asymptotic approximation is then made in order to design a numerical algorithm of predictor–corrector type to solve the integral equation in the unknown first-passage-time probability density function. Such algorithm, characterized by a reduced (linear) computation time, is seen to provide a high computation accuracy. Finally, it is shown that such an approach yields excellent approximations to the firing probability density function for a wide range of parameters, including the case of high stimulus frequencies.