Threshold shape corresponding to a gamma firing distribution in an Ornstein-Uhlenbeck neuronal model

We introduce two numerical methods to determine the shape of a time dependent boundary for the Ornstein-Uhlenbeck process that corresponds to an assigned first passage time probability density function. The application of these methods to the stochastic leaky integrate and fire neuronal model allows to check the reliability of specified densities as approximation of the interspike interval distribution. The cases of the Gamma and of the inverse Gaussian densities are discussed.