Fast and exact simulation methods applied on a broad range of neuron models

Recently van Elburg and van Ooyen (2009) published a generalization of the event-based integration scheme for an integrate-and-fire neuron model with exponentially decaying excitatory currents and double exponential inhibitory synaptic currents, introduced by Carnevale and Hines. In the paper, it was shown that the constraints on the synaptic time constants imposed by the Newton-Raphson iteration scheme, can be relaxed. In this note, we show that according to the results published in D'Haene, Schrauwen, Van Campenhout, and Stroobandt (2009), a further generalization is possible, eliminating any constraint on the time constants. We also demonstrate that in fact, a wide range of linear neuron models can be efficiently simulated with this computation scheme, including neuron models mimicking complex neuronal behavior. These results can change the way complex neuronal spiking behavior is modeled: instead of highly nonlinear neuron models with few state variables, it is possible to efficiently simulate linear models with a large number of state variables.