Fixed threshold modeling of an adjustable threshold integrate-and-fire neuronal model

An action potential is generated when the membrane potential of a spiking neuron reaches a certain threshold. Although it is well-known that the threshold level of a neuron is not a fixed value and changes with time and neuronal parameters, its variation is often ignored in neuronal modeling due to the complexity of the analysis. Assuming a fixed threshold level, however, may produce non-realistic results. If we find a model to incorporate the impact of the variation of the threshold in a fixed threshold model we can benefit from the simplicity of the existing fixed-threshold models yet obtain more realistic results. It is shown here that, with some approximations, we can create a fixed threshold model for an integrate-and-fire neuronal model from an adjustable threshold model by some simple operations. Both models generate the same spike (action potential) pattern.