The transfer function of neuron spike.

The mathematical modeling of neuronal signals is a relevant problem in neuroscience. The complexity of the neuron behavior, however, makes this problem a particularly difficult task. Here, we propose a discrete-time linear time-invariant (LTI) model with a rational function in order to represent the neuronal spike detected by an electrode located in the surroundings of the nerve cell. The model is presented as a cascade association of two subsystems: one that generates an action potential from an input stimulus, and one that represents the medium between the cell and the electrode. The suggested approach employs system identification and signal processing concepts, and is dissociated from any considerations about the biophysical processes of the neuronal cell, providing a low-complexity alternative to model the neuronal spike. The model is validated by using in vivo experimental readings of intracellular and extracellular signals. A computational simulation of the model is presented in order to assess its proximity to the neuronal signal and to observe the variability of the estimated parameters. The implications of the results are discussed in the context of spike sorting.