Nonlinear Oscillation Models for Spike Separation

Abstract

The present study reports an approach for automatic classification of extracellularly recorded action potentials (spikes). The recorded signal is observed at discrete times and characterized by high level of background noise and occurrence of the spikes at random time. The classification of spike waveform is considered as a pattern recognition problem of special segments of signal that correspond to the appearance of spikes. The spikes generated by one neuron should be recognized as members of the same class. We describe the spike waveform as an ordinary differential equation with perturbation. This allows us to characterize the signal distortions in both amplitude and phase. We have developed an iteration-learning algorithm that estimates the number of classes and their centers according to the distance between spike trajectories in phase space. The estimation of trajectories in phase space required calculation of the first and second order derivatives and the integral operators with piecewise polynomial kernels were used. This approach is computational efficient and of potential use for real time situations, in particular during neurosurgical procedures.