Efficient sequential Bayesian inference method for real-time detection and sorting of overlapped neural spikes

• Novel real-time spike sorting algorithm which can detect complexly-overlapped spikes.
• Efficient estimation procedure by sequential Bayesian inference with approximation.
• The algorithm can decompose overlaps of arbitrary numbers of spikes.
• Computational cost low enough for real-time processing of multi-channel recording.
• Accuracy much better than the conventional template matching in various conditions.

Overlapping of extracellularly recorded neural spike waveforms causes the original spike waveforms to become hidden and merged, confounding the real-time detection and sorting of these spikes. Methods proposed for solving this problem include using a multi-trode or placing a restriction on the complexity of overlaps. In this paper, we propose a rapid sequential method for the robust detection and sorting of arbitrarily overlapped spikes recorded with arbitrary types of electrodes. In our method, the probabilities of possible spike trains, including those that are overlapping, are evaluated by sequential Bayesian inference based on probabilistic models of spike-train generation and extracellular voltage recording. To reduce the high computational cost inherent in an exhaustive evaluation, candidates with low probabilities are considered as impossible candidates and are abolished at each sampling time to limit the number of candidates in the next evaluation. In addition, the data from a few subsequent sampling times are considered and used to calculate the “look-ahead probability”, resulting in improved calculation efficiency due to a more rapid elimination of candidates. These sufficiently reduce computational time to enable real-time calculation without impairing performance. We assessed the performance of our method using simulated neural signals and actual neural signals recorded in primary cortical neurons cultured on a multi-electrode array. Our results demonstrated that our computational method could be applied in real-time with a delay of less than 10 ms. The estimation accuracy was higher than that of a conventional spike sorting method, particularly for signals with multiple overlapping spikes.

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