Probability-based nonlinear modeling of neural dynamical systems with point-process inputs and outputs
© Sandler et al.; licensee BioMed Central Ltd. 2014
Published: 21 July 2014
One of the great challenges of contemporary neuroscience is understanding in a quantitative manner how neurons and neural ensembles encode and process information in the form of action potentials. The advent of multi-electrode arrays which can record large amounts of data simultaneously from several neurons has made this task more urgent. This task, however, is made difficult by the inherent complexity of neural systems which are highly nonlinear, interconnected, dynamic, and subject to stochastic variations. Furthermore, while several methods exist which offer good predictive performance for spike train modeling, their adoption in the broader neuroscience community has been limited due to their mathematical complexity and lack of interpretability.
This method may be extended to describe the contribution of n pairs spikes to the output in the form of the nth PBV kernel. We show that the PBV kernels are equivalent to the Wiener kernels when the input is a Poisson process, thus placing the PBV kernels in the context of a well-established and rigorous mathematical theory .
The proposed PBV methodology was applied to synthetic systems where the ground truth of the model was available. The PBV kernels were found to both accurately estimate the ground truth kernels and to reproduce the given output, thus validating the method. Finally, the proposed PBV methodology was applied to real neural data derived from the CA3 and CA1 regions of the rodent hippocampus . Although here ground truth was not available, the PBV kernels were able to reproduce the output as well as other models which have been validated both mathematically and in-vivo in the context of neural prosthetics .
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