System Identification of a Multi-timescale Adaptive Threshold Neuronal Model

1An abridged version (Jabalameli and Behal, 2015) of this paper was presented at the 2015 International Conference on Computational Advances in Bio and Medical Sciences.The study was supported by Award # R15NS062402 from NINDS. The content is solely the responsibility of the authors and does not necessarily represent the official views of the NINDS or the NIH. ar X iv :1 80 3. 04 23 6v 1 [ qbi o. N C ] 2 3 Fe b 20 18 In this paper, the parameter estimation problem for a multi-timescale adaptive threshold (MAT) neuronal model is investigated. By manipulating the system dynamics, which comprise of a non-resetting leaky integrator coupled with an adaptive threshold, the threshold voltage can be obtained as a realizable model that is linear in the unknown parameters. This linearly parametrized realizable model is then utilized inside a prediction error based framework to identify the threshold parameters with the purpose of predicting single neuron precise firing times. The iterative linear least squares estimation scheme is evaluated using both synthetic data obtained from an exact model as well as experimental data obtained from in vitro rat somatosensory cortical neurons. Results show the ability of this approach to fit the MAT model to different types of fluctuating reference data. The performance of the proposed approach is seen to be superior when comparing with existing identification approaches used by the neuronal community.