A numerical model for Hodgkin-Huxley neural stimulus reconstruction

The information about a neural activity is encoded in a neural response and usually the underlying stimulus that triggers the activity is unknown. This paper presents a numerical solution to reconstruct stimuli from Hodgkin-Huxley neural responses while retrieving the neural dynamics. The stimulus is reconstructed by first retrieving the maximal conductances of the ion channels and then solving the Hodgkin-Huxley equations for the stimulus. The results show that the reconstructed stimulus is a good approximation of the original stimulus, while the retrieved the neural dynamics, which represent the voltage-dependent changes in the ion channels, help to understand the changes in neural biochemistry. As high non-linearity of neural dynamics renders analytical inversion of a neuron an arduous task, a numerical approach provides a local solution to the problem of stimulus reconstruction and neural dynamics retrieval

A Toeplitz formulation of a real-time algorithm for time decoding machines

Abstract Time encoding is a real-time asynchronous mechanism for encoding the amplitude information of an analog bandlimited signal into a time sequence, or time codes, based on which the signal can be reconstructed. Using a Toeplitz formulation we propose an efficient real-time reconstruction procedure. As an illustration, time encoding is carried out by an asynchronous sigma-delta modulator. The proposed method is confirmed by numerical simulations