Linear control of neuronal spike timing using phase response curves.

We propose a simple, robust, linear method to control the spike timing of a periodically firing neuron. The control scheme uses the neuron's phase response curve to identify an area of optimal sensitivity for the chosen stimulation parameters. The spike advance as a function of current pulse amplitude is characterized at the optimal phase and a linear least-squares regression is fit to the data. The inverted regression is used as the control function for this method. The efficacy of this method is demonstrated through numerical simulations of a Hodgkin-Huxley style neuron model as well as in real neurons from rat hippocampal slice preparations. The study shows a proof of concept for the application of a linear control scheme to control neuron spike timing in-vitro. This study was done on an individual cell level, but translation to a tissue or network level is possible. Control schemes of this type could be implemented in a closed loop implantable device to treat neuromotor disorders involving pathologically neuronal activity such as epilepsy or Parkinson's disease.