Computation of reduced energy input current stimuli for neuron phase models

A regularly spiking neuron can be studied using a phase model. The effect of an input stimulus current on the phase time derivative is captured by a phase response curve. This paper adapts a technique that was previously applied to conductance-based models to discover optimal input stimulus currents for phase models. First, the neuron phase response θ(t) due to an input stimulus current i(t) is computed using a phase model. The resulting θ(t) is taken to be a reference phase r(t). Second, an optimal input stimulus current i^*(t) is computed to minimize a weighted sum of the square-integral `energy´ of i<sup>*</sup>(t) and the tracking error between the reference phase r(t) and the phase response due to i<sup>*</sup>(t). The balance between the conflicting requirements of energy and tracking error minimization is controlled by a single parameter. The generated optimal current i<sup>*</sup>t) is then compared to the input current i(t) which was used to generate the reference phase r(t). This technique was applied to two neuron phase models; in each case, the current i<sup>*</sup>(t) generates a phase response similar to the reference phase r(t), and the optimal current i<sup>*</sup>(t) has a lower `energy´ than the square-integral of i(t). For constant i(t), the optimal current i^*(t) need not be constant in time. In fact, i^*(t) is large (possibly even larger than i(t)) for regions where the phase response curve indicates a stronger sensitivity to the input stimulus current, and smaller in regions of reduced sensitivity.