Exploring optimal current stimuli that provide membrane voltage tracking in a neuron model

Evolution of extrema features reveals optimal stimuli for biological state transitions

The ability to define the unique features of an input stimulus needed to control switch-like behavior in biological systems is an important problem in computational biology and medicine. We show in this study how highly complex and intractable optimization problems can be simplified by restricting the search to the signal's extrema as key feature points, and evolving the extrema features towards optimal solutions that closely match solutions derived from gradient-based methods. Our results suggest a model-independent approach for solving a class of optimization problems related to controlling switch-like state transitions.

A new approach to optimal control of conductance-based spiking neurons

This paper presents an algorithm for solving the minimum-energy optimal control problem of conductance-based spiking neurons. The basic procedure is (1) to construct a conductance-based spiking neuron oscillator as an affine nonlinear system, (2) to formulate the optimal control problem of the affine nonlinear system as a boundary value problem based on Pontryagin's maximum principle, and (3) to solve the boundary value problem using the homotopy perturbation method. The construction of the minimum-energy optimal control in the framework of the homotopy perturbation technique is novel and valid for a broad class of nonlinear conductance-based neuron models. The applicability of our method in the FitzHugh-Nagumo and Hindmarsh-Rose models is validated by simulations.

Initial comparison of energy measures for neural stimulation in a single conductance channel

This paper considers the utility of several alternative energy measures to reduce the energy required by a stimulation current source to charge a neuron membrane capacitance to a prescribed value in the case of a single sodium channel. For a simple case, minimizing the energy of the nonlinear channel conductance provides improved efficiency in terms of stimulator energy as compared to minimizing a squared-integral measure of the stimulation current. This work lays the foundation for expanding this investigation to a full conductance-based Hodgkin-Huxley model.

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(*)(t) and the tracking error between the reference phase r(t) and the phase response due to i(*)(t). The balance between the conflicting requirements of energy and tracking error minimization is controlled by a single parameter. The generated optimal current i(*)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(*)(t) generates a phase response similar to the reference phase r(t), and the optimal current i(*)(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.