Minimum energy control for a two-compartment neuron to extracellular electric fields

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

“…Compute the ith order termsx (i) (t) andλ (i) (t) from the sequence of linear time-invariant BVP. Set M = i and calculate x (M ) (t) and λ (M ) (t) from (27), and then derive u (M ) (t) from (18).…”

“…Although the phase-reduced models using PRC is a parsimonious and effective way to describe how a neuron responds to a stimulus, it is only valid for periodic spiking or firing neurons. Therefore, some researchers have paid much attention to the control of spiking neurons in the context of conductance-based neuron models which are more intricate than phase-reduced models [14]- [18]. An event-based energy-optimal desynchronizing control for coupled reduced Hodgkin-Huxley neurons was established in [14] by means of the Hamilton-Jacobi-Bellman approach.…”

“…In [15], the tracking control with low energy input current stimuli of a reference membrane voltage in the reduced Hodgkin-Huxley neuron model was addressed to support investigations of neuron dynamics and energy efficiency. In [18], a low energy extracellular electric field input was designed for a reduced two-compartment model based on Pinsky-Rinzel model, and applied to drive the neuron to closely track a prescriptive spike train. However, it is generally impossible to solve analytically the optimal control problem of conductance-based neuron models.…”

Approximate optimal iterative approach for a class of oscillatory neuron models

“…In Wilson et al (2015), the authors developed an energy optimal control strategy to entrain heterogeneous noisy neurons and apply it to numerical models of noisy phase oscillators and to vitro hippocampal neurons. In spite of these advances, it has not received much attention until now with few results (Danzl, Hespanha, & Moehlis, 2009; CONTACT X. Lou louxy@jiangnan.edu.cn; Qian Ye qqianye@126.com Nabi, Mirzadeh, Gibou, & Moehlis, 2013;Yi, Wang, Li, Wei, & Deng, 2016) appearing on control of conductancebased neuron models which are more intricate than phase-reduced models. In particular, designed an event-based desynchronizing control stimulus for a network of pathologically synchronized coupled neurons and employed a Hamilton-Jacobi-Bellman (HJB) approach to transform the optimal control problem into solving numerical solution of an HJB partial differential equation by an level set method.…”

“…By using similar HJB framework, Danzl et al (2009) proposed an eventbased minimum-time optimal control for oscillatory neurons and the results were extended to a network of globally coupled neurons. From the view point of extracellular electric field stimulus, the optimization of stimulus energy for a reduced two-compartment neuron model was addressed in Yi et al (2016). Particular motivation for the study on optimal control of oscillatory neuron models using approximate iterative-type approach comes from its board application to approximate solution of optimal control problem for nonlinear systems and the rapid development of computer ability.…”