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

作者：Yi, Guo-Sheng; Wang, Jiang; Li, Hui-Yan^*; Wei, Xi-Le; Deng, Bin

来源：Communications in Nonlinear Science & Numerical Simulation, 2016, 40: 138-150.

DOI：10.1016/j.cnsns.2016.03.017

• Energy optimization
• Extracellular electric field
• Reduced two-compartment model
• Optimal control theory

The energy optimization of extracellular electric field (EF) stimulus for a neuron is considered in this paper. We employ the optimal control theory to design a low energy EF input for a reduced two-compartment model. It works by driving the neuron to closely track a prescriptive spike train. A cost function is introduced to balance the contradictory objectives, i.e., tracking errors and EF stimulus energy. By using the calculus of variations, we transform the minimization of cost function to a six-dimensional two-point boundary value problem (BVP). Through solving the obtained BVP in the cases of three fundamental bifurcations, it is shown that the control method is able to provide an optimal EF stimulus of reduced energy for the neuron to effectively track a prescriptive spike train. Further, the feasibility of the adopted method is interpreted from the point of view of the biophysical basis of spike initiation. These investigations are conducive to designing stimulating dose for extracellular neural stimulation, which are also helpful to interpret the effects of extracellular field on neural activity.

• 出版日期2016-11
• 单位天津大学; 天津职业技术师范大学