VIRTUS, IC Design Centre of Excellence, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798.
IEEE Trans Biomed Circuits Syst. 2012 Feb;6(1):64-75. doi: 10.1109/TBCAS.2011.2158314.
This paper introduces the use of the concept of small-signal analysis, commonly used in circuit design, for understanding neural models. We show that neural models, varying in complexity from Hodgkin-Huxley to integrate and fire have similar small-signal models when their corresponding differential equations are close to the same bifurcation with respect to input current. Three applications of small-signal neural models are shown. First, some of the properties of cortical neurons described by Izhikevich are explained intuitively through small-signal analysis. Second, we use small-signal models for deriving parameters for a simple neural model (such as resonate and fire) from a more complicated but biophysically relevant one like Morris-Lecar. We show similarity in the subthreshold behavior of the simple and complicated model when they are close to a Hopf bifurcation and a saddle-node bifurcation. Hence, this is useful to correctly tune simple neural models for large-scale cortical simulations. Finaly, the biasing regime of a silicon ion channel is derived by comparing its small-signal model with a Hodgkin-Huxley-type model.
本文介绍了小信号分析概念的应用，该概念通常用于电路设计，以帮助理解神经模型。我们表明，当相应的微分方程在输入电流方面接近相同的分岔时，从 Hodgkin-Huxley 到积分和点火的复杂程度不同的神经模型具有相似的小信号模型。展示了小信号神经模型的三个应用。首先，通过小信号分析直观地解释了 Izhikevich 描述的皮质神经元的一些特性。其次，我们使用小信号模型从更复杂但具有生理相关性的模型（如 Morris-Lecar）推导出简单神经模型（如谐振和点火）的参数。当它们接近 Hopf 分岔和鞍结分岔时，简单和复杂模型的亚阈值行为具有相似性。因此，这对于为大规模皮质模拟正确调整简单神经模型非常有用。最后，通过将硅离子通道的小信号模型与 Hodgkin-Huxley 型模型进行比较，推导出了其偏置状态。
