Eikenberry Steffen E, Marmarelis Vasilis Z
Department of Biomedical Engineering, University of Southern California, 1042 Downey Way, Los Angeles, CA 90089, USA.
Int J Neural Syst. 2015 Mar;25(2):1550001. doi: 10.1142/S012906571550001X. Epub 2014 Nov 20.
We develop an autoregressive model framework based on the concept of Principal Dynamic Modes (PDMs) for the process of action potential (AP) generation in the excitable neuronal membrane described by the Hodgkin-Huxley (H-H) equations. The model's exogenous input is injected current, and whenever the membrane potential output exceeds a specified threshold, it is fed back as a second input. The PDMs are estimated from the previously developed Nonlinear Autoregressive Volterra (NARV) model, and represent an efficient functional basis for Volterra kernel expansion. The PDM-based model admits a modular representation, consisting of the forward and feedback PDM bases as linear filterbanks for the exogenous and autoregressive inputs, respectively, whose outputs are then fed to a static nonlinearity composed of polynomials operating on the PDM outputs and cross-terms of pair-products of PDM outputs. A two-step procedure for model reduction is performed: first, influential subsets of the forward and feedback PDM bases are identified and selected as the reduced PDM bases. Second, the terms of the static nonlinearity are pruned. The first step reduces model complexity from a total of 65 coefficients to 27, while the second further reduces the model coefficients to only eight. It is demonstrated that the performance cost of model reduction in terms of out-of-sample prediction accuracy is minimal. Unlike the full model, the eight coefficient pruned model can be easily visualized to reveal the essential system components, and thus the data-derived PDM model can yield insight into the underlying system structure and function.
我们基于主动态模式（PDM）的概念，为霍奇金 - 赫胥黎（H - H）方程所描述的可兴奋神经元膜中动作电位（AP）的产生过程，开发了一种自回归模型框架。该模型的外部输入为注入电流，每当膜电位输出超过指定阈值时，就将其作为第二个输入反馈回来。PDM是根据先前开发的非线性自回归沃尔泰拉（NARV）模型估计得出的，代表了沃尔泰拉核展开的有效函数基。基于PDM的模型允许模块化表示，分别由前向和反馈PDM基组成，它们分别作为外部输入和自回归输入的线性滤波器组，其输出然后被馈送到一个静态非线性函数，该函数由对PDM输出以及PDM输出的成对乘积的交叉项进行运算的多项式组成。执行了一个两步的模型简化过程：首先，识别并选择前向和反馈PDM基的有影响子集作为简化后的PDM基。其次，修剪静态非线性函数的项。第一步将模型复杂度从总共65个系数降低到27个，而第二步进一步将模型系数减少到仅8个。结果表明，就样本外预测准确性而言，模型简化的性能代价最小。与完整模型不同，具有8个系数的修剪模型可以很容易地可视化以揭示基本的系统组件，因此基于数据的PDM模型可以深入了解潜在的系统结构和功能。
