Fellner Andreas, Heshmat Amirreza, Werginz Paul, Rattay Frank
Institute for Analysis and Scientific Computing, Vienna University of Technology, Vienna, Austria.
Laboratory for Inner Ear Biology, Department of Otorhinolaryngology, Medical University of Innsbruck, Innsbruck, Austria.
J Neural Eng. 2022 Apr 7;19(2). doi: 10.1088/1741-2552/ac6060.
Increasing complexity in extracellular stimulation experiments and neural implant design also requires realistic computer simulations capable of modeling the neural activity of nerve cells under the influence of an electrical stimulus. Classical model approaches are often based on simplifications, are not able to correctly calculate the electric field generated by complex electrode designs, and do not consider electrical effects of the cell on its surrounding. A more accurate approach is the finite element method (FEM), which provides necessary techniques to solve the Poisson equation for complex geometries under consideration of electrical tissue properties. Especially in situations where neurons experience large and non-symmetric extracellular potential gradients, a FEM solution that implements the cell membrane model can improve the computer simulation results. To investigate the response of neurons in an electric field generated by complex electrode designs, a FEM framework for extracellular stimulation was developed in COMSOL.Methods to implement morphologically- and biophysically-detailed neurons including active Hodgkin-Huxley (HH) cell membrane dynamics as well as the stimulation setup are described in detail. Covered methods are (a) development of cell and electrode geometries including meshing strategies, (b) assignment of physics for the conducting spaces and the realization of active electrodes, (c) implementation of the HH model, and (d) coupling of the physics to get a fully described model.Several implementation examples are briefly presented: (a) a full FEM implementation of a HH model cell stimulated with a honeycomb electrode, (b) the electric field of a cochlear electrode placed inside the cochlea, and (c) a proof of concept implementation of a detailed double-cable cell membrane model for myelinated nerve fibers.The presented concepts and methods provide basic and advanced techniques to realize a full FEM framework for innovative studies of neural excitation in response to extracellular stimulation.
细胞外刺激实验和神经植入设计的复杂性不断增加，这也需要能够对电刺激影响下神经细胞的神经活动进行建模的逼真计算机模拟。传统的模型方法通常基于简化，无法正确计算复杂电极设计产生的电场，也没有考虑细胞对其周围环境的电效应。一种更精确的方法是有限元法（FEM），它提供了必要的技术来求解考虑电组织特性的复杂几何形状的泊松方程。特别是在神经元经历大的非对称细胞外电位梯度的情况下，实现细胞膜模型的有限元法解决方案可以改善计算机模拟结果。为了研究复杂电极设计产生的电场中神经元的反应，在COMSOL中开发了一个用于细胞外刺激的有限元框架。详细描述了实现形态学和生物物理学详细神经元的方法，包括活跃的霍奇金-赫胥黎（HH）细胞膜动力学以及刺激设置。涵盖的方法有：（a）细胞和电极几何形状的开发，包括网格划分策略；（b）导电空间的物理属性分配和有源电极的实现；（c）HH模型的实现；（d）物理属性的耦合以获得一个完整描述的模型。简要介绍了几个实现示例：（a）用蜂窝电极刺激的HH模型细胞的完整有限元法实现；（b）置于耳蜗内的耳蜗电极的电场；（c）有髓神经纤维详细双电缆细胞膜模型的概念验证实现。所提出的概念和方法提供了基础和先进技术，以实现一个完整的有限元框架，用于响应细胞外刺激的神经兴奋的创新性研究。
