A Boundary Element Method of Bidomain Modeling for Predicting Cellular Responses to Electromagnetic Fields.
A Boundary Element Method of Bidomain Modeling for Predicting Cellular Responses to Electromagnetic Fields.
复制标题
用于预测细胞对电磁场响应的双域建模的边界元方法。
DOI：
10.1101/2023.12.15.571917
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发表时间：
2023
期刊：
影响因子：
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通讯作者：
Gomez,LuisJ
中科院分区：
文献类型：
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作者：
Czerwonky,DavidM;Aberra,AmanS;Gomez,LuisJ
目的 用于模拟电磁场对可兴奋细胞的影响的常用电缆方程方法做出了一些可能限制其预测能力的简化假设。双域或“整体”有限元方法已被开发用于完全耦合细胞和电场，以实现更真实的神经元建模。在这里，我们引入了一种新颖的双域积分方程，旨在确定刺激设备与神经元的细胞内、膜和细胞外区域之间的完全电磁耦合。方法我们提出的边界元公式为连接设备、组织不均匀性和细胞膜诱导电场的积分方程提供了解决方案。我们使用一阶节点元素和无条件稳定的 Crank-Nicholson 时间步长方案求解该积分方程。为了验证和演示我们的方法，我们在多个脑刺激场景中模拟了圆柱形霍奇金-赫胥黎轴突和球形细胞。主要结果比较研究表明，边界元方法可以为电刺激和磁刺激产生准确的结果。与双域有限元方法不同，双域边界元方法不需要包含多个尺度特征的体网格。因此，将微观特征嵌入宏观头部模型中的细胞或紧密排列的细胞群的建模得到简化，并且可以改变设备和细胞的相对位置，而无需生成新的网格。意义设备引起的电磁场通常用于调节大脑活动，用于研究和治疗应用。双域求解器可以完全结合真实的细胞几何形状、设备电场和神经元群。因此，高级神经元机制的多细胞研究将极大地受益于快速双域求解器的开发，以确保具有真实神经元形态的神经网络模拟的可扩展性和实际执行。
ObjectiveCommonly used cable equation approaches for simulating the effects of electromagnetic fields on excitable cells make several simplifying assumptions that could limit their predictive power. Bidomain or'whole'finite element methods have been developed to fully couple cells and electric fields for more realistic neuron modeling. Here, we introduce a novel bidomain integral equation designed for determining the full electromagnetic coupling between stimulation devices and the intracellular, membrane, and extracellular regions of neurons.ApproachOur proposed boundary element formulation offers a solution to an integral equation that connects the device, tissue inhomogeneity, and cell membrane-induced E-fields. We solve this integral equation using first-order nodal elements and an unconditionally stable Crank–Nicholson time-stepping scheme. To validate and demonstrate our approach, we simulated cylindrical Hodgkin–Huxley axons and spherical cells in multiple brain stimulation scenarios.Main ResultsComparison studies show that a boundary element approach produces accurate results for both electric and magnetic stimulation. Unlike bidomain finite element methods, the bidomain boundary element method does not require volume meshes containing features at multiple scales. As a result, modeling cells, or tightly packed populations of cells, with microscale features embedded in a macroscale head model, is simplified, and the relative placement of devices and cells can be varied without the need to generate a new mesh.SignificanceDevice-induced electromagnetic fields are commonly used to modulate brain activity for research and therapeutic applications. Bidomain solvers allow for the full incorporation of realistic cell geometries, device E-fields, and neuron populations. Thus, multi-cell studies of advanced neuronal mechanisms would greatly benefit from the development of fast-bidomain solvers to ensure scalability and the practical execution of neural network simulations with realistic neuron morphologies.