Department of Biological and Environmental Engineering, Cornell University, 321 Riley-Robb Hall, Ithaca, NY, 14850, USA.
Department of Biomedical Engineering, School of Electrical and Computing Engineering, University of Campinas, Campinas, SP, 1308-970, Brazil.
Med Biol Eng Comput. 2019 Dec;57(12):2617-2627. doi: 10.1007/s11517-019-02054-2. Epub 2019 Oct 30.
External electric fields (E) induce a spatially heterogeneous variation in the membrane potential (ΔV) of cardiomyocytes that, if sufficiently large, results in an action potential and contraction. Insights into the phenomenon of ΔV induction by E have been classically gained with electromagnetic models due to the lack of adequate experimental approaches. However, it is not clear yet how reliable these models are. To assess the accuracy of commonly used models, a reference 3D numerical model for cardiomyocytes (NMReal) was developed, consisting of the cell membrane shell reconstructed from rendered confocal microscopy images of freshly isolated ventricular myocytes. NMReal was used to estimate the E-induced maximum ΔV values (ΔV), which were compared with estimates from seven other electromagnetic models. Accurate ΔV estimates (average error < 2%) were obtained with a less complex 3D model (NM3D) based on the extruded 2D image of the cell longitudinal section. Acceptable ΔV estimates (average error < 5%) were obtained with the prolate spheroid analytical model (PSAM) when the angle of E incidence and the cell major axis was < 30°. In this case, PSAM, a much simpler model requiring only the measurement of the longitudinal and transversal cell dimensions, can be a suitable alternative for ΔV calculation. Graphical abstract (A) Confocal images of the cell were used to reconstruct the realistic geometry of cardiomyocytes (NMReal). (B) NMReal was used to estimate the maximum variation in the transmembrane potential (ΔV) induced by an external electric field (E) applied at different angles with respect to the cell major axis. Plus (anode) and minus (cathode) signs indicate electrode position (E direction is from minus to plus). (C) Relative error (vs. NMReal) of ΔV estimation with simplified electromagnetic models, presented in descending order of accuracy (left-to-right, top-to-bottom). NM2D: 2D numerical model based on the longitudinal cell image; NM3D: numerical model based on the z extrusion of NM2D; EAM, PSAM, and CAM: ellipsoidal, prolate spheroidal, and cylindrical analytical models, respectively; PNM and CNM: parallelepipedal and cylindrical numerical models, respectively.
外部电场 (E) 会引起心肌细胞膜电位 (ΔV) 的空间不均匀变化，如果电场足够大，就会导致动作电位和收缩。由于缺乏适当的实验方法，经典上通过电磁模型来深入了解 E 诱导 ΔV 的现象。然而，目前尚不清楚这些模型的可靠性如何。为了评估常用模型的准确性，开发了一个用于心肌细胞的参考 3D 数值模型 (NMReal)，该模型由从新鲜分离的心室肌细胞的共聚焦显微镜图像重建的细胞膜壳组成。NMReal 用于估计 E 诱导的最大 ΔV 值 (ΔV)，并将其与其他七个电磁模型的估计值进行比较。使用基于细胞纵向切片挤压 2D 图像的更简单的 3D 模型 (NM3D) 可以获得准确的 ΔV 估计值（平均误差<2%）。当 E 入射角度和细胞长轴<30°时，扁长球体解析模型 (PSAM) 可以获得可接受的 ΔV 估计值（平均误差<5%）。在这种情况下，PSAM 是一种更简单的模型，只需要测量细胞的纵向和横向尺寸，因此可以作为 ΔV 计算的合适替代方法。
