Medical & Biological Engineering & Computing

, Volume 57, Issue 12, pp 2617–2627 | Cite as

Accuracy of electromagnetic models to estimate cardiomyocyte membrane polarization

  • Hugo F. M. MilanEmail author
  • Rosana A. Bassani
  • Luiz E. C. Santos
  • Antonio C. G. Almeida
  • José W. M. Bassani
Original Article


External electric fields (E) induce a spatially heterogeneous variation in the membrane potential (ΔVm) of cardiomyocytes that, if sufficiently large, results in an action potential and contraction. Insights into the phenomenon of ΔVm 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 ΔVm values (ΔVmax), which were compared with estimates from seven other electromagnetic models. Accurate ΔVmax 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 ΔVmax 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 ΔVmax 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 (ΔVmax) 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 ΔVmax 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.


Finite element analysis Transmembrane electric potential Electric field Electric stimulation Myocardial cell 



The authors are grateful to the Brazilian National Center for High Performance Computing in the São Paulo State (CENAPAD-SP) for providing computational resources (Proj587) and to Ms. Elizângela S. Oliveira and Mr. Renato S. Moura from the Center for Biomedical Engineering of University of Campinas for technical support.

Funding information

This work was supported by São Paulo Research Foundation (FAPESP, Proc. 2013/05441-5), Brazilian National Council for Scientific and Technological Development (CNPq, Proc. 304010/2016-2, 203312/2014-7, 308092/2015-5), Minas Gerais Research Foundation (FAPEMIG, Proc. PPM-00666-16), and Coordination for the Improvement of Higher Education Personnel (CAPES).


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Copyright information

© International Federation for Medical and Biological Engineering 2019

Authors and Affiliations

  1. 1.Department of Biological and Environmental EngineeringCornell UniversityIthacaUSA
  2. 2.Department of Biomedical Engineering, School of Electrical and Computing EngineeringUniversity of CampinasCampinasBrazil
  3. 3.Center for Biomedical EngineeringUniversity of CampinasCampinasBrazil
  4. 4.Department of Biosystems EngineeringFederal University of São João del-ReiSão João del ReiBrazil

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