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Published in: Medical & Biological Engineering & Computing 12/2019

30-10-2019 | Original Article

Accuracy of electromagnetic models to estimate cardiomyocyte membrane polarization

Authors: Hugo F. M. Milan, Rosana A. Bassani, Luiz E. C. Santos, Antonio C. G. Almeida, José W. M. Bassani

Published in: Medical & Biological Engineering & Computing | Issue 12/2019

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Abstract

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.

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Literature
1.
go back to reference Bassani RA, Lima KA, Gomes PAP, Oliveira PX, Bassani JWM (2006) Combining stimulus direction and waveform for optimization of threshold stimulation of isolated ventricular myocytes. Physiol Meas 27:851–863CrossRef Bassani RA, Lima KA, Gomes PAP, Oliveira PX, Bassani JWM (2006) Combining stimulus direction and waveform for optimization of threshold stimulation of isolated ventricular myocytes. Physiol Meas 27:851–863CrossRef
2.
go back to reference Bensley JG, Matteo RD, Harding R, Black MJ (2016) Three-dimensional direct measurement of cardiomyocyte volume, nuclearity, and ploidy in thick histological sections. Sci Rep 6:23756CrossRef Bensley JG, Matteo RD, Harding R, Black MJ (2016) Three-dimensional direct measurement of cardiomyocyte volume, nuclearity, and ploidy in thick histological sections. Sci Rep 6:23756CrossRef
3.
go back to reference Bernhardt J, Pauly H (1973) On the generation of potential difference across the membranes of ellipsoidal cells in an alternating electrical field. Biophysics 10:89–98 Bernhardt J, Pauly H (1973) On the generation of potential difference across the membranes of ellipsoidal cells in an alternating electrical field. Biophysics 10:89–98
4.
go back to reference Bishop SP, Drummond JL (1979) Surface morphology and cell size measurement of isolated rat cardiac myocytes. J Mol Cell Cardiol 11:423–430CrossRef Bishop SP, Drummond JL (1979) Surface morphology and cell size measurement of isolated rat cardiac myocytes. J Mol Cell Cardiol 11:423–430CrossRef
5.
go back to reference Cartee LA, Plonsey R (1992) The transient subthreshold response of spherical and cylindrical cell models to extracellular stimulation. IEEE Trans Biomed Eng 39:76–85CrossRef Cartee LA, Plonsey R (1992) The transient subthreshold response of spherical and cylindrical cell models to extracellular stimulation. IEEE Trans Biomed Eng 39:76–85CrossRef
6.
go back to reference Coocklin M, Wallis WRJ, Sheridan DJ, Fry CH (1997) Changes in cell-to-cell electrical coupling associated with left ventricular hypertrophy. Circ Res 80:765–771CrossRef Coocklin M, Wallis WRJ, Sheridan DJ, Fry CH (1997) Changes in cell-to-cell electrical coupling associated with left ventricular hypertrophy. Circ Res 80:765–771CrossRef
7.
go back to reference Connolly A, Kelly A, Campos FO, Myles R, Smith G, Bishop MJ (2018) Ventricular endocardial tissue geometry affects stimulus threshold and effective refractory period. Biophys J 115:2486–2498CrossRef Connolly A, Kelly A, Campos FO, Myles R, Smith G, Bishop MJ (2018) Ventricular endocardial tissue geometry affects stimulus threshold and effective refractory period. Biophys J 115:2486–2498CrossRef
8.
go back to reference Fishler MG, Sobie AE, Tung L, Thakor NV (1995) Cardiac responses to premature monophasic and biphasic field stimuli: results from cell and tissue modeling studies. J Electrocardiol 28:174–179CrossRef Fishler MG, Sobie AE, Tung L, Thakor NV (1995) Cardiac responses to premature monophasic and biphasic field stimuli: results from cell and tissue modeling studies. J Electrocardiol 28:174–179CrossRef
9.
go back to reference Freitas JANLF, Leomil FSC, Zoccoler M, Antoneli PC, Oliveira PX (2018) Cardiomyocyte lethality by multidirectional stimuli. Med Biol Eng Comput 56:2177–2184CrossRef Freitas JANLF, Leomil FSC, Zoccoler M, Antoneli PC, Oliveira PX (2018) Cardiomyocyte lethality by multidirectional stimuli. Med Biol Eng Comput 56:2177–2184CrossRef
10.
go back to reference Fry CH, Salvage SC, Manazza A, Dupont E, Labeed FH, Hughes MP, Jabr RI (2012) Cytoplasm resistivity of mammalian atrial myocardium determined by dielectrophoresis and impedance methods. Biophys J 103:2287–2294CrossRef Fry CH, Salvage SC, Manazza A, Dupont E, Labeed FH, Hughes MP, Jabr RI (2012) Cytoplasm resistivity of mammalian atrial myocardium determined by dielectrophoresis and impedance methods. Biophys J 103:2287–2294CrossRef
11.
go back to reference Galappaththige S, Roth BJ (2015) Electrical pacing of cardiac tissue including potassium inward rectification. PLoS One 10:e0127837CrossRef Galappaththige S, Roth BJ (2015) Electrical pacing of cardiac tissue including potassium inward rectification. PLoS One 10:e0127837CrossRef
12.
go back to reference Geuzaine C, Remacle JF (2009) A three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. Int J Numer Methods Eng 79:1888–1896CrossRef Geuzaine C, Remacle JF (2009) A three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. Int J Numer Methods Eng 79:1888–1896CrossRef
13.
go back to reference Gimsa J, Wachner D (2001) Analytical description of the transmembrane voltage induced on arbitrarily oriented ellipsoidal and cylindrical cells. Biophys J 81:1888–1896CrossRef Gimsa J, Wachner D (2001) Analytical description of the transmembrane voltage induced on arbitrarily oriented ellipsoidal and cylindrical cells. Biophys J 81:1888–1896CrossRef
14.
go back to reference Gomes PAP, Bassani RA, Bassani JWM (2001) Electric field stimulation of cardiac myocytes during postnatal development. IEEE Trans Biomed Eng 48:630–636CrossRef Gomes PAP, Bassani RA, Bassani JWM (2001) Electric field stimulation of cardiac myocytes during postnatal development. IEEE Trans Biomed Eng 48:630–636CrossRef
15.
go back to reference Goulart JT, Oliveira PX, Bassani JWM, Bassani RA (2012) The influence of cell dimensions on the vulnerability of ventricular myocytes to lethal injury by high-intensity electrical fields. Braz J Biomed Eng 28:337–345 Goulart JT, Oliveira PX, Bassani JWM, Bassani RA (2012) The influence of cell dimensions on the vulnerability of ventricular myocytes to lethal injury by high-intensity electrical fields. Braz J Biomed Eng 28:337–345
16.
go back to reference IEEE Recommended Practices for Validation of Computational Electromagnetic Computer Modeling and Simulations (2011) IEEE Std 1597.2-2010. IEEE Recommended Practices for Validation of Computational Electromagnetic Computer Modeling and Simulations (2011) IEEE Std 1597.2-2010.
17.
go back to reference Jayasinghe ID, Clowsley AH, Munro M, Hou Y, Crossman DJ, Soeller C (2015) Revealing t-tubules in striated muscle with new optical super-resolution microscopy techniques. Eur J Transl Myol 25:15–26CrossRef Jayasinghe ID, Clowsley AH, Munro M, Hou Y, Crossman DJ, Soeller C (2015) Revealing t-tubules in striated muscle with new optical super-resolution microscopy techniques. Eur J Transl Myol 25:15–26CrossRef
18.
go back to reference Kishida H, Surawicz B, Fu LT (1979) Effect of K+ and K+-induced polarization on (dV/dt)max, threshold potential, and membrane input resistance in guinea pig and cat ventricular myocardium. Circ Res 44:800–814CrossRef Kishida H, Surawicz B, Fu LT (1979) Effect of K+ and K+-induced polarization on (dV/dt)max, threshold potential, and membrane input resistance in guinea pig and cat ventricular myocardium. Circ Res 44:800–814CrossRef
19.
go back to reference Klee M, Plonsey R (1976) Stimulation of spheroidal cells: the role of cell shape. IEEE Trans Biomed Eng 23:347–354CrossRef Klee M, Plonsey R (1976) Stimulation of spheroidal cells: the role of cell shape. IEEE Trans Biomed Eng 23:347–354CrossRef
20.
go back to reference Kotnik T, Miklavcic D (2000) Analytical description of transmembrane voltage induced by electric fields in spheroidal cells. Biophys J 79:670–679CrossRef Kotnik T, Miklavcic D (2000) Analytical description of transmembrane voltage induced by electric fields in spheroidal cells. Biophys J 79:670–679CrossRef
21.
go back to reference Krassowska W, Neu JC (1994) Response of a single cell to an external electric field. Biophys J 66:1768–1776CrossRef Krassowska W, Neu JC (1994) Response of a single cell to an external electric field. Biophys J 66:1768–1776CrossRef
22.
go back to reference Leon LJ, Roberge FA (1993) A model study of extracellular stimulation of cardiac cells. IEEE Trans Biomed Eng 40:1307–1319CrossRef Leon LJ, Roberge FA (1993) A model study of extracellular stimulation of cardiac cells. IEEE Trans Biomed Eng 40:1307–1319CrossRef
23.
go back to reference Malmivuo J, Plonsey R (1995) Bioelectromagnetism: principles and applications of bioelectric and biomagnetic fields. Oxford University Press, New YorkCrossRef Malmivuo J, Plonsey R (1995) Bioelectromagnetism: principles and applications of bioelectric and biomagnetic fields. Oxford University Press, New YorkCrossRef
24.
go back to reference Maswiwat K, Wachner D, Warnkoe R, Gimsa J (2007) Simplified equation for the transmembrane potential induced in ellipsoidal cells of rotational symmetry. J Phys D Appl Phys 40:914–923CrossRef Maswiwat K, Wachner D, Warnkoe R, Gimsa J (2007) Simplified equation for the transmembrane potential induced in ellipsoidal cells of rotational symmetry. J Phys D Appl Phys 40:914–923CrossRef
25.
go back to reference Maswiwat K, Wachner D, Gimsa J (2008) Effects of cell orientation and electric field frequency on the transmembrane potential induced in ellipsoidal cells. Bioelectrochemistry 74:130–141CrossRef Maswiwat K, Wachner D, Gimsa J (2008) Effects of cell orientation and electric field frequency on the transmembrane potential induced in ellipsoidal cells. Bioelectrochemistry 74:130–141CrossRef
26.
go back to reference Milan HFM, Bassani RA, Bassani JWM (2015) Testing electrode suitability for field stimulation of high-threshold biological preparations. Res Biomed Eng 31:273–276CrossRef Milan HFM, Bassani RA, Bassani JWM (2015) Testing electrode suitability for field stimulation of high-threshold biological preparations. Res Biomed Eng 31:273–276CrossRef
27.
go back to reference Oliveira PX, Bassani RA, Bassani JWM (2008) Lethal effect of electric field on isolated ventricular myocytes. IEEE Trans Biomed Eng 55:2635–2642CrossRef Oliveira PX, Bassani RA, Bassani JWM (2008) Lethal effect of electric field on isolated ventricular myocytes. IEEE Trans Biomed Eng 55:2635–2642CrossRef
28.
go back to reference Oshiyama NF, Bassani JWM, Bassani RA (2013). Differences in excitability of ventricular myocytes from neonatal and adult rats. VIII Iberoamerican Congress of Biophysics. Valparaíso, Chile. Proceedings, p. 49. Oshiyama NF, Bassani JWM, Bassani RA (2013). Differences in excitability of ventricular myocytes from neonatal and adult rats. VIII Iberoamerican Congress of Biophysics. Valparaíso, Chile. Proceedings, p. 49.
29.
go back to reference Penna LB, Bassani RA (2010) Increased spontaneous activity and reduced inotropic response to catecholamines in ventricular myocytes from footshock-stressed rats. Stress 13:73–82CrossRef Penna LB, Bassani RA (2010) Increased spontaneous activity and reduced inotropic response to catecholamines in ventricular myocytes from footshock-stressed rats. Stress 13:73–82CrossRef
30.
go back to reference Pham P, Cauffet G, Bardou A, Olivares J, Novakov E (2000) Development of linear transient model for stimulation of isolated cardiac cells. Eur Phys J Appl Phys 12:217–222CrossRef Pham P, Cauffet G, Bardou A, Olivares J, Novakov E (2000) Development of linear transient model for stimulation of isolated cardiac cells. Eur Phys J Appl Phys 12:217–222CrossRef
31.
go back to reference Pucihar G, Kotnik T, Valic B, Miklavcic D (2006) Numerical determination of transmembrane voltage induced on irregularly shaped cells. Ann Biomed Eng 34:642–652CrossRef Pucihar G, Kotnik T, Valic B, Miklavcic D (2006) Numerical determination of transmembrane voltage induced on irregularly shaped cells. Ann Biomed Eng 34:642–652CrossRef
33.
go back to reference Ranjan R, Thakor NV (1995) Electrical stimulation of cardiac myocytes. Ann Biomed Eng 23:812–821CrossRef Ranjan R, Thakor NV (1995) Electrical stimulation of cardiac myocytes. Ann Biomed Eng 23:812–821CrossRef
34.
go back to reference Satoh H, Delbridge LMD, Blatter LA, Bers DM (1996) Surface:volume relationship in cardiac myocytes studied with confocal microscopy and membrane capacitance measurements: species-dependence and development effects. Biophys J 70:1494–1504CrossRef Satoh H, Delbridge LMD, Blatter LA, Bers DM (1996) Surface:volume relationship in cardiac myocytes studied with confocal microscopy and membrane capacitance measurements: species-dependence and development effects. Biophys J 70:1494–1504CrossRef
35.
go back to reference Sevgi L (2014) Electromagnetic modeling and simulation: challenges in validation, verification, and calibration. IEEE Trans Electromagn Compat 56:750–758CrossRef Sevgi L (2014) Electromagnetic modeling and simulation: challenges in validation, verification, and calibration. IEEE Trans Electromagn Compat 56:750–758CrossRef
36.
go back to reference Sharma V, Tung L (2002) Spatial heterogeneity of transmembrane potential responses of single guinea-pig cardiac cells during electric field simulation. J Physiol 542:477–492CrossRef Sharma V, Tung L (2002) Spatial heterogeneity of transmembrane potential responses of single guinea-pig cardiac cells during electric field simulation. J Physiol 542:477–492CrossRef
37.
go back to reference Soeller C, Cannell MB (1999) Examination of the transverse tubular system in living cardiac rat myocytes by 2-photon microscopy and digital image: processing techniques. Circ Res 84:266–275CrossRef Soeller C, Cannell MB (1999) Examination of the transverse tubular system in living cardiac rat myocytes by 2-photon microscopy and digital image: processing techniques. Circ Res 84:266–275CrossRef
38.
go back to reference Stubbe M, Gimsa J (2018) Furthering the state of knowledge on the electric properties of hemi-ellipsoidal single cells and cell patches on electrodes. Biosens Bioelectron 105:166–172CrossRef Stubbe M, Gimsa J (2018) Furthering the state of knowledge on the electric properties of hemi-ellipsoidal single cells and cell patches on electrodes. Biosens Bioelectron 105:166–172CrossRef
39.
go back to reference Trayanova NA, Chang KC (2016) How computer simulations of the human heart can improve anti-arrhythmia therapy. J Physiol 594:2483–2502CrossRef Trayanova NA, Chang KC (2016) How computer simulations of the human heart can improve anti-arrhythmia therapy. J Physiol 594:2483–2502CrossRef
40.
go back to reference Tung L, Borderies JR (1992) Analysis of electric field stimulation of single cardiac muscle cell. Biophys J 63:371–386CrossRef Tung L, Borderies JR (1992) Analysis of electric field stimulation of single cardiac muscle cell. Biophys J 63:371–386CrossRef
41.
go back to reference Tung L, Sliz N, Mulligan MR (1991) Influence of electrical axis of stimulation on excitation of cardiac muscle cells. Circ Res 49:722–730CrossRef Tung L, Sliz N, Mulligan MR (1991) Influence of electrical axis of stimulation on excitation of cardiac muscle cells. Circ Res 49:722–730CrossRef
42.
go back to reference Viana MA, Bassani RA, Petrucci O, Marques DA, Bassani JWM (2014) Rapidly switching multidirectional defibrillation: reversal of ventricular fibrillation with lower energy shocks. J Thorac Cardiovasc Surg 148:3213–3218CrossRef Viana MA, Bassani RA, Petrucci O, Marques DA, Bassani JWM (2014) Rapidly switching multidirectional defibrillation: reversal of ventricular fibrillation with lower energy shocks. J Thorac Cardiovasc Surg 148:3213–3218CrossRef
43.
go back to reference Vigmond EJ, Hughes M, Plank G, Leon LJ (2003) Computational tools for modeling electrical activity in cardiac tissue. J Electrocardiol 36(suppl 1):69–74CrossRef Vigmond EJ, Hughes M, Plank G, Leon LJ (2003) Computational tools for modeling electrical activity in cardiac tissue. J Electrocardiol 36(suppl 1):69–74CrossRef
Metadata
Title
Accuracy of electromagnetic models to estimate cardiomyocyte membrane polarization
Authors
Hugo F. M. Milan
Rosana A. Bassani
Luiz E. C. Santos
Antonio C. G. Almeida
José W. M. Bassani
Publication date
30-10-2019
Publisher
Springer Berlin Heidelberg
Published in
Medical & Biological Engineering & Computing / Issue 12/2019
Print ISSN: 0140-0118
Electronic ISSN: 1741-0444
DOI
https://doi.org/10.1007/s11517-019-02054-2

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