Bassett, C. A. L. & Pawluk, R. J. Effects of electric currents on bone in vivo. Nature 204, 652–654 (1964).
Google Scholar
Brighton, C. T. et al. A multicenter study of the treatment of non-union with constant direct current. J. Bone Joint Surg. Am. 63, 2–13 (1981).
Google Scholar
Shigino, T., Ochi, M., Kagami, H., Sakaguchi, K. & Nakade, O. Application of capacitively coupled electric field enhances periimplant osteogenesis in the dog mandible. Int. J. Prosthodont. 13 (2000).
Mittelmeier, W. et al. Biss: Concept and biomechanical investigations of a new screw system for electromagnetically induced internal osteostimulation. Arch. Orthop. Trauma Surg. 124, 86–91 (2004).
Google Scholar
Wang, W., Wang, Z., Zhang, G., Clark, C. C. & Brighton, C. T. Up-regulation of chondrocyte matrix genes and products by electric fields. Clin. Orthop. Relat. Res. 427, S163–S173 (2004).
Lee, C., Grad, S., Wimmer, M. & Alini, M. The influence of mechanical stimuli on articular cartilage tissue engineering. Top. Tissue Eng. 2, 1–32 (2006).
Google Scholar
Xu, J., Wang, W., Clark, C. C. & Brighton, C. T. Signal transduction in electrically stimulated articular chondrocytes involves translocation of extracellular calcium through voltage-gated channels. Osteoarthr. Cartil. 17, 397–405 (2009).
Google Scholar
Balint, R., Cassidy, N. J. & Cartmell, S. H. Electrical stimulation: A novel tool for tissue engineering. Tissue Eng. Part B Rev. 19, 48–57 (2013).
Google Scholar
Jahr, H., Matta, C. & Mobasheri, A. Physicochemical and biomechanical stimuli in cell-based articular cartilage repair. Curr. Rheumatol. Rep. 17, 1–12 (2015).
Google Scholar
Thrivikraman, G., Boda, S. K. & Basu, B. Unraveling the mechanistic effects of electric field stimulation towards directing stem cell fate and function: A tissue engineering perspective. Biomaterials 150, 60–86 (2018).
Google Scholar
Chen, C., Bai, X., Ding, Y. & Lee, I. S. Electrical stimulation as a novel tool for regulating cell behavior in tissue engineering. Biomater. Res. 23, 1–12 (2019).
Google Scholar
Massari, L. et al. Biophysical stimulation of bone and cartilage: State of the art and future perspectives. Int. Orthop. 43, 539–551 (2019).
Google Scholar
Dauben, T. J. et al. A novel in vitro system for comparative analyses of bone cells and bacteria under electrical stimulation. BioMed Res. Int. 2016, 1–12 (2016).
Brighton, T., Wang, W. & Clark, C. C. The effect of electrical fields on gene and protein expression in human osteoarthritic cartilage explants. J. Bone Joint Surg. 90, 833–848 (2008).
Google Scholar
Krueger, S. et al. Re-differentiation capacity of human chondrocytes in vitro following electrical stimulation with capacitively coupled fields. J. Clin. Med. 8, 1771 (2019).
Google Scholar
Lorich, D. G. et al. Biochemical pathway mediating the response of bone cells to capacitive coupling. Clin. Orthop. Relat. Res. 350, 246–256 (1998).
Timoshkin, I. V., MacGregor, S. J., Fouracre, R. A., Crichton, B. H. & Anderson, J. G. Transient electrical field across cellular membranes: Pulsed electric field treatment of microbial cells. J. Phys. D Appl. Phys. 39, 596–603 (2006).
Google Scholar
Taghian, T., Narmoneva, D. A. & Kogan, A. B. Modulation of cell function by electric field: A high-resolution analysis. J. R. Soc. Interface 12, 20150153–20150153 (2015).
Google Scholar
Carter, E. L., Vresilovic, E. J., Pollack, S. R. & Brighton, C. T. Field distribution in vertebral bodies of the rat during electrical stimulation: A parameter study. IEEE Trans. Biomed. Eng. 36, 333–345 (1989).
Google Scholar
Clark, C. C., Wang, W. & Brighton, C. T. Up-regulation of expression of selected genes in human bone cells with specific capacitively coupled electric fields. J. Orthop. Res. 32, 894–903 (2014).
Google Scholar
Brady, M. A., Waldman, S. D. & Ethier, C. R. The application of multiple biophysical cues to engineer functional neocartilage for treatment of osteoarthritis. Part I: Cellular response. Tissue Eng. Part B Rev. 21, 1–19 (2015).
Google Scholar
Pall, M. L. Electromagnetic fields act via activation of voltage-gated calcium channels to produce beneficial or adverse effects. J. Cell. Mol. Med. 17, 958–965 (2013).
Google Scholar
Fear, E. C. & Stuchly, M. A. Biological cells with gap junctions in low-frequency electric fields. IEEE Trans. Biomed. Eng. 45, 856–866 (1998).
Google Scholar
Kadir, L. A., Stacey, M. & Barrett-Jolley, R. Emerging roles of the membrane potential: Action beyond the action potential. Front. Physiol. 9, 1–10 (2018).
Cho, M. R., Thatte, H. S., Silvia, M. T. & Golan, D. E. Transmembrane calcium influx induced by ac electric fields. FASEB J. 13, 677–683 (1999).
Google Scholar
Budde, K. et al. Requirements for documenting electrical cell stimulation experiments for replicability and numerical modeling. In 2019 41st Annu. Int. Conf. IEEE Eng. Med. Biol. Soc., 1082–1088 (2019).
Escobar, J. F., Vaca-González, J. J. & Garzón-Alvarado, D. A. Effect of magnetic and electric fields on plasma membrane of single cells: A computational approach. Eng. Rep. e12125, 1–14 (2020).
Pucihar, G., Kotnik, T., Valič, B. & Miklavčič, D. Numerical determination of transmembrane voltage induced on irregularly shaped cells. Ann. Biomed. Eng. 34, 642–652 (2006).
Google Scholar
Murovec, T., Sweeney, D. C., Latouche, E., Davalos, R. V. & Brosseau, C. Modeling of transmembrane potential in realistic multicellular structures before electroporation. Biophys. J. 111, 2286–2295. https://doi.org/10.1016/j.bpj.2016.10.005 (2016).
Google Scholar
Dirks, H. K. Quasi-stationary fields for microelectronic applications. Electr. Eng. 79, 145–155 (1996).
van Rienen, U. et al. Electro-quasistatic simulations in bio-systems engineering and medical engineering. Adv. Radio Sci. 3, 39–49 (2005).
Google Scholar
Vaca-González, J. J., Guevara, J. M., Vega, J. F. & Garzón-Alvarado, D. A. An in vitro chondrocyte electrical stimulation framework: A methodology to calculate electric fields and modulate proliferation, cell death and glycosaminoglycan synthesis. Cell. Mol. Bioeng. 9, 116–126 (2016).
Brighton, C. T., Wang, W. & Clark, C. C. Up-regulation of matrix in bovine articular cartilage explants by electric fields. Biochem. Biophys. Res. Commun. 342, 556–561 (2006).
Google Scholar
Vaca-González, J. J. et al. Capacitively coupled electrical stimulation of rat chondroepiphysis explants: A histomorphometric analysis. Bioelectrochemistry 126, 1–11. https://doi.org/10.1016/j.bioelechem.2018.11.004 (2019).
Google Scholar
Kotnik, T., Bobanović, F. & Miklavčič, D. Sensitivity of transmembrane voltage induced by applied electric fields—A theoretical analysis. Bioelectrochem. Bioenerg. 43, 285–291 (1997).
Google Scholar
Ermolina, I., Polevaya, Y. & Feldman, Y. Analysis of dielectric spectra of eukaryotic cells by computer modeling. Eur. Biophys. J. 29, 141–145 (2000).
Google Scholar
Stacey, M. W., Sabuncu, A. C. & Beskok, A. Dielectric characterization of costal cartilage chondrocytes. Biochim. Biophys. Acta Gen. Subj. 1840, 146–152 (2014).
Google Scholar
Braun, D. & Fromherz, P. Fluorescence interferometry of neuronal cell adhesion on microstructured silicon. Phys. Rev. Lett. 81, 5241–5244 (1998).
Google Scholar
Braun, D. & Fromherz, P. Imaging neuronal seal resistance on silicon chip using fluorescent voltage-sensitive dye. Biophys. J. 87, 1351–1359 (2004).
Google Scholar
Tennøe, S., Halnes, G. & Einevoll, G. T. Uncertainpy: A Python toolbox for uncertainty quantification and sensitivity analysis in computational neuroscience. Front. Neuroinform. 12, 1–29 (2018).
Huey, D. J., Hu, J. C. & Athanasiou, K. A. Unlike bone, cartilage regeneration remains elusive. Science 338, 917–921 (2012).
Google Scholar
Brighton, C. T., Okereke, E., Pollack, S. R. & Clark, C. C. In vitro bone-cell response to a capacitively coupled electrical field. Clin. Orthop. Relat. Res. 285, 255–262 (1992).
Meny, I., Burais, N., Buret, F. & Nicolas, L. Finite-element modeling of cell exposed to harmonic and transient electric fields. IEEE Trans. Magn. 43, 1773–1776 (2007).
Google Scholar
Agudelo-Toro, A. & Neef, A. Computationally efficient simulation of electrical activity at cell membranes interacting with self-generated and externally imposed electric fields. J. Neural Eng. 10, 026019 (2013).
Ellingsrud, A. J., Solbrå, A., Einevoll, G. T., Halnes, G. & Rognes, M. E. Finite element simulation of ionic electrodiffusion in cellular geometries. Front. Neuroinform. 14, 1–25 (2020).
Kuchta, M., Mardal, K.-A. & Rognes, M. E. Solving the EMI equations using finite element methods. In Modeling Excitable Tissue: The EMI Framework (eds Tveito, A. et al.) 56–69 (Springer International Publishing, 2021).
Google Scholar
Leguèbe, M., Poignard, C. & Weynans, L. A second-order Cartesian method for the simulation of electropermeabilization cell models. J. Comput. Phys. 292, 114–140 (2015).
Google Scholar
Guyomarc’h, G., Lee, C. O. & Jeon, K. A discontinuous Galerkin method for elliptic interface problems with application to electroporation. Commun. Numer. Methods Eng. 25, 991–1008 (2009).
Google Scholar
Perrussel, R. & Poignard, C. Asymptotic expansion of steady-state potential in a high contrast medium with a thin resistive layer. Appl. Math. Comput. 221, 48–65 (2013).
Google Scholar
Macdonald, J. R. & Johnson, W. B. Fundamentals of impedance spectroscopy. In Impedance Spectroscopy, chap. 1, 1–20 (Wiley, 2005).
Lojewska, Z., Farkas, D. L., Ehrenberg, B. & Loew, L. M. Analysis of the effect of medium and membrane conductance on the amplitude and kinetics of membrane potentials induced by externally applied electric fields. Biophys. J. 56, 121–128 (1989).
Google Scholar
Yang, X. et al. Imaging the electrochemical impedance of single cells via conductive polymer thin film. ACS Sensors 6, 485–492 (2021).
Google Scholar
Shamoon, D., Lasquellec, S. & Brosseau, C. Perspective: Towards understanding the multiscale description of cells and tissues by electromechanobiology. J. Appl. Phys. 123, 240902. https://doi.org/10.1063/1.5018723 (2018).
Google Scholar
Sabri, E. & Brosseau, C. Proximity-induced electrodeformation and membrane capacitance coupling between cells. Eur. Biophys. J. 50, 713–720 (2021).
Google Scholar
Merla, C. et al. Microdosimetry for nanosecond pulsed electric field applications: A parametric study for a single cell. IEEE Trans. Biomed. Eng. 58, 1294–1302 (2011).
Google Scholar
Leguèbe, M., Silve, A., Mir, L. M. & Poignard, C. Conducting and permeable states of cell membrane submitted to high voltage pulses: Mathematical and numerical studies validated by the experiments. J. Theor. Biol. 360, 83–94 (2014).
Google Scholar
Asami, K. Dielectric properties of microvillous cells simulated by the three-dimensional finite-element method. Bioelectrochemistry 81, 28–33 (2011).
Google Scholar
Ciuperca, I. S., Perrussel, R. & Poignard, C. Two-scale analysis for very rough thin layers. An explicit characterization of the polarization tensor. J. des Math. Pures Appl. 95, 277–295 (2011).
Google Scholar
Wenger, C. et al. A review on tumor-treating fields (TTFields): Clinical implications inferred from computational modeling. IEEE Rev. Biomed. Eng. 11, 195–207 (2018).
Google Scholar
Mistani, P., Guittet, A., Poignard, C. & Gibou, F. A parallel Voronoi-based approach for mesoscale simulations of cell aggregate electropermeabilization. J. Comput. Phys. 380, 48–64 (2019).
Google Scholar
Mollenhauer, J. A. Perspectives on articular cartilage biology and osteoarthritis. Injury 39, 5–12 (2008).
Nagarajan, M. B. et al. Computer-aided diagnosis in phase contrast imaging x-ray computed tomography for quantitative characterization of ex vivo human patellar cartilage. IEEE Trans. Biomed. Eng. 60, 2896–2903 (2013).
Google Scholar
Marzouk, Y. & Xiu, D. A stochastic collocation approach to Bayesian inference in inverse problems. Commun. Comput. Phys. 6, 826–847 (2009).
Google Scholar
Schmidt, C., Grant, P., Lowery, M. & van Rienen, U. Influence of uncertainties in the material properties of brain tissue on the probabilistic volume of tissue activated. IEEE Trans. Biomed. Eng. 60, 1378–1387 (2013).
Google Scholar
Tveito, A., Jæger, K. H., Kuchta, M., Mardal, K.-A. & Rognes, M. E. A cell-based framework for numerical modeling of electrical conduction in cardiac tissue. Front. Phys. 5, 1–18 (2017).
Poignard, C. et al. Ion fluxes, transmembrane potential, and osmotic stabilization: A new dynamic electrophysiological model for eukaryotic cells. Eur. Biophys. J. 40, 235–246 (2011).
Google Scholar
Casciola, M. & Tarek, M. A molecular insight into the electro-transfer of small molecules through electropores driven by electric fields. Biochim. Biophys. Acta Biomembr. 1858, 2278–2289. https://doi.org/10.1016/j.bbamem.2016.03.022 (2016).
Google Scholar
Haus, H. A. & Melcher, J. R. Electromagnetic Fields and Energy (Prentice Hall, 1989).
Bondeson, A., Rylander, T. & Ingelström, P. Computational Electromagnetics, Texts in Applied Mathematics Vol. 51 (Springer, 2005).
Google Scholar
Roy, C. J. & Oberkampf, W. L. A comprehensive framework for verification, validation, and uncertainty quantification in scientific computing. Comput. Methods Appl. Mech. Eng. 200, 2131–2144 (2011).
Google Scholar
Lemieux, C. Monte Carlo and Quasi-Monte Carlo Sampling, Springer Series in Statistics (Springer, 2009).
Google Scholar
Xiu, D. Numerical Methods for Stochastic Computations: A Spectral Method Approach (Princeton University Press, 2010).
Google Scholar
Eck, V. G. et al. A guide to uncertainty quantification and sensitivity analysis for cardiovascular applications. Int. J. Numer. Method. Biomed. Eng. 32, e02755 (2016).
Google Scholar
Mazzoleni, A. P., Sisken, B. F. & Kahler, R. L. Conductivity values of tissue culture medium from 20(^circ)C to 40(^circ)C. Bioelectromagnetics 7, 95–99 (1986).
Google Scholar
Svorčík, V., Ekrt, O., Rybka, V., Lipták, J. & Hnatowicz, V. Permittivity of polyethylene and polyethyleneterephtalate. J. Mater. Sci. Lett. 19, 1843–1845 (2000).
Zheng, Y., Nguyen, J., Wei, Y. & Sun, Y. Recent advances in microfluidic techniques for single-cell biophysical characterization. Lab Chip 13, 2464–2483 (2013).
Google Scholar
Funabashi, K., Fujii, M., Yamamura, H., Ohya, S. & Imaizumi, Y. Contribution of chloride channel conductance to the regulation of resting membrane potential in chondrocytes. J. Pharmacol. Sci. 113, 94–99 (2010).
Google Scholar
Lewis, R. et al. The role of the membrane potential in chondrocyte volume regulation. J. Cell. Physiol. 226, 2979–2986 (2011).
Google Scholar
Glen, G. & Isaacs, K. Estimating Sobol sensitivity indices using correlations. Environ. Model. Softw. 37, 157–166. https://doi.org/10.1016/j.envsoft.2012.03.014 (2012).
Google Scholar
