Numerical simulation of mechanoelectric feedback in a deformed myocardium
DOI:
https://doi.org/10.7242/1999-6691/2019.12.2.12Keywords:
electromechanical coupling, mechanoelectric feedback, stretch-activated channels, computational modelingAbstract
Mechanoelectric feedback is the effect of deformation on the contractile apparatus of the muscle cell, the change in myocardial conductivity, the appearance of additional transmembrane currents (stretch-activated channels). The first type of feedback is closely related to the electromechanical coupling process and is taken into account in the corresponding models. The derivation of the strain-to-conductance ratios was carried out based on the analysis of the microstructural model using the homogenization method. Cardiac tissue was considered as a periodic lattice, where cells are rectangular prisms filled with an isotropic electrolyte, and the conductivity of the gap junctions was taken into account through the boundary conditions on the sides of these prisms and was considered constant. It is shown that the tensor, the inverse of the myocardial conductivity tensor, can be represented as the sum of the inverse reduced conductivity tensors of myoplasma and gap junctions. A comparison was made with the model from the book F.B. Sachse. Computational Cardiology. Springer 2004. For longitudinal conductivity, both models are well matched for extensions, ranging from 0.8 to 1.2. When studying the propagation of an excitation wave, the effect of strain is “diluted” by extracellular conductivity. In the processes, where the extracellular and intracellular environments act individually, the effect of strain on myocardium is greater. The model describing the activation of channels under complex deformation has been constructed assuming that these channels are evenly distributed along the lateral surface of the cell and respond to the local increase in the region of a cell membrane segment. The model allows studying the activation of channels both during stretching along the fiber and during deformation in an arbitrary direction.
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References
Sundnes J., Lines G.T., Cai X., Nielsen B.F., Mardal K.-A., Tveito A. Computing the electrical activity in the heart. Springer, 2006. 321 p.
Ward M.L., Allen D.G. Stretch-activated channels in the heart: Contribution to cardiac performance. Mechanosensitivity of the heart, ed. A. Kamkin, I. Kiseleva. Springer, 2010. P. 141-167.
Nickerson D.P., Smith N.P., Hunter P.J. A model of cardiac cellular electromechanics. Phil. Trans. R. Soc. Lond. A, 2001, vol. 359, pp. 1159-1172. https://doi.org/10.1098/rsta.2001.0823">DOI
Sainte-Marie J., Chapelle D., Cimrman R., Sorine M. Modeling and estimation of the cardiac electromechanical activity. Comput. Struct., 2006, vol. 84, pp. 1743-1759. https://doi.org/10.1016/j.compstruc.2006.05.003">DOI
Izakov V.Ya., Katsnelson L.B., Blyakhman F.A., Markhasin V.S., Shklyar T.F. Cooperative effects due to calcium binding by troponin and their consequences for contraction and relaxation of cardiac muscle under various conditions of mechanical loading. Circ. Res., 1991, vol. 69, pp. 1171-1184. https://doi.org/10.1161/01.RES.69.5.1171">DOI
Syomin F.A., Tsaturyan A.K. A simple kinetic model of contraction of striated muscle: Full activation at full filament overlap in sarcomeres. Biophysics, 2012, vol. 57, pp. 651-657. https://doi.org/10.1134/S0006350912050181">DOI
Negroni J.A., Lascano E.C. A cardiac muscle model relating sarcomere dynamics to calcium kinetics. J. Mol. Cell. Cardiol., 1996, vol. 28, pp. 915-929. https://doi.org/10.1006/jmcc.1996.0086">DOI
Niederer S.A., Smith N.P. A mathematical model of the slow force response to stretch in rat ventricular myocytes. Biophys. J., 2007, vol. 92, pp. 4030-4044. https://doi.org/10.1529/biophysj.106.095463">DOI
Sachse F.B. Computational cardiology. Modelling of anatomy, electrophysiology and mechanics. Springer, 2004. 333 p.
Hand P.E., Griffith B.E., Peskin C.S. Deriving macroscopic myocardial conductivities by homogenization of microscopic models. Bull. Math. Biol., 2009, vol. 71, pp. 1707-1726. https://doi.org/10.1007/s11538-009-9421-y">DOI
Richardson G., Chapman S.J. Derivation of the bidomain equations for a beating heart with a general microstructure. SIAM J. Appl. Math., 2011, vol. 71, pp. 657-675. https://doi.org/10.1137/090777165">DOI
Vasserman I.N., Matveenko V.P., Shardakov I.N., Shestakov A.P. Derivation of the macroscopic intracellular conductivity of deformed myocardium on the basis of microstructure analysis. Biophysics, 2018, vol. 63, pp. 455-462. https://doi.org/10.1134/S0006350918030247">DOI
Vasserman I.N., Shardakov I.N., Shestakov A.P. Influence of the deformation on the propagation of waves of excitation in the heart tissue. Russian Journal of Biomechanics, 2018, vol. 22, no. 3, pp. 333-343. URL: http://vestnik.pstu.ru/biomech/archives/?id=&folder_id=7897">http://vestnik.pstu.ru/biomech/archives/?id=&folder_id=7897 (accessed 18 May 2019).
Kohl P., Bollensdorff C., Garny A. Effects of mechanosensitive ion channels on ventricular electrophysiology: experimental and theoretical models. Exp. Physiol., 2006, vol. 91, pp. 307-321. https://doi.org/10.1113/expphysiol.2005.031062">DOI
Timmermann V., Dejgaard L.A., Haugaa K.H., Edwards A.G., Sundnes J., McCulloch A.D., Wall S.T. An integrative appraisal of mechano-electric feedback mechanisms in the heart. Progr. Biophys. Mol. Biol., 2017, vol. 130, part B, pp. 404-417. https://doi.org/10.1016/j.pbiomolbio.2017.08.008">DOI
Kohl P., Sachs F. Mechanoelectric feedback in cardiac cells. Phil. Trans. R. Soc. Lond. A, 2001, vol. 359, pp. 1173-1185. https://doi.org/10.1098/rsta.2001.0824">DOI
Sackin H. Stretch-activated ion channels. Kidney Int., 1995, vol. 48, pp. 1134-1147. https://doi.org/10.1038/ki.1995.397">DOI
Guharay B.F., Sachs F. Stretch-activated single ion channel currents in tissue-cultured embriolitic chick skeletal muscle. J. Physiol., 1984, vol. 352, pp. 685-701.
Potse M., Dube B., Richer J., Vinet A., Gulrajani R.M. A comparison of monodomain and bidomain reaction-diffusion models for action potential propagation in the human heart. IEEE Trans. Biomed. Eng., 2006, vol. 53, pp. 2425-2435. https://doi.org/10.1109/TBME.2006.880875">DOI
Roth B.J. Proc. of the 2006 Int. Conf. of the IEEE Engineering in Medicine and Biology Society. New York, USA, August 30-September 3, 2006. Pp. 580-583. https://doi.org/10.1109/IEMBS.2006.260486">DOI
Roth B.J.Mechanism for polarisation of cardiac tissue at a sealed boundary. Med. Biol. Eng. Comput., 1999, vol. 37, pp. 523-525. https://doi.org/10.1007/BF02513340">DOI
Wikswo J.P., Lin S.-F., Abbas R.A. Virtual electrodes in cardiac tissue: A common mechanism for anodal and cathodal stimulation. Biophys. J., 1995, vol. 69, pp. 2195-2210. https://doi.org/10.1016/S0006-3495(95)80115-3">DOI
Sambelashvili A., Efimov I.R. Dynamics of virtual electrode-induced scroll-wave reentry in a 3D bidomain model. Am. J. Physiol. Heart. C., 2004, vol. 287, pp. H1570-H1581. https://doi.org/10.1152/ajpheart.01108.2003">DOI
Trayanova N., Skouibine K., Moore P. Virtual electrode effects in defibrillation. Progr. Biophys. Mol. Biol., 1998, vol. 69, pp. 387-403. https://doi.org/10.1016/S0079-6107(98)00016-9">DOI
Boukens B.J., Gutbrod S.R., Efimov I.R. Imaging of ventricular fibrillation and defibrillation: The virtual electrode hypothesis. Membrane potential imaging in the nervous system and heart, ed. M. Canepari, D. Zecevic, O. Bernus. Springer, 2015. P. 343-365. https://doi.org/10.1007/978-3-319-17641-3_14">DOI
http://fenicsproject.org/">http://fenicsproject.org/ (accessed 18 May 2019).
Roth B.J. A mathematical model of make and break electrical stimulation of cardiac tissue by unipolar anode or cathode. IEEE Trans. Biomed. Eng., 1995, vol. 42, pp. 1174-1184. https://doi.org/10.1109/10.476124">DOI
Goel V., Roth B.J. Proc. of the 13th Southern Biomedical Engineering Conf., Washington, USA, April 16-17, 1994, 5 p.
Sepulveda N.G., Roth B.J., Wikswo J.P. Current injection into a two-dimensional anisotropic bidomain. Biophys. J., 1989, vol. 55, pp. 987-999. https://doi.org/10.1016/S0006-3495(89)82897-8">DOI