DOI: https://doi.org/10.20535/RADAP.2018.72.69-77

A Computational Model of Electrophysiological Properties of Cardiomyocytes

N. G. Ivanushkina, E. O. Ivan'ko, Yu. V. Prokopenko, A. Redaelli, V. I. Tymofieiev, R. Visone

Abstract


Introduction. The method of electrical analogies for the analysis of bioelectric dynamic processes in cardiomyocytes is used in the study. This method allows for replacing investigation of phenomena in non-electrical systems by research of analogous phenomena in electrical circuits. The investigation of time processes in cardiac cells is based on the solution of the system of ordinary differential equations for an electrical circuit. Electrophysiological properties of cardiomyocytes such as refractory period, maximum capture rate and electrical restitution are studied.
Mathematical modeling. Computational simulation of the action potential and currents for $K^+$, $Na^+$, $Ca^{2+}$ ions in cardiomyocytes is performed by using the parallel conductance model. This model is based on the assumption of the presence of independent ion channels for $K^+$, $Na^+$, $Ca^{2+}$ ions, as well as leakage through the membrane of cardiac cell. Each branch of the electrical circuit reflects the contribution of one type of ions to total membrane current.
Results. The obtained electrical restitution curves for ventricular and atrial cardiomyocytes are presented in the paper. The proposed model makes it possible to identify the areas with the maximum slope on the restitution curves, which are crucial in the development of cardiac arrhythmias. Dependences of calcium current on stimulation frequency for atrial and ventricular cardiomyocytes are obtained. Analysis of the kinetics of calcium ions under various protocols of external influences can be useful for predicting the contractile force of cardiomyocytes.
Conclusion. The results of calculations can be used to interpret the experimental results obtained in investigations of cardiomyocytes using the "laboratory on a chip" technology, as well as in the design of new experiments with cardiomyocytes for drug screening, cell therapy and personalized studies of heart diseases.

Keywords


method of electrical analogies; cardiomyocyte; action potential; parallel conductance model; electrical restitution curve; lab-on-chip platform

Full Text:

PDF

References


Olson H.F. (2005) Dynamical Analogies. Van Nostrand's Scientific Encyclopedia. DOI: 10.1002/0471743984.vse2719

Sigorskii V.P. (1977) Matematicheskii apparat inzhenera [The mathematical tools of the engineer], Kiev, Tekhnika Publ., 768 p. (in Russian)

Hogan N. and Breedveld P. (2005) The Physical Basis of Analogies in Physical System Models. Mechatronics, pp. 8-1. DOI: 10.1201/9781420037241.ch8

Fu K., Moreno D., Yang M. and Wood K.L. (2014) Bio-Inspired Design: An Overview Investigating Open Questions From the Broader Field of Design-by-Analogy. Journal of Mechanical Design, Vol. 136, Iss. 11, pp. 111102. DOI: 10.1115/1.4028289

Glier M.W., McAdams D.A. and Linsey J.S. (2011) Concepts in Biomimetic Design: Methods and Tools to Incorporate Into a Biomimetic Design Course. Volume 7: 5th International Conference on Micro- and Nanosystems; 8th International Conference on Design and Design Education; 21st Reliability, Stress Analysis, and Failure Prevention Conference. DOI: 10.1115/detc2011-48571

Hodgkin A.L. and Huxley A.F. (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology, Vol. 117, Iss. 4, pp. 500. DOI: 10.1113/jphysiol.1952.sp004764

Ellis B.W., Acun A., Can U.I. and Zorlutuna P. (2017) Human iPSC-derived myocardium-on-chip with capillary-like flow for personalized medicine. Biomicrofluidics, Vol. 11, Iss. 2, pp. 024105. DOI: 10.1063/1.4978468

Liang P., Lan F., Lee A.S., Gong T., Sanchez-Freire V., Wang Y., Diecke S., Sallam K., Knowles J.W., Wang P.J., Nguyen P.K., Bers D.M., Robbins R.C. and Wu J.C. (2013) Drug Screening Using a Library of Human Induced Pluripotent Stem Cell-Derived Cardiomyocytes Reveals Disease-Specific Patterns of Cardiotoxicity. Circulation, Vol. 127, Iss. 16, pp. 1677. DOI: 10.1161/circulationaha.113.001883

Robinton D.A. and Daley G.Q. (2012) The promise of induced pluripotent stem cells in research and therapy. Nature, Vol. 481, Iss. 7381, pp. 295. DOI: 10.1038/nature10761

Zwi L., Caspi O., Arbel G., Huber I., Gepstein A., Park I. and Gepstein L. (2009) Cardiomyocyte Differentiation of Human Induced Pluripotent Stem Cells. Circulation, Vol. 120, Iss. 15, pp. 1513. DOI: 10.1161/circulationaha.109.868885

Ma J., Guo L., Fiene S.J., Anson B.D., Thomson J.A., Kamp T.J., Kolaja K.L., Swanson B.J. and January C.T. (2011) High purity human-induced pluripotent stem cell-derived cardiomyocytes: electrophysiological properties of action potentials and ionic currents. American Journal of Physiology-Heart and Circulatory Physiology, Vol. 301, Iss. 5, pp. H2006. DOI: 10.1152/ajpheart.00694.2011

Richardson E.S. and Xiao Y. (2010) Electrophysiology of Single Cardiomyocytes: Patch Clamp and Other Recording Methods. Cardiac Electrophysiology Methods and Models, pp. 329. DOI: 10.1007/978-1-4419-6658-2_16

Blazeski A., Zhu R., Hunter D.W., Weinberg S.H., Boheler K.R., Zambidis E.T. and Tung L. (2012) Electrophysiological and contractile function of cardiomyocytes derived from human embryonic stem cells. Progress in Biophysics and Molecular Biology, Vol. 110, Iss. 2-3, pp. 178. DOI: 10.1016/j.pbiomolbio.2012.07.012

Lee P., Klos M., Bollensdorff C., Hou L., Ewart P., Kamp T.J., Zhang J., Bizy A., Guerrero-Serna G., Kohl P., Jalife J. and Herron T.J. (2012) Simultaneous Voltage and Calcium Mapping of Genetically Purified Human Induced Pluripotent Stem Cell-Derived Cardiac Myocyte Monolayers. Circulation Research, Vol. 110, Iss. 12, pp. 1556. DOI: 10.1161/circresaha.111.262535

Shinnawi R., Huber I., Maizels L., Shaheen N., Gepstein A., Arbel G., Tijsen A. and Gepstein L. (2015) Monitoring Human-Induced Pluripotent Stem Cell-Derived Cardiomyocytes with Genetically Encoded Calcium and Voltage Fluorescent Reporters. Stem Cell Reports, Vol. 5, Iss. 4, pp. 582. DOI: 10.1016/j.stemcr.2015.08.009

Hansen A., Eder A., Bonstrup M., Flato M., Mewe M., Schaaf S., Aksehirlioglu B., Schworer A., Uebeler J. and Eschenhagen T. (2010) Development of a Drug Screening Platform Based on Engineered Heart Tissue. Circulation Research, Vol. 107, Iss. 1, pp. 35. DOI: 10.1161/circresaha.109.211458

Werdich A.A., Lima E.A., Ivanov B., Ges I., Anderson M.E., Wikswo J.P. and Baudenbacher F.J. (2004) A microfluidic device to confine a single cardiac myocyte in a sub-nanoliter volume on planar microelectrodes for extracellular potential recordings. Lab on a Chip, Vol. 4, Iss. 4, pp. 357. DOI: 10.1039/b315648f

Pavesi A., Adriani G., Rasponi M., Zervantonakis I. K., Fiore G. B. and Kamm R. D. (2015) Controlled electromechanical cell stimulation on-a-chip. Scientific Reports, Vol. 5, Iss. 1. DOI: 10.1038/srep11800

Marsano A., Conficconi C., Lemme M., Occhetta P., Gaudiello E., Votta E., Cerino G., Redaelli A. and Rasponi M. (2016) Beating heart on a chip: a novel microfluidic platform to generate functional 3D cardiac microtissues. Lab on a Chip, Vol. 16, Iss. 3, pp. 599. DOI: 10.1039/c5lc01356a

Plonsey R. and Barr R.C. (2007) Cardiac Electrophysiology. Bioelectricity, p. 267. DOI: 10.1007/978-0-387-48865-3_9

Luo C.H. and Rudy Y. (1994) A dynamic model of the cardiac ventricular action potential. I. Simulations of ionic currents and concentration changes. Circulation Research, Vol. 74, Iss. 6, pp. 1071. DOI: 10.1161/01.res.74.6.1071

Ivanko K., Ivanushkina N. and Prokopenko Y. (2017) Simulation of action potential in cardiomyocytes. 2017 IEEE 37th International Conference on Electronics and Nanotechnology (ELNANO). DOI: 10.1109/elnano.2017.7939777

Spiteri R.J. and Dean R.C. (2008) On the Performance of an Implicit–Explicit Runge--Kutta Method in Models of Cardiac Electrical Activity. IEEE Transactions on Biomedical Engineering, Vol. 55, Iss. 5, pp. 1488. DOI: 10.1109/tbme.2007.914677

Khuwaileh R. A. (2016) Electrical restitution and action potential repolarisation studies in acutely isolated cardiac ventricular myocytes, University of Leicester.

Traxel S.J. and Patwardhan A. (2009) A novel method to quantify contribution of electrical restitution to alternans of repolarization in cardiac myocytes: a simulation study. FASEB Journal, Vol. 23, No. 1, Suppl. 624.7.

Shattock M.J., Park K.C., Yang H., Yang H., Niederer S., MacLeod K.T. and Winter J. (2017) Restitution slope is principally determined by steady-state action potential duration. Cardiovascular Research, Vol. 113, Iss. 7, pp. 817. DOI: 10.1093/cvr/cvx063

Kanaporis G. and Blatter L.A. (2017) Alternans in atria: Mechanisms and clinical relevance. Medicina, Vol. 53, Iss. 3, pp. 139. DOI: 10.1016/j.medici.2017.04.004

Orini M., Taggart P., Srinivasan N., Hayward M. and Lambiase P.D. (2016) Interactions between Activation and Repolarization Restitution Properties in the Intact Human Heart: In-Vivo Whole-Heart Data and Mathematical Description. PLOS ONE, Vol. 11, Iss. 9, pp. e0161765. DOI: 10.1371/journal.pone.0161765


GOST Style Citations






Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.