Testing the limits of cardiac electrophysiology models through systematic variation of current

Binaya Tuladhar; Hana M. Dobrovolny; Binaya Tuladhar; Hana M. Dobrovolny

doi:10.3934/math.2020009

AIMS Mathematics

2020, Volume 5, Issue 1: 140-157. doi: 10.3934/math.2020009

Previous Article Next Article

Research article Topical Sections

Testing the limits of cardiac electrophysiology models through systematic variation of current

Binaya Tuladhar ,
Hana M. Dobrovolny ^,

Department of Physics & Astronomy, Texas Christian University, Fort Worth, TX, USA

Received: 29 January 2019 Accepted: 30 August 2019 Published: 23 October 2019
MSC : 92C37

Mathematical models of the electrical response of cardiac cells are used to help develop an understanding of the electrophysiological properties of cardiac cells. Increasingly complex models are being developed in an effort to enhance the biological fidelity of the models and potentially increase their ability to predict electrical dynamics observed in vivo and in vitro. However, as the models increase in size, they have a tendency to become unstable and are highly sensitive to changes in established parameters. This means that such models might be unable to accurately predict person-to-person variability, dynamical changes due to disease pathologies that alter ionic currents, or the effect of treatment with antiarrhythmics. In this paper, we test the predictive limits of two mathematical models by altering the conductance of Ca²⁺, Na⁺, and K⁺ channels. We assess changes in action potential duration (APD), rate dependence, hysteresis, dynamical behavior, and restitution as conductance is varied. We find model predictions of abrupt changes in measured quantities and differences in the predictions of the two models that might be missed in a less systematic approach. These features can be compared to experimental observations to help assess the fidelity of the models.
- mathematical modeling,
- cardiac electrophysiology,
- action potential duration,
- ionic currents,
- parameters
Citation: Binaya Tuladhar, Hana M. Dobrovolny. Testing the limits of cardiac electrophysiology models through systematic variation of current[J]. AIMS Mathematics, 2020, 5(1): 140-157. doi: 10.3934/math.2020009

Related Papers:

Abstract

Mathematical models of the electrical response of cardiac cells are used to help develop an understanding of the electrophysiological properties of cardiac cells. Increasingly complex models are being developed in an effort to enhance the biological fidelity of the models and potentially increase their ability to predict electrical dynamics observed in vivo and in vitro. However, as the models increase in size, they have a tendency to become unstable and are highly sensitive to changes in established parameters. This means that such models might be unable to accurately predict person-to-person variability, dynamical changes due to disease pathologies that alter ionic currents, or the effect of treatment with antiarrhythmics. In this paper, we test the predictive limits of two mathematical models by altering the conductance of Ca²⁺, Na⁺, and K⁺ channels. We assess changes in action potential duration (APD), rate dependence, hysteresis, dynamical behavior, and restitution as conductance is varied. We find model predictions of abrupt changes in measured quantities and differences in the predictions of the two models that might be missed in a less systematic approach. These features can be compared to experimental observations to help assess the fidelity of the models.

References

[1]	E. Anyukhovsky and M. Rosen, Electrophysiologic effects of alprafenone on canine cardiac tissue, J. Cardiovasc. Pharm., 24 (1994), 411-419.
[2]	R. Atanasiu, L. Gouin, M. A. Mateescu, et al. Class Ⅲ antiarrhythmic effects of ceruloplasmin on rat heart, Can. J. Physiol. Pharm., 74 (1999), 652-656.
[3]	T. Bányász, L. Bárándi, G. Harmati, et al. Mechanism of reverse rate-dependent action of cardioactive agents, Curr. Med. Chem., 18 (2011), 3597-3606.
[4]	T. Banyasz, B. Horvath, L. Virag, et al. Reverse rate dependency is an intrinsic property of canine cardiac preparations, Cardiovasc. Res., 84 (2009), 237-244.
[5]	L. Bárándi, L. Virág, N. Jost, et al. Reverse rate-dependent changes are determined by baseline action potential duration in mammalian and human ventricular preparations, Basic Res. Cardiol., 105 (2010), 315-323.
[6]	G. Beatch, D. Davis, S. Laganiere, et al. Rate-dependent effects of sematilide on ventricular monophasic action potential duration and delayed rectifier K⁺ current in rabbits, J. Cardiovasc. Pharm., 28 (1996), 618-630.
[7]	O. Bernus, R. Wilder, C. W. Zemlin, et al. A computationally efficient electrophysiological model of human ventricular cells, American Journal of Physiology-Heart and Circulatory Physiology, 282 (2002), 2296-2308.
[8]	K. Blinova, Q. Dang, D. Millard, et al. International multisite study of human-induced pluripotent stem cell-derived cardiomyocytes for drug proarrhythmic potential assessment, Cell Rep., 24 (2018), 3582-3592.
[9]	O. J. Britton, A. Bueno-Orovio, K. V. Ammel, et al. Experimentally calibrated population of models predicts and explains intersubject variability in cardiac cellular electrophysiology, Proceedings of the National Academy of Sciences of the United States of America, 110 (2013), E2098-E2105.
[10]	D. I. Cairns, F. H. Fenton and E. M. Cherry, Efficient parameterization of cardiac action potential models using a genetic algorithm, Chaos, 27 (2017), 093922.
[11]	T. J. Campbell, K. R. Wyse and R. Pallandi, Differential effects on action potential duration of class Ia, b and c antiarrhythmic drugs: modulation by stimulation rate and extracellular K⁺ concentration, Clin. Exp. Pharmacol. P., 18 (1991), 533-541.
[12]	J. Carro, J. F. Rodriguez-Matas, V. Monasterio, et al. Limitations in electrophysiological model development and validation caused by differences between simulations and experimental protocols, Prog. Biophys. Mol. Bio., 129 (2017), 53-64.
[13]	A. Carusi, K. Burrage and B. Rodriguez, Bridging experiments, models and simulations: an integrative approach to validation in computational cardiac electrophysiology, Am. J. Physiol.-Heart C., 303 (2012), H144-H155.
[14]	I. Cavero and H. Holzgrefe, Comprehensive in vitro proarrhythmia assay, a novel in vitro/in silico paradigm to detect ventricular proarrhythmic liability: a visionary 21st century initiative, Expert Opin. Drug Saf., 13 (2014), 745-758.
[15]	C.-E. Chiang, H.-N. Luk, T.-M. Wang, et al. Effects of sildenafil on cardiac repolarization, Cardiovasc. Res., 255 (2002), 290-299.
[16]	R. Clayton, O. Bernus, E. Cherry, et al. Models of cardiac tissue electrophysiology: Progress, challenges and open questions, Prog. Biophys. Mol. Bio., 104 (2011), 22-48.
[17]	J. Cooper, A. Corrias, D. Gavaghan, et al. Considerations for the use of cellular electrophysiology models within cardiac tissue simulations, Prog. Biophys. Mol. Bio., 107 (2011), 74-80.
[18]	D.-Z. Dai, F. Yu, H.-T. Li, et al. Blockade on sodium, potassium, and calcium channels by a new antiarrhythmic agent CPU 86017, Drug Develop. Res., 39 (1996), 138-146.
[19]	A. C. Daly, M. Clerx, K. A. Beattie, et al. Reproducible model development in the cardiac electrophysiology web lab, Prog. Biophys. Mol. Bio., 139 (2018), 3-14.
[20]	R. A. Devenyi, F. A. Ortega, W. Groenendaal, et al. Differential roles of two delayed rectifier potassium currents in regulation of ventricular action potential duration and arrhythmia susceptibility, J. Physiol., 595 (2017), 2301-2317.
[21]	H. J. Duff, R. S. Sheldon and N. J. Cannon, Tetrodotoxin: Sodium channel specific antiarrhythmic activity, Cardiovasc. Res., 22 (1988), 800-807.
[22]	J. Eastman, J. Sass, J. M. Gomes, et al. Using delay differential equations to induce alternans in a model of cardiac electrophysiology, J. Theor. Biol., 404 (2016), 262-272.
[23]	B. Fermini, N. Jurkiewicz, B. Jow, et al. Use-dependent effects of the class-Ⅲ antiarrhythmic agent NE-10064 (azimilide) on cardiac repolarization — block of delayed rectifier potassium and L-type calcium currents, J. Cardiovasc. Pharm., 26 (1995), 259-271.
[24]	J. J. Fox, J. L. McHarg and R. F. Gilmour, Ionic mechanism of electrical alternans, Am. J. Physiol.-Heart C., 282 (2002), H516-H530.
[25]	K. Fukuda, J. Watanabe, T. Yagi, et al. A sodium channel blocker, pilsicainide, produces atrial post-repolarization refractoriness through the reduction of sodium channel availability, Tohoku J. Exp. Med., 225 (2011), 35-42.
[26]	L. Geng, C.-W. Kong, A. O. Wong, et al. Probing flecainide block of I-Na using human pluripotent stem cell-derived ventricular cardiomyocytes adapted to automated patch-clamping and 2D monolayers, Toxicol. Lett., 294 (2018), 61-72.
[27]	J. K. Gibson, Y. Yue, J. Bronson, et al. Human stem cell-derived cardiomyocytes detect drugmediated changes in action potentials and ion currents, J. Pharmacol. Tox. Met., 70 (2014), 255-267.
[28]	G. Gintant, The class Ⅲ effect of azimilide is not associated with reverse use-dependence in open-chest dogs, J. Cardiovasc. Pharm., 31 (1998), 945-953.
[29]	R. A. Gray and P. Pathmanathan, Patient-specific cardiovascular computational modeling: Diversity of personalization and challenges, J. Cardiovasc. Trans. Res., 11 (2018), 80-88.
[30]	W. Groenendaal, F. A. Ortega, A. R. Kherlopian, et al. Cell-specific cardiac electrophysiology models, PLoS Comput. Biol., 11 (2015), e1004242.
[31]	R. N. Gutenkunst, J. J. Waterfall, F. P. Casey, et al. Universally sloppy parameter sensitivities in systems biology models, PLoS Comput. Biol., 3 (2007), e189.
[32]	G. Hall, S. Bahar and D. Gauthier, Prevalence of rate-dependent behaviors in cardiac muscle, Phys. Rev. Lett., 82 (1999), 2995-2998.
[33]	J. Heijman, S. Ghezelbash and D. Dobrev, Investigational antiarrhythmic agents: promising drugs in early clinical development, Expert Opin. Inv. Drug., 26 (2017), 897-907.
[34]	A. Hodgkin and A. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol., 117 (1952), 500-544.
[35]	J. W. Holmes and J. Lumens, Clinical applications of patient-specific models: The case for a simple approach, J. Cardiovasc. Trans. Res., 11 (2010), 71-79.
[36]	X. Huang, Y. Qian, X. Zhang, et al. Hysteresis and bistability in periodically paced cardiac tissue, Phys. Rev. E, 81 (2010), 051903.
[37]	I. Jacobson, G. Duker, M. Florentzson, et al. Experimental study electrophysiological characterization and antiarrhythmic efficacy of the mixed potassium channel-blocking antiarrhythmic agent AZ13395438 in vitro and in vivo, J. Cardiovasc. Pharmacol. Ther., 1 (2013), 290-300.
[38]	D. Jans, G. C. ad Olga Krylychkina, L. Hoffman, et al. Action potential-based MEA platform for in vitro screening of drug-induced cardiotoxicity using human iPSCs and rat neonatal myocytes, J. Pharmacol. Toxicol. Meth., 1 (2017), 290-300.
[39]	Q. Jin, X. Chen, W. M. Smith, et al. Effects of procainamide and sotalol on restitution properties, dispersion of refractoriness, and ventricular fibrillation activation patterns in pigs, J. Cardiovasc. Pharm., 19 (2008), 1090-1097.
[40]	Q. Jin, J. Zhou, N. Zhang, et al. Ibutilide decreases defibrillation threshold by the reduction of activation pattern complexity during ventricular fibrillation in canine hearts, Chinese Med. J., 125 (2012), 2701-2707.
[41]	N. K. Jurkiewicz and M. C. Sanguinetti, Rate-dependent prolongation of cardiac action potentials by a methanesulfonanilide class Ⅲ antiarrhythmic agent. Specific block of rapidly activating delayed rectifier K⁺ current by dofetilide, Circ. Res., 72 (1993), 75-83.
[42]	S. Kalb, H. Dobrovolny, E. Tolkacheva, et al. The restitution portrait: A new method of investigating rate-dependent restitution, J. Cardiovasc. Electr., 15 (2004), 698-709.
[43]	S. Kalb, J. Fox, E. Tolkacheva, et al. Parameter estimation in mapping models with memory, Anatomical Record A, 288 (2006), 579-86.
[44]	R. E. Klabunde, Cardiovascular Physiological Concepts, Lippincott Williams & Wilkins, Philadelphia, 2011.
[45]	I. Kodama, K. Kamiya and J. Toyama, Cellular electropharmacology of amiodarone, Cardiovasc. Res., 35 (1997), 13-29.
[46]	J.-Y. Le Guennec, J. Thireau, A. Ouille, et al. Inter-individual variability and modeling of electrical activity: a possible new approach to explore cardiac safety? Sci. Rep., 6 (2016), 37948.
[47]	L. Livshitz and Y. Rudy, Uniqueness and stability of action potential models during rest, pacing, and conduction using problem-solving environment, Biophys. J., 97 (2009), 1265-1276.
[48]	H. R. Lu, E. Vlaminckx, A. Teisman, et al. Choice of cardiac tissue plays an important role in the evaluation of drug-induced prolongation of the QT interval in vitro in rabbit, J. Pharmacol. Tox. Met., 52 (2005), 90-105.
[49]	D. lu Bai, W. zhou Chen, Y. xin Bo, et al. Discovery of N-(3, 5-bis(1-pyrrolidylmethyl)-4-hydroxy-benzyl)-4-methoxybenzenesulfamide (sulcardine) as a novel anti-arrhythmic agent, Acta Pharmacol. Sin., 33 (2012), 1176-1186.
[50]	H. Marschang, T. Beyer, L. Karolyi, et al. Differential rate and potassium dependent effects of class Ⅲ agents d-sotalol and dofetilide on guinea pig papillary muscle, Cardiovasc. Drug. Ther., 12 (1998), 573-583.
[51]	G. R. Mirams, M. R. Davies, Y. Cui, et al. Application of cardiac electrophysiology simulations to proarrhythmic safety testing, Brit. J. Pharmacol., 167 (2012), 932-945.
[52]	A. Muszkiewicz, O. J. Britton, P. Gemmell, et al. Variability in cardiac electrophysiology: Using experimentally-calibrated populations of models to move beyond the single virtual physiological human paradigm, Prog. Biophys. Mol. Biol., 120 (2016), 932-945.
[53]	S. Narayan, T-wave alternans and the susceptibility to ventricular arrhythmias, J. Am. Coll. Cardiol., 47 (2006), 269-281.
[54]	H. B. Ni, S. Morotti and E. Grandi, A heart for diversity: Simulating variability in cardiac arrhythmia research, Front. Physiol., 9 (2018), 958.
[55]	D. Noble, Modification of Hodgkin-Huxley equations applicable to Purkinje fibre action and pace-maker potentials, J. Physiol., 160 (1962), 317-52.
[56]	D. Noble, A. Garny and P. J. Noble, How the Hodgkin-Huxley equations inspired the Cardiac Physiome Project, J. Physiol., 590 (2012), 2613-2628.
[57]	K. Noguchi, J. Kase, M. Saitoh, et al. Effects of HNS-32, a novel antiarrhythmic agent, on guineapig myocardium, Pharmacology, 64 (2002), 36-42.
[58]	R. A. Oliver, G. M. Hall, S. Bahar, et al. Existence of bistability and correlation with arrhythmogenesis in paced sheep atria, J. Cardiovasc. Electr., 11 (2000), 797-805.
[59]	R. A. Oliver, C. S. Henriquez and W. Krassowska, Bistability and correlation with arrhythmogenesis in a model of the right atrium, Ann. Biomed. Eng., 33 (2005), 577-589.
[60]	C. Omichi, S. Zhou, M. Lee, et al. Effects of amiodarone on wave front dynamics during ventricular fibrillation in isolated swine right ventricle, Am. J. Physiol.-Heart. C., 282 (2002), H1063-H1070.
[61]	P. M. Orth, J. C. Hesketh, C. K. Mak, et al. RSD1235 blocks late I_Na and suppresses early afterdepolarizations and torsades de pointes induced by class Ⅲ agents, Cardiovasc. Res., 70 (2006), 486-496.
[62]	O. E. Osadchii, Dofetilide promotes repolarization abnormalities in perfused guinea-pig heart, Cardiovasc. Drug. Ther., 26 (2012), 489-500.
[63]	O. E. Osadchii, Quinidine elicits proarrhythmic changes in ventricular repolarization and refractoriness in guinea-pig, Can. J. Physiol. Pharmacol., 91 (2013), 306-315.
[64]	O. E. Osadchii, Effects of antiarrhythmics on the electrical restitution in perfused guinea-pig heart are critically determined by the applied cardiac pacing protocol, Exp. Physiol., 104 (2019), 490-504.
[65]	T. Osaka, E. Yokoyama, H. Hasebe, et al. Effects of chronic amiodarone on the electrical restitution in the human ventricle with reference to its antiarrhythmic efficacy, J. Cardiovasc. Eletr., 22 (2011), 669-676.
[66]	T. Osaka, E. Yokoyama, Y. Kushiyama, et al. Opposing effects of bepridil on ventricular repolarization in humans-inhomogeneous prolongation of the action potential duration vs flattening of its restitution kinetics, Circ. J., 73 (2009), 1612-1618.
[67]	M. Pan, P. J. Gawthrop, K. Tran, et al. Bond graph modelling of the cardiac action potential: implications for drift and non-unique steady states, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 474 (2018), 20180106.
[68]	C. Pankusci, T. Banyasz, J. Magyar, et al. Electrophysiological effects of EGIS-7229, a new antiarrhythmic agent, in isolated mammalian and human cardiac tissues, N-S Arch. Pharmacol., 355 (1997), 398-405.
[69]	J. M. Pastore, S. D. Girouard, K. R. Laurita, et al. Mechanism linking T-wave alternans to the genesis of cardiac fibrillation, Circulation, 99 (1999), 1385-1394.
[70]	P. Pathmanathan and R. A. Gray, Validation and trustworthiness of multiscale models of cardiac electrophysiology, Front. Physiol., 9 (2018), 106.
[71]	A. Pezhouman, S. Madahian, H. Stepanyan, et al. Selective inhibition of late sodium current suppresses ventricular tachycardia and fibrillation in intact rat hearts, Heart Rhythm, 11 (2014), 492-501.
[72]	A. S. Pickoff and A. Stolfi, Comparison of the rate dependent effects of dofetilide and ibutilide in the newborn heart, Pacing and Clinical Electrophysiology, 24 (2001), 816-823.
[73]	S. Polak, B. Wisniowska, K. Fijorek, et al. In vitro-in vivo extrapolation of drug-induced proarrhythmia predictions at the population level, General Pharmacology, 19 (2014), 275-281.
[74]	X. Qi, D. Newman and P. Dorian, The class Ⅲ effect of azimilide is not associated with reverse use-dependence in open-chest dogs, J. Cardiovasc. Pharm., 34 (1999), 898-903.
[75]	D. M. Roden, Antiarrhythmic drugs: from mechanisms to clinical practice, Heart, 84 (2000), 339-346.
[76]	D. S. Rosenbaum, L. E. Jackson, J. M. Smith, et al. Electrical alternans and vulnerability to ventricular arrhythmias, The New England Journal of Medicine, 330 (1994), 235-241.
[77]	P. T. Sager and M. Behboodikhah, Frequency-dependent electrophysiologic effects of d, l-sotalol and quinidine and modulation by beta-adrenergic stimulation, J. Cardiovasc. Pharm., 25 (1995), 1006-1011.
[78]	C. Sánchez, A. Bueno-Orovio, E. Wettwer, et al. Inter-subject variability in human atrial action potential in sinus rhythm versus chronic atrial fibrillation, PLoS ONE, 9 (2014), e105897.
[79]	A. A. Sher, K. Wang, A. Wathen, et al. A local sensitivity analysis method for developing biological models with identifiable parameters: Application to cardiac ionic channel modelling, Future Gener. Comp. Sy., 29 (2013), 591-598.
[80]	P. K. Shreenivasaiah, S.-H. Rho, T. Kim, et al. An overview of cardiac systems biology, J. Mol. Cell. Cardiol., 44 (2008), 460-469.
[81]	J. M. Smith, S. M. Clancy, R. Valeri, et al. Electrical alternans and cardiac electrical instability, Circulation, 77 (1988), 110-21.
[82]	E. A. Sosunov, E. P. Anyukhovsky and M. R. Rosen, Effects of quinidine on repolarization in canine epicardium, midmyocardium, and endocardium, Circulation, 96 (1997), 4011-4018.
[83]	M.-J. Su, G.-J. Chang, M.-H. Wu, et al. Electrophysiological basis for the antiarrhythmic action and positive inotropy of HA-7, a furoquinoline alkaloid derivative, in rat heart, Brit. J. Pharmacol., 122 (1997), 1285-1298.
[84]	J. Takacs, N. Iost, C. Lengyel, et al. Multiple cellular electrophysiological effects of azimilide in canine cardiac preparations, Eur. J. Pharmacol., 470 (2003), 163-170.
[85]	E. Tolkacheva, D. Schaeffer, D. Gauthier, et al. Condition for alternans and stability of the 1:1 response pattern in a 'memory' model of paced cardiac dynamics, Phys. Rev. E, 67 (2003), 031904.
[86]	M. R. Vagos, H. Arevalo, B. L. de Oliveira, et al. A computational framework for testing arrhythmia marker sensitivities to model parameters in functionally calibrated populations of atrial cells, Chaos, 27 (2017), 093941.
[87]	Z. Wang, B. Fermini and S. Nattel, Mechanism of flecainides rate-dependent actions on actionpotential duration in canine atrial tissue, J. Pharmacol. Exp. Ther., 267 (1993), 575-581.
[88]	M. Wilhelms, H. Hettmann, M. M. Maleckar, et al. Benchmarking electrophysiological models of human atrial myocytes, Front. Physiol., 3 (2013), 487.
[89]	B. A. Williams, D. R. Dickenson and G. N. Beatch, Kinetics of rate-dependent shortening of action potential duration in guinea-pig ventricle; effects of I_K1 and I_Kr blockade, Brit. J. Pharmacol., 126 (1999), 1426-1436.
[90]	B. Wisniowska, A. Mendyk, K. Fijorek, et al. Computer-based prediction of the drug proarrhythmic effect: problems, issues, known and suspected challenges, Europace, 16 (2014), 724-735.
[91]	R. Wu and A. Patwardhan, Effects of rapid and slow potassium repolarization currents and calcium dynamics on hysteresis in restitution of action potential duration, J. Electrocardiol., 40 (2007), 188-199.
[92]	K. Wyse, V. Ye and T. Campbell, Action-potential prolongation exhibits simple dose-dependence for sotalol, but reverse dose-dependence for quinidine and disopyramide — implications for proarrhythmia due to triggered activity, J. Cardiovasc. Pharm., 21 (1993), 316-322.
[93]	X. Yang, T. Yu and H. Kesteloot, Clinical and electrophysiologic studies of R61748 (transcainide) — a new class Ic antiarrhythmic drug, Acta Cardiol., 47 (1992), 43-56.
[94]	Z. I. Zhu and C. E. Clancy, Genetic mutations and arrhythmia: simulation from DNA to electrocardiogram, J. Electrocardiol., 40 (2007), S47-S50.

Reader Comments

Your name:*

Email:*
© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)