In-silico study of the ionic current gradients determining left-to-right atrial frequencies during paroxysmal atrial fibrillation

Atrial fibrillation is the most prevalent cardiac arrhythmia. Paroxysmal atrial fibrillation (pAF) may occur in episodes lasting from minutes to days. Recent studies suggest that some pAF episodes present a left-to-right dominant frequency gradient caused by ionic current gradients. However, how eac...

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oai_identifier_str oai:repository.udem.edu.co:11407/6086
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dc.title.none.fl_str_mv In-silico study of the ionic current gradients determining left-to-right atrial frequencies during paroxysmal atrial fibrillation
title In-silico study of the ionic current gradients determining left-to-right atrial frequencies during paroxysmal atrial fibrillation
spellingShingle In-silico study of the ionic current gradients determining left-to-right atrial frequencies during paroxysmal atrial fibrillation
title_short In-silico study of the ionic current gradients determining left-to-right atrial frequencies during paroxysmal atrial fibrillation
title_full In-silico study of the ionic current gradients determining left-to-right atrial frequencies during paroxysmal atrial fibrillation
title_fullStr In-silico study of the ionic current gradients determining left-to-right atrial frequencies during paroxysmal atrial fibrillation
title_full_unstemmed In-silico study of the ionic current gradients determining left-to-right atrial frequencies during paroxysmal atrial fibrillation
title_sort In-silico study of the ionic current gradients determining left-to-right atrial frequencies during paroxysmal atrial fibrillation
description Atrial fibrillation is the most prevalent cardiac arrhythmia. Paroxysmal atrial fibrillation (pAF) may occur in episodes lasting from minutes to days. Recent studies suggest that some pAF episodes present a left-to-right dominant frequency gradient caused by ionic current gradients. However, how each ionic current gradient affects the left-to-right dominant frequency gradient during pAF has not been studied. In this work, we use a 3D model of human atria to study how the ionic current gradients affect the dominant frequency gradient during pAF induced by continuous ectopic activity. The role of the specific gradients of acetylcholine-activated potassium current (I KACh ) and inward-rectifier potassium current (I K1 ) on determining the left-to-right dominant frequency gradient was assessed. The main outcome of this study is that either or both of the I KACh or I K1 gradients are necessary to induce a left-to-right dominant frequency gradient during pAF. However, both gradients are necessary to the left atrium maintaining, by itself, the pAF episode. These findings have potentially important implications for the development of atrial-selective therapeutic approaches. © The Author(s) 2019.
publishDate 2019
dc.date.accessioned.none.fl_str_mv 2021-02-05T14:59:17Z
dc.date.available.none.fl_str_mv 2021-02-05T14:59:17Z
dc.date.none.fl_str_mv 2019
dc.type.eng.fl_str_mv Article
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dc.identifier.issn.none.fl_str_mv 375497
dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/11407/6086
dc.identifier.doi.none.fl_str_mv 10.1177/0037549719837346
identifier_str_mv 375497
10.1177/0037549719837346
url http://hdl.handle.net/11407/6086
dc.language.iso.none.fl_str_mv eng
language eng
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dc.relation.references.none.fl_str_mv Kirchhof, P., Benussi, S., Kotecha, D., 2016 ESC Guidelines for the management of atrial fibrillation developed in collaboration with EACTS (2016) EP Europace, 18 (11), pp. 1609-1678
Nattel, S., Burstein, B., Dobrev, D., Atrial remodeling and atrial fibrillation: Mechanisms and implications (2008) Circ Arrhythm Electrophysiol, 1 (1), pp. 62-73
Niwano, S., Wakisaka, Y., Kojima, J., Monitoring the progression of the atrial electrical remodeling in patients with paroxysmal atrial fibrillation (2003) Circ J, 67 (2), pp. 133-138
Haissaguerre, M., Jais, P., Shah, D.C., Spontaneous initiation of atrial fibrillation by ectopic beats originating in the pulmonary veins (1998) N Engl J Med, 339 (10), pp. 659-666
Chen, S.A., Hsieh, M.H., Tai, C.T., Initiation of atrial fibrillation by ectopic beats originating from the pulmonary veins: Electrophysiological characteristics, pharmacological responses, and effects of radiofrequency ablation (1999) Circulation, 100 (18), pp. 1879-1886
Arentz, T., Haegeli, L., Sanders, P., High-density mapping of spontaneous pulmonary vein activity initiating atrial fibrillation in humans (2007) J Cardiovasc Electrophysiol, 18 (1), pp. 31-38
Patterson, E., Jackman, W.M., Beckman, K.J., Spontaneous pulmonary vein firing in man: Relationship to tachycardia-pause early afterdepolarizations and triggered arrhythmia in canine pulmonary veins in vitro (2007) J Cardiovasc Electrophysiol, 18 (10), pp. 1067-1075
Traykov, V.B., Pap, R., Gingl, Z., Role of triggering pulmonary veins in the maintenance of sustained paroxysmal atrial fibrillation (2013) Pacing Clin Electrophysiol, 36 (7), pp. 845-854
Jaïs, P., Haïssaguerre, M., Shah, D.C., A focal source of atrial fibrillation treated by discrete radiofrequency ablation (1997) Circulation, 95 (3), pp. 572-576
Kumagai, K., Gondo, N., Matsumoto, N., New technique for simultaneous catheter mapping of pulmonary veins for catheter ablation in focal atrial fibrillation (2000) Cardiology, 94 (4), pp. 233-238
Pison, L., Tilz, R., Jalife, J., Pulmonary vein triggers, focal sources, rotors and atrial cardiomyopathy: Implications for the choice of the most effective ablation therapy (2016) J Intern Med, 279 (5), pp. 449-456
Mandapati, R., Skanes, A., Chen, J., Stable microreentrant sources as a mechanism of atrial fibrillation in the isolated sheep heart (2000) Circulation, 101 (2), pp. 194-199
Jalife, J., Berenfeld, O., Mansour, M., Mother rotors and fibrillatory conduction: A mechanism of atrial fibrillation (2002) Cardiovasc Res, 54 (2), pp. 204-216
Belhassen, B., Glick, A., Viskin, S., Reentry in a pulmonary vein as a possible mechanism of focal atrial fibrillation (2004) J Cardiovasc Electrophysiol, 15 (7), pp. 824-828
Sanders, P., Berenfeld, O., Hocini, M., Spectral analysis identifies sites of high-frequency activity maintaining atrial fibrillation in humans (2005) Circulation, 112 (6), pp. 789-797
Yamazaki, M., Filgueiras-Rama, D., Berenfeld, O., Ectopic and reentrant activation patterns in the posterior left atrium during stretch-related atrial fibrillation (2012) Prog Biophys Mol Biol, 110 (2-3), pp. 269-277
Bingen, B.O., Engels, M.C., Schalij, M.J., Light-induced termination of spiral wave arrhythmias by optogenetic engineering of atrial cardiomyocytes (2014) Cardiovasc Res, 104 (1), pp. 194-205
Climent, A.M., Guillem, M.S., Fuentes, L., Role of atrial tissue remodeling on rotor dynamics: An in vitro study (2015) Am J Physiol Circ Physiol, 309 (11), pp. H1964-H1973
Varela, M., Colman, M.A., Hancox, J.C., Atrial heterogeneity generates re-entrant substrate during atrial fibrillation and anti-arrhythmic drug action: Mechanistic insights from canine atrial models (2016) PLoS Comput Biol, 12 (12), p. e1005245
Lim, H.S., Hocini, M., Dubois, R., Complexity and distribution of drivers in relation to duration of persistent atrial fibrillation (2017) J Am Coll Cardiol, 69 (10), pp. 1257-1269
Miller, J.M., Kalra, V., Das, M.K., Clinical benefit of ablating localized sources for human atrial fibrillation: The Indiana University FIRM registry (2017) J Am Coll Cardiol, 69 (10), pp. 1247-1256
Hasebe, H., Yoshida, K., Iida, M., Right-to-left frequency gradient during atrial fibrillation initiated by right atrial ectopies and its augmentation by adenosine triphosphate: Implications of right atrial fibrillation (2016) Heart Rhythm, 13 (2), pp. 354-363
Atienza, F., Almendral, J., Jalife, J., Real-time dominant frequency mapping and ablation of dominant frequency sites in atrial fibrillation with left-to-right frequency gradients predicts long-term maintenance of sinus rhythm (2009) Heart Rhythm, 6 (1), pp. 33-40
Zhou, Z., Jin, Q., Chen, L.Y., Noninvasive imaging of high-frequency drivers and reconstruction of global dominant frequency maps in patients with paroxysmal and persistent atrial fibrillation (2016) IEEE Trans Biomed Eng, 63 (6), pp. 1333-1340
Cervigón, R., Castells, F., Gómez-Pulido, J., Granger causality and Jensen–Shannon divergence to determine dominant atrial area in atrial fibrillation (2018) Entropy, 20 (1), p. 57
Csepe, T.A., Hansen, B.J., Fedorov, V.V., Atrial fibrillation driver mechanisms: Insight from the isolated human heart (2017) Trends Cardiovasc Med, 27 (1), pp. 1-11
Voigt, N., Trausch, A., Knaut, M., Left-to-right atrial inward rectifier potassium current gradients in patients with paroxysmal versus chronic atrial fibrillation (2010) Circ Arrhythm Electrophysiol, 3 (5), pp. 472-480
Samie, F.H., Berenfeld, O., Anumonwo, J., Rectification of the background potassium current: A determinant of rotor dynamics in ventricular fibrillation (2001) Circ Res, 89 (12), pp. 1216-1223
Sekar, R.B., Kizana, E., Cho, H.C., I K1 heterogeneity affects genesis and stability of spiral waves in cardiac myocyte monolayers (2009) Circ Res, 104 (3), pp. 355-364
Berenfeld, O., The major role of I K1 in mechanisms of rotor drift in the atria: A computational study (2016) Clin Med Insights Cardiol, 10 (1), pp. 71-79
Berenfeld, O., Jalife, J., Mechanisms of atrial fibrillation: Rotors, ionic determinants, and excitation frequency (2014) Cardiol Clin, 32 (4), pp. 495-506
Ehrlich, J.R., Inward rectifier potassium currents as a target for atrial fibrillation therapy (2008) J Cardiovasc Pharmacol, 52 (2), pp. 129-135
Sarmast, F., Kolli, A., Zaitsev, A., Cholinergic atrial fibrillation: I K,ACh gradients determine unequal left/right atrial frequencies and rotor dynamics (2003) Cardiovasc Res, 59 (4), pp. 863-873
Mansour, M., Mandapati, R., Berenfeld, O., Left-to-right gradient of atrial frequencies during acute atrial fibrillation in the isolated sheep heart (2001) Circulation, 103 (21), pp. 2631-2636
Tobón, C., Ruiz-Villa, C.A., Heidenreich, E., A three-dimensional human atrial model with fiber orientation. Electrograms and arrhythmic activation patterns relationship (2013) PLoS One, 8 (2), p. e50883
Saiz, J., Tobón, C., Supraventricular arrhythmias in a realistic 3D model of the human atria (2013) Cardiac electrophysiology: From cell to bedside, pp. 351-359. , Zipes D.P., Jalife J., (eds), 6th ed., Philadelphia, PA, USA, Elsevier Saunders, In:, (eds
Sanchez-Quintana, D., Anderson, R., Cabrera, J., The terminal crest: Morphological features relevant to electrophysiology (2002) Heart, 88 (4), pp. 406-411
Cabrera, J.A., Ho, S.Y., Climent, V., The architecture of the left lateral atrial wall: A particular anatomic region with implications for ablation of atrial fibrillation (2008) Eur Heart J, 29 (3), pp. 356-362
Ho, S.Y., Sánchez-Quintana, D., The importance of atrial structure and fibers (2009) Clin Anat, 22 (1), pp. 52-63
Courtemanche, M., Ramirez, R.J., Nattel, S., Ionic mechanisms underlying human atrial action potential properties: Insights from a mathematical model (1998) Am J Physiol, 275 (1), pp. H301-H321
Kneller, J., Zou, R., Vigmond, E.J., Cholinergic atrial fibrillation in a computer model of a two-dimensional sheet of canine atrial cells with realistic ionic properties (2002) Circ Res, 90 (9), pp. E73-E87
Feng, J., Yue, L., Wang, Z., Ionic mechanisms of regional action potential heterogeneity in the canine right atrium (1998) Circ Res, 83 (5), pp. 541-551
Cha, T.J., Ehrlich, J.R., Zhang, L., Atrial tachycardia remodeling of pulmonary vein cardiomyocytes: Comparison with left atrium and potential relation to arrhythmogenesis (2005) Circulation, 111 (6), pp. 728-735
Li, D., Zhang, L., Kneller, J., Potential ionic mechanism for repolarization differences between canine right and left atrium (2001) Circ Res, 88 (11), pp. 1168-1175
Heidenreich, E.A., Ferrero, J.M., Doblaré, M., Adaptive macro finite elements for the numerical solution of monodomain equations in cardiac electrophysiology (2010) Ann Biomed Eng, 38 (7), pp. 2331-2345
Boineau, J.P., Canavan, T.E., Schuessler, R.B., Demonstration of a widely distributed atrial pacemaker complex in the human heart (1988) Circulation, 77 (6), pp. 1221-1237
Shah, D.C., Haissaguerre, M., Jais, P., High-resolution mapping of tachycardia originating from the superior vena cava: Evidence of electrical heterogeneity, slow conduction, and possible circus movement reentry (2002) J Cardiovasc Electrophysiol, 13 (4), pp. 388-392
Ugarte, J.P., Orozco-Duque, A., Tobón, C., Dynamic approximate entropy electroanatomic maps detect rotors in a simulated atrial fibrillation model (2014) PLoS One, 9 (12), p. e114577
Schuessler, R.B., Grayson, T.M., Bromberg, B.I., Cholinergically mediated tachyarrhythmias induced by a single extrastimulus in the isolated canine right atrium (1992) Circ Res, 71 (5), pp. 1254-1267
Veenhuyzen, G.D., Simpson, C.S., Abdollah, H., Atrial fibrillation (2004) CMAJ, 171 (7), pp. 755-760
Tsai, C.F., Tai, C.T., Hsieh, M.H., Initiation of atrial fibrillation by ectopic beats originating from the superior vena cava: Electrophysiological characteristics and results of radiofrequency ablation (2000) Circulation, 102, pp. 67-74
Berenfeld, O., Zaitsev, A.V., Mironov, S.F., Frequency-dependent breakdown of wave propagation into fibrillatory conduction across the pectinate muscle network in the isolated sheep right atrium (2002) Circ Res, 90 (11), pp. 1173-1180
Berenfeld, O., Ionic and substrate mechanism of atrial fibrillation: Rotors and the exitation frequency approach (2010) Arch Cardiol Mex, 80 (4), pp. 301-314
Atienza, F., Almendral, J., Moreno, J., Activation of inward rectifier potassium channels accelerates atrial fibrillation in humans: Evidence for a reentrant mechanism (2006) Circulation, 114 (23), pp. 2434-2442
Lazar, S., Dixit, S., Marchlinski, F.E., Presence of left-to-right atrial frequency gradient in paroxysmal but not persistent atrial fibrillation in humans (2004) Circulation, 110 (20), pp. 3181-3186
Ehrlich, J.R., Biliczki, P., Hohnloser, S.H., Atrial-selective approaches for the treatment of atrial fibrillation (2008) J Am Coll Cardiol, 51 (8), pp. 787-792
Nadimi, A.E., Ebrahimipour, S.Y., Afshar, E.G., Nano-scale drug delivery systems for antiarrhythmic agents (2018) Eur J Med Chem, 157, pp. 1153-1163
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_16ec
rights_invalid_str_mv http://purl.org/coar/access_right/c_16ec
dc.publisher.none.fl_str_mv SAGE Publications Ltd
dc.publisher.faculty.spa.fl_str_mv Facultad de Ciencias Básicas
publisher.none.fl_str_mv SAGE Publications Ltd
dc.source.none.fl_str_mv Simulation
institution Universidad de Medellín
repository.name.fl_str_mv Repositorio Institucional Universidad de Medellin
repository.mail.fl_str_mv repositorio@udem.edu.co
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spelling 20192021-02-05T14:59:17Z2021-02-05T14:59:17Z375497http://hdl.handle.net/11407/608610.1177/0037549719837346Atrial fibrillation is the most prevalent cardiac arrhythmia. Paroxysmal atrial fibrillation (pAF) may occur in episodes lasting from minutes to days. Recent studies suggest that some pAF episodes present a left-to-right dominant frequency gradient caused by ionic current gradients. However, how each ionic current gradient affects the left-to-right dominant frequency gradient during pAF has not been studied. In this work, we use a 3D model of human atria to study how the ionic current gradients affect the dominant frequency gradient during pAF induced by continuous ectopic activity. The role of the specific gradients of acetylcholine-activated potassium current (I KACh ) and inward-rectifier potassium current (I K1 ) on determining the left-to-right dominant frequency gradient was assessed. The main outcome of this study is that either or both of the I KACh or I K1 gradients are necessary to induce a left-to-right dominant frequency gradient during pAF. However, both gradients are necessary to the left atrium maintaining, by itself, the pAF episode. These findings have potentially important implications for the development of atrial-selective therapeutic approaches. © The Author(s) 2019.engSAGE Publications LtdFacultad de Ciencias Básicashttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85063608650&doi=10.1177%2f0037549719837346&partnerID=40&md5=b79cafb32842cb1361a71288d4bc8286Kirchhof, P., Benussi, S., Kotecha, D., 2016 ESC Guidelines for the management of atrial fibrillation developed in collaboration with EACTS (2016) EP Europace, 18 (11), pp. 1609-1678Nattel, S., Burstein, B., Dobrev, D., Atrial remodeling and atrial fibrillation: Mechanisms and implications (2008) Circ Arrhythm Electrophysiol, 1 (1), pp. 62-73Niwano, S., Wakisaka, Y., Kojima, J., Monitoring the progression of the atrial electrical remodeling in patients with paroxysmal atrial fibrillation (2003) Circ J, 67 (2), pp. 133-138Haissaguerre, M., Jais, P., Shah, D.C., Spontaneous initiation of atrial fibrillation by ectopic beats originating in the pulmonary veins (1998) N Engl J Med, 339 (10), pp. 659-666Chen, S.A., Hsieh, M.H., Tai, C.T., Initiation of atrial fibrillation by ectopic beats originating from the pulmonary veins: Electrophysiological characteristics, pharmacological responses, and effects of radiofrequency ablation (1999) Circulation, 100 (18), pp. 1879-1886Arentz, T., Haegeli, L., Sanders, P., High-density mapping of spontaneous pulmonary vein activity initiating atrial fibrillation in humans (2007) J Cardiovasc Electrophysiol, 18 (1), pp. 31-38Patterson, E., Jackman, W.M., Beckman, K.J., Spontaneous pulmonary vein firing in man: Relationship to tachycardia-pause early afterdepolarizations and triggered arrhythmia in canine pulmonary veins in vitro (2007) J Cardiovasc Electrophysiol, 18 (10), pp. 1067-1075Traykov, V.B., Pap, R., Gingl, Z., Role of triggering pulmonary veins in the maintenance of sustained paroxysmal atrial fibrillation (2013) Pacing Clin Electrophysiol, 36 (7), pp. 845-854Jaïs, P., Haïssaguerre, M., Shah, D.C., A focal source of atrial fibrillation treated by discrete radiofrequency ablation (1997) Circulation, 95 (3), pp. 572-576Kumagai, K., Gondo, N., Matsumoto, N., New technique for simultaneous catheter mapping of pulmonary veins for catheter ablation in focal atrial fibrillation (2000) Cardiology, 94 (4), pp. 233-238Pison, L., Tilz, R., Jalife, J., Pulmonary vein triggers, focal sources, rotors and atrial cardiomyopathy: Implications for the choice of the most effective ablation therapy (2016) J Intern Med, 279 (5), pp. 449-456Mandapati, R., Skanes, A., Chen, J., Stable microreentrant sources as a mechanism of atrial fibrillation in the isolated sheep heart (2000) Circulation, 101 (2), pp. 194-199Jalife, J., Berenfeld, O., Mansour, M., Mother rotors and fibrillatory conduction: A mechanism of atrial fibrillation (2002) Cardiovasc Res, 54 (2), pp. 204-216Belhassen, B., Glick, A., Viskin, S., Reentry in a pulmonary vein as a possible mechanism of focal atrial fibrillation (2004) J Cardiovasc Electrophysiol, 15 (7), pp. 824-828Sanders, P., Berenfeld, O., Hocini, M., Spectral analysis identifies sites of high-frequency activity maintaining atrial fibrillation in humans (2005) Circulation, 112 (6), pp. 789-797Yamazaki, M., Filgueiras-Rama, D., Berenfeld, O., Ectopic and reentrant activation patterns in the posterior left atrium during stretch-related atrial fibrillation (2012) Prog Biophys Mol Biol, 110 (2-3), pp. 269-277Bingen, B.O., Engels, M.C., Schalij, M.J., Light-induced termination of spiral wave arrhythmias by optogenetic engineering of atrial cardiomyocytes (2014) Cardiovasc Res, 104 (1), pp. 194-205Climent, A.M., Guillem, M.S., Fuentes, L., Role of atrial tissue remodeling on rotor dynamics: An in vitro study (2015) Am J Physiol Circ Physiol, 309 (11), pp. H1964-H1973Varela, M., Colman, M.A., Hancox, J.C., Atrial heterogeneity generates re-entrant substrate during atrial fibrillation and anti-arrhythmic drug action: Mechanistic insights from canine atrial models (2016) PLoS Comput Biol, 12 (12), p. e1005245Lim, H.S., Hocini, M., Dubois, R., Complexity and distribution of drivers in relation to duration of persistent atrial fibrillation (2017) J Am Coll Cardiol, 69 (10), pp. 1257-1269Miller, J.M., Kalra, V., Das, M.K., Clinical benefit of ablating localized sources for human atrial fibrillation: The Indiana University FIRM registry (2017) J Am Coll Cardiol, 69 (10), pp. 1247-1256Hasebe, H., Yoshida, K., Iida, M., Right-to-left frequency gradient during atrial fibrillation initiated by right atrial ectopies and its augmentation by adenosine triphosphate: Implications of right atrial fibrillation (2016) Heart Rhythm, 13 (2), pp. 354-363Atienza, F., Almendral, J., Jalife, J., Real-time dominant frequency mapping and ablation of dominant frequency sites in atrial fibrillation with left-to-right frequency gradients predicts long-term maintenance of sinus rhythm (2009) Heart Rhythm, 6 (1), pp. 33-40Zhou, Z., Jin, Q., Chen, L.Y., Noninvasive imaging of high-frequency drivers and reconstruction of global dominant frequency maps in patients with paroxysmal and persistent atrial fibrillation (2016) IEEE Trans Biomed Eng, 63 (6), pp. 1333-1340Cervigón, R., Castells, F., Gómez-Pulido, J., Granger causality and Jensen–Shannon divergence to determine dominant atrial area in atrial fibrillation (2018) Entropy, 20 (1), p. 57Csepe, T.A., Hansen, B.J., Fedorov, V.V., Atrial fibrillation driver mechanisms: Insight from the isolated human heart (2017) Trends Cardiovasc Med, 27 (1), pp. 1-11Voigt, N., Trausch, A., Knaut, M., Left-to-right atrial inward rectifier potassium current gradients in patients with paroxysmal versus chronic atrial fibrillation (2010) Circ Arrhythm Electrophysiol, 3 (5), pp. 472-480Samie, F.H., Berenfeld, O., Anumonwo, J., Rectification of the background potassium current: A determinant of rotor dynamics in ventricular fibrillation (2001) Circ Res, 89 (12), pp. 1216-1223Sekar, R.B., Kizana, E., Cho, H.C., I K1 heterogeneity affects genesis and stability of spiral waves in cardiac myocyte monolayers (2009) Circ Res, 104 (3), pp. 355-364Berenfeld, O., The major role of I K1 in mechanisms of rotor drift in the atria: A computational study (2016) Clin Med Insights Cardiol, 10 (1), pp. 71-79Berenfeld, O., Jalife, J., Mechanisms of atrial fibrillation: Rotors, ionic determinants, and excitation frequency (2014) Cardiol Clin, 32 (4), pp. 495-506Ehrlich, J.R., Inward rectifier potassium currents as a target for atrial fibrillation therapy (2008) J Cardiovasc Pharmacol, 52 (2), pp. 129-135Sarmast, F., Kolli, A., Zaitsev, A., Cholinergic atrial fibrillation: I K,ACh gradients determine unequal left/right atrial frequencies and rotor dynamics (2003) Cardiovasc Res, 59 (4), pp. 863-873Mansour, M., Mandapati, R., Berenfeld, O., Left-to-right gradient of atrial frequencies during acute atrial fibrillation in the isolated sheep heart (2001) Circulation, 103 (21), pp. 2631-2636Tobón, C., Ruiz-Villa, C.A., Heidenreich, E., A three-dimensional human atrial model with fiber orientation. 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