Spontaneous activation under atrial fibrosis: A model using complex order derivatives

The computational modeling of the cardiac electrophysiology allows assertive and quantitative study of the atrial fibrosis under fibrillation conditions. The cardiac electrical propagation is described by the so-called monodomain model, that consists of a nonlinear parabolic reaction-diffusion equat...

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Fecha de publicación:: 2020

Institución:: Universidad de Medellín

Repositorio:: Repositorio UDEM

Idioma:: eng

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network_acronym_str	REPOUDEM2
network_name_str	Repositorio UDEM
repository_id_str
dc.title.none.fl_str_mv	Spontaneous activation under atrial fibrosis: A model using complex order derivatives
title	Spontaneous activation under atrial fibrosis: A model using complex order derivatives
spellingShingle	Spontaneous activation under atrial fibrosis: A model using complex order derivatives Atrial fibrosis Complex order derivatives Spontaneous activation Stability analysis Cell culture Computation theory Electrophysiology Fibroblasts Linear equations Nonlinear equations Cardiac electrophysiology Complex-order derivatives Computational modelling Electrophysiological properties Fibroblast proliferation Mathematical descriptions Nonlinear parabolic reaction Structural interactions Chemical activation
title_short	Spontaneous activation under atrial fibrosis: A model using complex order derivatives
title_full	Spontaneous activation under atrial fibrosis: A model using complex order derivatives
title_fullStr	Spontaneous activation under atrial fibrosis: A model using complex order derivatives
title_full_unstemmed	Spontaneous activation under atrial fibrosis: A model using complex order derivatives
title_sort	Spontaneous activation under atrial fibrosis: A model using complex order derivatives
dc.subject.spa.fl_str_mv	Atrial fibrosis Complex order derivatives Spontaneous activation Stability analysis
topic	Atrial fibrosis Complex order derivatives Spontaneous activation Stability analysis Cell culture Computation theory Electrophysiology Fibroblasts Linear equations Nonlinear equations Cardiac electrophysiology Complex-order derivatives Computational modelling Electrophysiological properties Fibroblast proliferation Mathematical descriptions Nonlinear parabolic reaction Structural interactions Chemical activation
dc.subject.keyword.eng.fl_str_mv	Cell culture Computation theory Electrophysiology Fibroblasts Linear equations Nonlinear equations Cardiac electrophysiology Complex-order derivatives Computational modelling Electrophysiological properties Fibroblast proliferation Mathematical descriptions Nonlinear parabolic reaction Structural interactions Chemical activation
description	The computational modeling of the cardiac electrophysiology allows assertive and quantitative study of the atrial fibrosis under fibrillation conditions. The cardiac electrical propagation is described by the so-called monodomain model, that consists of a nonlinear parabolic reaction-diffusion equation. Fibroblast proliferation, which is an essential component of the fibrotic process, can be modeled by considering the membrane ionic kinetics as a reactive component. However, such a mathematical description does not account the structural feature of fibroblasts. In this work, the electrophysiological properties of fibroblast proliferation and coupling with cardiomyocytes are investigated, using mathematical and computational modelling. The study is focused on the conditions under which spontaneous activations occur in a fibrotic domain. The proposed fibrosis model takes account the electrical and structural interactions of fibroblasts within the myocardium. The electrical component is described through an ionic kinetics formalism, while the structural component is obtained by means of a triplet of complex order derivatives that constructs the diffusion operator. A theoretical analysis determines the model parameters that generate unstable solutions, and numerical simulations illustrate and validate the analytical outcomes. The results evince a strong modulation of the stability conditions of the fibrotic model by the real and imaginary part of the fractional derivative order. The fibrosis structural complexity, controlled by the fractional order, determines the extent of the parameter space that generates spontaneous activation. Moreover, not all the unstable parameter configurations generate electrical propagation. In the cases of electrical conduction after spontaneous activation, the conduction velocity in the fibrotic domain is significantly slower than the one observed in healthy atrial tissue. The results give a new perspective for the development of atrial fibrosis models including the ectopic activity as an initiation factor for fibrillation activity. Indeed, the proposed design exploits the complex order fractional derivatives, to generate a wide set of electrophysiological scenarios. © 2020 Elsevier B.V.
publishDate	2020
dc.date.accessioned.none.fl_str_mv	2021-02-05T14:58:47Z
dc.date.available.none.fl_str_mv	2021-02-05T14:58:47Z
dc.date.none.fl_str_mv	2020
dc.type.eng.fl_str_mv	Article
dc.type.coarversion.fl_str_mv	http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.coar.fl_str_mv	http://purl.org/coar/resource_type/c_6501 http://purl.org/coar/resource_type/c_2df8fbb1
dc.type.driver.none.fl_str_mv	info:eu-repo/semantics/article
dc.identifier.issn.none.fl_str_mv	10075704
dc.identifier.uri.none.fl_str_mv	http://hdl.handle.net/11407/6018
dc.identifier.doi.none.fl_str_mv	10.1016/j.cnsns.2020.105618
identifier_str_mv	10075704 10.1016/j.cnsns.2020.105618
url	http://hdl.handle.net/11407/6018
dc.language.iso.none.fl_str_mv	eng
language	eng
dc.relation.isversionof.none.fl_str_mv	https://www.scopus.com/inward/record.uri?eid=2-s2.0-85097110396&doi=10.1016%2fj.cnsns.2020.105618&partnerID=40&md5=1ba48af7022d3f6c99d6d5e692e5b342
dc.relation.references.none.fl_str_mv	Corradi, D., Atrial fibrillation from the pathologist's perspective (2014) Cardiovas Pathol, 23, pp. 71-84 Kallergis, E.M., Goudis, C.A., Vardas, P.E., Atrial fibrillation: a progressive atrial myopathy or a distinct disease? (2014) Int J Cardiol, 171, pp. 126-133 Kirchhof, P., Benussi, S., Kotecha, D., Ahlsson, A., Atar, D., Casadei, B., 2016 ESC Guidelines for the management of atrial fibrillation developed in collaboration with EACTS (2016) Europace, 18 (11), pp. 1609-1678 Haïssaguerre, M., Jaïs, P., Shah, D.C., Takahashi, A., Hocini, M., Quiniou, G., Spontaneous initiation of atrial fibrillation by ectopic beats originating in the pulmonary veins (1998) N Engl J Med, 339 (10), pp. 659-666 Dilaveris, P., Antoniou, C.-K., Manolakou, P., Tsiamis, E., Gatzoulis, K., Tousoulis, D., Biomarkers associated with atrial fibrosis and remodeling (2018) Curr Med Chem, 26 (5), pp. 780-802 Quinn, T.A., Camelliti, P., Rog-Zielinska, E.A., Siedlecka, U., Poggioli, T., O'Toole, E.T., Electrotonic coupling of excitable and nonexcitable cells in the heart revealed by optogenetics (2016) Proc Natl Acad Sci, 113 (51), pp. 14852-14857 Camelliti, P., Green, C.R., LeGrice, I., Kohl, P., Fibroblast network in rabbit sinoatrial node: structural and functional identification of homogeneous and heterogeneous cell coupling. (2004) Circ Res, 94 (6), pp. 828-835 Miragoli, M., Salvarani, N., Rohr, S., Myofibroblasts induce ectopic activity in cardiac tissue (2007) Circ Res, 101, pp. 755-758 Brown, T.R., Krogh-Madsen, T., Christini, D.J., Computational approaches to understanding the role of fibroblast-myocyte interactions in cardiac arrhythmogenesis (2015) BioMed Res Int, 2015 Greisas, A., Zlochiver, S., Modulation of spiral-wave dynamics and spontaneous activity in a fibroblast/myocyte heterocellular tissue–a computational study. (2012) IEEE Trans Biomed Eng, 59 (5), pp. 1398-1407 Tveito, A., Lines, G., Artebrant, R., Skavhaug, O., Maleckar, M.M., Existence of excitation waves for a collection of cardiomyocytes electrically coupled to fibroblasts (2011) Math Biosci, 230 (2), pp. 79-86 Maccannell, K.A., Bazzazi, H., Chilton, L., Shibukawa, Y., Clark, R.B., Giles, W.R., A mathematical model of electrotonic interactions between ventricular myocytes and fibroblasts (2007) Byophys J, 92 (June), pp. 4121-4132 Maleckar, M.M., Greenstein, J.L., Giles, W.R., Trayanova, N.A., Electrotonic coupling between human atrial myocytes and fibroblasts alters myocyte excitability and repolarization (2009) Biophys J, 97, pp. 2179-2190 Clayton, R.H., Bernus, O., Cherry, E.M., Dierckx, H., Fenton, F.H., Mirabella, L., Models of cardiac tissue electrophysiology: progress, challenges and open questions (2011) Prog Biophys Mol Biol, 104, pp. 22-48 Bezekci, B., Biktashev, V.N., Strength-duration relationship in an excitable medium (2020) Commun Nonlinear Sci NumerSimul, 80 Trayanova, N.A., Boyle, P.M., Arevalo, H.J., Zahid, S., Exploring susceptibility to atrial and ventricular arrhythmias resulting from remodeling of the passive electrical properties in the heart: a simulation approach (2014) Front Physiol, 5 Morgan, R., Colman, M.A., Chubb, H., Seemann, G., Aslanidi, O.V., Slow conduction in the border zones of patchy fibrosis stabilizes the drivers for atrial fibrillation: insights from multi-scale human atrial modeling (2016) Front Physiol, 7 (OCT), pp. 1-15 Chen, R., Wen, C., Fu, R., Li, J., Wu, J., The effect of complex intramural microstructure caused by structural remodeling on the stability of atrial fibrillation: insights from a three-dimensional multi-layer modeling study (2018) PLoS ONE, 13 (11), pp. 1-23 Aronis, K.N., Ali, R., Trayanova, N.A., The role of personalized atrial modeling in understanding atrial fibrillation mechanisms and improving treatment (2019) Int J Cardiol, 287, pp. 139-147 Bueno-Orovio, A., Kay, D., Grau, V., Rodriguez, B., Burrage, K., Fractional diffusion models of cardiac electrical propagation: role of structural heterogeneity in dispersion of repolarization (2014) J R Soc Interface, 11 (97) Ugarte, J.P., Tobón, C., Lopes, A.M., Tenreiro Machado, J.A., Atrial rotor dynamics under complex fractional order diffusion (2018) Front Physiol, 9 (JUL), pp. 1-14 Cusimano, N., Gizzi, A., Fenton, F.H., Filippi, S., Gerardo-Giorda, L., Key aspects for effective mathematical modelling of fractional-diffusion in cardiac electrophysiology: a quantitative study (2020) Commun Nonlinear Sci NumerSimul, 84 Captur, G., Karperien, A.L., Li, C., Zemrak, F., Tobon-Gomez, C., Gao, X., Fractal frontiers in cardiovascular magnetic resonance: towards clinical implementation (2015) J Cardiovasc Magn Reson, 17 (1), pp. 1-10 Captur, G., Karperien, A.L., Hughes, A.D., Francis, D.P., Moon, J.C., The fractal heart-embracing mathematics in the cardiology clinic (2016) Nat Rev Cardiol, 14 (1), pp. 56-64 Huo, Y., Kassab, G.S., Scaling laws of coronary circulation in health and disease (2016) J Biomech, 49 (12), pp. 2531-2539 Butera, S., Di Paola, M., A physically based connection between fractional calculus and fractal geometry (2014) Ann Phys, 350, pp. 146-158 Liang, Y.S., Su, W.Y., The relationship between the Box dimension of the Besicovitch functions and the orders of their fractional calculus (2008) Appl Math Comput, 200 (1), pp. 297-307 Nigmatullin, R.R., Zhang, W., Gubaidullin, I., Accurate relationships between fractals and fractional integrals: new approaches and evaluations (2017) Fract Calc Appl Anal, 20 (5), pp. 1263-1280 Tarasov, V.E., Electromagnetic waves in non-integer dimensional spaces and fractals (2015) Chaos Solitons Fractals, 81, pp. 38-42 Yao, K., Liang, Y.S., Zhang, F., On the connection between the order of the fractional derivative and the Hausdorff dimension of a fractal function (2009) Chaos Solitons Fractals, 41 (5), pp. 2538-2545 Nigmatullin, R.R., Le Mehaute, A., Is there geometrical/physical meaning of the fractional integral with complex exponent? (2005) J Non-Cryst Solids, 351 (33–36 SPEC. ISS.), pp. 2888-2899 Nigmatullin, R.R., Baleanu, D., New relationships connecting a class of fractal objects and fractional integrals in space (2013) Fract Calc Appl Anal, 16 (4), pp. 911-936 Nigmatullin, R.R., Baleanu, D., Relationships between 1D and space fractals and fractional integrals and their applications in physics (2019) Applications in Physics, Part A, pp. 183-220. , Tarasov V.E. De Gruyter Berlin, Boston Sornette, D., Discrete-scale invariance and complex dimensions (1998) Phys Rep, 297 (5), pp. 239-270 Karamitsos, T.D., Arvanitaki, A., Karvounis, H., Neubauer, S., Ferreira, V.M., Myocardial tissue characterization and fibrosis by imaging (2020) JACC Cardiovasc Imaging, 13 (5), pp. 1221-1234 Ugarte, J.P., Tobon, C., Lopes, A.M., Machado, J.A.T., A complex order model of atrial electrical propagation from fractal porous cell membrane (2020) Fractals Ortigueira, M.D., Machado, J.A.T., On fractional vectorial calculus (2018) Bull Polish Acad Sci Tech Sci, 66 (4), pp. 389-402 Ortigueira, M., Machado, J., Which Derivative? (2017) Fractal Fract, 1 (1) Tveito, A., Lines, G.T., A condition for setting off ectopic waves in computational models of excitable cells (2008) Math Biosci, 213 (2), pp. 141-150 Szekeres, B.J., Izsák F. Numerical solution of fractional order diffusion problems with Neumann boundary conditions2014;:1–27 Ilić, M., Liu, F., Turner, I., Anh, V., Numerical approximation of a fractional-in-space diffusion equation (II)-with nonhomogeneous boundary conditions (2006) Fract Calc Appl Anal, 9 (4), pp. 333-349 Maleckar, M.M., Greenstein, J.L., Giles, W.R., Trayanova, N.A., K+ current changes account for the rate dependence of the action potential in the human atrial myocyte (2009) Am J Physiol HeartCir Physiol, 297, pp. H1398-H1410 Bueno-Orovio, A., Kay, D., Burrage, K., Fourier spectral methods for fractional-in-space reaction-diffusion equations (2014) BIT Numer Math, 54 (4), pp. 937-954 Rudy, Y., Electrotonic cell-cell interactions in cardiac tissue: effects on action potential propagation and repolarization (2005) Ann New York Acad Sci, 1047, pp. 308-313 Graux, P., Carlioz, R., Rivat, P., Bera, J., Guyomar, Y., Dutoit, A., Wavelength and atrial vulnerability: an endocavitary approach in humans (1998) Pacing Clin Electrophysiol PACE, 21 (1), pp. 202-208 Hansson, A., Holm, M., Blomström, P., Johansson, R., Lührs, C., Brandt, J., Right atrial free wall conduction velocity and degree of anisotropy in patients with stable sinus rhythm studied during open heart surgery (1998) Eur Heart J, 19 (2), pp. 293-300 Zheng, Y., Xia, Y., Carlson, J., Kongstad, O., Yuan, S., Atrial average conduction velocity in patients with and without paroxysmal atrial fibrillation (2017) Clin Physiol Funct Imaging, 37 (6), pp. 596-601 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 Shah, D.C., Häissaguerre, M., Jäis, P., Clémenty, J., 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
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	Elsevier B.V.
dc.publisher.faculty.spa.fl_str_mv	Facultad de Ciencias Básicas
publisher.none.fl_str_mv	Elsevier B.V.
dc.source.none.fl_str_mv	Communications in Nonlinear Science and Numerical 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	20202021-02-05T14:58:47Z2021-02-05T14:58:47Z10075704http://hdl.handle.net/11407/601810.1016/j.cnsns.2020.105618The computational modeling of the cardiac electrophysiology allows assertive and quantitative study of the atrial fibrosis under fibrillation conditions. The cardiac electrical propagation is described by the so-called monodomain model, that consists of a nonlinear parabolic reaction-diffusion equation. Fibroblast proliferation, which is an essential component of the fibrotic process, can be modeled by considering the membrane ionic kinetics as a reactive component. However, such a mathematical description does not account the structural feature of fibroblasts. In this work, the electrophysiological properties of fibroblast proliferation and coupling with cardiomyocytes are investigated, using mathematical and computational modelling. The study is focused on the conditions under which spontaneous activations occur in a fibrotic domain. The proposed fibrosis model takes account the electrical and structural interactions of fibroblasts within the myocardium. The electrical component is described through an ionic kinetics formalism, while the structural component is obtained by means of a triplet of complex order derivatives that constructs the diffusion operator. A theoretical analysis determines the model parameters that generate unstable solutions, and numerical simulations illustrate and validate the analytical outcomes. The results evince a strong modulation of the stability conditions of the fibrotic model by the real and imaginary part of the fractional derivative order. The fibrosis structural complexity, controlled by the fractional order, determines the extent of the parameter space that generates spontaneous activation. Moreover, not all the unstable parameter configurations generate electrical propagation. In the cases of electrical conduction after spontaneous activation, the conduction velocity in the fibrotic domain is significantly slower than the one observed in healthy atrial tissue. The results give a new perspective for the development of atrial fibrosis models including the ectopic activity as an initiation factor for fibrillation activity. Indeed, the proposed design exploits the complex order fractional derivatives, to generate a wide set of electrophysiological scenarios. © 2020 Elsevier B.V.engElsevier B.V.Facultad de Ciencias Básicashttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85097110396&doi=10.1016%2fj.cnsns.2020.105618&partnerID=40&md5=1ba48af7022d3f6c99d6d5e692e5b342Corradi, D., Atrial fibrillation from the pathologist's perspective (2014) Cardiovas Pathol, 23, pp. 71-84Kallergis, E.M., Goudis, C.A., Vardas, P.E., Atrial fibrillation: a progressive atrial myopathy or a distinct disease? (2014) Int J Cardiol, 171, pp. 126-133Kirchhof, P., Benussi, S., Kotecha, D., Ahlsson, A., Atar, D., Casadei, B., 2016 ESC Guidelines for the management of atrial fibrillation developed in collaboration with EACTS (2016) Europace, 18 (11), pp. 1609-1678Haïssaguerre, M., Jaïs, P., Shah, D.C., Takahashi, A., Hocini, M., Quiniou, G., Spontaneous initiation of atrial fibrillation by ectopic beats originating in the pulmonary veins (1998) N Engl J Med, 339 (10), pp. 659-666Dilaveris, P., Antoniou, C.-K., Manolakou, P., Tsiamis, E., Gatzoulis, K., Tousoulis, D., Biomarkers associated with atrial fibrosis and remodeling (2018) Curr Med Chem, 26 (5), pp. 780-802Quinn, T.A., Camelliti, P., Rog-Zielinska, E.A., Siedlecka, U., Poggioli, T., O'Toole, E.T., Electrotonic coupling of excitable and nonexcitable cells in the heart revealed by optogenetics (2016) Proc Natl Acad Sci, 113 (51), pp. 14852-14857Camelliti, P., Green, C.R., LeGrice, I., Kohl, P., Fibroblast network in rabbit sinoatrial node: structural and functional identification of homogeneous and heterogeneous cell coupling. (2004) Circ Res, 94 (6), pp. 828-835Miragoli, M., Salvarani, N., Rohr, S., Myofibroblasts induce ectopic activity in cardiac tissue (2007) Circ Res, 101, pp. 755-758Brown, T.R., Krogh-Madsen, T., Christini, D.J., Computational approaches to understanding the role of fibroblast-myocyte interactions in cardiac arrhythmogenesis (2015) BioMed Res Int, 2015Greisas, A., Zlochiver, S., Modulation of spiral-wave dynamics and spontaneous activity in a fibroblast/myocyte heterocellular tissue–a computational study. (2012) IEEE Trans Biomed Eng, 59 (5), pp. 1398-1407Tveito, A., Lines, G., Artebrant, R., Skavhaug, O., Maleckar, M.M., Existence of excitation waves for a collection of cardiomyocytes electrically coupled to fibroblasts (2011) Math Biosci, 230 (2), pp. 79-86Maccannell, K.A., Bazzazi, H., Chilton, L., Shibukawa, Y., Clark, R.B., Giles, W.R., A mathematical model of electrotonic interactions between ventricular myocytes and fibroblasts (2007) Byophys J, 92 (June), pp. 4121-4132Maleckar, M.M., Greenstein, J.L., Giles, W.R., Trayanova, N.A., Electrotonic coupling between human atrial myocytes and fibroblasts alters myocyte excitability and repolarization (2009) Biophys J, 97, pp. 2179-2190Clayton, R.H., Bernus, O., Cherry, E.M., Dierckx, H., Fenton, F.H., Mirabella, L., Models of cardiac tissue electrophysiology: progress, challenges and open questions (2011) Prog Biophys Mol Biol, 104, pp. 22-48Bezekci, B., Biktashev, V.N., Strength-duration relationship in an excitable medium (2020) Commun Nonlinear Sci NumerSimul, 80Trayanova, N.A., Boyle, P.M., Arevalo, H.J., Zahid, S., Exploring susceptibility to atrial and ventricular arrhythmias resulting from remodeling of the passive electrical properties in the heart: a simulation approach (2014) Front Physiol, 5Morgan, R., Colman, M.A., Chubb, H., Seemann, G., Aslanidi, O.V., Slow conduction in the border zones of patchy fibrosis stabilizes the drivers for atrial fibrillation: insights from multi-scale human atrial modeling (2016) Front Physiol, 7 (OCT), pp. 1-15Chen, R., Wen, C., Fu, R., Li, J., Wu, J., The effect of complex intramural microstructure caused by structural remodeling on the stability of atrial fibrillation: insights from a three-dimensional multi-layer modeling study (2018) PLoS ONE, 13 (11), pp. 1-23Aronis, K.N., Ali, R., Trayanova, N.A., The role of personalized atrial modeling in understanding atrial fibrillation mechanisms and improving treatment (2019) Int J Cardiol, 287, pp. 139-147Bueno-Orovio, A., Kay, D., Grau, V., Rodriguez, B., Burrage, K., Fractional diffusion models of cardiac electrical propagation: role of structural heterogeneity in dispersion of repolarization (2014) J R Soc Interface, 11 (97)Ugarte, J.P., Tobón, C., Lopes, A.M., Tenreiro Machado, J.A., Atrial rotor dynamics under complex fractional order diffusion (2018) Front Physiol, 9 (JUL), pp. 1-14Cusimano, N., Gizzi, A., Fenton, F.H., Filippi, S., Gerardo-Giorda, L., Key aspects for effective mathematical modelling of fractional-diffusion in cardiac electrophysiology: a quantitative study (2020) Commun Nonlinear Sci NumerSimul, 84Captur, G., Karperien, A.L., Li, C., Zemrak, F., Tobon-Gomez, C., Gao, X., Fractal frontiers in cardiovascular magnetic resonance: towards clinical implementation (2015) J Cardiovasc Magn Reson, 17 (1), pp. 1-10Captur, G., Karperien, A.L., Hughes, A.D., Francis, D.P., Moon, J.C., The fractal heart-embracing mathematics in the cardiology clinic (2016) Nat Rev Cardiol, 14 (1), pp. 56-64Huo, Y., Kassab, G.S., Scaling laws of coronary circulation in health and disease (2016) J Biomech, 49 (12), pp. 2531-2539Butera, S., Di Paola, M., A physically based connection between fractional calculus and fractal geometry (2014) Ann Phys, 350, pp. 146-158Liang, Y.S., Su, W.Y., The relationship between the Box dimension of the Besicovitch functions and the orders of their fractional calculus (2008) Appl Math Comput, 200 (1), pp. 297-307Nigmatullin, R.R., Zhang, W., Gubaidullin, I., Accurate relationships between fractals and fractional integrals: new approaches and evaluations (2017) Fract Calc Appl Anal, 20 (5), pp. 1263-1280Tarasov, V.E., Electromagnetic waves in non-integer dimensional spaces and fractals (2015) Chaos Solitons Fractals, 81, pp. 38-42Yao, K., Liang, Y.S., Zhang, F., On the connection between the order of the fractional derivative and the Hausdorff dimension of a fractal function (2009) Chaos Solitons Fractals, 41 (5), pp. 2538-2545Nigmatullin, R.R., Le Mehaute, A., Is there geometrical/physical meaning of the fractional integral with complex exponent? (2005) J Non-Cryst Solids, 351 (33–36 SPEC. ISS.), pp. 2888-2899Nigmatullin, R.R., Baleanu, D., New relationships connecting a class of fractal objects and fractional integrals in space (2013) Fract Calc Appl Anal, 16 (4), pp. 911-936Nigmatullin, R.R., Baleanu, D., Relationships between 1D and space fractals and fractional integrals and their applications in physics (2019) Applications in Physics, Part A, pp. 183-220. , Tarasov V.E. De Gruyter Berlin, BostonSornette, D., Discrete-scale invariance and complex dimensions (1998) Phys Rep, 297 (5), pp. 239-270Karamitsos, T.D., Arvanitaki, A., Karvounis, H., Neubauer, S., Ferreira, V.M., Myocardial tissue characterization and fibrosis by imaging (2020) JACC Cardiovasc Imaging, 13 (5), pp. 1221-1234Ugarte, J.P., Tobon, C., Lopes, A.M., Machado, J.A.T., A complex order model of atrial electrical propagation from fractal porous cell membrane (2020) FractalsOrtigueira, M.D., Machado, J.A.T., On fractional vectorial calculus (2018) Bull Polish Acad Sci Tech Sci, 66 (4), pp. 389-402Ortigueira, M., Machado, J., Which Derivative? (2017) Fractal Fract, 1 (1)Tveito, A., Lines, G.T., A condition for setting off ectopic waves in computational models of excitable cells (2008) Math Biosci, 213 (2), pp. 141-150Szekeres, B.J., Izsák F. Numerical solution of fractional order diffusion problems with Neumann boundary conditions2014;:1–27Ilić, M., Liu, F., Turner, I., Anh, V., Numerical approximation of a fractional-in-space diffusion equation (II)-with nonhomogeneous boundary conditions (2006) Fract Calc Appl Anal, 9 (4), pp. 333-349Maleckar, M.M., Greenstein, J.L., Giles, W.R., Trayanova, N.A., K+ current changes account for the rate dependence of the action potential in the human atrial myocyte (2009) Am J Physiol HeartCir Physiol, 297, pp. H1398-H1410Bueno-Orovio, A., Kay, D., Burrage, K., Fourier spectral methods for fractional-in-space reaction-diffusion equations (2014) BIT Numer Math, 54 (4), pp. 937-954Rudy, Y., Electrotonic cell-cell interactions in cardiac tissue: effects on action potential propagation and repolarization (2005) Ann New York Acad Sci, 1047, pp. 308-313Graux, P., Carlioz, R., Rivat, P., Bera, J., Guyomar, Y., Dutoit, A., Wavelength and atrial vulnerability: an endocavitary approach in humans (1998) Pacing Clin Electrophysiol PACE, 21 (1), pp. 202-208Hansson, A., Holm, M., Blomström, P., Johansson, R., Lührs, C., Brandt, J., Right atrial free wall conduction velocity and degree of anisotropy in patients with stable sinus rhythm studied during open heart surgery (1998) Eur Heart J, 19 (2), pp. 293-300Zheng, Y., Xia, Y., Carlson, J., Kongstad, O., Yuan, S., Atrial average conduction velocity in patients with and without paroxysmal atrial fibrillation (2017) Clin Physiol Funct Imaging, 37 (6), pp. 596-601Belhassen, 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. 824-828Shah, D.C., Häissaguerre, M., Jäis, P., Clémenty, J., 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. 388-392Communications in Nonlinear Science and Numerical SimulationAtrial fibrosisComplex order derivativesSpontaneous activationStability analysisCell cultureComputation theoryElectrophysiologyFibroblastsLinear equationsNonlinear equationsCardiac electrophysiologyComplex-order derivativesComputational modellingElectrophysiological propertiesFibroblast proliferationMathematical descriptionsNonlinear parabolic reactionStructural interactionsChemical activationSpontaneous activation under atrial fibrosis: A model using complex order derivativesArticleinfo:eu-repo/semantics/articlehttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Ugarte, J.P., GIMSC, Universidad de San Buenaventura, Medellín, ColombiaTobón, C., MATBIOM, Universidad de Medellín, Medellín, ColombiaSaiz, J., CI2B, Universitat Politècnica de València, Valencia, SpainLopes, A.M., UISPA-LAETA/INEGI, Faculty of Engineering, University of Porto, Porto, PortugalTenreiro Machado, J.A., Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, Porto, Portugalhttp://purl.org/coar/access_right/c_16ecUgarte J.P.Tobón C.Saiz J.Lopes A.M.Tenreiro Machado J.A.11407/6018oai:repository.udem.edu.co:11407/60182021-02-05 09:58:47.254Repositorio Institucional Universidad de Medellinrepositorio@udem.edu.co

Spontaneous activation under atrial fibrosis: A model using complex order derivatives

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