A COMPLEX ORDER MODEL of ATRIAL ELECTRICAL PROPAGATION from FRACTAL POROUS CELL MEMBRANE
Cardiac tissue is characterized by structural and cellular heterogeneities that play an important role in the cardiac conduction system. Under persistent atrial fibrillation (persAF), electrical and structural remodeling occur simultaneously. The classical mathematical models of cardiac electrophysi...
- Autores:
- Tipo de recurso:
- Fecha de publicación:
- 2020
- Institución:
- Universidad de Medellín
- Repositorio:
- Repositorio UDEM
- Idioma:
- eng
- OAI Identifier:
- oai:repository.udem.edu.co:11407/5904
- Acceso en línea:
- http://hdl.handle.net/11407/5904
- Palabra clave:
- Atrial Electrophysiology
Atrial Fibrillation
Complex Order Derivatives
Fractals
Myocardium Heterogeneities
Cytology
Electrophysiology
Heart
Structural properties
Tissue
Cardiac conductions
Complex-order derivatives
Electrical and structural properties
Electrical propagation
Electrophysiological properties
Mathematical equations
Numerical procedures
Structural remodeling
Fractal dimension
- Rights
- License
- http://purl.org/coar/access_right/c_16ec
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| dc.title.none.fl_str_mv |
A COMPLEX ORDER MODEL of ATRIAL ELECTRICAL PROPAGATION from FRACTAL POROUS CELL MEMBRANE |
| title |
A COMPLEX ORDER MODEL of ATRIAL ELECTRICAL PROPAGATION from FRACTAL POROUS CELL MEMBRANE |
| spellingShingle |
A COMPLEX ORDER MODEL of ATRIAL ELECTRICAL PROPAGATION from FRACTAL POROUS CELL MEMBRANE Atrial Electrophysiology Atrial Fibrillation Complex Order Derivatives Fractals Myocardium Heterogeneities Cytology Electrophysiology Heart Structural properties Tissue Cardiac conductions Complex-order derivatives Electrical and structural properties Electrical propagation Electrophysiological properties Mathematical equations Numerical procedures Structural remodeling Fractal dimension |
| title_short |
A COMPLEX ORDER MODEL of ATRIAL ELECTRICAL PROPAGATION from FRACTAL POROUS CELL MEMBRANE |
| title_full |
A COMPLEX ORDER MODEL of ATRIAL ELECTRICAL PROPAGATION from FRACTAL POROUS CELL MEMBRANE |
| title_fullStr |
A COMPLEX ORDER MODEL of ATRIAL ELECTRICAL PROPAGATION from FRACTAL POROUS CELL MEMBRANE |
| title_full_unstemmed |
A COMPLEX ORDER MODEL of ATRIAL ELECTRICAL PROPAGATION from FRACTAL POROUS CELL MEMBRANE |
| title_sort |
A COMPLEX ORDER MODEL of ATRIAL ELECTRICAL PROPAGATION from FRACTAL POROUS CELL MEMBRANE |
| dc.subject.spa.fl_str_mv |
Atrial Electrophysiology Atrial Fibrillation Complex Order Derivatives Fractals Myocardium Heterogeneities |
| topic |
Atrial Electrophysiology Atrial Fibrillation Complex Order Derivatives Fractals Myocardium Heterogeneities Cytology Electrophysiology Heart Structural properties Tissue Cardiac conductions Complex-order derivatives Electrical and structural properties Electrical propagation Electrophysiological properties Mathematical equations Numerical procedures Structural remodeling Fractal dimension |
| dc.subject.keyword.eng.fl_str_mv |
Cytology Electrophysiology Heart Structural properties Tissue Cardiac conductions Complex-order derivatives Electrical and structural properties Electrical propagation Electrophysiological properties Mathematical equations Numerical procedures Structural remodeling Fractal dimension |
| description |
Cardiac tissue is characterized by structural and cellular heterogeneities that play an important role in the cardiac conduction system. Under persistent atrial fibrillation (persAF), electrical and structural remodeling occur simultaneously. The classical mathematical models of cardiac electrophysiological showed remarkable progress during recent years. Among those models, it is of relevance the standard diffusion mathematical equation, that considers the myocardium as a continuum. However, the modeling of structural properties and their influence on electrical propagation still reveal several limitations. In this paper, a model of cardiac electrical propagation is proposed based on complex order derivatives. By assuming that the myocardium has an underlying fractal process, the complex order dynamics emerges as an important modeling option. In this perspective, the real part of the order corresponds to the fractal dimension, while the imaginary part represents the log-periodic corrections of the fractal dimension. Indeed, the imaginary part in the derivative implies characteristic scales within the cardiac tissue. The analytical and numerical procedures for solving the related equation are presented. The sinus rhythm and persAF conditions are implemented using the Courtemanche formalism. The electrophysiological properties are measured and analyzed on different scales of observation. The results indicate that the complex order modulates the electrophysiology of the atrial system, through the variation of its real and imaginary parts. The combined effect of the two components yields a broad range of electrophysiological conditions. Therefore, the proposed model can be a useful tool for modeling electrical and structural properties during cardiac conduction. © 2020 World Scientific Publishing Company. |
| publishDate |
2020 |
| dc.date.accessioned.none.fl_str_mv |
2021-02-05T14:57:44Z |
| dc.date.available.none.fl_str_mv |
2021-02-05T14:57:44Z |
| 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 |
0218348X |
| dc.identifier.uri.none.fl_str_mv |
http://hdl.handle.net/11407/5904 |
| dc.identifier.doi.none.fl_str_mv |
10.1142/S0218348X20501066 |
| identifier_str_mv |
0218348X 10.1142/S0218348X20501066 |
| url |
http://hdl.handle.net/11407/5904 |
| 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-s2.0-85092934157&doi=10.1142%2fS0218348X20501066&partnerID=40&md5=2bc51c714df3d9a0472daa62a3960d18 |
| dc.relation.citationvolume.none.fl_str_mv |
28 |
| dc.relation.citationissue.none.fl_str_mv |
6 |
| dc.relation.references.none.fl_str_mv |
Kirchhof, P., Benussi, S., Kotecha, D., Ahlsson, A., Atar, D., Casadei, B., Castella, M., Vardas, P., 2016 ESC Guidelines for the management of atrial fibrillation developed in collaboration with EACTS (2016) Europace, 18, pp. 1609-1678 Haissaguerre, M, Jais, P, Shah, D C, Garrigue, S, Takahashi, A., Lavergne, T., Hocini, M., Clementy, J., Electrophysiological End Point for Catheter Ablation of Atrial Fibrillation Initiated From Multiple Pulmonary Venous Foci (2000) Circulation, 101, pp. 1409-1417 Jalife, J., Mechanisms of persistent atrial fibrillation (2014) Curr. Opini. Cardiol, 29, pp. 20-27 Yoshida, K., Aonuma, K., Catheter ablation of atrial fibrillation: Past, present, and future directions (2012) J. Arrhythmia, 28, pp. 83-90 Corradi, D., Atrial fibrillation from the pathologist's perspective (2014) Cardiovasc. Pathol, 23, pp. 71-84 Grandi, E., Workman, A. J., Pandit, S. V., Altered Excitation-Contraction Coupling in Human Chronic Atrial Fibrillation (2012) J. Atr. Fibrillation, 4, pp. 37-53 Workman, A. J., Kane, K. A., Rankin, A. C., The contribution of ionic currents to changes in refractoriness of human atrial myocytes associated with chronic atrial fibrillation (2001) Cardiovasc. Res, 52, pp. 226-235 Burstein, B., Nattel, S., Atrial fibrosis: Mechanisms and clinical relevance in atrial fibrillation (2008) J. Am. Coll. Cardiol, 51, pp. 802-809 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 Clayton, R. H., Bernus, O., Cherry, E. M., Dierckx, H., Fenton, F. H., Mirabella, L., Panfilov, A. V., Zhang, H., Models of cardiac tissue electrophysiology: Progress, challenges and open questions (2011) Progr. Biophys. Mol. Biol, 104, pp. 22-48 Nattel, S., Harada, M., Atrial remodeling and atrial fibrillation: Recent advances and translational perspectives (2014) J. Am. Coll. Cardiol, 63, pp. 2335-2345 Allessie, M., Ausma, J., Schotten, U., Electrical, contractile and structural remodeling during atrial fibrillation (2002) Cardiovascu. Res, 54, pp. 230-246 Vandersickel, N., Watanabe, M., Tao, Q., Fostier, J., Zeppenfeld, K., Panfilov, A. V., Dynamical anchoring of distant arrhythmia sources by fibrotic regions via restructuring of the activation pattern (2018) PLoS Comput. Biol, 14, pp. 1-19 Campos, F. O., Shiferaw, Y., Weber, R., Plank, G., Microscopic isthmuses and fibrosis within the border zone of infarcted hearts promote calcium-mediated ectopy and conduction block (2018) Front. Physiol, 6, pp. 1-14 Vigmond, E., Pashaei, A., Amraoui, S., Cochet andM, H., Hassaguerre. Percolation as a mechanism to explain atrial fractionated electrograms and reentry in a fibrosis model based on imaging data (2016) Heart Rhythm, 13, pp. 1536-1543 Zhan, H.-q., Xia, L., Shou, G.-f., Zang, Y.-l., Liu, F., Crozier, S., Fibroblast proliferation alters cardiac excitation conduction and contraction: A computational study (2014) J. Zhejiang Univ. Sci. B, 15, pp. 225-242 Alonso, S., Bär, M., Reentry near the percolation threshold in a heterogeneous discrete model for cardiac tissue (2013) Phys. Rev. Lett, 110, pp. 1-5 Duverger, J. E., Jacquemet, V., Vinet, A., Comtois, P., In silico study of multicellular automaticity of heterogeneous cardiac cell monolayers: Effects of automaticity strength and structural linear anisotropy (2018) PLoS Computat. Biol, 14, p. e1005978 Deng, D., Murphy, M. J., Hakim, J. B., Franceschi, W. H., Zahid, S., Pashakhanloo, F., Trayanova, N. A., Boyle, P. M., Sensitivity of reentrant driver localization to electrophysiological parameter variability in image-based computational models of persistent atrial fibrillation sustained by a fibrotic substrate (2017) Chaos, 27, p. 093932 Krogh-Madsen, T., Abbott, G. W., Christini, D. J., Effects of electrical and structural remodeling on atrial fibrillation maintenance: A simulation study (2012) PLoS Computa. Biol, 8, p. e1002390 Spach, M. S., Heidlage, J. F., The stochastic nature of cardiac propagation at a microscopic level. electrical description of myocardial architecture and its application to conduction (1995) Circul. Res, 76, pp. 366-380 Lim, H., Cun, W., Wang, Y., Gray, R. A., Glimm, J., The role of conductivity discontinuities in design of cardiac defibrillation (2018) Chaos, 28, p. 013106 Zahid, S., Cochet, H., Boyle, P. M., Schwarz, E. L., Whyte, K. N., Vigmond, E. J., Dubois, R., Trayanova, N. A., Patient-derived models link re-entrant driver localization in atrial fibrillation to fibrosis spatial pattern (2016) Cardiovasc. Res, 110, pp. 443-454 Coudière, Y., Henry, J., Labarthe, S., A two layers monodomain model of cardiac electrophysiology of the atria (2015) J. Math. Biol, 71, pp. 1607-1641 Lin, J., Keener, J. P., Microdomain effects on transverse cardiac propagation (2014) Biophys. J, 106, pp. 925-931 Stinstra, J., Macleod, R., Henriquez, C., Incorporating histology into a 3D microscopic computer model of myocardium to study propagation at a cellular level (2010) Ann. Biomed. Eng, 38, pp. 1399-1414 Liu, F., Turner, I., Anh, V., Yang, Q., Burrage, K., A numerical method for the fractional Fitzhugh-Nagumo monodomain model (2012) Math. Soc, 54, pp. 608-629 Bueno-Orovio, A., Kay, D., Burrage, K., Fourier spectral methods for fractional-in-space reactiondiffusion equations (2014) BIT Numer. Math, 54, pp. 937-954 Cusimano, N., Bueno-Orovio, A., Turner, I., Burrage, K., On the order of the fractional Laplacian in determining the spatio-temporal evolution of a space-fractional model of cardiac electrophysiology (2015) PLoS ONE, 10, p. e0143938 Sun, H., Zhang, Y., Baleanu, D., Chen, W., Chen, Y., A new collection of real world applications of fractional calculus in science and engineering (2018) Commun. Nonlinear Sci. Numer. Simul, 64, pp. 213-231 Sopasakis, P., Sarimveis, H., Macheras, P., Dokoumetzidis, A., Fractional calculus in pharmacokinetics (2018) J. Pharmacokinet. Pharmacodyn, 45, pp. 107-125 Tenreiro Machado, J. A., Kiryakova, V., The chronicles of fractional calculus (2017) Fract. Calc. Appl. Anal, 20, pp. 307-336 Ionescu, C., Lopes, A., Copot, D., Machado, J. A. T., Bates, J. H. T., The role of fractional calculus in modeling biological phenomena: A review (2017) Commun. Nonlinear Sc. Numer. Simul, 51, pp. 141-159 Maione, G., Nigmatullin, R. R., Tenreiro Machado, J. A., Sabatier, J., New challenges in fractional systems 2014 (2015) Math. Prob. Eng, 2015, pp. 1-3 Oldham, K., Spanier, J., The Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order (1974) Mathematics in Science and Engineering, , (Elsevier Science) Miller, K. S., Ross, B., (1993) An Introduction to the Fractional Calculus and Fractional Differential Equations, , (Wiley) Pozrikidis, C., (2016) The Fractional Laplacian, , (Taylor & Francis) Baleanu, D., Fernandez, A., On some new properties of fractional derivatives with Mittag-Leffler kernel (2018) Commun. Nonlinear Sci. Numer. Simul, 59, pp. 444-462 Samko, S. G., Kilbas, A. A., Marichev, O. I., (1993) Fractional Integrals and Derivatives: Theory and Applications, , (CRC) Tarasov, V. E., Map of discrete system into continuous (2006) J. Math. Phys, 47 Tarasov, V. E., Continuous limit of discrete systems with long-range interaction (2006) J. Phys. A: Math. Gene, 39, pp. 14895-14910 Bessonov, L., (1973) Applied Electricity for Engineers, , (Izdat. Mir) Raab, R. E., De Lange, O. L., de Lange, O. L., (2005) Multipole Theory in Electromagnetism: Classical, Quantum, and Symmetry Aspects, with Applications, , Oxford University Press, International Series of Monographs on Physics (OUP Oxford) Tenreiro Machado, J. A., Jesus, I. S., Galhano, A., Cunha, J. B., Fractional order electromagnetics (2006) Signal Process, 86, pp. 2637-2644 Engheta, N., On fractional calculus and fractional multipoles in electromagnetism (1996) IEEE Trans. Antennas Propag, 44, pp. 554-566 Spira, A. W., The nexus in the intercalated disc of the canine heart: Quantitative data for an estimation of its resistance (1971) J. Ultrastruct. Res, 34, pp. 409-425 Weidmann, S., Hodgkin, A. L., The diffusion of radiopotassium across intercalated disks of mammalian cardiac muscle (1966) J. Phys, 187, pp. 323-342 Page, E., Shibata, Y., Permeable junctions between cardiac cells (1981) Ann. Rev. Phys, 43, pp. 431-441 Harris, A. L., Emerging issues of connexin channels: Biophysics fills the gap (2001) Q. Rev.Biophy, 34, pp. 325-472 Prudat, Y., Kucera, J. P., Nonlinear behaviour of conduction and block in cardiac tissue with heterogeneous expression of connexin 43 (2014) Curr. Ther. Res. Clin. Exp, 76, pp. 46-54 Howard Evans, W., Cell communication across gap junctions: A historical perspective and current developments (2015) Biochem. Soc. Trans, 43, pp. 450-459 Hülser, D. F., Eckert, R., Irmer, U., Kriŝciukaitis, A., Mindermann, A., Pleiss, J., Rehkopf, B., Traub, O., Intercellular communication via gap junction channels (1998) Bioelectrochem. Bioenerge, 45, pp. 55-65 Sosinsky, G. E., Nicholson, B. J., Structural organization of gap junction channels (2005) Biochim. Biophys. Acta Biomembr, 1711, pp. 99-125 Berkowitz, B., Klafter, J., Metzler, R., Scher, H., Physical pictures of transport in heterogeneous media: Advection-dispersion, random walk and fractional derivative formulations (2002) Water Res. Res, 38, pp. 1-12 Havlin, S., Ben-Avraham, D., Diffusion in disordered media (2002) Adv. Phys, 51, pp. 187-292 Tarasov, V. E., Zaslavsky, G. M., Fractional dynamics of coupled oscillators with long-range interaction (2006) Chaos, 16, pp. 1-13 Ortigueira, M. D., Machado, J. A. T., On fractional vectorial calculus (2018) Bull. Pol. Acad. Sci. Tech. Sci, 66, pp. 389-402 Tenreiro Machado, J. A., Pinto, C. M.A., Lopes, A. M., A review on the characterization of signals and systems by power law distributions (2015) Signal Process, 107, pp. 246-253 Li, Y., Farrher, G., Kimmich, R., Sub-and superdiffusive molecular displacement laws in disordered porous media probed by nuclear magnetic resonance (2006) Phys. Rev. E, Stat. Nonlinear Soft Matter Phys, 74, pp. 1-7 Kimmich, R., Strange kinetics, porous media, and NMR (2002) Chem. Phys, 284, pp. 253-285 Ben-Avraham, D., Diffusion in disordered media (1991) Chemomet. Intell. Lab. Syst, 10, pp. 117-122 Mandelbrot, B. B., (1983) The Fractal Geometry of Nature Einaudi Paperbacks, , (Henry Holt and Company) Miao, T., Chen, A., Xu, Y., Cheng, S., Yu, B., A fractal permeability model for porous-fracture media with the transfer of fluids from porous matrix to fracture (2019) Fractals, 27, p. 1950121 Zheng, Q., Fan, J., Li, X., Wang, S., Fractal model of gas diffusion in fractured porous media (2018) Fractals, 26, p. 1850065 Cai, J., Wei, W., Hu, X., Wood, D. A., Electrical conductivity models in saturated porous media: A review (2017) Earth-Sci. Rev, 171, pp. 419-433 Wei, W., Cai, J., Hu, X., Han, Q., An electrical conductivity model for fractal porous media (2015) Geophys. Res. Lett, 42, pp. 4833-4840 Tenreiro Machado, J. A., Galhano, A. M. S. F., Fractional order inductive phenomena based on the skin effect (2012) Nonlinear Dyn, 68, pp. 107-115 Amadu, M., Pegg, M. J., A mathematical determination of the pore size distribution and fractal dimension of a porous sample using spontaneous imbibition dynamics theory (2018) J. Pet. Expl. Prod. Technol, 9, pp. 1-9 Amadu, M., Pegg, M. J., Theoretical and experimental determination of the fractal dimension and pore size distribution index of a porous sample using spontaneous imbibition dynamics theory Mumuni (2018) J. Pet. Sci. Eng, 167, pp. 785-795 Zheng, Q., Li, X., Gas diffusion coefficient of fractal porous media by Monte Carlo simulations (2015) Fractals, 23, p. 1550012 Plonsey, R., Barr, R. C., (2007) Bioelectricity: A Quantitative Approach, , (Springer, US) Weinberg, S. H., Spatial discordance and phase reversals during alternate pacing in discrete-time kinematic and cardiomyocyte ionic models (2015) Chaos, 25 Lemay, M., de Lange, E., Kucera, J. P., Uncovering the dynamics of cardiac systems using stochastic pacing and frequency domain analyses (2012) PLoS Comput. Biol, 8, p. e1002399 De Lange, E., Kucera, J. P., The transfer functions of cardiac tissue during stochastic pacing (2009) Biophys. J, 96, pp. 294-311 Méhauté, A. L., Nigmatullin, R. R., Nivanen, L., Flèches du temps et géométrie fractale (1998) Collection Systèmes Complexes, , (Hermès) Nigmatullin, R. R., Le Mehaute, A., Is there geometrical/ physicalmeaning of the fractional integral with complex exponent? (2005) J. Non-Cryst. Solids, 351, pp. 2888-2899 Hartley, T. T, Tomhartleyaolcom, E., Lorenzo, C. F., Adams, J. L., Conjugated-order differintegrals (2005) ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, pp. 1597-1602. , (2005) Sornette, D., Discrete-scale invariance and complex dimensions (1998) Phys. Rep, 297, pp. 239-270 Marchuk, G. I., On the construction and comparison of difference schemes (1968) Apl. Mat, 13, pp. 103-132 Strang, G., On the construction and comparison of difference schemes (1968) J. Numer. Anal, 5, pp. 506-517 Ugarte, J. P., Tobón, C., Lopes, A. M., Tenreiro Machado, J. A., Atrial rotor dynamics under complex fractional order diffusion (2018) Front. Physiol, 9, pp. 1-14 Courtemanche, M., Ramirez, R. J., Nattel, S., Ionic mechanisms underlying human atrial action potential properties: Insights from a mathematical model (1998) Amer. J. Phys, 275, pp. H301-H321 Wilhelms, M., Hettmann, H., Maleckar, M. M., Koivumäki, J. T., Dössel, O., Seemann, G., Benchmarking electrophysiological models of human atrial myocytes (2013) Front. Physiol, 3, pp. 1-16 Xu, Y., Sharma, D., Li, G., Liu, Y., Atrial remodeling: New pathophysiological mechanism of atrial fibrillation (2013) Med. Hypotheses, 80, pp. 53-56 Heijman, J., Algalarrondo, V., Voigt, N., Melka, J., Wehrens, X. H. T., Dobrev, D., Nattel, S., The value of basic research insights into atrial fibrillation mechanisms as a guide to therapeutic innovation: A critical analysis (2016) Cardiovasc. Res, 109, pp. 467-479 Miragoli, M., Gaudesius, G., Rohr, S., Electrotonic modulation of cardiac impulse conduction by myofibroblasts (2006) Circul. Res, 98, pp. 801-810 Bode, F., Kilborn, M., Karasik, P., Franz, M. R., The repolarization-excitability relationship in the human right atrium is unaffected by cycle length, recording site and prior arrhythmias (2001) J. Am. Coll. Cardiol, 37, pp. 920-925 Boutjdir, M., Le Heuzey, J. Y., Lavergne, T., Chauvaud, S., Guize, L., Carpentier, A., Peronneau, P., Inhomogeneity of Cellular Refractoriness in Human Atrium: Factor of Arrhythmia? L'hétérogénéité des périodes réfractaires cellulaires de l'oreillette humaine: Un facteur d'arythmie? (1986) Pac. Clin. Electrophysiol, 9, pp. 1095-1100 Kamalvand, K., Tan, K., Lloyd, G., Gill, J., Bucknall, C., Sulke, N., Alterations in atrial electrophysiology associated with chronic atrial fibrillation in man (1999) Eur. Heart J, 20, pp. 888-895 Bueno-orovio, A., Kay, D., Grau, V., Rodriguez, Blanca, Burrage, Kevin, Soc Interface, J. R., Fractional diffusion models of cardiac electrical propagation: role of structural heterogeneity in dispersion of repolarization (2014) J. R. Soc. Interface, 11, p. 20140352 Spach, M. S., Heidlage, J. F., Dolber, P. C., Barr, R. C., Extracellular discontinuities in cardiac muscle: Evidence for capillary effects on the action potential foot (1998) Circul. Res, 83, pp. 1144-1164 Hanson, B., Suton, P., Elameri, N., Gray, M., Critchley, H., Gill, J. S., Taggart, P., Interaction of activation-repolarization coupling and restitution properties in humans (2009) Circul. Arrhythmia Electrophysiol, 2, pp. 162-170 Boyett, M. R., Honjo, H., Yamamoto, M., Nikmaram, M. R., Niwa, R., Kodama, I., Downward gradient in action potential duration along conduction path in and around the sinoatrial node (1999) Amer. J. Phys. Heart and Circul. Physiol, 276, pp. H686-H698 Li, Z., Liu, Y., Hertervig, E., Kongstad, O., Yuan, S., Regional heterogeneity of right atrial repolarization. Monophasic action potential mapping in swine (2011) Scand. Cardiovasc. J, 45, pp. 336-341 Ridler, M. E., Lee, M., McQueen, D., Peskin, C., Vigmond, E., Arrhythmogenic consequences of action potential duration gradients in the atria (2011) Can. J. Cardiol, 27, pp. 112-119 Hurtado, D. E., Castro, S., Gizzi, A., Computational modeling of non-linear diffusion in cardiac electrophysiology: A novel porous-medium approach (2016) Comput. Methods Appl. Mech. Eng, 300, pp. 70-83 Liebovitch, L. S., Scheurle, D., Rusek, M., Zochowski, M., Fractal methods to analyze ion channel kinetics (2001) Methods, 24, pp. 359-375 Nigmatullin, R. R., Baleanu, D., New relationships connecting a class of fractal objects and fractional integrals in space (2013) Fract. Calc. Appl. Anal, 16, pp. 911-936 Nigmatullin, R. R., Zhang, W., Gubaidullin, I., Accurate relationships between fractals and fractional integrals: New approaches and evaluations (2017) Fract. Calc. Appl. Anal, 20, pp. 1263-1280 Sornette, D., Johansen, A., Arneodo, A., Muzy, J. F., Saleur, H., Complex fractal dimensions describe the hierarchical structure of diffusionlimited-aggregate clusters (1996) Phys. Rev. Lett, 76, pp. 251-254 Mondal, A., Sachse, F. B., Moreno, A. P., Modulation of asymmetric flux in heterotypic gap junctions by pore shape, particle size and charge (2017) Front. Physiol, 8, pp. 1-15 Hall, J. E., Gourdie, R. G., Spatial organization of cardiac gap junctions can affect access resistance (1995) Microsc. Res. Techn, 31, pp. 446-451 Zamir, M., On fractal properties of arterial trees (1999) J. Theor. Biol, 197, pp. 517-526 Zenin, O. K., Kizilova, N. N., Filippova, E. N., Studies on the structure of human coronary vasculature (2007) Biophysics, 52, pp. 499-503 Goldberger, A. L., West, B. J., Fractals in physiology and medicine (1987) Yale J. Biol. Med, 60, pp. 421-435 Goldberger, A. L., Rigney, D. R., West, B. J., Chaos Fractals Human Physiology (1990) Sci. Pict, 262, pp. 42-49 Dickinson, R. B., Guido, S., Tranquillo, R. T., Biased cell migration of fibroblasts exhibiting contact guidance in oriented collagen gels (1994) Ann. Biomed. Eng, 22, pp. 342-356 Nogueira, I. R., Alves, S. G., Ferreira, S. C., Scaling laws in the diffusion limited aggregation of persistent random walkers (2011) Phys. A, Stat.Mech. Appl, 390, pp. 4087-4094 Meerschaert, M. M., Mortensen, J., Wheatcraft, S. W., Fractional vector calculus for fractional advection-dispersion (2006) Phys. A, Stat. Mech. Appl, 367, pp. 181-190 Tarasov, V. E., Fractional vector calculus and fractional Maxwell's equations (2008) Anna. Phys, 323, pp. 2756-2778 Magin, R. L., Abdullah, O., Baleanu, D., Zhou, X. J., Anomalous diffusion expressed through fractional order differential operators in the Bloch-Torrey equation (2008) J. Magn. Reson, 190, pp. 255-270 Qin, S., Liu, F., Turner, I. W., Yang, Q., Yu, Q., Modelling anomalous diffusion using fractional Bloch-Torrey equations on approximate irregular domains (2018) Comput. Math. Appl, 75, pp. 7-21 Yu, Q., Reutens, D., O'Brien, K., Vegh, V., Tissue microstructure features derived from anomalous diffusion measurements in magnetic resonance imaging (2017) Human Brain Mapp, 38, pp. 1068-1081 Bueno-Orovio, A., Teh, I., Schneider, J. E., Burrage, K., Grau, V., Anomalous Diffusion in Cardiac Tissue as an Index of Myocardial Microstructure (2016) IEEE Trans. Med. Imag, 35, pp. 2200-2207 |
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World Scientific |
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Facultad de Ciencias Básicas |
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World Scientific |
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Fractals |
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Repositorio Institucional Universidad de Medellin |
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repositorio@udem.edu.co |
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20202021-02-05T14:57:44Z2021-02-05T14:57:44Z0218348Xhttp://hdl.handle.net/11407/590410.1142/S0218348X20501066Cardiac tissue is characterized by structural and cellular heterogeneities that play an important role in the cardiac conduction system. Under persistent atrial fibrillation (persAF), electrical and structural remodeling occur simultaneously. The classical mathematical models of cardiac electrophysiological showed remarkable progress during recent years. Among those models, it is of relevance the standard diffusion mathematical equation, that considers the myocardium as a continuum. However, the modeling of structural properties and their influence on electrical propagation still reveal several limitations. In this paper, a model of cardiac electrical propagation is proposed based on complex order derivatives. By assuming that the myocardium has an underlying fractal process, the complex order dynamics emerges as an important modeling option. In this perspective, the real part of the order corresponds to the fractal dimension, while the imaginary part represents the log-periodic corrections of the fractal dimension. Indeed, the imaginary part in the derivative implies characteristic scales within the cardiac tissue. The analytical and numerical procedures for solving the related equation are presented. The sinus rhythm and persAF conditions are implemented using the Courtemanche formalism. The electrophysiological properties are measured and analyzed on different scales of observation. The results indicate that the complex order modulates the electrophysiology of the atrial system, through the variation of its real and imaginary parts. The combined effect of the two components yields a broad range of electrophysiological conditions. Therefore, the proposed model can be a useful tool for modeling electrical and structural properties during cardiac conduction. © 2020 World Scientific Publishing Company.engWorld ScientificFacultad de Ciencias Básicashttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85092934157&doi=10.1142%2fS0218348X20501066&partnerID=40&md5=2bc51c714df3d9a0472daa62a3960d18286Kirchhof, P., Benussi, S., Kotecha, D., Ahlsson, A., Atar, D., Casadei, B., Castella, M., Vardas, P., 2016 ESC Guidelines for the management of atrial fibrillation developed in collaboration with EACTS (2016) Europace, 18, pp. 1609-1678Haissaguerre, M, Jais, P, Shah, D C, Garrigue, S, Takahashi, A., Lavergne, T., Hocini, M., Clementy, J., Electrophysiological End Point for Catheter Ablation of Atrial Fibrillation Initiated From Multiple Pulmonary Venous Foci (2000) Circulation, 101, pp. 1409-1417Jalife, J., Mechanisms of persistent atrial fibrillation (2014) Curr. Opini. Cardiol, 29, pp. 20-27Yoshida, K., Aonuma, K., Catheter ablation of atrial fibrillation: Past, present, and future directions (2012) J. Arrhythmia, 28, pp. 83-90Corradi, D., Atrial fibrillation from the pathologist's perspective (2014) Cardiovasc. Pathol, 23, pp. 71-84Grandi, E., Workman, A. J., Pandit, S. V., Altered Excitation-Contraction Coupling in Human Chronic Atrial Fibrillation (2012) J. Atr. Fibrillation, 4, pp. 37-53Workman, A. J., Kane, K. A., Rankin, A. C., The contribution of ionic currents to changes in refractoriness of human atrial myocytes associated with chronic atrial fibrillation (2001) Cardiovasc. Res, 52, pp. 226-235Burstein, B., Nattel, S., Atrial fibrosis: Mechanisms and clinical relevance in atrial fibrillation (2008) J. Am. Coll. Cardiol, 51, pp. 802-809Kallergis, E. M., Goudis, C. A., Vardas, P. E., Atrial fibrillation: A progressive atrial myopathy or a distinct disease? (2014) Int. J. Cardiol, 171, pp. 126-133Clayton, R. H., Bernus, O., Cherry, E. M., Dierckx, H., Fenton, F. H., Mirabella, L., Panfilov, A. V., Zhang, H., Models of cardiac tissue electrophysiology: Progress, challenges and open questions (2011) Progr. Biophys. Mol. Biol, 104, pp. 22-48Nattel, S., Harada, M., Atrial remodeling and atrial fibrillation: Recent advances and translational perspectives (2014) J. Am. Coll. Cardiol, 63, pp. 2335-2345Allessie, M., Ausma, J., Schotten, U., Electrical, contractile and structural remodeling during atrial fibrillation (2002) Cardiovascu. Res, 54, pp. 230-246Vandersickel, N., Watanabe, M., Tao, Q., Fostier, J., Zeppenfeld, K., Panfilov, A. V., Dynamical anchoring of distant arrhythmia sources by fibrotic regions via restructuring of the activation pattern (2018) PLoS Comput. Biol, 14, pp. 1-19Campos, F. O., Shiferaw, Y., Weber, R., Plank, G., Microscopic isthmuses and fibrosis within the border zone of infarcted hearts promote calcium-mediated ectopy and conduction block (2018) Front. Physiol, 6, pp. 1-14Vigmond, E., Pashaei, A., Amraoui, S., Cochet andM, H., Hassaguerre. Percolation as a mechanism to explain atrial fractionated electrograms and reentry in a fibrosis model based on imaging data (2016) Heart Rhythm, 13, pp. 1536-1543Zhan, H.-q., Xia, L., Shou, G.-f., Zang, Y.-l., Liu, F., Crozier, S., Fibroblast proliferation alters cardiac excitation conduction and contraction: A computational study (2014) J. Zhejiang Univ. Sci. B, 15, pp. 225-242Alonso, S., Bär, M., Reentry near the percolation threshold in a heterogeneous discrete model for cardiac tissue (2013) Phys. Rev. Lett, 110, pp. 1-5Duverger, J. E., Jacquemet, V., Vinet, A., Comtois, P., In silico study of multicellular automaticity of heterogeneous cardiac cell monolayers: Effects of automaticity strength and structural linear anisotropy (2018) PLoS Computat. Biol, 14, p. e1005978Deng, D., Murphy, M. J., Hakim, J. B., Franceschi, W. H., Zahid, S., Pashakhanloo, F., Trayanova, N. A., Boyle, P. M., Sensitivity of reentrant driver localization to electrophysiological parameter variability in image-based computational models of persistent atrial fibrillation sustained by a fibrotic substrate (2017) Chaos, 27, p. 093932Krogh-Madsen, T., Abbott, G. W., Christini, D. J., Effects of electrical and structural remodeling on atrial fibrillation maintenance: A simulation study (2012) PLoS Computa. Biol, 8, p. e1002390Spach, M. S., Heidlage, J. F., The stochastic nature of cardiac propagation at a microscopic level. electrical description of myocardial architecture and its application to conduction (1995) Circul. Res, 76, pp. 366-380Lim, H., Cun, W., Wang, Y., Gray, R. A., Glimm, J., The role of conductivity discontinuities in design of cardiac defibrillation (2018) Chaos, 28, p. 013106Zahid, S., Cochet, H., Boyle, P. M., Schwarz, E. L., Whyte, K. N., Vigmond, E. J., Dubois, R., Trayanova, N. A., Patient-derived models link re-entrant driver localization in atrial fibrillation to fibrosis spatial pattern (2016) Cardiovasc. Res, 110, pp. 443-454Coudière, Y., Henry, J., Labarthe, S., A two layers monodomain model of cardiac electrophysiology of the atria (2015) J. Math. Biol, 71, pp. 1607-1641Lin, J., Keener, J. P., Microdomain effects on transverse cardiac propagation (2014) Biophys. J, 106, pp. 925-931Stinstra, J., Macleod, R., Henriquez, C., Incorporating histology into a 3D microscopic computer model of myocardium to study propagation at a cellular level (2010) Ann. Biomed. Eng, 38, pp. 1399-1414Liu, F., Turner, I., Anh, V., Yang, Q., Burrage, K., A numerical method for the fractional Fitzhugh-Nagumo monodomain model (2012) Math. Soc, 54, pp. 608-629Bueno-Orovio, A., Kay, D., Burrage, K., Fourier spectral methods for fractional-in-space reactiondiffusion equations (2014) BIT Numer. Math, 54, pp. 937-954Cusimano, N., Bueno-Orovio, A., Turner, I., Burrage, K., On the order of the fractional Laplacian in determining the spatio-temporal evolution of a space-fractional model of cardiac electrophysiology (2015) PLoS ONE, 10, p. e0143938Sun, H., Zhang, Y., Baleanu, D., Chen, W., Chen, Y., A new collection of real world applications of fractional calculus in science and engineering (2018) Commun. Nonlinear Sci. Numer. Simul, 64, pp. 213-231Sopasakis, P., Sarimveis, H., Macheras, P., Dokoumetzidis, A., Fractional calculus in pharmacokinetics (2018) J. Pharmacokinet. Pharmacodyn, 45, pp. 107-125Tenreiro Machado, J. A., Kiryakova, V., The chronicles of fractional calculus (2017) Fract. Calc. Appl. Anal, 20, pp. 307-336Ionescu, C., Lopes, A., Copot, D., Machado, J. A. T., Bates, J. H. T., The role of fractional calculus in modeling biological phenomena: A review (2017) Commun. Nonlinear Sc. Numer. Simul, 51, pp. 141-159Maione, G., Nigmatullin, R. R., Tenreiro Machado, J. A., Sabatier, J., New challenges in fractional systems 2014 (2015) Math. Prob. Eng, 2015, pp. 1-3Oldham, K., Spanier, J., The Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order (1974) Mathematics in Science and Engineering, , (Elsevier Science)Miller, K. S., Ross, B., (1993) An Introduction to the Fractional Calculus and Fractional Differential Equations, , (Wiley)Pozrikidis, C., (2016) The Fractional Laplacian, , (Taylor & Francis)Baleanu, D., Fernandez, A., On some new properties of fractional derivatives with Mittag-Leffler kernel (2018) Commun. Nonlinear Sci. Numer. Simul, 59, pp. 444-462Samko, S. G., Kilbas, A. A., Marichev, O. I., (1993) Fractional Integrals and Derivatives: Theory and Applications, , (CRC)Tarasov, V. E., Map of discrete system into continuous (2006) J. Math. Phys, 47Tarasov, V. E., Continuous limit of discrete systems with long-range interaction (2006) J. Phys. A: Math. Gene, 39, pp. 14895-14910Bessonov, L., (1973) Applied Electricity for Engineers, , (Izdat. Mir)Raab, R. E., De Lange, O. L., de Lange, O. L., (2005) Multipole Theory in Electromagnetism: Classical, Quantum, and Symmetry Aspects, with Applications, , Oxford University Press, International Series of Monographs on Physics (OUP Oxford)Tenreiro Machado, J. A., Jesus, I. S., Galhano, A., Cunha, J. B., Fractional order electromagnetics (2006) Signal Process, 86, pp. 2637-2644Engheta, N., On fractional calculus and fractional multipoles in electromagnetism (1996) IEEE Trans. Antennas Propag, 44, pp. 554-566Spira, A. W., The nexus in the intercalated disc of the canine heart: Quantitative data for an estimation of its resistance (1971) J. Ultrastruct. Res, 34, pp. 409-425Weidmann, S., Hodgkin, A. L., The diffusion of radiopotassium across intercalated disks of mammalian cardiac muscle (1966) J. Phys, 187, pp. 323-342Page, E., Shibata, Y., Permeable junctions between cardiac cells (1981) Ann. Rev. Phys, 43, pp. 431-441Harris, A. L., Emerging issues of connexin channels: Biophysics fills the gap (2001) Q. Rev.Biophy, 34, pp. 325-472Prudat, Y., Kucera, J. P., Nonlinear behaviour of conduction and block in cardiac tissue with heterogeneous expression of connexin 43 (2014) Curr. Ther. Res. Clin. Exp, 76, pp. 46-54Howard Evans, W., Cell communication across gap junctions: A historical perspective and current developments (2015) Biochem. Soc. Trans, 43, pp. 450-459Hülser, D. F., Eckert, R., Irmer, U., Kriŝciukaitis, A., Mindermann, A., Pleiss, J., Rehkopf, B., Traub, O., Intercellular communication via gap junction channels (1998) Bioelectrochem. Bioenerge, 45, pp. 55-65Sosinsky, G. E., Nicholson, B. J., Structural organization of gap junction channels (2005) Biochim. Biophys. Acta Biomembr, 1711, pp. 99-125Berkowitz, B., Klafter, J., Metzler, R., Scher, H., Physical pictures of transport in heterogeneous media: Advection-dispersion, random walk and fractional derivative formulations (2002) Water Res. Res, 38, pp. 1-12Havlin, S., Ben-Avraham, D., Diffusion in disordered media (2002) Adv. Phys, 51, pp. 187-292Tarasov, V. E., Zaslavsky, G. M., Fractional dynamics of coupled oscillators with long-range interaction (2006) Chaos, 16, pp. 1-13Ortigueira, M. D., Machado, J. A. T., On fractional vectorial calculus (2018) Bull. Pol. Acad. Sci. Tech. Sci, 66, pp. 389-402Tenreiro Machado, J. A., Pinto, C. M.A., Lopes, A. M., A review on the characterization of signals and systems by power law distributions (2015) Signal Process, 107, pp. 246-253Li, Y., Farrher, G., Kimmich, R., Sub-and superdiffusive molecular displacement laws in disordered porous media probed by nuclear magnetic resonance (2006) Phys. Rev. E, Stat. Nonlinear Soft Matter Phys, 74, pp. 1-7Kimmich, R., Strange kinetics, porous media, and NMR (2002) Chem. Phys, 284, pp. 253-285Ben-Avraham, D., Diffusion in disordered media (1991) Chemomet. Intell. Lab. Syst, 10, pp. 117-122Mandelbrot, B. B., (1983) The Fractal Geometry of Nature Einaudi Paperbacks, , (Henry Holt and Company)Miao, T., Chen, A., Xu, Y., Cheng, S., Yu, B., A fractal permeability model for porous-fracture media with the transfer of fluids from porous matrix to fracture (2019) Fractals, 27, p. 1950121Zheng, Q., Fan, J., Li, X., Wang, S., Fractal model of gas diffusion in fractured porous media (2018) Fractals, 26, p. 1850065Cai, J., Wei, W., Hu, X., Wood, D. A., Electrical conductivity models in saturated porous media: A review (2017) Earth-Sci. Rev, 171, pp. 419-433Wei, W., Cai, J., Hu, X., Han, Q., An electrical conductivity model for fractal porous media (2015) Geophys. Res. Lett, 42, pp. 4833-4840Tenreiro Machado, J. A., Galhano, A. M. S. F., Fractional order inductive phenomena based on the skin effect (2012) Nonlinear Dyn, 68, pp. 107-115Amadu, M., Pegg, M. J., A mathematical determination of the pore size distribution and fractal dimension of a porous sample using spontaneous imbibition dynamics theory (2018) J. Pet. Expl. Prod. Technol, 9, pp. 1-9Amadu, M., Pegg, M. J., Theoretical and experimental determination of the fractal dimension and pore size distribution index of a porous sample using spontaneous imbibition dynamics theory Mumuni (2018) J. Pet. Sci. Eng, 167, pp. 785-795Zheng, Q., Li, X., Gas diffusion coefficient of fractal porous media by Monte Carlo simulations (2015) Fractals, 23, p. 1550012Plonsey, R., Barr, R. C., (2007) Bioelectricity: A Quantitative Approach, , (Springer, US)Weinberg, S. H., Spatial discordance and phase reversals during alternate pacing in discrete-time kinematic and cardiomyocyte ionic models (2015) Chaos, 25Lemay, M., de Lange, E., Kucera, J. P., Uncovering the dynamics of cardiac systems using stochastic pacing and frequency domain analyses (2012) PLoS Comput. Biol, 8, p. e1002399De Lange, E., Kucera, J. P., The transfer functions of cardiac tissue during stochastic pacing (2009) Biophys. J, 96, pp. 294-311Méhauté, A. L., Nigmatullin, R. R., Nivanen, L., Flèches du temps et géométrie fractale (1998) Collection Systèmes Complexes, , (Hermès)Nigmatullin, R. R., Le Mehaute, A., Is there geometrical/ physicalmeaning of the fractional integral with complex exponent? (2005) J. Non-Cryst. Solids, 351, pp. 2888-2899Hartley, T. T, Tomhartleyaolcom, E., Lorenzo, C. F., Adams, J. L., Conjugated-order differintegrals (2005) ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, pp. 1597-1602. , (2005)Sornette, D., Discrete-scale invariance and complex dimensions (1998) Phys. Rep, 297, pp. 239-270Marchuk, G. I., On the construction and comparison of difference schemes (1968) Apl. Mat, 13, pp. 103-132Strang, G., On the construction and comparison of difference schemes (1968) J. Numer. Anal, 5, pp. 506-517Ugarte, J. P., Tobón, C., Lopes, A. M., Tenreiro Machado, J. A., Atrial rotor dynamics under complex fractional order diffusion (2018) Front. Physiol, 9, pp. 1-14Courtemanche, M., Ramirez, R. J., Nattel, S., Ionic mechanisms underlying human atrial action potential properties: Insights from a mathematical model (1998) Amer. J. Phys, 275, pp. H301-H321Wilhelms, M., Hettmann, H., Maleckar, M. M., Koivumäki, J. T., Dössel, O., Seemann, G., Benchmarking electrophysiological models of human atrial myocytes (2013) Front. Physiol, 3, pp. 1-16Xu, Y., Sharma, D., Li, G., Liu, Y., Atrial remodeling: New pathophysiological mechanism of atrial fibrillation (2013) Med. Hypotheses, 80, pp. 53-56Heijman, J., Algalarrondo, V., Voigt, N., Melka, J., Wehrens, X. H. T., Dobrev, D., Nattel, S., The value of basic research insights into atrial fibrillation mechanisms as a guide to therapeutic innovation: A critical analysis (2016) Cardiovasc. Res, 109, pp. 467-479Miragoli, M., Gaudesius, G., Rohr, S., Electrotonic modulation of cardiac impulse conduction by myofibroblasts (2006) Circul. Res, 98, pp. 801-810Bode, F., Kilborn, M., Karasik, P., Franz, M. R., The repolarization-excitability relationship in the human right atrium is unaffected by cycle length, recording site and prior arrhythmias (2001) J. Am. Coll. Cardiol, 37, pp. 920-925Boutjdir, M., Le Heuzey, J. Y., Lavergne, T., Chauvaud, S., Guize, L., Carpentier, A., Peronneau, P., Inhomogeneity of Cellular Refractoriness in Human Atrium: Factor of Arrhythmia? L'hétérogénéité des périodes réfractaires cellulaires de l'oreillette humaine: Un facteur d'arythmie? (1986) Pac. Clin. Electrophysiol, 9, pp. 1095-1100Kamalvand, K., Tan, K., Lloyd, G., Gill, J., Bucknall, C., Sulke, N., Alterations in atrial electrophysiology associated with chronic atrial fibrillation in man (1999) Eur. Heart J, 20, pp. 888-895Bueno-orovio, A., Kay, D., Grau, V., Rodriguez, Blanca, Burrage, Kevin, Soc Interface, J. R., Fractional diffusion models of cardiac electrical propagation: role of structural heterogeneity in dispersion of repolarization (2014) J. R. Soc. Interface, 11, p. 20140352Spach, M. S., Heidlage, J. F., Dolber, P. C., Barr, R. C., Extracellular discontinuities in cardiac muscle: Evidence for capillary effects on the action potential foot (1998) Circul. Res, 83, pp. 1144-1164Hanson, B., Suton, P., Elameri, N., Gray, M., Critchley, H., Gill, J. S., Taggart, P., Interaction of activation-repolarization coupling and restitution properties in humans (2009) Circul. Arrhythmia Electrophysiol, 2, pp. 162-170Boyett, M. R., Honjo, H., Yamamoto, M., Nikmaram, M. R., Niwa, R., Kodama, I., Downward gradient in action potential duration along conduction path in and around the sinoatrial node (1999) Amer. J. Phys. Heart and Circul. Physiol, 276, pp. H686-H698Li, Z., Liu, Y., Hertervig, E., Kongstad, O., Yuan, S., Regional heterogeneity of right atrial repolarization. Monophasic action potential mapping in swine (2011) Scand. Cardiovasc. J, 45, pp. 336-341Ridler, M. E., Lee, M., McQueen, D., Peskin, C., Vigmond, E., Arrhythmogenic consequences of action potential duration gradients in the atria (2011) Can. J. Cardiol, 27, pp. 112-119Hurtado, D. E., Castro, S., Gizzi, A., Computational modeling of non-linear diffusion in cardiac electrophysiology: A novel porous-medium approach (2016) Comput. Methods Appl. Mech. Eng, 300, pp. 70-83Liebovitch, L. S., Scheurle, D., Rusek, M., Zochowski, M., Fractal methods to analyze ion channel kinetics (2001) Methods, 24, pp. 359-375Nigmatullin, R. R., Baleanu, D., New relationships connecting a class of fractal objects and fractional integrals in space (2013) Fract. Calc. Appl. Anal, 16, pp. 911-936Nigmatullin, R. R., Zhang, W., Gubaidullin, I., Accurate relationships between fractals and fractional integrals: New approaches and evaluations (2017) Fract. Calc. Appl. Anal, 20, pp. 1263-1280Sornette, D., Johansen, A., Arneodo, A., Muzy, J. F., Saleur, H., Complex fractal dimensions describe the hierarchical structure of diffusionlimited-aggregate clusters (1996) Phys. Rev. Lett, 76, pp. 251-254Mondal, A., Sachse, F. B., Moreno, A. P., Modulation of asymmetric flux in heterotypic gap junctions by pore shape, particle size and charge (2017) Front. Physiol, 8, pp. 1-15Hall, J. E., Gourdie, R. G., Spatial organization of cardiac gap junctions can affect access resistance (1995) Microsc. Res. Techn, 31, pp. 446-451Zamir, M., On fractal properties of arterial trees (1999) J. Theor. Biol, 197, pp. 517-526Zenin, O. K., Kizilova, N. N., Filippova, E. N., Studies on the structure of human coronary vasculature (2007) Biophysics, 52, pp. 499-503Goldberger, A. L., West, B. J., Fractals in physiology and medicine (1987) Yale J. Biol. Med, 60, pp. 421-435Goldberger, A. L., Rigney, D. R., West, B. J., Chaos Fractals Human Physiology (1990) Sci. Pict, 262, pp. 42-49Dickinson, R. B., Guido, S., Tranquillo, R. T., Biased cell migration of fibroblasts exhibiting contact guidance in oriented collagen gels (1994) Ann. Biomed. Eng, 22, pp. 342-356Nogueira, I. R., Alves, S. G., Ferreira, S. C., Scaling laws in the diffusion limited aggregation of persistent random walkers (2011) Phys. A, Stat.Mech. Appl, 390, pp. 4087-4094Meerschaert, M. M., Mortensen, J., Wheatcraft, S. W., Fractional vector calculus for fractional advection-dispersion (2006) Phys. A, Stat. Mech. Appl, 367, pp. 181-190Tarasov, V. E., Fractional vector calculus and fractional Maxwell's equations (2008) Anna. Phys, 323, pp. 2756-2778Magin, R. L., Abdullah, O., Baleanu, D., Zhou, X. J., Anomalous diffusion expressed through fractional order differential operators in the Bloch-Torrey equation (2008) J. Magn. Reson, 190, pp. 255-270Qin, S., Liu, F., Turner, I. W., Yang, Q., Yu, Q., Modelling anomalous diffusion using fractional Bloch-Torrey equations on approximate irregular domains (2018) Comput. Math. Appl, 75, pp. 7-21Yu, Q., Reutens, D., O'Brien, K., Vegh, V., Tissue microstructure features derived from anomalous diffusion measurements in magnetic resonance imaging (2017) Human Brain Mapp, 38, pp. 1068-1081Bueno-Orovio, A., Teh, I., Schneider, J. E., Burrage, K., Grau, V., Anomalous Diffusion in Cardiac Tissue as an Index of Myocardial Microstructure (2016) IEEE Trans. Med. Imag, 35, pp. 2200-2207FractalsAtrial ElectrophysiologyAtrial FibrillationComplex Order DerivativesFractalsMyocardium HeterogeneitiesCytologyElectrophysiologyHeartStructural propertiesTissueCardiac conductionsComplex-order derivativesElectrical and structural propertiesElectrical propagationElectrophysiological propertiesMathematical equationsNumerical proceduresStructural remodelingFractal dimensionA COMPLEX ORDER MODEL of ATRIAL ELECTRICAL PROPAGATION from FRACTAL POROUS CELL MEMBRANEArticleinfo: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, Facultad de Ingenieriás, Universidad de San Buenaventura, Medellín, ColombiaTobón, C., MATBIOM, Facultad de Ciencias Básicas, Universidad de Medellín, Medellín, ColombiaLopes, A.M., UISPA-LAETA/INEGI, Faculty of Engineering, University of Porto, Porto, PortugalMachado, J.A.T., Institute of Engineering, Polytechnic of Porto, Dept. of Electrical Engineering, Porto, Portugalhttp://purl.org/coar/access_right/c_16ecUgarte J.P.Tobón C.Lopes A.M.Machado J.A.T.11407/5904oai:repository.udem.edu.co:11407/59042021-02-05 09:57:44.844Repositorio Institucional Universidad de Medellinrepositorio@udem.edu.co |