Show simple item record

dc.creatorUgarte J.P.
dc.creatorTobón C.
dc.creatorLopes A.M.
dc.creatorMachado J.A.T.
dc.date2020
dc.date.accessioned2021-02-05T14:57:44Z
dc.date.available2021-02-05T14:57:44Z
dc.identifier.issn0218348X
dc.identifier.urihttp://hdl.handle.net/11407/5904
dc.descriptionCardiac 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.
dc.language.isoeng
dc.publisherWorld Scientific
dc.relation.isversionofhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85092934157&doi=10.1142%2fS0218348X20501066&partnerID=40&md5=2bc51c714df3d9a0472daa62a3960d18
dc.sourceFractals
dc.subjectAtrial Electrophysiologyspa
dc.subjectAtrial Fibrillationspa
dc.subjectComplex Order Derivativesspa
dc.subjectFractalsspa
dc.subjectMyocardium Heterogeneitiesspa
dc.titleA COMPLEX ORDER MODEL of ATRIAL ELECTRICAL PROPAGATION from FRACTAL POROUS CELL MEMBRANE
dc.typeArticleeng
dc.rights.accessrightsinfo:eu-repo/semantics/restrictedAccess
dc.identifier.doi10.1142/S0218348X20501066
dc.subject.keywordCytologyeng
dc.subject.keywordElectrophysiologyeng
dc.subject.keywordHearteng
dc.subject.keywordStructural propertieseng
dc.subject.keywordTissueeng
dc.subject.keywordCardiac conductionseng
dc.subject.keywordComplex-order derivativeseng
dc.subject.keywordElectrical and structural propertieseng
dc.subject.keywordElectrical propagationeng
dc.subject.keywordElectrophysiological propertieseng
dc.subject.keywordMathematical equationseng
dc.subject.keywordNumerical procedureseng
dc.subject.keywordStructural remodelingeng
dc.subject.keywordFractal dimensioneng
dc.relation.citationvolume28
dc.relation.citationissue6
dc.publisher.facultyFacultad de Ciencias Básicasspa
dc.affiliationUgarte, J.P., GIMSC, Facultad de Ingenieriás, Universidad de San Buenaventura, Medellín, Colombia
dc.affiliationTobón, C., MATBIOM, Facultad de Ciencias Básicas, Universidad de Medellín, Medellín, Colombia
dc.affiliationLopes, A.M., UISPA-LAETA/INEGI, Faculty of Engineering, University of Porto, Porto, Portugal
dc.affiliationMachado, J.A.T., Institute of Engineering, Polytechnic of Porto, Dept. of Electrical Engineering, Porto, Portugal
dc.relation.referencesKirchhof, 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
dc.relation.referencesHaissaguerre, 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
dc.relation.referencesJalife, J., Mechanisms of persistent atrial fibrillation (2014) Curr. Opini. Cardiol, 29, pp. 20-27
dc.relation.referencesYoshida, K., Aonuma, K., Catheter ablation of atrial fibrillation: Past, present, and future directions (2012) J. Arrhythmia, 28, pp. 83-90
dc.relation.referencesCorradi, D., Atrial fibrillation from the pathologist's perspective (2014) Cardiovasc. Pathol, 23, pp. 71-84
dc.relation.referencesGrandi, E., Workman, A. J., Pandit, S. V., Altered Excitation-Contraction Coupling in Human Chronic Atrial Fibrillation (2012) J. Atr. Fibrillation, 4, pp. 37-53
dc.relation.referencesWorkman, 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
dc.relation.referencesBurstein, B., Nattel, S., Atrial fibrosis: Mechanisms and clinical relevance in atrial fibrillation (2008) J. Am. Coll. Cardiol, 51, pp. 802-809
dc.relation.referencesKallergis, 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
dc.relation.referencesClayton, 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
dc.relation.referencesNattel, S., Harada, M., Atrial remodeling and atrial fibrillation: Recent advances and translational perspectives (2014) J. Am. Coll. Cardiol, 63, pp. 2335-2345
dc.relation.referencesAllessie, M., Ausma, J., Schotten, U., Electrical, contractile and structural remodeling during atrial fibrillation (2002) Cardiovascu. Res, 54, pp. 230-246
dc.relation.referencesVandersickel, 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
dc.relation.referencesCampos, 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
dc.relation.referencesVigmond, 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
dc.relation.referencesZhan, 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
dc.relation.referencesAlonso, S., Bär, M., Reentry near the percolation threshold in a heterogeneous discrete model for cardiac tissue (2013) Phys. Rev. Lett, 110, pp. 1-5
dc.relation.referencesDuverger, 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
dc.relation.referencesDeng, 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
dc.relation.referencesKrogh-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
dc.relation.referencesSpach, 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
dc.relation.referencesLim, 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
dc.relation.referencesZahid, 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
dc.relation.referencesCoudière, Y., Henry, J., Labarthe, S., A two layers monodomain model of cardiac electrophysiology of the atria (2015) J. Math. Biol, 71, pp. 1607-1641
dc.relation.referencesLin, J., Keener, J. P., Microdomain effects on transverse cardiac propagation (2014) Biophys. J, 106, pp. 925-931
dc.relation.referencesStinstra, 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
dc.relation.referencesLiu, 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
dc.relation.referencesBueno-Orovio, A., Kay, D., Burrage, K., Fourier spectral methods for fractional-in-space reactiondiffusion equations (2014) BIT Numer. Math, 54, pp. 937-954
dc.relation.referencesCusimano, 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
dc.relation.referencesSun, 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
dc.relation.referencesSopasakis, P., Sarimveis, H., Macheras, P., Dokoumetzidis, A., Fractional calculus in pharmacokinetics (2018) J. Pharmacokinet. Pharmacodyn, 45, pp. 107-125
dc.relation.referencesTenreiro Machado, J. A., Kiryakova, V., The chronicles of fractional calculus (2017) Fract. Calc. Appl. Anal, 20, pp. 307-336
dc.relation.referencesIonescu, 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
dc.relation.referencesMaione, G., Nigmatullin, R. R., Tenreiro Machado, J. A., Sabatier, J., New challenges in fractional systems 2014 (2015) Math. Prob. Eng, 2015, pp. 1-3
dc.relation.referencesOldham, K., Spanier, J., The Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order (1974) Mathematics in Science and Engineering, , (Elsevier Science)
dc.relation.referencesMiller, K. S., Ross, B., (1993) An Introduction to the Fractional Calculus and Fractional Differential Equations, , (Wiley)
dc.relation.referencesPozrikidis, C., (2016) The Fractional Laplacian, , (Taylor & Francis)
dc.relation.referencesBaleanu, D., Fernandez, A., On some new properties of fractional derivatives with Mittag-Leffler kernel (2018) Commun. Nonlinear Sci. Numer. Simul, 59, pp. 444-462
dc.relation.referencesSamko, S. G., Kilbas, A. A., Marichev, O. I., (1993) Fractional Integrals and Derivatives: Theory and Applications, , (CRC)
dc.relation.referencesTarasov, V. E., Map of discrete system into continuous (2006) J. Math. Phys, 47
dc.relation.referencesTarasov, V. E., Continuous limit of discrete systems with long-range interaction (2006) J. Phys. A: Math. Gene, 39, pp. 14895-14910
dc.relation.referencesBessonov, L., (1973) Applied Electricity for Engineers, , (Izdat. Mir)
dc.relation.referencesRaab, 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)
dc.relation.referencesTenreiro Machado, J. A., Jesus, I. S., Galhano, A., Cunha, J. B., Fractional order electromagnetics (2006) Signal Process, 86, pp. 2637-2644
dc.relation.referencesEngheta, N., On fractional calculus and fractional multipoles in electromagnetism (1996) IEEE Trans. Antennas Propag, 44, pp. 554-566
dc.relation.referencesSpira, 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
dc.relation.referencesWeidmann, S., Hodgkin, A. L., The diffusion of radiopotassium across intercalated disks of mammalian cardiac muscle (1966) J. Phys, 187, pp. 323-342
dc.relation.referencesPage, E., Shibata, Y., Permeable junctions between cardiac cells (1981) Ann. Rev. Phys, 43, pp. 431-441
dc.relation.referencesHarris, A. L., Emerging issues of connexin channels: Biophysics fills the gap (2001) Q. Rev.Biophy, 34, pp. 325-472
dc.relation.referencesPrudat, 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
dc.relation.referencesHoward Evans, W., Cell communication across gap junctions: A historical perspective and current developments (2015) Biochem. Soc. Trans, 43, pp. 450-459
dc.relation.referencesHülser, 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
dc.relation.referencesSosinsky, G. E., Nicholson, B. J., Structural organization of gap junction channels (2005) Biochim. Biophys. Acta Biomembr, 1711, pp. 99-125
dc.relation.referencesBerkowitz, 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
dc.relation.referencesHavlin, S., Ben-Avraham, D., Diffusion in disordered media (2002) Adv. Phys, 51, pp. 187-292
dc.relation.referencesTarasov, V. E., Zaslavsky, G. M., Fractional dynamics of coupled oscillators with long-range interaction (2006) Chaos, 16, pp. 1-13
dc.relation.referencesOrtigueira, M. D., Machado, J. A. T., On fractional vectorial calculus (2018) Bull. Pol. Acad. Sci. Tech. Sci, 66, pp. 389-402
dc.relation.referencesTenreiro 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
dc.relation.referencesLi, 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
dc.relation.referencesKimmich, R., Strange kinetics, porous media, and NMR (2002) Chem. Phys, 284, pp. 253-285
dc.relation.referencesBen-Avraham, D., Diffusion in disordered media (1991) Chemomet. Intell. Lab. Syst, 10, pp. 117-122
dc.relation.referencesMandelbrot, B. B., (1983) The Fractal Geometry of Nature Einaudi Paperbacks, , (Henry Holt and Company)
dc.relation.referencesMiao, 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
dc.relation.referencesZheng, Q., Fan, J., Li, X., Wang, S., Fractal model of gas diffusion in fractured porous media (2018) Fractals, 26, p. 1850065
dc.relation.referencesCai, 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
dc.relation.referencesWei, W., Cai, J., Hu, X., Han, Q., An electrical conductivity model for fractal porous media (2015) Geophys. Res. Lett, 42, pp. 4833-4840
dc.relation.referencesTenreiro Machado, J. A., Galhano, A. M. S. F., Fractional order inductive phenomena based on the skin effect (2012) Nonlinear Dyn, 68, pp. 107-115
dc.relation.referencesAmadu, 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
dc.relation.referencesAmadu, 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
dc.relation.referencesZheng, Q., Li, X., Gas diffusion coefficient of fractal porous media by Monte Carlo simulations (2015) Fractals, 23, p. 1550012
dc.relation.referencesPlonsey, R., Barr, R. C., (2007) Bioelectricity: A Quantitative Approach, , (Springer, US)
dc.relation.referencesWeinberg, S. H., Spatial discordance and phase reversals during alternate pacing in discrete-time kinematic and cardiomyocyte ionic models (2015) Chaos, 25
dc.relation.referencesLemay, 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
dc.relation.referencesDe Lange, E., Kucera, J. P., The transfer functions of cardiac tissue during stochastic pacing (2009) Biophys. J, 96, pp. 294-311
dc.relation.referencesMéhauté, A. L., Nigmatullin, R. R., Nivanen, L., Flèches du temps et géométrie fractale (1998) Collection Systèmes Complexes, , (Hermès)
dc.relation.referencesNigmatullin, 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
dc.relation.referencesHartley, 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)
dc.relation.referencesSornette, D., Discrete-scale invariance and complex dimensions (1998) Phys. Rep, 297, pp. 239-270
dc.relation.referencesMarchuk, G. I., On the construction and comparison of difference schemes (1968) Apl. Mat, 13, pp. 103-132
dc.relation.referencesStrang, G., On the construction and comparison of difference schemes (1968) J. Numer. Anal, 5, pp. 506-517
dc.relation.referencesUgarte, 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
dc.relation.referencesCourtemanche, 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
dc.relation.referencesWilhelms, 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
dc.relation.referencesXu, Y., Sharma, D., Li, G., Liu, Y., Atrial remodeling: New pathophysiological mechanism of atrial fibrillation (2013) Med. Hypotheses, 80, pp. 53-56
dc.relation.referencesHeijman, 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
dc.relation.referencesMiragoli, M., Gaudesius, G., Rohr, S., Electrotonic modulation of cardiac impulse conduction by myofibroblasts (2006) Circul. Res, 98, pp. 801-810
dc.relation.referencesBode, 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
dc.relation.referencesBoutjdir, 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
dc.relation.referencesKamalvand, 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
dc.relation.referencesBueno-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
dc.relation.referencesSpach, 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
dc.relation.referencesHanson, 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
dc.relation.referencesBoyett, 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
dc.relation.referencesLi, 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
dc.relation.referencesRidler, 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
dc.relation.referencesHurtado, 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
dc.relation.referencesLiebovitch, L. S., Scheurle, D., Rusek, M., Zochowski, M., Fractal methods to analyze ion channel kinetics (2001) Methods, 24, pp. 359-375
dc.relation.referencesNigmatullin, 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
dc.relation.referencesNigmatullin, 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
dc.relation.referencesSornette, 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
dc.relation.referencesMondal, 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
dc.relation.referencesHall, J. E., Gourdie, R. G., Spatial organization of cardiac gap junctions can affect access resistance (1995) Microsc. Res. Techn, 31, pp. 446-451
dc.relation.referencesZamir, M., On fractal properties of arterial trees (1999) J. Theor. Biol, 197, pp. 517-526
dc.relation.referencesZenin, O. K., Kizilova, N. N., Filippova, E. N., Studies on the structure of human coronary vasculature (2007) Biophysics, 52, pp. 499-503
dc.relation.referencesGoldberger, A. L., West, B. J., Fractals in physiology and medicine (1987) Yale J. Biol. Med, 60, pp. 421-435
dc.relation.referencesGoldberger, A. L., Rigney, D. R., West, B. J., Chaos Fractals Human Physiology (1990) Sci. Pict, 262, pp. 42-49
dc.relation.referencesDickinson, 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
dc.relation.referencesNogueira, 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
dc.relation.referencesMeerschaert, M. M., Mortensen, J., Wheatcraft, S. W., Fractional vector calculus for fractional advection-dispersion (2006) Phys. A, Stat. Mech. Appl, 367, pp. 181-190
dc.relation.referencesTarasov, V. E., Fractional vector calculus and fractional Maxwell's equations (2008) Anna. Phys, 323, pp. 2756-2778
dc.relation.referencesMagin, 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
dc.relation.referencesQin, 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
dc.relation.referencesYu, 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
dc.relation.referencesBueno-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
dc.type.versioninfo:eu-repo/semantics/publishedVersion
dc.type.driverinfo:eu-repo/semantics/article


Files in this item

FilesSizeFormatView

There are no files associated with this item.

This item appears in the following Collection(s)

Show simple item record