Urdeitx, Pau; Doweidar, Mohamed H. Mechanical stimulation of cell microenvironment for cardiac muscle tissue regeneration: a 3D in-silico model. (English) Zbl 07304571 Comput. Mech. 66, No. 4, 1003-1023 (2020). MSC: 74 PDF BibTeX XML Cite \textit{P. Urdeitx} and \textit{M. H. Doweidar}, Comput. Mech. 66, No. 4, 1003--1023 (2020; Zbl 07304571) Full Text: DOI
Colorado Cervantes, Ivan; Sansalone, Vittorio; Teresi, Luciano The heart function as a motor-brake system. (English) Zbl 1409.92068 J. Theor. Biol. 467, 23-30 (2019). MSC: 92C30 92C10 PDF BibTeX XML Cite \textit{I. Colorado Cervantes} et al., J. Theor. Biol. 467, 23--30 (2019; Zbl 1409.92068) Full Text: DOI
Hayashi, Tatsuya; Tokihiro, Tetsuji; Kurihara, Hiroki; Nomura, Fumimasa; Yasuda, Kenji Integrate and fire model with refractory period for synchronization of two cardiomyocytes. (English) Zbl 1394.92033 J. Theor. Biol. 437, 141-148 (2018). MSC: 92C37 92B25 PDF BibTeX XML Cite \textit{T. Hayashi} et al., J. Theor. Biol. 437, 141--148 (2018; Zbl 1394.92033) Full Text: DOI
Syomin, Fyodor A.; Tsaturyan, Andrey K. Mechanical model of the left ventricle of the heart approximated by axisymmetric geometry. (English) Zbl 1379.92005 Russ. J. Numer. Anal. Math. Model. 32, No. 5, 327-337 (2017). MSC: 92C10 74L15 92C30 PDF BibTeX XML Cite \textit{F. A. Syomin} and \textit{A. K. Tsaturyan}, Russ. J. Numer. Anal. Math. Model. 32, No. 5, 327--337 (2017; Zbl 1379.92005) Full Text: DOI
Syomin, Fyodor A.; Tsaturyan, Andrey K. A simple model of cardiac muscle for multiscale simulation: passive mechanics, crossbridge kinetics and calcium regulation. (English) Zbl 1370.92025 J. Theor. Biol. 420, 105-116 (2017). MSC: 92C10 92C30 92C05 PDF BibTeX XML Cite \textit{F. A. Syomin} and \textit{A. K. Tsaturyan}, J. Theor. Biol. 420, 105--116 (2017; Zbl 1370.92025) Full Text: DOI
Griswold, Cortland K. A model of the physiological basis of a multivariate phenotype that is mediated by Ca\(^{2+}\) signaling and controlled by ryanodine receptor composition. (English) Zbl 1397.92191 J. Theor. Biol. 282, 14-22 (2011). MSC: 92C40 92C20 PDF BibTeX XML Cite \textit{C. K. Griswold}, J. Theor. Biol. 282, 14--22 (2011; Zbl 1397.92191) Full Text: DOI
Krejčí, Pavel; Sainte-Marie, Jacques; Sorine, Michel; Urquiza, José M. Solutions to muscle fiber equations and their long time behaviour. (English) Zbl 1105.35306 Nonlinear Anal., Real World Appl. 7, No. 4, 535-558 (2006). MSC: 35B40 35K60 74L15 92C10 35B35 PDF BibTeX XML Cite \textit{P. Krejčí} et al., Nonlinear Anal., Real World Appl. 7, No. 4, 535--558 (2006; Zbl 1105.35306) Full Text: DOI
Sperelakis, N.; Murali, K. P. V. Effect of external resistance on propagation of action potentials in cardiac muscle and visceral smooth muscle in PSpice simulation. (English) Zbl 1045.92013 Math. Comput. Modelling 37, No. 12-13, 1443-1467 (2003). MSC: 92C30 78A70 PDF BibTeX XML Cite \textit{N. Sperelakis} and \textit{K. P. V. Murali}, Math. Comput. Modelling 37, No. 12--13, 1443--1467 (2003; Zbl 1045.92013) Full Text: DOI
Clayton, R. H. (ed.); Holden, A. V. (ed.) Special issue: Virtual tissue engineering of cardiac muscle. Proceedings of an EPSRC workshop, Leeds, GB, June 2000. (English) Zbl 0992.00064 Chaos Solitons Fractals 13, No. 8, 1579-1762 (2002). MSC: 00B25 92-06 PDF BibTeX XML Cite \textit{R. H. Clayton} (ed.) and \textit{A. V. Holden} (ed.), Chaos Solitons Fractals 13, No. 8, 1579--1762 (2002; Zbl 0992.00064) Full Text: DOI
Sanfelici, Simona Convergence of the Galerkin approximation of a degenerate evolution problem in electrocardiology. (English) Zbl 1002.65100 Numer. Methods Partial Differ. Equations 18, No. 2, 218-240 (2002). Reviewer: K.T.S.R.Iyengar (Bangalore) MSC: 65M12 35K65 78A70 65M60 35K57 92C10 PDF BibTeX XML Cite \textit{S. Sanfelici}, Numer. Methods Partial Differ. Equations 18, No. 2, 218--240 (2002; Zbl 1002.65100) Full Text: DOI
Biktasheva, I. V.; Biktashev, V. N. Response functions of spiral wave solutions of the complex Ginzburg-Landau equation. (English) Zbl 0976.35077 J. Nonlinear Math. Phys. 8, Suppl., 28-34 (2001). MSC: 35Q55 92C30 35K57 PDF BibTeX XML Cite \textit{I. V. Biktasheva} and \textit{V. N. Biktashev}, J. Nonlinear Math. Phys. 8, 28--34 (2001; Zbl 0976.35077) Full Text: DOI
Vendelin, M.; Engelbrecht, J. Microstructure described by hierarchical internal variables. (English) Zbl 1072.74043 Rend. Semin. Mat., Torino 58, No. 1, 83-91 (2000). Reviewer: Alain Brillard (Mulhouse) MSC: 74J30 74A60 92C05 PDF BibTeX XML Cite \textit{M. Vendelin} and \textit{J. Engelbrecht}, Rend. Semin. Mat., Torino 58, No. 1, 83--91 (2000; Zbl 1072.74043)
Engelbrecht, Jüri; Vendelin, Marko; Maugin, Gérard A. Hierarchical internal variables reflecting microstructural properties: Application to cardiac muscle contraction. (English) Zbl 0970.74046 J. Non-Equilibrium Thermodyn. 25, No. 2, 119-130 (2000). MSC: 74L15 74A15 92C10 PDF BibTeX XML Cite \textit{J. Engelbrecht} et al., J. Non-Equilibrium Thermodyn. 25, No. 2, 119--130 (2000; Zbl 0970.74046) Full Text: DOI
Bestel, J.; Clairambault, J.; Médigue, C.; Monti, A.; Sorine, M. The cardio-vascular system and it’s control by the autonomous nervous system: Modelleing and measurement. (Le système cardio-vasculaire et sa régulation par le système nerveux autonome: Modélisation et mesures.) (French) Zbl 0946.92005 ESAIM, Proc. 9, 65-92 (2000). MSC: 92C30 92C20 93C95 PDF BibTeX XML Cite \textit{J. Bestel} et al., ESAIM, Proc. 9, 65--92 (2000; Zbl 0946.92005) Full Text: DOI Link
Chopra, G. C.; Sleeman, B. D.; Brindley, J.; Knapp, D. G.; Holden, A. V. Velocity and stability of solitary planar travelling wave solutions of intracellular [Ca]\(^{2+}\). (English) Zbl 1323.92082 Bull. Math. Biol. 61, No. 2, 273-301 (1999). MSC: 92C40 92C37 35C07 PDF BibTeX XML Cite \textit{G. C. Chopra} et al., Bull. Math. Biol. 61, No. 2, 273--301 (1999; Zbl 1323.92082) Full Text: DOI
Holden, Arun V. Defibrillation in models of cardiac muscle. (English) Zbl 0901.92019 J. Theor. Med. 1, No. 2, 91-102 (1997). MSC: 92C50 92C30 35K57 92C05 PDF BibTeX XML Cite \textit{A. V. Holden}, J. Theor. Med. 1, No. 2, 91--102 (1997; Zbl 0901.92019) Full Text: DOI EuDML
Redaelli, Alberto; Pietrabissa, Riccardo A structural model of the left ventricle including muscle fibres and coronary vessels: Mechanical behaviour in normal conditions. (English) Zbl 0874.92007 Meccanica 32, No. 1, 53-70 (1997). MSC: 92C10 92C50 92C35 PDF BibTeX XML Cite \textit{A. Redaelli} and \textit{R. Pietrabissa}, Meccanica 32, No. 1, 53--70 (1997; Zbl 0874.92007) Full Text: DOI
van Campen, D. H.; Huyghe, J. M.; Bovendeerd, P. H. M.; Arts, T. Biomechanics of the heart muscle. (English) Zbl 0815.73045 Eur. J. Mech., A 13, Spec. Iss., 19-41 (1994). MSC: 74L15 74S05 92C10 PDF BibTeX XML Cite \textit{D. H. van Campen} et al., Eur. J. Mech., A 13, 19--41 (1994; Zbl 0815.73045)
Grenander, Ulf; Miller, Michael I. Representations of knowledge in complex systems. (With discussion). (English) Zbl 0814.62009 J. R. Stat. Soc., Ser. B 56, No. 4, 549-603 (1994). MSC: 62A01 62P10 92C50 PDF BibTeX XML Cite \textit{U. Grenander} and \textit{M. I. Miller}, J. R. Stat. Soc., Ser. B 56, No. 4, 549--603 (1994; Zbl 0814.62009)
Di Cola, G.; Guerri, L.; Macchi, E.; Morrea, T.; Pennacchio, M.; Taccardi, B. Identification of dipolar sources in tridimensional anisotropic cardiac muscle. (English) Zbl 0790.92010 Math. Model. Sci. Comput. 2(Sect.A), 592-599 (1993). MSC: 92C30 78A70 92-08 PDF BibTeX XML Cite \textit{G. Di Cola} et al., Math. Model. Sci. Comput. 2(Sect.A), 592--599 (1993; Zbl 0790.92010)
Shumaker, J. M.; Clark, J. W.; Giles, W. R. Simulations of passive properties and action potential conduction in an idealized bullfrog atrial trabeculum. (English) Zbl 0777.92005 Math. Biosci. 116, No. 2, 127-167 (1993). MSC: 92C30 PDF BibTeX XML Cite \textit{J. M. Shumaker} et al., Math. Biosci. 116, No. 2, 127--167 (1993; Zbl 0777.92005) Full Text: DOI
Roth, Bradley J. How the anisotropy of the intracellular and extracellular conductivities influences stimulation of cardiac muscle. (English) Zbl 0748.92004 J. Math. Biol. 30, No. 6, 633-646 (1992). MSC: 92C30 92C05 78A70 PDF BibTeX XML Cite \textit{B. J. Roth}, J. Math. Biol. 30, No. 6, 633--646 (1992; Zbl 0748.92004) Full Text: DOI
Colli, Pierluigi; Comincioli, Valeriano; Naldi, Giovanni; Torelli, Alessandro A mathematical study of the plasticity effects in muscle contraction. (English) Zbl 0739.73028 Appl. Math. Optimization 22, No. 1, 1-26 (1990). Reviewer: H.Demiray (İstanbul) MSC: 74L15 74C99 74S30 74P10 49J40 92C10 PDF BibTeX XML Cite \textit{P. Colli} et al., Appl. Math. Optim. 22, No. 1, 1--26 (1990; Zbl 0739.73028) Full Text: DOI
Peskin, Charles S. Fiber architecture of the left ventricular wall: An asymptotic analysis. (English) Zbl 0664.92005 Commun. Pure Appl. Math. 42, No. 1, 79-113 (1989). MSC: 92Cxx 74L15 76Z05 PDF BibTeX XML Cite \textit{C. S. Peskin}, Commun. Pure Appl. Math. 42, No. 1, 79--113 (1989; Zbl 0664.92005) Full Text: DOI
Colli Franzone, P.; Guerri, Luciano; Rovida, S. Macroscopic cardiac source model and propagation waves in excitable media. (English) Zbl 0679.92005 Biomathematics and related computational problems, Proc. Workshop, Naples and Anacapri/Italy 1987, 615-627 (1988). MSC: 92Cxx 35Q99 78A70 92C50 35B25 PDF BibTeX XML
Favella, L.; Balossino, N.; Reineri, M. T. Electrical excitation propagation front in the cardiac muscle. (English) Zbl 0645.92007 Biomathematics and related computational problems, Proc. Workshop, Naples and Anacapri/Italy 1987, 649-658 (1988). MSC: 92Cxx 78A70 92C05 PDF BibTeX XML
Sorek, Shaul; Sideman, Samuel A porous-medium approach for modelling heart mechanics. I. Theory. (English) Zbl 0606.92007 Math. Biosci. 81, 1-14 (1986). Reviewer: G.Eason MSC: 92Cxx 76Z05 74L15 PDF BibTeX XML Cite \textit{S. Sorek} and \textit{S. Sideman}, Math. Biosci. 81, 1--14 (1986; Zbl 0606.92007) Full Text: DOI
Greensite, Fred Topological foundations of electrocardiology. (English) Zbl 0597.92004 Adv. Appl. Math. 6, 230-258 (1985). Reviewer: J.Cronin MSC: 92C50 58E05 PDF BibTeX XML Cite \textit{F. Greensite}, Adv. Appl. Math. 6, 230--258 (1985; Zbl 0597.92004) Full Text: DOI
Gastaldi, Lucia; Tomarelli, Franco Existence and uniqueness for a nonlinear Cauchy problem of hyperbolic type. (English) Zbl 0569.92011 Mathematics in biology and medicine, Proc. Int. Conf., Bari/Italy 1983, Lect. Notes Biomath. 57, 504-509 (1985). MSC: 92Cxx 35L60 35L50 PDF BibTeX XML
Gastaldi, Lucia; Tomarelli, Franco A uniqueness result for a nonlinear hyperbolic equation. (English) Zbl 0563.35046 Ann. Mat. Pura Appl., IV. Ser. 137, 175-205 (1984). Reviewer: J.Smoller MSC: 35L60 35A05 92Cxx PDF BibTeX XML Cite \textit{L. Gastaldi} and \textit{F. Tomarelli}, Ann. Mat. Pura Appl. (4) 137, 175--205 (1984; Zbl 0563.35046) Full Text: DOI
Colli Franzone, P.; Guerri, L.; Magenes, E. Oblique double layer potentials for the direct and inverse problems of electrocardiology. (English) Zbl 0558.92007 Math. Biosci. 68, 23-55 (1984). Reviewer: J.Cronin MSC: 92Cxx 92C50 35J55 PDF BibTeX XML Cite \textit{P. Colli Franzone} et al., Math. Biosci. 68, 23--55 (1984; Zbl 0558.92007) Full Text: DOI
Moskowitz, Samuel E. A duality principle for viscoelastic relaxation of cardiac muscle. (English) Zbl 0541.92009 Math. Biosci. 70, 57-64 (1984). MSC: 92Cxx 74L15 74D05 74D10 PDF BibTeX XML Cite \textit{S. E. Moskowitz}, Math. Biosci. 70, 57--64 (1984; Zbl 0541.92009) Full Text: DOI
Torelli, Alessandro A non linear hyperbolic equation related to the dynamics of cardiac muscle. (English) Zbl 0548.92001 Port. Math. 41, 171-188 (1982). Reviewer: J.Cronin MSC: 92Cxx 35J60 PDF BibTeX XML Cite \textit{A. Torelli}, Port. Math. 41, 171--188 (1982; Zbl 0548.92001) Full Text: EuDML
Wong, Alan Y. K.; Bassingthwaighte, James B. The kinetics of Ca-Na exchange in excitable tissue. (English) Zbl 0487.92008 Math. Biosci. 53, 275-310 (1981). MSC: 92Cxx 76Z05 PDF BibTeX XML Cite \textit{A. Y. K. Wong} and \textit{J. B. Bassingthwaighte}, Math. Biosci. 53, 275--310 (1981; Zbl 0487.92008) Full Text: DOI
Wong, Alan Y. K. Some comments on the conductance of slow inward current in cardiac muscle. (English) Zbl 0456.92004 Bull. Math. Biol. 43, 183-199 (1981). MSC: 92Cxx 76Z05 93B30 93C99 93C57 PDF BibTeX XML Cite \textit{A. Y. K. Wong}, Bull. Math. Biol. 43, 183--199 (1981; Zbl 0456.92004) Full Text: DOI
Smolyaninov, V. V. Mathematical models of biological tissues. (Matematicheskie modeli biologicheskikh tkanej). (Russian) Zbl 0482.92001 Teoreticheskaya i Prikladnaya Biofizika. Moskva: ”Nauka”. 368 p. R. 3.70 (1980). MSC: 92B05 92Cxx 92-02 92C50 PDF BibTeX XML