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Advantages in the torsional performances of a simplified cylindrical geometry due to transmural differential contractile properties. (English) Zbl 1348.74245
Summary: A question which has not been addressed so far in the analysis of the twisting motion of the heart, relates to the existence of any advantages in energetic expenditure due to differential contractile properties across the wall of the ventricles. The question is addressed in this paper by a highly simplified analytical model of the ventricular cavity, based on a cylindrical geometry and set in the context of the linear theory of elasticity; however, the anisotropy of contraction is also taken into account. It is concluded, that when oppositely directed spirals of fibres in the internal and external layers of the cylinder keep the torsion within suitable limits, i.e. mimicking the biological context, a smaller energetic expenditure is related to a transmural pattern of contraction which is not uniform, and presents a larger epicardial contraction.

MSC:
74L15 Biomechanical solid mechanics
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[1] Ambrosi, D.; Arioli, G.; Nobile, F.; Quarteroni, A., Electromechanical coupling in cardiac dynamics: the active strain approach, SIAM J. appl. math., 71, 2, 605-621, (2011) · Zbl 1419.74174
[2] Arts, T.; Reneman, R.S.; Veenstra, P.C., A model of the mechanics of the left ventricle, Ann. biomed. eng., 7, 299-318, (1979)
[3] Bovendeerd, P.H.M.; Arts, T.; Huyghe, J.M.; van Campen, D.H.; Reneman, R.S., Dependence of local left ventricular wall mechanics on myocardial fiber orientation: a model study, J. biomech., 25, 10, 1129-1140, (1992)
[4] Bueno-Orovio, A.; Cherry, E.M.; Fenton, F.H., Minimal model of human ventricular action potentials in tissue, J. theor. biol., 253, 544-560, (2008) · Zbl 1398.92052
[5] Burgert, I.; Eder, M.; Gierlinger, N.; Fraztl, P., Tensile and compressive stresses in tracheids are induced by swelling based on geometrical constraints of the wood cell, Planta, 226, 981-987, (2007)
[6] Chadwick, R.S., Mechanics of the left ventricle, Biophys. J., 39, 279-288, (1982)
[7] DeAnda, A.; Komeda, M.; Nikolic, S.D.; Daughters, G.T.; Ingels, N.B.; Miller, D.C., Left ventricular function, twist, and recoil after mitral valve replacement, Circulation, 92, 458-466, (1995)
[8] DiCarlo, A.; Nardinocchi, P.; Svaton, T.; Teresi, L., Passive and active deformation process in cardiac tissue, (), 1-4
[9] Evangelista, A.; Nardinocchi, P.; Puddu, P.E.; Teresi, L.; Torromeo, C.; Varano, V., Torsion of the human left ventricle: experimental analysis and computational modelling, Prog. biophys. mol. biol, (2011)
[10] Fink, M.; Niederer, S.A.; Cherry, E.M.; Fenton, F.H.; Koivumaki, J.T.; Seemann, G.; Thul, R.; Zhang, H.; Sachse, F.B.; Beard, D.; Crampin, E.J.; Smith, N.P., Cardiac cell modelling: observations from the heart of the cardiac physiome project, Prog. biophys. mol. biol., 104, 2-21, (2011)
[11] Geyer, H.; Caracciolo, G.; Abe, H.; Wilansky, S.; Carerji, S.; Gentile, F.; Nesser, H.J.; Khandheria, B.; Narula, J.; Sengupta, P.P., Assessment of myocardial mechanics using Speckle tracking echocardiography: fundamentals and clinical applications, J. am. soc. echocardiogr., 23, 4, 351-369, (2010)
[12] Glukhov, A.V.; Fedorov, V.V.; Lou, Q.; Ravikumar, V.K.; Kalish, P.W.; Schuessler, R.B.; Moazami, N.; Efimov, I.R., Transmural dispersion of repolarization in failing and nonfailing human ventricle, Circ. res., 106, 981-991, (2010)
[13] Grosberg, A.; Gharib, M., Modeling the macro-structure of the heart: healthy and diseased, Med. biol. eng. comput., 47, 301-311, (2009)
[14] Grosberg, A.; Gharib, M., Computational models of heart pumping efficiences based on contraction waves in spiral elastic bands, J. theor. biol., 257, 359-370, (2009) · Zbl 1400.92137
[15] Helle-Valle, T.; Remme, E.W.; Lyseggen, E.; Pettersen, E.; Vartdal, T.; Opdahl, A.; Smith, H.J.; Osman, N.F.; Ihlen, H.; Edvardsen, T.; Smiseth, O.A., Clinical assessment of left ventricular rotation and strain: a novel approach for quantification of function in infarcted myocardium and its border zones, Am. J. physiol. heart. circ. physiol., 297, H257-H267, (2009)
[16] Lou, Q.; Fedorov, V.V.; Glukhov, A.V.; Moazami, N.; Fast, V.G.; Efimov, I.R., Transmural heterogeneity and remodeling of ventricular excitation-contraction coupling in human heart failure, Circulation, 123, 1881-1890, (2011)
[17] Nardinocchi, P.; Teresi, L., On the active response of soft living tissues, J. elast., 88, 27-39, (2007) · Zbl 1115.74349
[18] Nardinocchi, P.; Teresi, L.; Varano, V., A simplified mechanical modeling for myocardial contraction and the ventricular pressure – volume relationships, Mech. res. commun., 38, 532-535, (2011) · Zbl 1272.74477
[19] Nash, M.P.; Hunter, P.J., Computational mechanics of the heart: from tissue structure to ventricular function, J. elast., 61, 113-141, (2000) · Zbl 1071.74659
[20] Rijcken, J.; Bovendeerd, P.H.M.; Schoofs, A.J.G.; van Campen, D.H.; Arts, T., Optimization of cardiac fiber orientation for homogeneous fiber strain during ejection, Ann. biomed. eng., 27, 289-297, (1999)
[21] Rodriguez, E.K.; Hoger, A.; McCulloch, A.D., Stress-dependent finite growth in soft elastic tissues, J. biomech., 27, 455, (1994)
[22] Sengupta, P.P.; Tajik, J.A.; Chandrasekaran, K.; Khandheria, B.K., Twist mechanics of the left ventricle: principles and application, J. am. coll. cardiol. img., 1, 366-376, (2008)
[23] Shaw, S.M.; Fox, D.J.; Williams, S.G., The development of left ventricular torsion and its clinical relevance, Int. J. cardiol., 130, 319-325, (2008)
[24] Smerup, M.; Nielsen, E.; Agger, P.; Frandsen, J.; Vestergaard-Poulsen, P.; Andersen, J.; Nyengaard, J.; Pedersen, M.; Ringgaard, S.; Hjortdal, V.; Lunkenheimer, P.P.; Anderson, R.H., The three-dimensional arrangement of the myocites aggregated together within the Mammalian ventricular myocardium, Anat. rec., 292, 1-11, (2009)
[25] Streeter, D.D.; Spotnitz, H.M.; Patel, D.P.; Ross, J.; Sonnenblick, E.H., Fiber orientation in the canine left ventricle during diastole and systole, Circ. res., 24, 339-347, (1969)
[26] Vendelin, M.; Bovendeerd, P.H.M.; Engelbrecht, J.R.; Arts, T., Optimizing ventricular fibers: uniform strain or stress, but not ATP consumption, leads to high efficiency, Am. J. physiol. heart. circ. physiol., 283, H1072-H1081, (2002)
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