Abstract
This chapter discusses a phenomenological approach to simulate active contraction within the framework of elasticity theory. The concepts of an evolving zero-stress configuration and time-varying elasticity are introduced. These ideas are used to model the fundamental behavior of contractile structures. The theory is then used to study the mechanics of the beating heart.
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Notes
- 1.
Unfortunately, we need to use K for “contraction,” as C is already taken for the deformation tensor.
- 2.
Although active stresses also can be exerted in the transverse direction (Zahalak 1996), we assume that the stress parallel to the filaments is predominant and treat stress in a CE as 1D.
- 3.
The second assumption characterizes a constrained mixture.
- 4.
The idealized plots shown in Fig. 5.8 are based on constitutive equations developed in the following subsection.
- 5.
The ventricle can deform regionally as it contracts, but the cavity volume cannot change as blood is essentially incompressible. (Think about squeezing a water-filled balloon.)
- 6.
Because the undeformed and deformed base vectors differ for this problem, the dyadic bases are indicated on matrices, with I, J = R, Θ, Z and i, j = r, θ, z.
References
Alberts B, Johnson A, Lewis J, Morgan D, Raff M, Roberts K, Walter P (2014) Molecular biology of the cell, 6th edn. W.W. Norton, New York
An SS, Fredberg JJ (2007) Biophysical basis for airway hyperresponsiveness. Can J Physiol Pharmacol 85(7):700–714
Beyar R, Yin FCP, Hausknecht M, Weisfeldt ML, Kass DA (1989) Dependence of left ventricular twist-radial shortening relations on cardiac cycle phase. Am J Physiol Heart Circ Physiol 257(4):H1119–H1126
Dahl KN, Ribeiro AJ, Lammerding J (2008) Nuclear shape, mechanics, and mechanotransduction. Circ Res 102(11):1307–1318
Fredberg JJ, Inouye D, Miller B, Nathan M, Jafari S, Raboudi SH, Butler JP, Shore SA (1997) Airway smooth muscle, tidal stretches, and dynamically determined contractile states. Am J Respir Crit Care Med 156:1752–1759
Fung YC (1993) Biomechanics: mechanical properties of living tissues. Springer, New York
Fung YC (1997) Biomechanics: circulation, 2nd edn. Springer, New York
Herzog W (2017) Skeletal muscle mechanics: questions, problems and possible solutions. J Neuroeng Rehabil 14(1):98
Howard J (2001) Mechanics of motor proteins and the cytoskeleton. Sinauer, Sunderland
Hu S, Chen J, Butler JP, Wang N (2005). Prestress mediates force propagation into the nucleus. Biochem Biophys Res Commun 329(2):423–428
LeGrice IJ, Smaill BH, Chai LZ, Edgar SG, Gavin JB, Hunter PJ (1995) Laminar structure of the heart: Ventricular myocyte arrangement and connective tissue architecture in the dog. Am J Physiol Heart Circ Physiol 269(2):H571–H582
Martin AC, Kaschube M, Wieschaus EF (2009) Pulsed contractions of an actin-myosin network drive apical constriction. Nature 457:495–499
McMahon TA (1984) Muscles, reflexes, and locomotion. Princeton University Press, Princeton
Sagawa K, Maughan L, Suga H, Sunagaw K (1988) Cardiac contraction and the pressure-volume relationship. Oxford University Press, New York
Szczesny SE, Mauck RL (2017) The nuclear option: evidence implicating the cell nucleus in mechanotransduction. J Biomech Eng 139(2): 021006
Taber LA, Yang M, Podszus WW (1996) Mechanics of ventricular torsion. J Biomech 29:745–752
Tajik A, Zhang Y, Wei F, Sun J, Jia Q, Zhou W, Singh R, Khanna N, Belmont AS, Wang N (2016) Transcription upregulation via force-induced direct stretching of chromatin. Nat Mater 15:1287–1296
Vilfan A, Duke T (2003) Instabilities in the transient response of muscle. Biophys J 85:818–827
Waldman LK, Fung YC, Covell JW (1985) Transmural myocardial deformation in the canine left ventricle. Normal in vivo three-dimensional finite strains. Circ Res 57:152–163
Wang N, Suo Z (2005) Long-distance propagation of forces in a cell. Biochem Biophys Res Commun 328(4):1133–1138
Wang V, Nielsen P, Nash M (2015) Image-based predictive modeling of heart mechanics. Annu Rev Biomed Eng 17:351–383
Woods RH (1892) A few applications of a physical theorem to membranes in the human body in a state of tension. J Anat Physiol 26:362–370
Zahalak GI (1996) Non-axial muscle stress and stiffness. J Theor Biol 182:59–84
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Taber, L.A. (2020). Contraction. In: Continuum Modeling in Mechanobiology. Springer, Cham. https://doi.org/10.1007/978-3-030-43209-6_5
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