252
5 Contraction
If p i = 250 Pa, λ = 1.1, and c a = 400 Pa at end systole, use trialand-error to determine the value of K needed to make the inner radius at
this time approximately equal to the undeformed radius a 0 . Then, plot the
distribution of circumferential stress across the wall at end systole.
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
5 Contraction
If p i = 250 Pa, λ = 1.1, and c a = 400 Pa at end systole, use trialand-error to determine the value of K needed to make the inner radius at
this time approximately equal to the undeformed radius a 0 . Then, plot the
distribution of circumferential stress across the wall at end systole.
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