Abstract
This manuscript presents a chemomechanically coupled three-dimensional model, describing the contractile behavior of smooth muscles. It bases on a strain-energy function, additively decomposed into passive parts and an active calcium-driven part related to the chemical contraction of smooth muscle cells. For the description of the calcium phase the four state cross-bridge model of Hai and Murphy (Am. J. Physiol. 254:C99–106, 1988) has been used. Before the features and applicability of the proposed approach are illustrated in terms of three-dimensional boundary-value problems, the model is validated by experiments on porcine smooth muscle tissue strips.
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References
Arner A (1982) Mechanical characteristics of chemically skinned guinea-pig taenia coli. Pflügers Arch 395:277–284
Bates JHT, Lauzon A-M (2007) Parenchymal tethering, airway wall stiffness, and the dynamics of bronchoconstriction. J Appl Physiol 102:1912–1920
Bursztyn L, Eytan O, Jaffa AJ, Elad D (2007) Mathematical model of excitation-contraction in a uterine smooth muscle cell. Am J Physiol, Cell Physiol 292:C1816–1829
Bond M, Somlyo AV (1982) Dense bodies and actin polarity in vertebrate smooth muscle. J Cell Biol 95:403–413
Dahl SLM, Vaughn ME, Niklason LE (2007) An ultrastructural analysis of collagen in tissue engineered arteries. Ann Biomed Eng 35:1749–1755
Fay FS, Delise CM (1973) Contraction of isolated smooth-muscle cells-structural changes. Proc Natl Acad Sci USA 70:641–645
Fritsch H, Kuehnel W (2007) Color atlas and textbook of human anatomy, vol 2. Internal organs. Thieme, Stuttgart
Gestrelius S, Borgström P (1986) A dynamic model of smooth muscle contraction. Biophys J 50:157–169
Hai CM, Murphy RA (1988) Cross-bridge phosphorylation and regulation of latch state in smooth muscle. Am J Physiol 254:C99–106
Herlihy JT, Murphy RA (1973) Length-tension relationship of smooth muscle of the hog carotid artery. Circ Res 33:275–283
Herrera AM, McParland BE, Bienkowska A, Tait R, Paré PD, Seow CY (2005) ‘Sarcomeres’ of smooth muscle: functional characteristics and ultrastructural evidence. J Cell Sci 118:2381–2392
Hodgkinson JL, Newman TM, Marston SB, Severs NJ (1995) The structure of the contractile apparatus in ultrarapidly frozen smooth muscle: freeze-fracture, deep-etch, and freeze-substitution studies. J Struct Biol 114:93–104
Holzapfel GA, Gasser TC, Ogden RW (2000) A new constitutive framework for arterial wall mechanics and a comparative study of material models. J Elast 61:1–48
Kuo K-H, Seow CY (2004) Contractile filament architecture and force transmission in swine airway smooth muscle. J Cell Sci 117:1503–1511
Lee S, Schmid-Schönbein GW (1996a) Biomechanical model for the myogenic response in the microcirculation: Part I—Formulation and initial testing. J Biomech Eng 118:145–151
Lee S, Schmid-Schönbein GW (1996b) Biomechanical model for the myogenic response in the microcirculation: Part II—Experimental evaluation in rat cremaster muscle. J Biomech Eng 118:152–157
Miftakhov RN, Abdusheva GR (1996) Numerical simulation of excitation-contraction coupling in a locus of the small bowel. Biol Cybern 74:455–467
Murtada S-I, Kroon M, Holzapfel GA (2010) A calcium-driven mechanochemical model for prediction of force generation in smooth muscle. Biomech Model Mechanobiol 9:749–762
Rachev A, Hayashi K (1999) Theoretical study of the effects of vascular smooth muscle contraction on strain and stress distributions in arteries. Ann Biomed Eng 27:459–468
Rhoades RA, Bell DR (2008) Medical physiology: principles for clinical medicine, 3rd edn. Lippincott Williams & Wilkins, Baltimore
Schmitz A, Böl M (2011) On a phenomenological model for active smooth muscle contraction. J Biomech 44:2090–2095
Seow CY, Paré PD (2007) Ultrastructural basis of airway smooth muscle contraction. Can J Physiol Pharm 85:659–665
Singer HA, Murphy RA (1987) Maximal rates of activation in electrically stimulated swine carotid media. Circ Res 60:438–445
Stålhand J, Klarbring A, Holzapfel GA (2008) Smooth muscle contraction: mechanochemical formulation for homogeneous finite strains. Prog Biophys Mol Biol 96:465–481
Walmsley JG, Murphy RA (1987) Force-length dependence of arterial lamellar smooth muscle and myofilament orientations. Am J Physiol 253:H1141–H1147
Wang C, Garcia M, Lu X, Lanir Y, Kassab GS (2006) Three-dimensional mechanical properties of porcine coronary arteries: a validated two-layer model. Am J Physiol, Heart Circ Physiol 291:H1200–1209
Yang J, Clark JW, Bryan RM, Robertson CS (2003a) The myogenic response in isolated rat cerebrovascular arteries: smooth muscle cell model. Med Eng Phys 25:691–709
Yang J, Clark JW, Bryan RM, Robertson CS (2003b) The myogenic response in isolated rat cerebrovascular arteries: vessel model. Med Eng Phys 25:711–717
Zulliger MA, Rachev A, Stergiopulos A (2004) A constitutive formulation of arterial mechanics including vascular smooth muscle tone. Am J Physiol, Heart Circ Physiol 287:H1335–H1343
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Böl, M., Schmitz, A. (2013). A Coupled Chemomechanical Model for Smooth Muscle Contraction. In: Holzapfel, G., Kuhl, E. (eds) Computer Models in Biomechanics. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5464-5_5
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DOI: https://doi.org/10.1007/978-94-007-5464-5_5
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