Introducing mesoscopic information into constitutive equations for arterial walls

Biomechanics and Modeling in Mechanobiology

Volumn 6, Issue 5, 2007, Pages 333-344

  Ogden, Ray W ^a   Saccomandi, Giuseppe ^b  

^a UNIVERSITY OF GLASGOW   (United Kingdom)

^b UNIVERSITY OF SALENTO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

COLLAGEN; DEGRADATION; FIBERS; MATHEMATICAL MODELS; TISSUE;

ARTERIAL WALLS; ELASTIC CONSTITUTIVE LAWS; FIBRE NETWORKS; POLYMERIC CHAINS;

CONSTITUTIVE EQUATIONS;

COLLAGEN; ELASTIN;

ANIMAL; ARTERY; ARTICLE; BIOLOGICAL MODEL; COMPUTER SIMULATION; ELASTICITY; HUMAN; MECHANICAL STRESS; PHYSIOLOGY;

ANIMALS; ARTERIES; COLLAGEN; COMPUTER SIMULATION; ELASTICITY; ELASTIN; HUMANS; MODELS, CARDIOVASCULAR; STRESS, MECHANICAL;

EID: 34548273197     PISSN: 16177959     EISSN: 16822978     Source Type: Journal    
DOI: 10.1007/s10237-006-0064-8     Document Type: Article

References (47)

1. Avolio A, Jones D, Tafazzoli-Shadpour M (1998) Quantification of alterations in structure and function of elastin in the arterial media. Hypertension 32:170-175
2. Beatty MF (1987) Topics in finite elasticity: hyperelasticity of rubber, elastomers, and biological tissues-with examples. Appl Mech Rev 40:1699-1733
3. (Reprinted with minor modifications as Introduction to non-linear elasticity. In: Carroll MM, Hayes MA (eds) Non-linear effects in fluids and solids. Plenum Press, New York (1996), pp 16-112)
4. Bischoff JE, Arruda EM, Grosh K (2002) A microstructurally based orthotropic hyperelastic constitutive law. J Appl Mech 69:570-579
5. Bischoff JE, Arruda EM, Grosh K (2004) A rheological network model for the continuum anisotropic and viscoelastic behavior of soft tissue. Biomech Modeling Mechanobiol 3:56-65
6. Cameron J (1999) Estimation of arterial mechanics in clinical practice and as a research technique. Clin Exptl Pharm Physiol 26:285-294
7. Demiray H (1972) A note on the elasticity of soft biological tissues. J Biomech 5:309-311
8. Edwards SF, Vilgis T (1986) The effect of entanglements in rubber elasticity. Polymer 27:483-492
9. Erman B (2004) Molecular aspects of rubber elasticity. In: Saccomandi G, Ogden RW (eds) Mechanics and thermomechanics of rubberlike solids, CISM courses and lecture notes, vol 452. Springer, Vienna, pp 63-89
10. Fung YC (1967) Elasticity of soft tissues in simple elongation. Am J Physiol 213:1532-1544
11. Gasser TC, Ogden RW, Holzapfel GA (2006) Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. J Royal Soc Interface 3:15-35
12. Gent AN (1996) A new constitutive relation for rubber. Rubber Chem Technol 69:59-61
13. Holzapfel GA (2000) Non-linear solid mechanics. Wiley, Chichester
14. Holzapfel GA (2005) Similarities between soft biological tissues and rubberlike materials. In: Austrell P-E, Keri L (eds), Constitutive models for rubber, vol IV. A.A. Balkema Publishers, Leiden, pp 607-617
15. Holzapfel GA, Gasser TC, Ogden RW (2000) A new constitutive framework for arterial wall mechanics and a comparative study of material models. J Elasticity 61:1-48
16. Holzapfel GA, Gasser TC, Ogden RW (2004) Comparison of a multi-layer structural model for arterial walls with a Fung-type model, and issues of material stability. J Biomech Eng 126:264-275
17. Horgan CO, Saccomandi G (1999a) Simple torsion of isotropic, hyperelastic, incompressible materials with limiting chain extensibility. J Elasticity 56:159-170
18. Horgan CO, Saccomandi G (1999b) Pure axial shear of isotropic, hyperelastic, incompressible non-linear elastic materials with limiting chain extensibility. J Elasticity 57:307-319
19. Horgan CO, Saccomandi G (2002a) A molecular-statistical basis for the Gent model of rubber elasticity. J Elasticity 68:167-176
20. Horgan CO, Saccomandi G (2002b) Constitutive modelling of rubber-like and biological materials with limiting chain extensibility. Math Mech Solids 7:353-371
21. Horgan CO, Saccomandi G (2003a) Finite thermoelasticity with limiting chain extensibility. J Mech Phys Solids 51:1127-1146
22. Horgan CO, Saccomandi G (2003b) A description of arterial wall mechanics using limiting chain extensibilty constitutive models. Biomech Modeling Mechanobiol 1:251-266
23. Horgan CO, Saccomandi G (2005) A new constitutive theory for fibre-reinforced incompressible non-linearly elastic solids. J Mech Phys Solids 53:1985-2025
24. Horgan CO, Saccomandi G (2006) Phenomenological hyperelastic strain-stiffening constitutive models for rubber. Rubber Chem Technol 71:152-169
25. Horgan CO, Ogden RW, Saccomandi G (2004) A theory of stress softening of elastomers based on finite chain extensibility. Proc R Soc Lond A 460:1737-1754
26. Humphrey JD (2002) Cardiovascular solid mechanics. Springer, Berlin Heidelberg New York
27. Kilian HG (1981) Equation of state of real networks. Polymer 22:209-217
28. Kuhn W, Grün F (1942) Beziehungen zwischen elastischen Konstanten und Dehnungsdoppelbrechung höchelastischer Stoffe. Kolloid Z 101:248-271
29. Lawton RW, King AL (1951) Free longitudinal vibrations of rubber and tissue strips. J Appl Phys 22:1340-1343
30. Marque V, Kieffer P, Atkinson J, Lartaud-Idjouadiene I (1999) Elastic properties and composition of the aortic wall in old spontaneously hypertensive rats. Hypertension 34: 415-422
31. Nash MP, Hunter PJ (2000) Computational mechanics of the heart: from tissue structure to ventricular function. J Elasticity 61:113-141
32. Ogden RW (1997) Non-linear elastic deformations. Dover, New York
33. Ogden RW (2003) non-linear elasticity, anisotropy, material stability and residual stresses in soft tissue. In: Holzapfel GA, Ogden RW (eds), Biomechanics of soft tissue in cardiovascular systems, CISM Courses and Lecture Notes, vol 441. Springer, Wien, pp 65-108
34. Ogden RW, Roxburgh DG (1999) A pseudo-elastic model for the Mullins effect in filled rubber. Proc R Soc Lond A 455: 2861-2877
35. Ogden RW, Schulze-Bauer CAJ (2000) Phenomenological and structural aspects of the mechanical response of arteries. In: Casey J, Bao G (eds) Mechanics in biology, ASME AMD-vol 242/BED-vol 46. ASME, New York, pp 125-140
36. Ogden RW, Saccomandi G, Sgura I (2006) A phenomenological three-dimensional theory of the wormlike chain. Proc R Soc Lond A 462:749-768
37. Puso MA (1994) Mechanistic constitutive models for rubber elasticity and viscoelasticity. Doctoral dissertation, University of California, Davis
38. Saccomandi G (2001) Universal results in finite elasticity. In: Fu YB, Ogden RW (eds) non-linear elasticity: theory and applications, London Mathematical Society lecture notes, vol 283. Cambridge University Press, Cambridge, pp 97-134
39. Schulze-Bauer CAJ, Mörth C, Holzapfel GA (2003) Passive biaxial mechanical response of aged human iliac arteries. J Biomech Eng 125:395-406
40. Spencer AJM (1984) Constitutive theory for strongly anisotropic solids. In: Spencer AJM (eds) Continuum theory of the mechanics of fibre-reinforced composites, CISM courses and lecture notes, vol 282. Springer, Wien, pp 1-32
41. Sun Y-L, Luo Z-P, Fertala A, An KN (2004) Stretching type II collagen with opyical tweezers. J Biomech 37:1665-1669
42. Takamizawa K, Hayashi K (1987) Strain energy density function and uniform strain hypothesis for arterial mechanics. J Biomech 20:7-17
43. Urry DW, Hugel T, Seitz M, Gaub HE, Sheiba L, Dea J, Xu J, Parker T (2002) Elastin: a representative ideal protein elastomer. Phil Trans R Soc Lond B 357:169-184
44. Villani V, Tamburro AM (1999) Conformational chaos of an -related peptide in aqueous solution. Ann N Y Acad Sci 30:284-287
45. Wu X, Levenston ME, Chaikof EL (2006) A constitutive model for protein-based materials. Biomaterials 27:5315-5325
46. Wuyts PR, Vanhuyse VJ, Langewouters GJ, Decraemer WF, Raman ER, Buyle S (1995) Elastic properties of human aortas in relation to age and atherosclerosis: a structural model. Phys Med Biol 40:1577-1597
47. Zulliger MA, Fridez P, Hayashi K, Stergiopulos N (2004) A strain energy function for arteries accounting for wall composition and structure. J Biomech 37:989-1000