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Differential histomechanical response of carotid artery in relation to species and region: mathematical description accounting for elastin and collagen anisotropy

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Abstract

The selection of a mathematical descriptor for the passive arterial mechanical behavior has been long debated in the literature and customarily constrained by lack of pertinent data on the underlying microstructure. Our objective was to analyze the response of carotid artery subjected to inflation/extension with phenomenological and microstructure-based candidate strain-energy functions (SEFs), according to species (rabbit vs. pig) and region (proximal vs. distal). Histological variations among segments were examined, aiming to explicitly relate them with the differential material response. The Fung-type model could not capture the biphasic response alone. Combining a neo-Hookean with a two-fiber family term alleviated this restraint, but force data were poorly captured, while consideration of low-stress anisotropy via a quadratic term allowed improved simulation of both pressure and force data. The best fitting was achieved with the quadratic and Fung-type or four-fiber family SEF. The latter simulated more closely than the two-fiber family the high-stress response, being structurally justified for all artery types, whereas the quadratic term was justified for transitional and muscular arteries exhibiting notable elastin anisotropy. Diagonally arranged fibers were associated with pericellular medial collagen, and circumferentially and longitudinally arranged fibers with medial and adventitial collagen bundles, evidenced by the significant correlations of SEF parameters with quantitative histology.

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References

  1. Baaijens F, Bouten C, Driessen N (2010) Modeling collagen remodeling. J Biomech 43:166–175

    Article  PubMed  Google Scholar 

  2. Chuong CJ, Fung YC (1986) On residual stresses in arteries. J Biomech Eng 108:189–191

    Article  PubMed  CAS  Google Scholar 

  3. Clark JM, Glagov S (1985) Transmural organization of the arterial media. The lamellar unit revisited. Arteriosclerosis 5:19–34

    Article  PubMed  CAS  Google Scholar 

  4. Cox RH (1978) Comparison of carotid artery mechanics in the rat, rabbit, and dog. Am J Physiol 234:H280–H288

    PubMed  CAS  Google Scholar 

  5. Crissman RS (1986) SEM observations of the elastic networks in canine femoral artery. Am J Anat 175:481–492

    Article  PubMed  CAS  Google Scholar 

  6. Delfino A, Stergiopulos N, Moore JE et al (1997) Residual strain effects on the stress field in a thick wall finite element model of the human carotid bifurcation. J Biomech 18:777–786

    Article  Google Scholar 

  7. Demiray H, Weizsäcker HW, Pascale K (1986) A mechanical model for passive behaviour of rats carotid artery. Biomed Tech (Berl) 31:46–52

    Article  CAS  Google Scholar 

  8. Driessen NJ, Bouten CV, Baaijens FP (2005) A structural constitutive model for collagenous cardiovascular tissues incorporating the angular fiber distribution. J Biomech Eng 127:494–503

    Article  PubMed  Google Scholar 

  9. Finlay HM, McCullough L, Canham PB (1995) Three-dimensional collagen organization of human brain arteries at different transmural pressures. J Vasc Res 32:301–312

    PubMed  CAS  Google Scholar 

  10. Fung YC (1993) Biomechanics: mechanical properties of living tissues. Springer, New York

    Google Scholar 

  11. Fung YC, Fronek K, Patitucci P (1979) Pseudoelasticity of arteries and the choice of its mathematical expression. Am J Physiol 237:H620–H631

    PubMed  CAS  Google Scholar 

  12. Gleason RL, Dye WW, Wilson E et al (2008) Quantification of the mechanical behavior of carotid arteries from wild-type, dystrophin-deficient, and sarcoglycan-d knockout mice. J Biomech 41:3213–3218

    Article  PubMed  Google Scholar 

  13. Gosline JM (1980) The elastic properties of rubber-like proteins and highly extensible tissues. Cambridge University Press, Cambridge

    Google Scholar 

  14. Gundiah N, Ratcliffe MB, Pruitt LA (2007) Determination of strain energy function for arterial elastin: experiments using histology and mechanical tests. J Biomech 40:586–594

    Article  PubMed  Google Scholar 

  15. Hansen L, Wan W, Gleason RL (2009) Microstructurally motivated constitutive modeling of mouse arteries cultured under altered axial stretch. J Biomech Eng 131:101015

    Article  PubMed  Google Scholar 

  16. Holzapfel GA, Ogden RW (2010) Constitutive modelling of arteries. Proc R Soc A 466:1551–1597

    Article  Google Scholar 

  17. Holzapfel GA, Weizsäcker HW (1998) Biomechanical behavior of the arterial wall and its numerical characterization. Comput Biol Med 28:377–392

    Article  PubMed  CAS  Google Scholar 

  18. Holzapfel GA, Gasser CT, Ogden RW (2000) A new constitutive framework for arterial wall mechanics and a comparative study of material models. J Elast 61:1–48

    Article  Google Scholar 

  19. Humphrey JD (1995) Mechanics of the arterial wall: review and directions. Crit Rev Biomed Eng 23:1–162

    PubMed  CAS  Google Scholar 

  20. Humphrey JD (1999) An evaluation of pseudoelastic descriptors used in arterial mechanics. J Biomech Eng 121:259–262

    Article  PubMed  CAS  Google Scholar 

  21. Lillie MA, Gosline JM (2007) Mechanical properties of elastin along the thoracic aorta in the pig. J Biomech 40:2214–2221

    Article  PubMed  CAS  Google Scholar 

  22. O’Connell MK, Murthy S, Phan S et al (2008) The three-dimensional micro- and nano-structure of the aortic medial lamellar unit measured using 3D confocal and electron microscopy imaging. Matrix Biol 27:171–181

    Article  PubMed  Google Scholar 

  23. Pandit A, Lu X, Wang C et al (2005) Biaxial elastic material properties of porcine coronary media and adventitia. Am J Physiol 288:H2581–H2587

    CAS  Google Scholar 

  24. Pasquali-Ronchetti I, Alessandrini A, Baccarani Contri M et al (1998) Study of elastic fiber organization by scanning force microscopy. Matrix Biol 17:75–83

    Article  PubMed  CAS  Google Scholar 

  25. Pianosi C, Burattini AR, Desch GW et al (1999) Biphasic stress-strain relationship of arteries: dependence on topography and animal species. Proceedings of the 1st European Medical and Biological Engineering Conference EMBEC’99, Vienna, Austria. Med Biol Eng Comput 37:1432–1433

    Google Scholar 

  26. Rezakhaniha R, Stergiopulos N (2008) A structural model of the venous wall considering elastin anisotropy. J Biomech Eng 130:031017

    Article  PubMed  Google Scholar 

  27. Rezakhaniha R, Fonck E, Genoud C, Stergiopulos N (2010) Role of elastin anisotropy in structural strain energy functions of arterial tissue. Biomech Model Mechanobiol. doi:10.1007/s10237-010-0259-x

  28. Rhodin JAG (1980) Architecture of the vessel wall. In: Bohr DF, Somlyo AD, Sparks HV Jr (eds) Handbook of physiology, section 2: the cardiovascular system, vol ii: vascular smooth muscle. American Physiological Society, Bethesda, pp 1–31

    Google Scholar 

  29. Roach MR, Song SH (1988) Arterial elastin as seen with scanning electron microscopy: a review. Scan Microsc 2:994–1004

    CAS  Google Scholar 

  30. Sherebrin MH, Song SH, Roach MR (1982) Mechanical anisotropy of purified elastin from the thoracic aorta of dog and sheep. Can J Biochem Physiol 61:539–545

    Google Scholar 

  31. Sokolis DP (2008) Passive mechanical properties and constitutive modeling of blood vessels in relation to microstructure. Med Biol Eng Comput 46:1187–1199

    Article  PubMed  Google Scholar 

  32. Sokolis DP (2010) A passive strain-energy function for elastic and muscular arteries: correlation of material parameters with histological data. Med Biol Eng Comput 48:507–518

    Article  PubMed  Google Scholar 

  33. Sokolis DP, Kefaloyannis EM, Kouloukoussa M et al (2006) A structural basis for the aortic stress-strain relation in uniaxial tension. J Biomech 39:1651–1662

    Article  PubMed  Google Scholar 

  34. Sommer G, Regitnig P, Költringer L, Holzapfel GA (2010) Biaxial mechanical properties of intact and layer-dissected human carotid arteries at physiological and supraphysiological loadings. Am J Physiol Heart Circ Physiol 298:H898–H912

    Article  PubMed  CAS  Google Scholar 

  35. Stavropoulou E, Dafalias YF, Sokolis DP (2009) Biomechanical and histological characteristics of passive esophagus: Experimental investigation and comparative constitutive modeling. J Biomech 42:2654–2663

    Article  PubMed  Google Scholar 

  36. Takamizawa K, Hayashi K (1987) Strain energy density function and uniform strain hypothesis for arterial mechanics. J Biomech 20:7–17

    Article  PubMed  CAS  Google Scholar 

  37. Takamizawa K, Hayashi K (1988) Uniform strain hypothesis and thin-walled theory in arterial mechanics. Biorheology 25:555–565

    PubMed  CAS  Google Scholar 

  38. Tong P, Fung YC (1976) The stress–strain relationship for skin. J Biomech 9:649–657

    Article  PubMed  CAS  Google Scholar 

  39. Vito RP, Dixon SA (2003) Blood vessel constitutive models—1995–2002. Ann Rev Biomed Eng 5:413–439

    Article  CAS  Google Scholar 

  40. von Maltzahn WW, Warriyar RG, Keitzer WF (1984) Experimental measurements of elastic properties of media and adventitia of bovine carotid arteries. J Biomech 17:839–847

    Article  Google Scholar 

  41. Watton PN, Ventikos Y, Holzapfel GA (2009) Modelling the mechanical response of elastin for arterial tissue. J Biomech 42:1320–1325

    Article  PubMed  Google Scholar 

  42. Weizsäcker HW, Holzapfel GA, Desch GW et al (1995) Strain energy density function for arteries from different topographical sites. Biomed Tech (Berl) 2:139–141

    Article  Google Scholar 

  43. Wicker BK, Hutchens HP, Wu Q, Yeh AT, Humphrey JD (2008) Normal basilar artery structure and biaxial mechanical behavior. Comput Methods Biomech Biomed Eng 11:539–551

    Article  CAS  Google Scholar 

  44. Zhou J, Fung YC (1996) The degree of nonlinearity and anisotropy of blood vessel elasticity. Proc Natl Acad Sci USA 94:14255–14260

    Article  Google Scholar 

  45. Zou Y, Zhang Y (2009) An experimental and theoretical study on the anisotropy of elastin network. Ann Biomed Eng 37:1572–1583

    Article  PubMed  Google Scholar 

  46. Zulliger MA, Fridez P, Hayashi K et al (2004) A strain energy function for arteries accounting for wall composition and structure. J Biomech 37:989–1000

    Article  PubMed  Google Scholar 

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Authors and Affiliations

  1. Laboratory of Biomechanics, Center for Experimental Surgery, Foundation of Biomedical Research, Academy of Athens, Athens, Greece

    Dimitrios P. Sokolis, Sofia Sassani & Eleftherios P. Kritharis

  2. Laboratory of Biofluid Mechanics and Biomedical Engineering, School of Mechanical Engineering, National Technical University, Athens, Greece

    Sofia Sassani, Eleftherios P. Kritharis & Sokrates Tsangaris

  3. 35, Lefkados St., 15354, Athens, Greece

    Dimitrios P. Sokolis

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  1. Dimitrios P. Sokolis
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  2. Sofia Sassani
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  3. Eleftherios P. Kritharis
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  4. Sokrates Tsangaris
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Correspondence to Dimitrios P. Sokolis.

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Sokolis, D.P., Sassani, S., Kritharis, E.P. et al. Differential histomechanical response of carotid artery in relation to species and region: mathematical description accounting for elastin and collagen anisotropy. Med Biol Eng Comput 49, 867–879 (2011). https://doi.org/10.1007/s11517-011-0784-5

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  • DOI: https://doi.org/10.1007/s11517-011-0784-5

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