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Origin of axial prestretch and residual stress in arteries

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Abstract

The structural protein elastin endows large arteries with unique biological functionality and mechanical integrity, hence its disorganization, fragmentation, or degradation can have important consequences on the progression and treatment of vascular diseases. There is, therefore, a need in arterial mechanics to move from materially uniform, phenomenological, constitutive relations for the wall to those that account for separate contributions of the primary structural constituents: elastin, fibrillar collagens, smooth muscle, and amorphous matrix. In this paper, we employ a recently proposed constrained mixture model of the arterial wall and show that prestretched elastin contributes significantly to both the retraction of arteries that is observed upon transection and the opening angle that follows the introduction of a radial cut in an unloaded segment. We also show that the transmural distributions of elastin and collagen, compressive stiffness of collagen, and smooth muscle tone play complementary roles. Axial prestresses and residual stresses in arteries contribute to the homeostatic state of stress in vivo as well as adaptations to perturbed loads, disease, or injury. Understanding better the development of and changes in wall stress due to individual extracellular matrix constituents thus promises to provide considerable clinically important insight into arterial health and disease.

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References

  • Alastrue V, Pena E, Martinez MA, Doblare M (2007) Assessing the use of the “opening angle method” to enforce residual stresses in patient-specific arteries. Ann Biomed Eng 35: 1821–1837

    Article  Google Scholar 

  • Alford PW, Humphrey JD, Taber LA (2008) Growth and remodeling in a thick-walled artery model: effects of spatial variations in wall constituents. Biomech Model Mechanobiol 7: 245–262

    Article  Google Scholar 

  • Arribas SM, Hinek A, Gonzalez MC (2006) Elastic fibres and vascular structure in hypertension. Pharmacol Therapeu 111: 771–791

    Article  Google Scholar 

  • Azeloglu EU, Albro MB, Thimmappa VA, Ateshian GA, Costa KD (2008) Heterogeneous transmural proteoglycan distribution provides a mechanism for regulating residual stresses in the aorta. Am J Physiol 294: H1197–1205

    Google Scholar 

  • Badrek-Amoudi A, Patel CK, Kane TPC, Greenwald SE (1996) The effect of age on residual strain in the rat aorta. J Biomech Eng 118: 189–192

    Google Scholar 

  • Baek S, Rajagopal KR, Humphrey JD (2006) A theoretical model of enlarging intracranial fusiform aneurism. J Biomech Eng 128: 142–149

    Article  Google Scholar 

  • Bergel DH (1960) The visco-elastic properties of the arterial wall. PhD Thesis, University of London, UK

  • Brankov G, Rachev A, Stoychev S (1975) A composite model of large blood vessels. Mechanics of Biological Solids. Bulgaria, pp 71–78

  • Briones AM, Gonzalez JM, Somoza B, Giraldo J, Daly CJ, Vila E, Gonzalez MC, McGrath JC, Arribas SM (2003) Role of elastin in spontaneously hypertensive rat small mesenteric artery remodeling. J Physiol 552: 185–195

    Article  Google Scholar 

  • Burton AC (1954) Relation of structure to function of the tissues of the wall of blood vessels. Physiol Rev 34: 619–642

    Google Scholar 

  • Chuong CJ, Fung YC (1984) Compressibility and constitutive equation of arterial wall in radial compression experiments. J Biomech 17: 35–40

    Article  Google Scholar 

  • Chuong CJ, Fung YC (1986) On residual stress in artery. J Biomech Eng 108: 189–192

    Article  Google Scholar 

  • Cox RH (1975) Anisotropic properties of the canine carotid artery in vitro. J Biomech 8: 293–300

    Article  Google Scholar 

  • Davis EC (1995) Elastic lamina growth in the developing mouse aorta. J Histochem Cytochem 43: 1115–1123

    Google Scholar 

  • Delfino A, Stergiopulos N, Moore JE, Meister JJ (1997) Residual strain effects on the stress field in a thick wall finite element model of the human carotid bifurcation. J Biomech 30: 777–786

    Article  Google Scholar 

  • Dobrin PB, Canfield T, Sinha S (1975) Development of longitudinal retraction of carotid arteries in neonatal dogs. Experientia 31: 1295–1296

    Article  Google Scholar 

  • Dobrin PB, Schwarcz TH, Mrkvicka R (1990) Longitudinal retractive force in pressurized dog and human arteries. J Surg Res 48: 116–120

    Article  Google Scholar 

  • Dorrington KL, McCrum NG (1977) Elastin as rubber. Biopolymers 16: 1201–1222

    Article  Google Scholar 

  • Faury G (2001) Function–structure relationship of elastic arteries in evolution: from microfibrils to elastin and elastic fibres. Pathol Biol 49: 310–325

    Article  Google Scholar 

  • Feldman SA, Glagov S (1971) Transmural collagen and elastin in human aortas: reversal with age. Atherosclerosis 13: 385–394

    Article  Google Scholar 

  • Fonck E, Prod’hom G, Roy S, Augsburger L, Rufenacht AD, Stergiopulos N (2006) Effect of elastin degradation on carotid wall mechanics as assessed by a constituent-based biomechanical model. Am J Physiol 292: H2754–2763

    Google Scholar 

  • Fridez P (2000) The role of vascular smooth muscle in biomechanical adaptation of the arterial wall to induced hypertension. PhD, Swiss Federal Institute of Technology

  • Fung YC (1983) What principle governs the stress distribution in Living organism? In: Fung YC, Fukada E, Wang JJ (eds) Biomechanics in China, Japan and USA. Science Press, Beijing, pp 1–13

    Google Scholar 

  • Fung YC (1991) What are residual stresses doing in our blood vessels? Annl Biomed Eng 19: 237–249

    Article  MathSciNet  Google Scholar 

  • Fung YC (1993) Biomechanics: motion, flow, stress, and growth. Springer, New York

    Google Scholar 

  • Gerrity RG, Cliff WJ (1975) The aortic tunica media of the developing rat. I. Quantitative stereological and biochemical analysis. Lab Invest 32: 585–600

    Google Scholar 

  • Gleason RL, Taber LA, Humphrey JD (2004) A 2-D model of flow-induced alterations in the geometry, structure, and properties of carotid arteries. J Biomech Eng 126: 371–381

    Article  Google Scholar 

  • Greenwald SE, Moore JE, Rachev A, Kane TPC, Meister J-J (1997) Experimental investigation of the distribution of residual strains in the artery wall. J Biomech Eng 119: 438–444

    Article  Google Scholar 

  • Guillou A, Ogden RW (2006) Growth of soft biological tissue and residual stress development. In: Holzapfel GA, Ogden RW (eds) Mechanics of biological tissue. Springer, Berlin

    Google Scholar 

  • Holzapfel GA, Ogden RW (2006) Mechanics of biological tissues. Springer, Berlin

    Book  Google Scholar 

  • 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

    Article  MATH  MathSciNet  Google Scholar 

  • Holzapfel GA, Sommer G, Auer M, Regitnig P, Ogden RW (2007) Layer-specific residual deformations of human aortas with non-atherosclerotic intimal thickening. Ann Biomed Eng 35: 530–545

    Article  Google Scholar 

  • Humphrey JD (2002) Cardiovascular solid mechanics: cells, tissues and organs. Springer, New York

    Google Scholar 

  • Humphrey JD, Na S (2002) Elastodynamics and arterial wall stress. Ann Biomed Eng 30: 509–523

    Article  Google Scholar 

  • Humphrey JD, Rajagopal KR (2002) A constrained mixture model for growth and remodeling of soft tissues. Math Model Meth Appl Sci 12: 407–430

    Article  MATH  MathSciNet  Google Scholar 

  • Humphrey JD, Rajagopal KR (2003) A constrained mixture model for arterial adaptations to a sustained step change in blood flow. Biomech Model Mechanobiol 2: 109–126

    Article  Google Scholar 

  • Kang T, Humphrey JD (1991) Finite deformation of an inverted artery. In: Vanderby R (eds) Advances in bioengineering. ASME, New York

    Google Scholar 

  • Langille BL (1996) Arterial remodeling: relation to hemodynamics. Can J Physiol Pharmacol 74: 834–841

    Article  Google Scholar 

  • Masson I, Boutouyrie P, Laurent S, Humphrey JD, Zidi M (2008) Characterization of arterial wall mechanical behavior and stress from human clinical data. J Biomech 41: 2618–2627

    Article  Google Scholar 

  • Matsumoto T, Tsuchida M, Sato M (1996) Change in intramural strain distribution in rat aorta due to smooth muscle contraction and relaxation. Am J Physiol 271: H1711–1716

    Google Scholar 

  • Mithieux SM, Weiss AS (2005) Elastin. Adv Protein Chem 70: 437–461

    Article  Google Scholar 

  • Nevo E, Lanir Y (1989) Strucutural finite deformation model of the left ventricle during diastole and systole. J Biomech Eng 111: 342– 349

    Article  Google Scholar 

  • Patel DJ, Fry DL (1966) Longitudinal tethering of arteries in dogs. Circ Res 19: 1011–1021

    Google Scholar 

  • Rachev A, Greenwald SE (2003) Residual strains in conduit arteries. J Biomech 36: 661–670

    Article  Google Scholar 

  • Rachev A, Hayashi K (1999) Theoretical study of the effects of vascular smooth muscle contraction on strain and stress distributions in arteries. Annl Biomed Eng 27: 459–468

    Article  Google Scholar 

  • Saini A, Berry CL, Greenwald SE (1995) The effect of age and sex on residual stress in the aorta. J Vasc Res 32: 398–405

    Google Scholar 

  • Stalhand J, Karlsson A, Klarbrang M (2004) Towards in vivo aorta material identification and stress estimation. Biomech Model Mechanobiol 2: 169–186

    Article  Google Scholar 

  • Stergiopulos N, Vulliemoz S, Rachev A, Meister JJ, Greenwald SE (2001) Assessing the homogeneity of the elastic properties and composition of the pig aortic media. J Vasc Res 38: 237–246

    Article  Google Scholar 

  • Taber LA, Humphrey JD (2001) Stress-modulated growth, residual stress, and vascular heterogeneity. J Biomech Eng 123: 528–535

    Article  Google Scholar 

  • Tickner EG, Sacks AH (1967) A theory for the static elastic behavior of blood vessels. Biorheology 4: 151–168

    Google Scholar 

  • Tomasek JJ, Gabbiani G, Hinz B, Chaponnier C, Brown RA (2002) Myofibroblasts and mechano-regulation of connective tissue remodeling. Nat Rev 3: 349363

    Article  Google Scholar 

  • Vaishnav RN, Vossoughi J (1983) Estimation of residual strain in aortic segment. In: Hall CW (eds) Biomedical Engineering II, Recent developments. Pergamon Press, New York, pp 330–333

    Google Scholar 

  • Valentín A, Cardamone L, Baek S, Humphrey JD (2008) Complementary vasoactivity and matrix remodeling in arterial adaptations to altered flow and pressure. J Roy Soc Interface (in press)

  • Van Dyke TJ, Hoger A (2002) A new method for predicting the opening angle for soft tissues. J Biomech Eng 124: 347–354

    Article  Google Scholar 

  • Van Loon P, Klip W, Bradley EL (1977) Length-force and volume–pressure relationships in arteries. Biorheology 14: 181–201

    Google Scholar 

  • Vossoughi J, Hedjazi H, Borris FSI, (1993) Intimal residual stress and strain in large arteries. ASME Bioengineering Conference, ASME, New York, pp 434–437

  • Wagenseil JE, Mecham RP (2007) New insights into elastic fiber assembly. Birth Defects Res 81: 229–240

    Article  Google Scholar 

  • Wicker BK, Hutchens HP, Wu Q, Yeh AT, Humphrey JD (2008) Normal basilar artery structure and biaxial mechanical behavior. Comp Meth Biomech Biomed Eng (in press)

  • Zeller PJ, Skalak TC (1998) Contribution of individual structural components in determining the zero-stress state in small arteries. J Vasc Res 35: 8–17

    Article  Google Scholar 

  • Zhou X, Lu J (2008) Estimation of vascular open configuration using finite element inverse elastostatic method. Eng Comp (ePub ahead of press)

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Authors and Affiliations

  1. Dipartimento di Ingegneria Civile, Università degli Studi di Salerno, Fisciano, Italy

    L. Cardamone

  2. Department of Biomedical Engineering, Texas A&M University, 337 Zachry Engineering Center, 3120 TAMU, College Station, TX, 77843-3120, USA

    A. Valentín, J. F. Eberth & J. D. Humphrey

Authors
  1. L. Cardamone
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  2. A. Valentín
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  3. J. F. Eberth
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  4. J. D. Humphrey
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Correspondence to J. D. Humphrey.

Additional information

This work is dedicated to Prof. Dr. Y. C. Fung in celebration of his 90th birthday.

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Cardamone, L., Valentín, A., Eberth, J.F. et al. Origin of axial prestretch and residual stress in arteries. Biomech Model Mechanobiol 8, 431–446 (2009). https://doi.org/10.1007/s10237-008-0146-x

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