Skip to main content
SpringerLink
Log in

Growth and remodeling in a thick-walled artery model: effects of spatial variations in wall constituents

  • Original Paper
  • Published:
Biomechanics and Modeling in Mechanobiology Aims and scope Submit manuscript

Abstract

A mathematical model is presented for growth and remodeling of arteries. The model is a thick-walled tube composed of a constrained mixture of smooth muscle cells, elastin and collagen. Material properties and radial and axial distributions of each constituent are prescribed according to previously published data. The analysis includes stress-dependent growth and contractility of the muscle and turnover of collagen fibers. Simulations were conducted for homeostatic conditions and for the temporal response following sudden hypertension. Numerical pressure–radius relations and opening angles (residual stress) show reasonable agreement with published experimental results. In particular, for realistic material and structural properties, the model predicts measured variations in opening angles along the length of the aorta with reasonable accuracy. These results provide a better understanding of the determinants of residual stress in arteries and could lend insight into the importance of constituent distributions in both natural and tissue-engineered blood vessels.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Berry C, Greenwald SE, Rivett JF (1975) Static mechanical properties of the developing and mature rat aorta. Cadiovasc Res 9:669–78

    Article  Google Scholar 

  • Bunce DFM (1974) Atlas of arterial histology. Warren H. Green, St Louis

    Google Scholar 

  • Chuong CJ, Fung YC (1986) On residual stresses in arteries. J Biomech Eng 108:189–92

    Article  Google Scholar 

  • Conte MS (1998) The ideal small arterial substitute: a search for the Holy Grail? FASEB J 12:43–5

    MathSciNet  Google Scholar 

  • Cox RH (1975) Arterial wall mechanics and composition and the effects of smooth muscle activation. Am J Physiol 229:807–12

    Google Scholar 

  • Davidson JM, Hill KE, Alford JL (1986) Developmental changes in collagen and elastin biosynthesis in the porcine aorta. Dev Biol 118:103–11

    Article  Google Scholar 

  • Davis EC (1993) Stability of elastin in the developing mouse aorta: a quantitative radioautographic study. Histochemistry 100:17–6

    Article  Google Scholar 

  • Dobrin P (1997) Physiology and pathophysiology of blood vessels. In: Sidawy ANSB, DePalma RG (eds) The basic science of vascular disease. Futura, New York, pp 69–05

    Google Scholar 

  • Feldman SA, Glagov S (1971) Transmedial collagen and elastin gradients in human aortas: reversal with age. Atherosclerosis 13:385–94

    Article  Google Scholar 

  • Fischer GM, Llaurado JG (1966) Collagen and elastin content in canine arteries selected from functionally different vascular beds. Circ Res 19:394–99

    Google Scholar 

  • Fridez P, Makino A, Kakoi D, Miyazaki H, Meister JJ, Hayashi K, Stergiopulos N (2002) Adaptation of conduit artery vascular smooth muscle tone to induced hypertension. Ann Biomed Eng 30:905–16

    Article  Google Scholar 

  • Friedman MH, O’Brien V, Ehrlich LW (1975) Calculations of pulsatile flow through a branch: implications for the hemodynamics of atherogenesis. Circ Res 36:277–85

    Google Scholar 

  • Fung YC, Liu SQ (1989) Change of residual strains in arteries due to hypertrophy caused by aortic constriction. Circ Res 65:1340–349

    Google Scholar 

  • Fung YC, Liu SQ (1991) Changes of zero-stress state of rat pulmonary arteries in hypoxic hypertension. J Appl Physiol 70:2455–470

    Article  Google Scholar 

  • Furchgott RF, Zawadzki JV (1980) The obligatory role of endothelial cells in the relaxation of arterial smooth muscle by acetylcholine. Nature 288:373–76

    Article  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 126:371–81

    Article  Google Scholar 

  • Gleason RL, Humphrey JD (2005) A mixture model of arterial growth and remodeling in hypertension: Altered muscle tone and tissue turnover. J Vasc Res 41:352–63

    Article  Google Scholar 

  • Greenwald SE, Moore JE Jr, Rachev A, Kane TP, Meister JJ (1997) Experimental investigation of the distribution of residual strains in the artery wall. J Biomech Eng 119:438–44

    Article  Google Scholar 

  • Guo X, Kono Y, Mattrey R, Kassab GS (2002) Morphometry and strain distribution of the C57BL/6 mouse aorta. Am J Physiol Heart Circ Physiol 283:H1829–H1837

    Google Scholar 

  • Han HC, Fung YC (1991) Species dependence of the zero-stress state of aorta: pig versus rat. J Bio Eng 126:371–81

    Google Scholar 

  • Holtz J, Forstermann U, Pohl U, Giesler M, Bassenge E (1984) Flow-dependent, endothelium-mediated dilation of epicardial coronary arteries in conscious dogs: effects of cyclooxygenase inhibition. J Cardiovasc Pharmacol 6:1161–169

    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 Elasticity 61:1–8

    Article  MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  • Humphrey JD, Rajagopal KR (2002) A constrained mixture model for growth and remodeling of soft tissues. Math Models Methods Appl Sci 12:407–30

    Article  MATH  MathSciNet  Google Scholar 

  • Johnson P (1981) The myogenic response. In: Bohr DF, Somlyo AP, Sparks HV Jr (eds) Handbook of physiology. The cardiovascular system. vascular smooth muscle. Sec. II. American Physiological Society, Bethesda, pp 409–42

    Google Scholar 

  • Kamiya A, Togawa T (1980) Adaptive regulation of wall shear stress to flow change in the canine carotid artery. Am J Physiol 239:H14–H21

    Google Scholar 

  • Langille BL (1993) Remodeling of developing and mature arteries: endothelium, smooth muscle, and matrix. J Cardiovasc Pharmacol 21 (Suppl 1):S11–S17

    Google Scholar 

  • Lefevre M, Rucker RB (1980) Aorta elastin turnover in normal and hypercholesterolemic Japanese quail. Biochim Biophys Acta 630:519–29

    Google Scholar 

  • Liu SQ, Fung YC (1988) Zero-stress states of arteries. J Biomech Eng 110:82–4

    Article  Google Scholar 

  • MacKenna DA, Vaplon SM, McCulloch AD (1997) Microstructural model of perimysial collagen fibers for resting myocardial mechanics during ventricular filling. Am J Physiol 273:H1576–H1586

    Google Scholar 

  • Matsumoto T, Hayashi K (1996) Stress and strain distribution in hypertensive and normotensive rat aorta considering residual strain. J Biomech Eng 118:62–3

    Article  Google Scholar 

  • Mirnajafi A, Raymer J, Scott MJ, Sacks MS (2005) The effects of collagen fiber orientation on the flexural properties of pericardial heterograft biomaterials. Biomaterials 26:795–04

    Article  Google Scholar 

  • Nissen R, Cardinale GJ, Udenfriend S (1978) Increased turnover of arterial collagen in hypertensive rats. Proc Natl Acad Sci U S A 75:451–53

    Article  Google Scholar 

  • Olivetti G, Anversa P, Melissari M, Loud AV (1980) Morphometry of medial hypertrophy in the rat thoracic aorta. Lab Invest 42:559–65

    Google Scholar 

  • 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 27:459–68

    Article  Google Scholar 

  • Rachev A, Stergiopulos N, Meister JJ (1998) A model for geometric and mechanical adaptation of arteries to sustained hypertension. J Biomech Eng 120:9–7

    Article  Google Scholar 

  • Rhodin J (1979) Architecture of the Vessel Wall. In: Berne RM (ed) Handbook of physiology, Sect 2, vol 2. American Physiological Society

  • Rodriguez EK, Hoger A, McCulloch AD (1994) Stress-dependent finite growth in soft elastic tissues. J Biomech 27:455–67

    Article  Google Scholar 

  • Sacks MS (2003) Incorporation of experimentally-derived fiber orientation into a structural constitutive model for planar collagenous tissues. J Biomech Eng 125:280–87

    Article  Google Scholar 

  • Saini A, Berry C, Greenwald S (1995) Effect of age and sex on residual stress in the aorta. J Vasc Res 32:398–05

    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 38:237–46

    Article  Google Scholar 

  • Taber LA (2000) Pattern formation in a nonlinear membrane model for epithelial morphogenesis. Acta Biotheoretica 48:47–3

    Article  Google Scholar 

  • Taber LA (1998) A model for aortic growth based on fluid shear and fiber stresses. J Biomech Eng 120:348–54

    Article  Google Scholar 

  • Taber LA (2004) Nonlinear theory of elasticity: applications in biomechanics. World Scientific, Singapore

    MATH  Google Scholar 

  • Taber LA, Eggers DW (1996) Theoretical study of stress-modulated growth in the aorta. J Theor Biol 180:343–57

    Article  Google Scholar 

  • Taber LA, Humphrey JD (2001) Stress-modulated growth, residual stress, and vascular heterogeneity. J Biomech Eng 123:528–35

    Article  Google Scholar 

  • von Maltzahn WW, Warriyar RG, Keitzer WF (1984) Experimental measurements of elastic properties of media and adventitia of bovine carotid arteries. J Biomech 17:839–47

    Article  Google Scholar 

  • Vossoughi J, Hedjazi Z, Borris F (1993) Intimal residual stress and strain in large arteries. In: Langrana NA, Friedman MH, Grood ES (eds) Proc summer bioengineering conf. ASME, New York, pp 434–37

    Google Scholar 

  • Zeller PJ, Skalak TC (1998) Contribution of individual structural components in determining the zero-stress state in small arteries. J Vasc Res 35:8–7

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Biomedical Engineering, Washington University, Campus Box 1097, St Louis, MO, 63130, USA

    Patrick W. Alford & Larry A. Taber

  2. Department of Biomedical Engineering and M.E. DeBakey Institute, Texas A&M University, College Station, TX, 77843, USA

    Jay D. Humphrey

Authors
  1. Patrick W. Alford
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jay D. Humphrey
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Larry A. Taber
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Larry A. Taber.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alford, P.W., Humphrey, J.D. & Taber, L.A. Growth and remodeling in a thick-walled artery model: effects of spatial variations in wall constituents. Biomech Model Mechanobiol 7, 245–262 (2008). https://doi.org/10.1007/s10237-007-0101-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10237-007-0101-2

Keywords

Search

Navigation