Hyperelastic modelling of arterial layers with distributed collagen fibre orientations

Journal of the Royal Society Interface - Tập 3 Số 6 - Trang 15-35 - 2006
Thomas C. Gasser1, Ray W. Ogden2, Gerhard A. Holzapfel3,1
1School of Engineering Sciences, Royal Institute of Technology (KTH)Osquars backe 1, 100 44 Stockholm, Sweden
2Department of Mathematics University Gardens, University of GlasgowGlasgow G12 8QW, UK
3Computational Biomechanics, Graz University of TechnologySchiesstattgasse 14-B, 8010 Graz, Austria

Tóm tắt

Constitutive relations are fundamental to the solution of problems in continuum mechanics, and are required in the study of, for example, mechanically dominated clinical interventions involving soft biological tissues. Structural continuum constitutive models of arterial layers integrate information about the tissue morphology and therefore allow investigation of the interrelation between structure and function in response to mechanical loading. Collagen fibres are key ingredients in the structure of arteries. In the media (the middle layer of the artery wall) they are arranged in two helically distributed families with a small pitch and very little dispersion in their orientation (i.e. they are aligned quite close to the circumferential direction). By contrast, in the adventitial and intimal layers, the orientation of the collagen fibres is dispersed, as shown by polarized light microscopy of stained arterial tissue. As a result, continuum models that do not account for the dispersion are not able to capture accurately the stress–strain response of these layers. The purpose of this paper, therefore, is to develop a structural continuum framework that is able to represent the dispersion of the collagen fibre orientation. This then allows the development of a new hyperelastic free-energy function that is particularly suited for representing the anisotropic elastic properties of adventitial and intimal layers of arterial walls, and is a generalization of the fibre-reinforced structural model introduced by Holzapfel & Gasser (Holzapfel & Gasser 2001 Comput. Meth. Appl. Mech. Eng . 190 , 4379–4403) and Holzapfel et al . (Holzapfel et al . 2000 J. Elast . 61 , 1–48). The model incorporates an additional scalar structure parameter that characterizes the dispersed collagen orientation. An efficient finite element implementation of the model is then presented and numerical examples show that the dispersion of the orientation of collagen fibres in the adventitia of human iliac arteries has a significant effect on their mechanical response.

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Tài liệu tham khảo

Abè H Hayashi K& Sato M Data book on mechanical properties of living cells tissues and organs. 1996 New York:Springer.

Bergel D. H. 1960 The visco-elastic properties of the arterial wall. Ph.D. thesis University of London.

10.1115/1.1287158

10.1016/0002-9149(84)90750-1

10.1115/1.1318906

10.1093/cvr/23.11.973

10.1161/01.RES.23.1.61

10.1115/1.3138417

10.1016/0021-9290(84)90077-0

10.1115/1.3138600

Clark J.M, 1979, Structural integration of the arterial wall, Lab. Invest, 40, 587

10.1161/01.ATV.5.1.19

10.1152/ajpcell.1978.234.5.C146

10.1016/0021-9290(80)90338-3

10.1016/S0021-9290(97)00025-0

10.1016/0021-9290(72)90047-4

10.1159/000159104

10.1161/01.STR.29.8.1595

Fisher N.I Lewis T.L& Embleton B.J.J Statistical analysis of spherical data. 1987 Cambridge:Cambridge University Press.

10.1039/tf9615700829

Freed A. D. Einstein D. R. & Vesely I. In press. Invariant formulation for dispersed transverse isotropy in aortic heart valves. An efficient means for modeling fiber splay. Biomech. Model. Mechanobiol.

Fuchs R.F, 1900, Zur Physiologie und Wachstumsmechanik des Blutgefäßsystems, Arch. Ges. Physiol, 28

Fung Y.C Biomechanics: mechanical properties of living tissue. 2nd edn. 1993 New York:Springer.

Fung Y.C, 1979, Pseudoelasticity of arteries and the choice of its mathematical expression, Am. J. Physiol, 237, H620

10.1007/s00466-002-0347-6

10.1115/1.1485284

Glagov S, 1993, Mechanical functional role of non-atherosclerotic intimal thickening, Front. Med. Biol. Eng, 5, 37

10.1115/1.2798291

Hartman J.D, 1977, Structural changes within the media of coronary arteries related to intimal thickening, Am. J. Pathology, 89, 13

10.1007/978-3-7091-2736-0_2

Holzapfel G.A, 2000, A continuum approach for engineering

10.1016/S0045-7825(00)00323-6

Holzapfel G.A& Ogden R.W Biomechanics of soft tissue in cardiovascular systems. 2003 Wien:Springer CISM courses and lectures no. 441.

Holzapfel G.A& Ogden R.W Mechanics of biological tissue. In press Heidelberg:Springer.

Holzapfel G. A. & Ogden R. W. Submitted. Three-dimensional residual stress distributions of human aorta layers: a mathematical model.

10.1016/S0010-4825(98)00022-5

10.1023/A:1010835316564

10.1016/S0997-7538(01)01206-2

10.1114/1.1492812

10.1115/1.1695572

10.1115/1.1800557

Holzapfel G. A. Sommer G. Auer M. & Regitnig P. Submitted. Layer-specific three-dimensional geometry of dissected human aortas with intimal thickening.

Holzapfel G. A. Sommer G. Gasser T. C. & Regitnig P. In press. Determination of the layer-specific mechanical properties of human coronary arteries with non-atherosclerotic intimal thickening and related constitutive modelling. Am. J. Physiol ..

10.1007/s10237-002-0022-z

10.1115/1.1406131

Humphrey J.D, 2002, Cells, tissues, and organs

10.1098/rspa.2002.1060

10.1023/A:1010989418250

10.1142/S0218202502001714

10.1007/s10237-003-0033-4

10.1115/1.2798284

10.1016/0020-7225(84)90090-9

Krajcinovic D Damage mechanics. 1996 Amsterdam:North-Holland.

10.1016/0021-9290(83)90041-6

10.1115/1.2795944

10.1016/S0020-7683(02)00352-9

Mathematica 5.1.2005 Wolfram Research Inc.

10.1002/nme.1620371202

10.1016/0020-7683(95)00274-X

10.1016/j.compscitech.2003.11.010

10.1016/0022-5096(78)90012-1

Ogden R.W Non-linear elastic deformations. 1997 New York:Dover.

Oktay H.S, 1991, ASME 1991 Biomechanics Symp., AMD

10.1161/01.RES.24.1.1

10.1016/S0021-9150(01)00766-3

10.1016/S0021-9290(97)00032-8

Rhodin J.A.G, 1980, Handbook of physiology, the cardiovascular system, 1

10.1139/y57-080

Roach M.R, 1994, Variations in strength of the porcine aorta as a function of location, Clin. Invest. Med, 17, 308

10.1113/jphysiol.1881.sp000088

10.1115/1.1544508

10.1139/y81-160

Schmid F. Sommer G. Rappolt M. Schulze-Bauer C. A. J. Regitnig P. Holzapfel G. A. Laggner P. & Amenitsch H. In press. In situ tensile testing of human aortas by time-resolved small angle X-ray scattering. Synchro. Rad.

Schultze-Jena B.S, 1939, Über die schraubenförmige Struktur der Arterienwand, Gegenbauers Morphol. Jahrbuch, 83, 230

Schulze-Bauer C.A.J, 2002, Proc. 13th Conf. European Society of Biomechanics, Wroclaw, Poland

10.1115/1.1574331

10.1016/S0174-173X(85)80024-8

Silver F.H, 1989, Mechanical properties of the aorta: a review, Crit. Rev. Biomed. Eng, 17, 323

10.1016/0045-7825(91)90100-K

10.1115/1.2895529

10.1007/978-3-7091-4336-0_1

Stålhand J. 2005 Arterial mechanics. Noninvasive identification of constitutive parameters and residual stress. Ph.D. thesis Linköping University Sweden.

Stary H.C Atlas of atherosclerosis: progression and regression. 2003 Boca Raton:Parthenon Publishing Group Limited.

Staubesand J, 1959, Angiology, ch. 2, 23

10.1023/A:1011587522951

10.1016/0021-9290(87)90262-4

Taylor R.L. 2000 Berkeley:University of California.

10.1161/01.RES.32.5.577

10.3233/BIR-1977-14405

Vito R.P, 1982, Proc. 35th Ann. Conf. Engineering in Medicine and Biology (ACEMB), Pennsylvania

10.1016/B978-0-12-363709-3.50012-7

10.1016/0021-9290(81)90056-7

Weisstein E. W. 2005 Erfi. MathWorld—a Wolfram web resource. Available at http://mathworld.wolfram.com/Erfi.html.

10.1016/0021-9290(88)90240-0

10.1016/0021-9290(83)90080-5

10.1088/0031-9155/40/10/002

10.1016/j.jbiomech.2003.11.026

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Journal of the Royal Society Interface

Tập 3 Số 6

15-35

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