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Mechanics of formation and rupture of human aneurysm. (English) Zbl 1378.92037

Summary: The mechanical response of the human arterial wall under the combined loading of inflation, axial extension, and torsion is examined within the framework of the large deformation hyper-elastic theory. The probability of the aneurysm formation is explained with the instability theory of structure, and the probability of its rupture is explained with the strength theory of material. Taking account of the residual stress and the smooth muscle activities, a two layer thick-walled circular cylindrical tube model with fiber-reinforced composite-based incompressible anisotropic hyper-elastic materials is employed to model the mechanical behavior of the arterial wall. The deformation curves and the stress distributions of the arterial wall are given under normal and abnormal conditions. The results of the deformation and the structure instability analysis show that the model can describe the uniform inflation deformation of the arterial wall under normal conditions, as well as formation and growth of an aneurysm under abnormal conditions such as the decreased stiffness of the elastic and collagen fibers. From the analysis of the stresses and the material strength, the rupture of an aneurysm may also be described by this model if the wall stress is larger than its strength.

MSC:

92C50 Medical applications (general)
74B20 Nonlinear elasticity
74L15 Biomechanical solid mechanics
92C10 Biomechanics
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[1] Humphrey, J. D. Cardiovascular Solid Mechanics, Cells, Tissues and Organs, Springer-Verlag, New York (2002)
[2] Vorp, D. A. Biomechanics of abdominal aortic aneurysm. Journal of Biomechanics 40(9), 1887–1902 (2007) · doi:10.1016/j.jbiomech.2006.09.003
[3] Volokh, K. Y. and Vorp, D. A. A model of growth and rupture of abdominal aortic aneurysm. Journal of Biomechanics 41(5), 1015–1021 (2008) · doi:10.1016/j.jbiomech.2007.12.014
[4] Humphrey, J. D. Continuum biomechanics of soft biological tissues. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 459(1), 3–46 (2003) · Zbl 1116.74385 · doi:10.1098/rspa.2002.1060
[5] Watton, P. N., Hill, N. A., and Heil, M. A mathematical model for the growth of abdominal aortic aneurysm. Biomechanics and Modeling in Mechanobiology 3(2), 98–113 (2004) · doi:10.1007/s10237-004-0052-9
[6] Humphrey, J. D. Intracranial saccular aneurysms. Biomechanics of Soft Tissue in Cardiovascular Systems, Springer Wien, New York (2003)
[7] David, G. and Humphrey, J. D. Further evidence for the dynamic stability of intracranial saccular aneurysms. Journal of Biomechanics 36(7), 1043–1150 (2003) · doi:10.1016/S0021-9290(03)00083-6
[8] Humphrey, J. D. and Canham, P. B. Structure, mechanical properties, and mechanics of intracranial saccular aneurysms. Journal of Elasticity 61(1–3), 49–81 (2000) · Zbl 0973.92016 · doi:10.1023/A:1010989418250
[9] Kroon, M. and Holzapfel, G. A. Estimation of the distributions of anisotropic, elastic properties and wall stresses of saccular cerebral aneurysms by inverse analysis. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464(6), 807–825 (2008) · Zbl 1174.74004 · doi:10.1098/rspa.2007.0332
[10] Holzapfel, G. A., Gasser, T. C., and Stadler, M. A structural model for the viscoelastic behavior of arterial walls: continuum formulations and finite element analysis. European Journal of Mechanics A/Solids 21(3), 441–463 (2002) · Zbl 1100.74597 · doi:10.1016/S0997-7538(01)01206-2
[11] Taber, L. A. Nonlinear Theory of Elasticity: Applications in Biomechanics, World Scientific Publishing Company, New Jersy (2004) · Zbl 1052.74001
[12] Holzapfel, G. A., Gasser, T. C., and Ogden, R. W. A new constitutive framework for arterial wall mechanics and a comparative study of material models. Journal of Elasticity 61(1–3), 1–48 (2000) · Zbl 1023.74033 · doi:10.1023/A:1010835316564
[13] Holzapfel, G. A., Sommer, G., and Regitnig, P. Anisotropic mechanical properties of tissue components in human atherosclerotic plaques. Journal of Biomechanical Engineering 126(5), 657–665 (2004) · doi:10.1115/1.1800557
[14] Driessen, N. J. B., Wilson, W., Bouten, C. V. C., and Baaijens, F. P. T. A computational model for collagen fiber remodeling in the arterial wall. Journal of Theoretical Biology 226(1), 53–64 (2004) · doi:10.1016/j.jtbi.2003.08.004
[15] Gasser, T. C., Ogden, R. W., and Holzapfel, G. A. Hyperelastic modeling of arterial layers with distributed collagen fiber orientations. Journal of the Royal Society Interface 3(1), 15–35 (2006) · doi:10.1098/rsif.2005.0073
[16] Vito, R. P. and Dixon, S. A. Blood vessel constitutive models–1995–2002. Annual Review of Biomedical Engineering 5(4), 413–439 (2003) · doi:10.1146/annurev.bioeng.5.011303.120719
[17] Fung, Y. C. Biomechanics: Motion, Flow, Stress and Growth, Springer-Verlag, New York (1990) · Zbl 0743.92007
[18] Baek, S., Gleason, R. L., Rajagopal, K. R., and Humphrey, J. D. Theory of small on large: potential utility in computations of fluid-solid interactions in arteries. Computer Methods in Applied Mechanics and Engineering 196(15), 3070–3078 (2007) · Zbl 1127.74026 · doi:10.1016/j.cma.2006.06.018
[19] Masson, I., Boutouyrie, P., Laurent, S., Humphrey, J. D., and Zidi, M. Characterization of arterial wall mechanical behavior and stresses from human clinical data. Journal of Biomechanics 41(12), 2618–2627 (2008) · doi:10.1016/j.jbiomech.2008.06.022
[20] Vena, P., Gastadi, D., Socci, L., and Pennati, G. An anisotropic model for tissue growth and remodeling during early development of cerebral aneurysms. Computational Materials Science 43(3), 565–577 (2008) · doi:10.1016/j.commatsci.2007.12.023
[21] Baek, S., Rajagopal, K. R., and Humphrey, J. D. A theoretical model of enlarging intracranial fusiform aneurysm. Journal of Biomechanical Engineering 128(1), 142–149 (2006) · doi:10.1115/1.2132374
[22] Haughton, D. M. and Ogden, R. W. On the incremental equations in non-linear elasticity-II: bifurcation of pressurized spherical shells. Journal of the Mechanics and Physics of Solids 26(2), 111–138 (1978) · Zbl 0401.73077 · doi:10.1016/0022-5096(78)90017-0
[23] Kroon, M. and Holzapfel, G. A. A theoretical model for fibroblast-controlled growth of saccular cerebral aneurysms. Journal of Theoretical Biology 257(1), 73–83 (2009) · Zbl 1400.92097 · doi:10.1016/j.jtbi.2008.10.021
[24] Holzapfel, G. A., and Gasser, T. C. Computational stress-deformation analysis of arterial walls including high-pressure response. International Journal of Cardiology 116(1), 78–85 (2007) · doi:10.1016/j.ijcard.2006.03.033
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