Mechanics of the Formation and Rupture of Human Aneurysms
-
摘要: 在大变形超弹性理论框架下研究了内压、轴向拉伸和扭转联合作用下人体动脉壁的力学响应,应用结构不稳定性理论对动脉瘤生成的可能性进行了解释,应用材料强度理论对动脉瘤破裂的可能性进行了分析.考虑动脉壁中残余应力和平滑肌主动作用的影响,用纤维加强各向异性不可压超弹性复合材料两层厚壁圆筒模型来模拟动脉壁的力学特性.给出了正常和几种非正常状态下动脉壁的变形曲线和应力分布.变形和稳定性分析结果表明该文模型可以模拟正常状态下动脉壁的均匀变形,还可以模拟在动脉壁中弹性蛋白纤维和胶原蛋白纤维强度降低的非正常状态下动脉瘤生成的可能性及动脉瘤的增长.应力和强度分析结果表明该文模型可以模拟当动脉瘤中的最大应力超过管壁的强度时动脉瘤破裂的可能性.Abstract: Mechanical response of human arterial wall under the combined loading of in flation, axial extension and torsion was examined with in the framework of the large deformation hyperelastic theory. The probability for the formation of aneurysm was explained with the instability theory of structure and the probability for its rupture was explained with the strength theory of material. Taking account of the residual stress and the smooth muscleactivity, a two layer thick-walled circular cylindrical tube model with fiber-rein forced composite-based incompressible anisotropic hyper-elastic materials was employed to model the mechanical behavior of the arterial wall. The deformation curves and the stress distributions of the arterial wall are given both under normal conditions and abnormal conditions. With the results of the deformation and the structureins tability analysis, that not only the uniform in flation deformation of the arterial wall under normal conditions, but also the formation and growth of ananeurysm underabnormal conditions such as the stiffness of the elastic and collagen fibers is decreased to a certain degree may be described by this model. With the results of the stresses and the material strength analysis, that the rupture of aneurysm if the wall stress is larger than its strength may be described by this model, too.
-
[1] Humphrey J D. Cardiovascular Solid Mechanics, Cells, Tissures and Organs[M]. New York: Springer-Verlag, 2002. [2] Vorp D A. Biomechanics of abdominal aortic aneurysm[J]. J Biomech, 2007, 40(9): 1887-1902. doi: 10.1016/j.jbiomech.2006.09.003 [3] Volokh K Y, Vorp D A. A model of growth and rupture of abdominal aortic aneurysm[J]. J Biomech, 2008, 41(5): 1015-1021. doi: 10.1016/j.jbiomech.2007.12.014 [4] Humphrey J D. Continuum biomechanics of soft biological tissues[J]. Proc R Soc A, 2003, 459(1): 1-44. doi: 10.1098/rspa.2002.1109 [5] Watton P N, Hill N A, Heil M. A mathematical model for the growth of abdominal aortic aneurysm[J]. Biomechan Model Mechanobiol, 2004, 3(1): 98-113. doi: 10.1007/s10237-004-0052-9 [6] Humphrey J D. Intracranial saccular aneurysms[C]Biomechanics of Soft Tissue in Cardiovascular Systems. New York: Springer Wien, 2003. [7] David G, Humphrey J D. Further evidence for the dynamic stability of intracranial saccular aneurysms[J]. J Biomech, 2003, 36(7): 1043-1150. doi: 10.1016/S0021-9290(03)00034-4 [8] Humphrey J D, Canham P B. Structure, mechanical properties and mechanics of intracranial saccular aneurysms[J]. J Elasticity, 2000, 61(1): 49-81. doi: 10.1023/A:1010989418250 [9] Kroon M, Holzapfel G A. Estimation of the distributions of anisotropic, elastic properties and wall stresses of saccular cerebral aneurysms by inverse analysis[J]. Proceedings of the Royal Society A, 2008, 464(6): 807-825. doi: 10.1098/rspa.2007.0332 [10] Holzapfel G A, Gasser T C, Stadler M. Structural model for the viscoelastic behavior of arterial walls, continuum formulations and finite element analysis[J]. Eur J Mech A/Solids, 2002, 21(3): 441-463. doi: 10.1016/S0997-7538(01)01206-2 [11] Taber L A. Nonlinear Theory of Elasticity: Applications in Biomechanics[M]. NJ: World Scientific, River Edge, 2004. [12] Holzapfel G A, Gasser T C, Ogden R W. A new constitutive framework for arterial wall mechanics and a comparative study of material models[J]. J Elasticity, 2000, 61(1): 1-48. doi: 10.1023/A:1010835316564 [13] Holzapfel G A, Sommer G, Regitnig P. Anisotropic mechanical properties of tissue components in human atherosclerotic plaques[J]. J Biomech Eng, 2004, 126(5): 657-665. doi: 10.1115/1.1800557 [14] Driessen N J B, Wilson W, Bouten C V C, et al. A computational model for collagen fiber remodeling in the arterial wall[J]. J Theoretical Biology, 2004, 226(1): 53-64. doi: 10.1016/j.jtbi.2003.08.004 [15] Gasser T C, Ogden R W, Holzapfel G A. Hyperelastic modeling of arterial layers with distributed collagen fiber orientations[J]. J R Soc Interface, 2006, 3(1): 15-35. doi: 10.1098/rsif.2005.0073 [16] Vito R P, Dixon S A. Blood vessel constitutive models-1995-2002[J]. Annu Rev Biomed Eng, 2003, 5(4): 413-439. doi: 10.1146/annurev.bioeng.5.011303.120719 [17] Fung Y C. Biomechanics: Motion, Flow, Stress and Growth[M]. New York :Springer-Verlag, 1990. [18] Baek S, Gleason R L, Rajagopal K R, et al. Theory of small on large; potential utility in computations of fluid-solid interactions in arteries[J]. Computer Methods in Applied Mechanics and Engineering, 2007, 196(15) 3070-3078. [19] Masson I, Boutouyrie P, Laurent S, et al. Characterization of arterial wall mechanical behavior and stresses from human clinical data[J]. J Biomech, 2008, 41(12): 2618-2627. doi: 10.1016/j.jbiomech.2008.06.022 [20] Vena P, Gastadi D, Socci L, et al. An anisotropic model for tissue growth and remodeling during early development of cerebral aneurysms[J]. Computational Materials Science, 2008, 43(3): 565-577. doi: 10.1016/j.commatsci.2007.12.023 [21] Baek S, Rajagopal K R, Humphrey J D. A theoretical model of enlarging intracranial fusiform aneurysm[J]. J Biomechanical Engineering, 2006, 128(1): 142-149. doi: 10.1115/1.2132374 [22] Haughton D M. Ogden R W. On the incremental equations in non-linear elasticity—Ⅱ: Bifurcation of pressurized spherical shells[J]. J Mech Phys Solids, 1978, 26(1): 111-138. doi: 10.1016/0022-5096(78)90017-0 [23] Kroon M, Holzapfel G A. A theoretical model for fibroblast-controlled growth of saccular cerebral aneurysms[J]. J Theoretical Biology, 2009, 257(1): 73-83. doi: 10.1016/j.jtbi.2008.10.021 [24] Holzapfel G A, Gasser T C. Computational stress-deformation analysis of arterial wall including high-pressure response[J]. Int J Cardiology, 2007, 116(1): 78-85. doi: 10.1016/j.ijcard.2006.03.033
点击查看大图
计量
- 文章访问数: 1454
- HTML全文浏览量: 113
- PDF下载量: 936
- 被引次数: 0