EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 17 (2022) Math. Model. Nat. Phenom., 17 (2022) 20 References
Open Access
Issue
Math. Model. Nat. Phenom.
Volume 17, 2022
Article Number 20
Number of page(s) 20
DOI https://doi.org/10.1051/mmnp/2022022
Published online 11 July 2022
  1. H. Adams, V.S. Ban, V. Leinonen, S.G. Aoun, J. Huttunen, T. Saavalainen, A. Lindgren, J. Frosen, M. Fraunberg, T. Koivisto, J. Hernesniemi, B.G. Welch, J.E. Jaaskelainen and T.J. Huttunen, Risk of shunting after aneurysmal subarachnoid hemorrhage: a collaborative study and initiation of a consortium. Stroke 47 (2016) 2488–2496. [CrossRef] [PubMed] [Google Scholar]
  2. D. Balzani, J. Schröder and D. Gross, Simulation of discontinuous damage incorporating residual stresses in circumferentially overstretched atherosclerotic arteries. Acta Biomater. 2 (2006) 609–618. [CrossRef] [Google Scholar]
  3. D. Balzani, J. Schröder and D. Gross, Numerical simulation of residual stresses in arterial walls. Comput. Mater. Sci. 39 (2007) 117–123. [CrossRef] [Google Scholar]
  4. J.V. Beck and K.J. Arnold, Parameter Estimation in Engineering and Science. Wiley, New York (1977). [Google Scholar]
  5. F.A. Braeu, A. Seitz, R.C. Aydin and C.J. Cyron, Homogenized constrained mixture models for anisotropic volumetric growth and remodeling. Biomech. Model. Mechan. 16 (2017) 889–906. [CrossRef] [PubMed] [Google Scholar]
  6. S. Brandstaeter, S.L. Fuchs, J. Biehler, R.C. Aydin, W.A. Wall and C.J. Cyron, Global sensitivity analysis of a homogenized constrained mixture model of arterial growth and remodeling. J. Elast. 145 (2021) 191–221. [CrossRef] [Google Scholar]
  7. F. Cacho, M. Doblare and G.A. Holzapfel, A procedure to simulate coronary artery bypass graft surgery. Med. Biol. Eng. Comput. 45 (2007) 819–827. [CrossRef] [PubMed] [Google Scholar]
  8. D.B. Camasao and D. Mantovani, The mechanical characterization of blood vessels and their substitutes in the continuous quest for physiological-relevant performances. A critical review. Mater. Today Biol. 10 (2021) 100106. [CrossRef] [Google Scholar]
  9. P.B. Canham, H.M. Finlay, J.A. Kiernan and G.G. Ferguson, Layered structure of saccular aneurysms assessed by collagen birefringence. Neurol. Res. 21 (1999) 618–626. [CrossRef] [PubMed] [Google Scholar]
  10. C.J. Chuong and Y.C. Fung, Three-dimensional stress distribution in arteries. J. Biomech. Eng. 105 (1983) 268–274. [CrossRef] [PubMed] [Google Scholar]
  11. J.T. Connell, Saphenovenous graft aneurysm: a rare complication of CABG. Case Rep. Cardiol. 2017 (2017) 8101489. [Google Scholar]
  12. C.J. Cyron and J.D. Humphrey, Growth and remodeling of load-bearing biological soft tissues. Meccanica 52 (2016) 645–664. [Google Scholar]
  13. M. Diodato and E.G. Chedrawy, Coronary artery bypass graft surgery: the past, present, and future of myocardial revascularisation. Surg. Res. Pract. 2014 (2014) 726158. [Google Scholar]
  14. Y.C. Fung, Biomechanics: Motion, Flow, Stress, and Growth. Springer, New York (1990). [Google Scholar]
  15. T.C. Gasser, R.W. Ogden and G.A. Holzapfel, Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. J. R. Soc. Interface 3 (2005) 15–35. [Google Scholar]
  16. M.A. Geith, L. Nothdurfter, M. Heiml, E. Agrafiotis, M. Gruber, G. Sommer, T.G. Schratzenstaller and G.A. Holzapfel, Quantifying stent-induced damage in coronary arteries by investigating mechanical and structural alterations. Acta Biomater. 116 (2020) 285–301. [CrossRef] [PubMed] [Google Scholar]
  17. M. Gierig, P. Wriggers and M. Marino, Computational model of damage-induced growth in soft biological tissues considering the mechanobiology of healing. Biomech. Model. Mechanobiol. 20 (2021) 1297–1315. [CrossRef] [PubMed] [Google Scholar]
  18. H. Gu, A. Chua, T. Bien-Kemm and K.C. Hung, Nonlinear finite element simulation to elucidate the efficacy of slit arteriotomy for end-to-side arterial anastomosis in microsurgery. J. Biomech. 39 (2006) 435–443. [CrossRef] [Google Scholar]
  19. B. Guerciotti, C. Vergara, L. Azzimonti, L. Forzenigo, A. Buora, P. Biondetti and M. Domanin, Computational study of the fluid-dynamics in carotids before and after endarterectomy. J. Biomech. 49 (2016) 26–38. [CrossRef] [Google Scholar]
  20. K. Guevorkian, M.-J. Colbert, M. Durth, S. Dufour and F. Brochard-Wyart, Aspiration of biological viscoelastic drops. Phys. Rev. Lett. 104 (2010) 218101. [CrossRef] [PubMed] [Google Scholar]
  21. A. Hamedzadeh, T.C. Gasser and S. Federico, On the constitutive modelling of recruitment and damage of collagen fibres in soft biological tissues. Eur. J. Mech. A-Solid. 72 (2018) 483–496. [CrossRef] [Google Scholar]
  22. J. Helfenstein, M. Jabareen, E. Mazza and S. Govindjee, On non-physical response in models for fiber-reinforced hyperelastic materials. Int. J. Solids Struct. 47 (2010) 2056–2061. [CrossRef] [Google Scholar]
  23. M. Hofer, G. Rappitsch, K. Perktold, W. Trubel and H. Schima, Numerical study of wall mechanics and fluid dynamics in end-to-side anastomoses and correlation to intimal hyperplasia. J. Biomech. 29 (1996) 1297–1308. [CrossRef] [Google Scholar]
  24. G.A. Holzapfel, T.C. Gasser and R.W. Ogden, A new constitutive framework for arterial wall mechanics and a comparative study of material models. J. Elast. 61 (2000) 1–48. [CrossRef] [Google Scholar]
  25. G.A. Holzapfel and T.C. Gasser, A viscoelastic model for fiber-reinforced composites at finite stains: continuum basis, computational aspects and applications. Comput. Method. Appl. Mech. Eng. 190 (2001) 4379–4403. [CrossRef] [Google Scholar]
  26. G.A. Holzapfel, G. Sommer, M. Auer, P. Regitnig and R.W. Ogden, Layer-specific 3D residual deformations of human aortas with non-atherosclerotic intimal thickening Ann. Biomed. Eng. 35 (2007) 530–545. [CrossRef] [PubMed] [Google Scholar]
  27. G.A. Holzapfel and R.W. Ogden, Modelling the layer-specific three-dimensional residual stresses in arteries, with an application to the human aorta. J. R. Soc. Interface 7 (2010) 787–799. [CrossRef] [PubMed] [Google Scholar]
  28. R. Huang, R.W. Ogden and R. Penta, Mathematical modelling of residual-stress based volumetric growth in soft matter. J. Elast. 145 (2021) 223–241. [CrossRef] [Google Scholar]
  29. J.D. Humphrey, Constrained mixture models of soft tissue growth and remodeling - twenty years after. J. Elast. 145 (2021) 49–75. [CrossRef] [Google Scholar]
  30. C. Hurschler, B. Loitz-Ramage and R. Vanderby Jr., A structurally based stress-stretch relationship for tendon and ligament. J. Biomech. Eng. 119 (1997) 392–399. [CrossRef] [PubMed] [Google Scholar]
  31. S. Iqbal, A comprehensive study of the anatomical variations of the circle of Willis in adult human brains. J. Clin. Diagn. Res. 7 (2013) 2423–2427. [Google Scholar]
  32. M.Y.S. Kalani, J.M. Zabramski, P. Nakaji and R.F. Spetzler, Bypass and flow reduction for complex basilar and vertebrobasilar junction aneurysms. Neurosurgery 72 (2013) 763–775. [CrossRef] [PubMed] [Google Scholar]
  33. M. Keshavarzian, C.A. Meyer and H.N. Hayenga, Mechanobiological model of arterial growth and remodeling. Biomech. Model. Mechanobiol. 17 (2018) 87–101. [CrossRef] [PubMed] [Google Scholar]
  34. J.H. Koolstra, E. Tanaka and T.M.G.J. Van Eijden, Viscoelastic material model for the temporomandibular joint disc derived from dynamic shear tests or strain-relaxation tests. J. Biomech. 40 (2007) 2330–2334. [CrossRef] [Google Scholar]
  35. I. Kuianova, A. Dubovoy and D. Parshin, Using swarm intelligence optimization methods for transport functions of vascular bypasses: first results and perspectives. J. Phys. Conf. Ser. 1666 (2020) 012061. [CrossRef] [Google Scholar]
  36. Y.O. Kuyanova, S.S. Presnyakov, A.V. Dubovoi, A.P. Chupakhin and D.V. Parshin, Numerical study of the tee hydrodynamics in the model problem of optimizing the low-flow vascular bypass angle. J. Appl. Mech. Tech. Phys. 60 (2019) 1038–1045. [CrossRef] [MathSciNet] [Google Scholar]
  37. M. Latorre and F.J. Montans, Anisotropic finite strain viscoelasticity based on the Sidoroff multiplicative decomposition and logarithmic strains. Comput. Mech. 56 (2015) 503–531. [CrossRef] [MathSciNet] [Google Scholar]
  38. D.W. Laurence, H. Homburg, F. Yan, Q. Tang, K.M. Fung, B.N. Bohnstedt, G.A. Holzapfel and C.H. Lee, A pilot study on biaxial mechanical, collagen microstructural, and morphological characterizations of a resected human intracranial aneurysm tissue. Sci. Rep. 11 (2021) 3525. [CrossRef] [Google Scholar]
  39. A. Leuprecht, K. Perktold, M. Prosi, T. Berk, W. Trubel and H. Schima, Numerical study of hemodynamics and wall mechanics in distal end-to-side anastomoses of bypass grafts. J. Biomech. 35 (2002) 225–236. [CrossRef] [Google Scholar]
  40. M. Marino, M. von Hoegen, J. Schröder and P. Wriggers, Direct and inverse identification of constitutive parameters from the structure of soft tissues. Part 1: micro- and nanostructure of collagen fibers. Biomech. Model. Mechanobiol. 17 (2018) 1011–1036. [CrossRef] [PubMed] [Google Scholar]
  41. J.G. Murphy and G.A. Rogerson, Modelling slight compressibility for hyperelastic anisotropic materials. J. Elast. 131 (2018) 171–181. [CrossRef] [Google Scholar]
  42. A. Niemann, S. Voß, R. Tulamo, S. Weigand, B. Preim, P. Berg and S. Saalfeld, Complex wall modeling for hemodynamic simulations of intracranial aneurysms based on histologic images. Int. J. Comput. Ass. Rad. 16 (2021) 597–607. [Google Scholar]
  43. B. Owen, N. Bojdo, A. Jivkov, B. Keavney and A. Revell, Structural modelling of the cardiovascular system. Biomech. Model. Mechanobiol. 17 (2018) 1217–1242. [CrossRef] [PubMed] [Google Scholar]
  44. D.V. Parshin, A.I. Lipovka, A.S. Yunoshev, K.S. Ovsyannikov, A.V. Dubovoy and A.P. Chupakhin, On the optimal choice of a hyperelastic model of ruptured and unruptured cerebral aneurysm. Sci. Rep. 9 (2019) 15865. [CrossRef] [Google Scholar]
  45. K. Perktold, A. Leuprecht, M. Prosi, T. Berk, M. Czerny, W. Trubel and H. Schima, Fluid dynamics, wall mechanics, and oxygen transfer in peripheral bypass anastomoses. Ann. Biomed. Eng. 30 (2002) 447–460. [CrossRef] [PubMed] [Google Scholar]
  46. M. Ramezanpour, F. Rikhtegar Nezami, N. Ramezanpour, F. Kabinejadian, M. Maerefat, G.A. Holzapfel and J.L. Bull, Role of vessel microstructure in the longevity of end-to-side grafts. J. Biomech. Eng. 142 (2020) 021008. [CrossRef] [PubMed] [Google Scholar]
  47. J.A.G. Rhodin, Architecture of the Vessel Wall. Comprehensive Physiology, edited by R. Terjung (2014) 1–31. [PubMed] [Google Scholar]
  48. S.N. Sanders, R.G.P. Lopata, L.C.A. van Breemen, F.N. van de Vosse and M.C.M. Rutten, A novel technique for the assessment of mechanical properties of vascular tissue. Biomech. Model. Mechanobiol. 19 (2020) 1585–1594. [CrossRef] [PubMed] [Google Scholar]
  49. C. Sansour, On the physical assumptions underlying the volumetric-isochoric split and the case of anisotropy. Eur. J. Mech. A Solid. 27 (2007) 28–39. [Google Scholar]
  50. J.S. Sheltes, C.J. van Andel, P.V. Pistecky and C. Borst, Coronary anastomotic devices: blood-exposed non-intimal surface and coronary wall stress. J. Thorac. Cardiovasc. Surg. 126 (2003) 191–199. [CrossRef] [Google Scholar]
  51. A.V. Shutov, Efficient time stepping for the multiplicative Maxwell fluid including the Mooney-Rivlin hyperelasticity. Int. J. Numer. Methods Eng. 113 (2018) 1851–1869. [CrossRef] [Google Scholar]
  52. A.V. Shutov and J. Ihlemann, Analysis of some basic approaches to finite strain elasto-plasticity in view of reference change. Int. J. Plasticity 63 (2014) 183–197. [CrossRef] [Google Scholar]
  53. A.V. Shutov and A.A. Kaygorodtseva, Parameter identification in elasto-plasticity: distance between parameters and impact of measurement errors. ZAMM-Z. Angew. Math. Me. 99 (2019) e201800340. [Google Scholar]
  54. A.V. Shutov, R. Landgraf and J. Ihlemann, An explicit solution for implicit time stepping in multiplicative finite strain viscoelasticity. Comput. Methods Appl. Mech. Eng. 265 (2013) 213–225. [CrossRef] [Google Scholar]
  55. A.V. Shutov and I.I. Tagiltsev, Efficient integration of evolution equations for a fiber-like Maxwell body. J. Phys. Conf. Ser. 1268 (2019) 012078. [CrossRef] [Google Scholar]
  56. A.V. Shutov and I.I. Tagiltsev, Efficient numerics for the analysis of fibre-reinforced composites subjected to large viscoplastic strains. State of the Art and Future Trends in Material Modelling, edited by H. Altenbach, A. Oöchsner (2019) 367–380. [Google Scholar]
  57. J.C. Simo and C. Miehe, Associative coupled thermoplasticity at finite strains: Formulation, numerical analysis and implementation. Comput. Methods Appl. Mech. Eng. 98 (1992) 41–104. [CrossRef] [Google Scholar]
  58. D.P. Sokolis, Regional distribution of layer-specific circumferential residual deformations and opening angles in the porcine aorta. J. Biomech. 96 (2019) 109335. [CrossRef] [Google Scholar]
  59. D.P. Sokolis, N. Gouskou, S.A. Papadodima and S.K. Kourkoulis, Layer-specific residual deformations and their variation along the human aorta. J. Biomech. Eng. 143 (2021) 094504. [CrossRef] [PubMed] [Google Scholar]
  60. K.R. Stenmark, M.E. Yeager, K.C. El Kasmi, Nozik-E. Grayck, E.V. Gerasimovskaya, M. Li, S.R. Riddle and M.G. Frid, The adventitia: essential regulator of vascular wall structure and function. Annu. Rev. Physiol. 75 (2013) 23–47. [CrossRef] [PubMed] [Google Scholar]
  61. I.I. Tagiltsev, P.P. Laktionov and A.V. Shutov, Simulation of fiber-reinforced viscoelastic structures subjected to finite strains: multiplicative approach. Meccanica 53 (2018) 3779–3794. [CrossRef] [MathSciNet] [Google Scholar]
  62. I.I. Tagiltsev and A.V. Shutov, Geometrically nonlinear modelling of pre-stressed viscoelastic fibre-reinforced composites with application to arteries. Biomech. Model. Mechanobiol. 20 (2021) 323–337. [CrossRef] [PubMed] [Google Scholar]
  63. I.I. Tagiltsev and A.V. Shutov, Combined experimental/theoretical approach to residual stresses within multiplicative elasto-plasticity. (2021) arXiv:2104.01951. [Google Scholar]
  64. I.I. Tagiltsev and A.V. Shutov, Assessment of residual stresses in a T-joint weld by combined experimental/theoretical approach. J. Phys. Conf. Ser. 1945 (2021) 012059. [CrossRef] [Google Scholar]
  65. M.J. Thubrikar, Vascular Mechanics and Pathology. Springer, Boston, MA (2007). [Google Scholar]
  66. S.M. Vartanian and M.S. Conte, Circ. Res. 116 (2015) 1614–1628. [CrossRef] [PubMed] [Google Scholar]
  67. W.W. Von Maltzahn, R.G. Warriyar and W.F. Keitzer, Experimental measurements of elastic properties of media and adventitia of bovine carotid arteries J. Biomech. 17 (1984) 839–847. [CrossRef] [Google Scholar]
  68. J. Xie, J. Zhou and Y.C. Fung, Bending of blood vessel wall: stress-strain laws of the intima-media and adventitial layers. J. Biomech. Eng. 117 (1995) 136–145. [CrossRef] [PubMed] [Google Scholar]
  69. Q. Yu, J. Zhou and Y.C. Fung, Neutral axis location in bending and Young's modulus of different layers of arterial wall. Am,. J. Physiol. 265 (1993) H52–H60. [Google Scholar]
  70. W. Zhang, A. Capilnasiu and D. Nordsletten, Comparative analysis of nonlinear viscoelastic models across common biomechanical experiments. J. Elast. 145 (2021) 117–152. [CrossRef] [Google Scholar]
  71. W. Zhang, G. Sommer, J.A. Niestrawska, G.A. Holzapfel and D. Nordsletten, The effects of viscoelasticity on residual strain in aortic soft tissues. Acta Biomater. (2021) In press. [Google Scholar]
  72. Y. Zhao, S. Yu, J. Lu, L. Yu, J. Li, Y. Zhang, R. Wang and Y. Zhao, Direct bypass surgery vs. combined bypass surgery for hemorrhagic moyamoya disease: a comparison of angiographic outcomes. Front. Neurol. 9 (2018) 1121. [CrossRef] [Google Scholar]
  73. X. Zhuan and X. Luo, Residual stress estimates from multi-cut opening angles of the left ventricle. Cardiovasc. Eng. Technol. 11 (2020) 381–393. [CrossRef] [PubMed] [Google Scholar]
  74. D. Zuo, Y. He, S. Avril, H. Yang and K. Hackl, A thermodynamic framework for unified continuum models for the healing of damaged soft biological tissue. J. Mech. Phys. Solids 158 (2022) 104662. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.