Computational Modeling and Simulation Examples in Bioengineering

49 49 Zhang, Y., Barocas, V.H., Berceli, S.A. et al. (2016). Multi‐scale modeling of the cardiovascular system: disease development, progression, and clinical intervention. Ann. Biomed. Eng. 44 (9): 2642–2660.

50 50 Guidoboni, G., Glowinski, R., Cavallini, N. et al. (2009). A kinematically coupled time‐splitting scheme for fluid–structure interaction in blood flow. Appl. Math. Lett. 22 (5): 684–688.

51 51 Guidoboni, G., Glowinski, R., Cavallini, N., and Čanić, S. (2009). Stable loosely‐coupled‐type algorithm for fluid–structure interaction in blood flow. J. Comput. Phys. 228 (18): 6916–6937.

52 52 Bukač, M., Čanić, S., Glowinski, R. et al. (2013). Fluid–structure interaction in blood flow capturing non‐zero longitudinal structure displacement. J. Comput. Phys. 235: 515–541.

53 53 Quarteroni, A. and Formaggia, L. (2004). Mathematical modelling and numerical simulation of the cardiovascular system in modelling of living systems. In: 12 of Handbook of Numerical Analysis, 3–127. Amsterdam: North‐Holland.

54 54 Formaggia, L., Gerbeau, J.F., Nobile, F., and Quarteroni, A. (2001). On the coupling of 3D and 1D Navier–Stokes equations for flow problems in compliant vessels. Comput. Methods Appl. Mech. Eng. 191 (6–7): 561–582.

55 55 Formaggia, L., Lamponi, D., and Quarteroni, A. One‐dimensional models for blood flow in arteries. J. Eng. Math. 47 (3–4): 251–276.

56 56 Nobile, F. and Vergara, C. (2008). An effective fluid–structure interaction formulation for vascular dynamics by generalized Robin conditions. SIAM J. Sci. Comput. 30 (2): 731–763.

57 57 Causin, P., Gerbeau, J.F., and Nobile, F. (2005). Added‐mass effect in the design of partitioned algorithms for fluid–structure problems. Comput. Methods Appl. Mech. Eng. 194 (42–44): 4506–4527.

58 58 Čanić, S., Mikelić, A., and Tambača, J. (2005). A two‐dimensional effective model describing fluid–structure interaction in blood flow: analysis, simulation and experimental validation. Comptes Rendus. 333 (12): 867–883.

59 59 Čanić, S., Tambača, J., Guidoboni, G. et al. (2006). Modeling viscoelastic behavior of arterial walls and their interaction with pulsatile blood flow. SIAM J. Appl. Math. 67 (1): 164–193.

60 60 Čanić, S., Hartley, C.J., Rosenstrauch, D. et al. (2006). Blood flow in compliant arteries: an effective viscoelastic reduced model, numerics, and experimental validation. Ann. Biomed. Eng. 34 (4): 575–575.

61 61 Heil, A., Hazel, L., and Boyle, J. (2008). Solvers for large‐displacement fluid–structure interaction problems: segregated versus monolithic approaches. Comput. Mech. 43 (1): 91–101.

62 62 MacSweeney, S.T.R., Powell, J.T., and Greenhalgh, R.M. (1994). Pathogenesis of abdominal aortic aneurysm. Br. J. Surg. 81: 935–941.

63 63 van't Veer, M., Buth, J., Merkx, M. et al. (2008). Biomechanical properties of abdominal aortic aneurysms assessed by simultaneously measured pressure and volume changes in humans. J. Vasc. Surg. 48 (6): 1401–1407.

64 64 Ganten, M.K., Krautter, U., von Tengg‐Kobligk, H. et al. (2008). Quantification of aortic distensibility in abdominal aortic aneurysm using ecg‐gated multi‐detector computed tomography. Vasc. Intervent. 18 (5): 966–973.

65 65 Molacek, J., Baxa, J., Houdek, K. et al. (2011). Assessment of abdominal aortic aneurysm wall distensibility with electrocardiography‐gated computed tomography. Ann. Vasc. Surg. 25 (8): 1036–1042.

66 66 Di Puccio, F., Celi, S., and Forte, P. (2012). Review of experimental investigations on compressibility of arteries and the introduction of a new apparatus. Exp. Mech. 52 (7): 1–8. https://doi.org/10.1007/s11340‐012‐9614‐4.

67 67 Humphrey, J.D. and Yin, F.C. (1987). A new constitutive formulation for characterizing the mechanical behavior of soft tissues. Biophys. J. 52 (4): 563–570.

68 68 Ogden, R.W. (2009). Anisotropy and nonlinear elasticity in arterial wall mechanics. In: Biomechanical Modelling at the Molecular, Cellular and Tissue Levels. CISM Courses and Lectures, vol. 508 (eds. G.A. Holzapfel, R.W. Ogden, F. Pfeiffer, et al.), 179–258. Vienna: Springer.

69 69 Vande Geest, J.P., Sacks, M.S., and Vorp, D.A. (2004). Age dependency of the biaxial biomechanical behavior of human abdominal aorta. J. Biomech. Eng. 12: 815–822.

70 70 Vande Geest, J.P., Sacks, M.S., and Vorp, D.A. (2006). The effects of aneurysm on the biaxial mechanical behavior of human abdominal aorta. J. Biomech. 39: 1324–1334.

71 71 Koncar, I., Nikolic, D., Pantovic, S. et al. (2013). Modeling of abdominal aortic aneurysm rupture by using bubble inflation test. Bioinform. Bioeng. (BIBE) https://doi.org/10.1109/BIBE.2013.6701612.

72 72 Vande Geest, J.P., Di Martino, E.S., Bohra, A. et al. (2006). A biomechanics‐based rupture potential index for abdominal aortic aneurysm risk assessment. Ann. N. Y. Acad. Sci. 1085: 11–21.

73 73 Thubrikar, M.J., Labrosse, M., Robicsek, F. et al. (2001). Mechanical properties of abdominal aortic aneurysm wall. J. Med. Eng. Techn. 25 (4): 133–142.

74 74 Stamatopoulos, C., Mathioulakis, D.S., Papaharilaou, Y., and Katsamouris, A. (2011). Experimental unsteady flow study in a patientspecific abdominal aortic aneurysm model. Exp. Fluids 50 (6): 1695–1709.

75 75 Holzapfel, G.A. (2006). Determination of material models for arterial walls from uniaxial extension tests and histological structure. J. Theor. Biol. 238 (2): 290–302.

76 76 Simsek, F.G. and Kwon, Y.W. (2015). Investigation of material modeling in fluid–structure interaction analysis of an idealized three layered abdominal aorta: aneurysm initiation and fully developed aneurysms. J. Biol. Phys. 41 (2): 173–201.

77 77 Taghizadeh, H., Tafazzoli‐Shadpour, M., Shadmehr, M., and Fatouraee, N. (2015). Evaluation of biaxial mechanical properties of aortic media based on the lamellar microstructure. Materials 8 (1): 302–316.

78 78 Sokolis, D.P., Kefaloyannis, E.M., Kouloukoussa, M. et al. (2006). A structural basis for the aortic stress–strain relation in uniaxial tension. J. Biomech. 39 (9): 1651–1662.

79 79 Karimi, A., Navidbakhsh, M., Shojaei, A., and Faghihi, S. (2013). Measurement of the uniaxial mechanical properties of healthy and atherosclerotic human coronary arteries. Mater. Sci. Eng. C 33 (5): 2550–2554.

80 80 Taylor, C.A. and Humphrey, J.D. (2009). Open problems in computational vascular biomechanics: hemodynamics and arterial wall mechanics. Comput. Methods Appl. Mech. Eng. 198 (45–46): 3514–3523.

81 81 Raut, S.S., Chandra, S., Shum, J., and Finol, E.A. (2013). The role of geometric and biomechanical factors in abdominal aortic aneurysm rupture risk assessment. Ann. Biomed. Eng. 41 (7): 1459–1477.

82 82 Stenbaek, J., Kalin, B., and Swedenborg, J. (2000). Growth of thrombus may be a better predictor of rupture than diameter in patients with abdominal aortic aneurysms. Eur. J. Vasc. Endovasc. Surg. 20 (5): 466–469.

83 83 Li, Z.‐Y., U‐King‐Im, J., Tang, T.Y. et al. (2008). Impact of calcification and intraluminal thrombus on the computed wall stresses of abdominal aortic aneurysm. J. Vasc. Surg. 47 (5): 928–936.

84 84 Di Martino, E.S. and Vorp, D.A. (2003). Effect of variation in intraluminal thrombus constitutive properties on abdominal aortic aneurysm wall stress. Ann. Biomed. Eng. 31 (7): 804–809.

85 85 O'Leary, S.A., Kavanagh, E.G., Grace, P.A. et al. (2014). The biaxial mechanical behaviour of abdominal aortic aneurysm intraluminal thrombus: classification of morphology and the determination of layer and region specific properties. J. Biomech. 47 (6): 1430–1437.

86 86 Tong, J., Schriefl, A.J., Cohnert, T., and Holzapfel, G.A. (2013). Gender differences in biomechanical properties, thrombus age, mass fraction and clinical factors of abdominal aortic aneurysms. Eur. J. Vasc. Endovasc. Surg. 45 (4): 364–372.