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**Role of 0D peripheral vasculature model in fluid-structure interaction modeling of aneurysms.**
*(English)*
Zbl 1301.92020

Summary: Patient-specific simulations based on medical images such as CT and MRI offer information on the hemodynamic and wall tissue stress in patient-specific aneurysm configurations. These are considered important in predicting the rupture risk for individual aneurysms but are not possible to measure directly. In this paper, fluid-structure interaction (FSI) analyses of a cerebral aneurysm at the middle cerebral artery (MCA) bifurcation are presented. A 0D structural recursive tree model of the peripheral vasculature is incorporated and its impedance is coupled with the 3D FSI model to compute the outflow through the two branches accurately. The results are compared with FSI simulation with prescribed pressure variation at the outlets. The comparison shows that the pressure at the two outlets are nearly identical even with the peripheral vasculature model and the flow division to the two branches is nearly the same as what we see in the simulation without the peripheral vasculature model. This suggests that the role of the peripheral vasculature in FSI modeling of the MCA aneurysm is not significant.

### Keywords:

fluid-structure interaction; cerebral aneurysm; outflow boundary condition; structural tree model
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\textit{R. Torii} et al., Comput. Mech. 46, No. 1, 43--52 (2010; Zbl 1301.92020)

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[1] | van Gijn J, Rinkel GJE (2001) Subarachnoid heamorrhage: diagnosis, cause and management. Brain 124: 249–278 |

[2] | Steiger HJ (1990) Pathophysiology of development and rupture of cerebral aneurysms. Acta Neurochir Suppl 48: 1–57 |

[3] | Humphrey JD (2008) Vascular adaptation and mechanical homeostasis at tissue, cellular, and sub-cellular levels. Cell Biochem Biophys 50: 53–78 |

[4] | The International Study of Unruptured Intracranial Aneurysms Investigators (1998) Unruptured intracranial aneurysms–risk of rupture and risks of surgical intervention. New Engl J Med 339(24):1725–1733 |

[5] | Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2004) Influence of wall elasticity on image-based blood flow simulation. Jpn Soc Mech Eng J Ser A 70:1224–1231 (in Japanese) |

[6] | Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2006) Computer modeling of cardiovascular fluid–structure interactions with the Deforming-Spatial-Domain/Stabilized Space–Time formulation. Comput Methods Appl Mech Eng 195: 1885–1895 · Zbl 1178.76241 |

[7] | Gerbeau J-F, Vidrascu M, Frey P (2008) Fluid–structure interaction in blood flow on geometries based on medical images. Comput Struct 83: 155–165 |

[8] | Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2006) Fluid–structure interaction modeling of aneurysmal conditions with high and normal blood pressures. Comput Mech 38: 482–490 · Zbl 1160.76061 |

[9] | Bazilevs Y, Calo VM, Zhang Y, Hughes TJR (2006) Isogeometric fluid–structure interaction analysis with applications to arterial blood flow. Comput Mech 38: 310–322 · Zbl 1161.74020 |

[10] | Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2007) Influence of wall elasticity in patient-specific hemodynamic simulations. Comput Fluids 36: 160–168 · Zbl 1113.76105 |

[11] | Tezduyar TE, Sathe S, Cragin T, Nanna B, Conklin BS, Pausewang J, Schwaab M (2007) Modeling of fluid–structure interactions with the space–time finite elements: Arterial fluid mechanics. Int J Numer Methods Fluids 54: 901–922 · Zbl 1276.76043 |

[12] | Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2007) Numerical investigation of the effect of hypertensive blood pressure on cerebral aneurysm–dependence of the effect on the aneurysm shape. Int J Numer Methods Fluids 54: 995–1009 · Zbl 1317.76107 |

[13] | Tezduyar TE, Sathe S, Schwaab M, Conklin BS (2008) Arterial fluid mechanics modeling with the stabilized space–time fluid–structure interaction technique. Int J Numer Methods Fluids 57: 601–629 · Zbl 1230.76054 |

[14] | Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) Isogeometric fluid–structure interaction: theory, algorithms, and computations. Comput Mech 43: 3–37 · Zbl 1169.74015 |

[15] | Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2008) Fluid–structure interaction modeling of a patient-specific cerebral aneurysm: influence of structural modeling. Comput Mech 43: 151–159 · Zbl 1169.74032 |

[16] | Isaksen JG, Bazilevs Y, Kvamsdal T, Zhang Y, Kaspersen JH, Waterloo K, Romner B, Ingebrigtsen T (2008) Determination of wall tension in cerebral artery aneurysms by numerical simulation. Stroke 39: 3172–3178 |

[17] | Tezduyar TE, Schwaab M, Sathe S (2009) Sequentially-coupled arterial fluid–structure interaction (SCAFSI) technique. Comput Methods Appl Mech Eng 198: 3524–3533 · Zbl 1229.74100 |

[18] | Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2009) Fluid–structure interaction modeling of blood flow and cerebral aneurysm: significance of artery and aneurysm shapes. Comput Methods Appl Mech Eng 198: 3613–3621 · Zbl 1229.74101 |

[19] | Bazilevs Y, Gohean JR, Hughes TJR, Moser RD, Zhang Y (2009) Patient-specific isogeometric fluid–structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device. Comput Methods Appl Mech Eng 198: 3534–3550 · Zbl 1229.74096 |

[20] | Takizawa K, Christopher J, Tezduyar TE, Sathe S (2009) Space–time finite element computation of arterial fluid–structure interactions with patient-specific data. Commun Numer Methods Eng. published online, doi: 10.1002/cnm.1241 · Zbl 1180.92023 |

[21] | Tezduyar TE, Takizawa K, Christopher J (2009) Multiscale sequentially-coupled arterial fluid–structure interaction (SCAFSI) technique. In: Hartmann S, Meister A, Schaefer M, Turek S (eds) International workshop on fluid–structure interaction–theory, numerics and applications. Kassel University Press |

[22] | Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2009) Influence of wall thickness on fluid–structure interaction computations of cerebral aneurysms. Commun Numer Methods Eng. published online, doi: 10.1002/cnm.1289 · Zbl 1183.92050 |

[23] | Bazilevs Y, Hsu M-C, Benson D, Sankaran S, Marsden A (2009) Computational fluid-structure interaction: methods and application to a total cavopulmonary connection. Comput Mech (in the same issue) · Zbl 1398.92056 |

[24] | Bazilevs Y, Hsu M-C, Zhang Y, Wang W, Liang X, Kvamsdal T, Brekken R, Isaksen J (2009) A fully-coupled fluid–structure interaction simulation of cerebral aneurysms. Comput Mech (in the same issue) · Zbl 1301.92014 |

[25] | Tezduyar TE, Takizawa K, Moorman C, Wright S, Christopher J (2009) Multiscale sequentially-coupled arterial FSI technique. Comput Mech. published online, doi: 10.1007/s00466-009-0423-2 · Zbl 1261.92010 |

[26] | Takizawa K, Moorman C, Wright S, Christopher J, Tezduyar TE (2009) Wall shear stress calculations in space–time finite element computation of arterial fluid–structure interactions. Comput Mech. published online, doi: 10.1007/s00466-009-0425-0 · Zbl 1301.92019 |

[27] | Meng H, Wang W, Hoi Y, Gao L, Metaxa E, Swartz DD, Kolega J (2007) Complex hemodynamics at the apex of an arterial bifurcation induces vascular remodeling resembling cerebral aneurysm initiation. Stroke 38: 1924–1931 |

[28] | Frank O (1899) Die grundform des arteriellen pulses. Zeitung fur Biol 37: 483–586 |

[29] | Alastruey J, Parker KH, Peiro J, Sherwin SJ (2008) Lumped parameter outflow models for 1-D blood flow simulations: effect on pulse waves and parameter estimation. Commun Comput Phys 4: 317–336 · Zbl 1364.76248 |

[30] | Olufsen MS (1999) Structured tree outflow condition for blood flow in largar systemic arteries. Am J Physiol Heart Circulatory Physiol 276(1): 257–268 |

[31] | Vignon IE, Taylor CA (2004) Outflow boundary conditions for one-dimensional finite element modeling of blood flow and pressure waves in arteries. Wave Motion 39(4): 361–374 · Zbl 1163.74453 |

[32] | Vignon-Clementel IE, Figueroa CA, Jansen KE, Taylor CA (2005) Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries. CMAME 195: 3776–3796 · Zbl 1175.76098 |

[33] | Migliavacca F, Balossino R, Pennati G, Dubini G, Hsia T, de Leval MR, Bove EL (2006) Multiscale modelling in biofluidynamics: application to reconstructive paediatric cardiac surgery. J Biomech 39: 1010–1020 |

[34] | Spilker RL, Feinstein JA, Parker DW, Reddy VM, Taylor CA (2007) Morphometry-based impedance boundary conditions for patient-specific modeling of blood flow in pulmonary arteries. Ann Biomed Eng 35: 546–559 |

[35] | Tezduyar TE (1992) Stabilized finite element formulations for incompressible flow computations. Adv Appl Mech 28: 1–44 · Zbl 0747.76069 |

[36] | Tezduyar TE, Behr M, Liou J (1992) A new strategy for finite element computations involving moving boundaries and interfaces–the deforming-spatial-domain/space–time procedure: I. The concept and the preliminary numerical tests. Comput Methods Appl Mech Eng 94(3): 339–351 · Zbl 0745.76044 |

[37] | Tezduyar TE, Behr M, Mittal S, Liou J (1992) A new strategy for finite element computations involving moving boundaries and interfaces–the deforming-spatial-domain/space–time procedure: II. Computation of free-surface flows, two-liquid flows, and flows with drifting cylinders. Comput Methods Appl Mech Eng 94(3): 353–371 · Zbl 0745.76045 |

[38] | Tezduyar TE (2003) Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Methods Fluids 43: 555–575 · Zbl 1032.76605 |

[39] | Brooks AN, Hughes TJR (1982) Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations. Comput Methods Appl Mech Eng 32: 199–259 · Zbl 0497.76041 |

[40] | Tezduyar TE, Mittal S, Ray SE, Shih R (1992) Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements. Comput Methods Appl Mech Eng 95: 221–242 · Zbl 0756.76048 |

[41] | Tezduyar T, Aliabadi S, Behr M, Johnson A, Mittal S (1993) Parallel finite-element computation of D flows. Computer 26(10): 27–36 · Zbl 05090697 |

[42] | Tezduyar TE, Aliabadi SK, Behr M, Mittal S (1994) Massively parallel finite element simulation of compressible and incompressible flows. Comput Methods Appl Mech Eng 119: 157–177 · Zbl 0848.76040 |

[43] | Mittal S, Tezduyar TE (1994) Massively parallel finite element computation of incompressible flows involving fluid-body interactions. Comput Methods Appl Mech Eng 112: 253–282 · Zbl 0846.76048 |

[44] | Tezduyar T, Aliabadi S, Behr M, Johnson A, Kalro V, Litke M (1996) Flow simulation and high performance computing. Comput Mech 18: 397–412 · Zbl 0893.76046 |

[45] | Johnson AA, Tezduyar TE (1997) Parallel computation of incompressible flows with complex geometries. Int J Numer Methods Fluids 24: 1321–1340 · Zbl 0882.76044 |

[46] | Johnson AA, Tezduyar TE (1999) Advanced mesh generation and update methods for 3D flow simulations. Comput Mech 23: 130–143 · Zbl 0949.76049 |

[47] | Tezduyar TE (2001) Finite element methods for flow problems with moving boundaries and interfaces. Arch Comput Methods Eng 8: 83–130 · Zbl 1039.76037 |

[48] | Tezduyar TE (2007) Finite elements in fluids: stabilized formulations and moving boundaries and interfaces. Comput Fluids 36: 191–206 · Zbl 1177.76202 |

[49] | Mittal S, Tezduyar TE (1995) Parallel finite element simulation of 3D incompressible flows–fluid-structure interactions. Int J Numer Methods Fluids 21: 933–953 · Zbl 0873.76047 |

[50] | Kalro V, Tezduyar TE (2000) A parallel 3D computational method for fluid–structure interactions in parachute systems. Comput Methods Appl Mech Eng 190: 321–332 · Zbl 0993.76044 |

[51] | Stein K, Benney R, Kalro V, Tezduyar TE, Leonard J, Accorsi M (2000) Parachute fluid–structure interactions: 3-D computation. Comput Methods Appl Mech Eng 190: 373–386 · Zbl 0973.76055 |

[52] | Tezduyar T, Osawa Y (2001) Fluid–structure interactions of a parachute crossing the far wake of an aircraft. Comput Methods Appl Mech Eng 191: 717–726 · Zbl 1113.76407 |

[53] | Stein K, Tezduyar T, Benney R (2003) Mesh moving techniques for fluid–structure interactions with large displacements. J Appl Mech 70: 58–63 · Zbl 1110.74689 |

[54] | Stein K, Tezduyar TE, Benney R (2004) Automatic mesh update with the solid-extension mesh moving technique. Comput Methods Appl Mech Eng 193: 2019–2032 · Zbl 1067.74587 |

[55] | Tezduyar TE, Sathe S, Keedy R, Stein K (2006) Space–time finite element techniques for computation of fluid–structure interactions. Comput Methods Appl Mech Eng 195: 2002–2027 · Zbl 1118.74052 |

[56] | Tezduyar TE, Sathe S, Stein K (2006) Solution techniques for the fully-discretized equations in computation of fluid–structure interactions with the space–time formulations. Comput Methods Appl Mech Eng 195: 5743–5753 · Zbl 1123.76035 |

[57] | Tezduyar TE, Sathe S (2007) Modeling of fluid–structure interactions with the space–time finite elements: solution techniques. Int J Numer Methods Fluids 54: 855–900 · Zbl 1144.74044 |

[58] | MacDonald DJ, Finlay HM, Canham PB (2000) Directional wall strength in saccular brain aneurysms from polarized light microscopy. Ann Biomed Eng 28: 533–542 |

[59] | Kataoka K, Taneda M, Asai T, Kinoshita A, Ito M, Kuroda R (1999) Structural fragility and inflammatory response of ruptured cerebral aneurysms. Stroke 30: 1396–1401 |

[60] | Frösen J, Piippo A, Paetau A, Kangasniemi M, Niemelä M, Hernesniemi J, Jääskeläinen J (2004) Remodeling of saccular cerebral artery aneurysm wall is associated with rupture: histological analysis of 24 unruptured and 42 ruptured cases. Stroke 35: 2287–2293 |

[61] | Flamini V, Kerskens C, Lally C (2008) Characterization of the 3D fibre distribution in a porcine aorta using diffusion tensor imaging. In: 16th congress of European Society of Biomechanics, Lucerne, Switzerland |

[62] | Tang D, Yang C, Zheng J, Woodard PK, Sicard GA, Saffitz JE, Yuan C (2004) 3d mri-based multicomponent fsi models for atherosclerotic plaques. Ann Biomed Eng 32(7): 947–960 |

[63] | Rodriguez-Granillo GA, Garcia-Garcia HM, McFadden EP, Valgimigli M, Aoki J, de Feyter P, Serruys PW (2005) In vivo intravascular ultrasound-derived thin-cap fibroatheroma detection using ultrasound radiofrequency data analysis. J Am College Cardiol 46: 2038–2042 |

[64] | Williamson SD, Lam Y, Younis HF, Huang H, Patel S, Kaazempur-Mofrad MR, Kamm RD (2003) On the sensitivity of wall stresses in diseased arteries to variable material properties. J Biomech Eng 125: 147–155 |

[65] | Delfino A, Stergiopulos N, Moore JE Jr, Meister JJ (1997) Residual strain effects on the stress field in a thick wall finite element model of the human carotid bifurcation. J Biomech 30: 777–786 |

[66] | Kuroda H, Katagiri T, Kudoh M, Kanada Y (2001) Ilib_gmres: an auto-tuning parallel iterative solver for linear equations. In: SC2001, Denver, USA |

[67] | Nagano K (2002) A hemodynamic study on the middle cerebral artery aneurysm using numerical simulations (in Japanese). Master’s thesis, The University of Tokyo |

[68] | Shinozaki K (2003) A study on the effect of arterial morphology on haemodynamics in cerebral aneurysms (in Japanese). Master’s thesis, The University of Tokyo |

[69] | Hayashi K, Handa H, Nagasawa S, Okumura A, Moritake K (1980) Stiffness and elastic behavior of human intracranial and extracranial arteries. J Biomech 13: 175–184 |

[70] | Womersley JR (1955) Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known. J Physiol 127: 553–563 |

[71] | Ogoh S, Fadel PJ, Zhang R, Selmer C, Jans O, Secher NH, Raven PB (2005) Middle cerebral artery flow velocity and pulse pressure during dynamic exercise in humans. Am J Physiol Heart Circul Physiol 288: H1526–H1531 |

[72] | Olufsen MS (1998) Modeling the arterial system with reference to anesthesia simulator. PhD thesis, Roskilde University, Denmark |

[73] | Olufsen MS, Peskin CS, Kim WY, Pedersen EM (2000) Numerical simulation and experimental validation of blood flow in arteries with structured-tree outflow conditions. Ann Biomed Eng 28: 1281–1299 |

[74] | Steele BN, Olufsen MS, Taylor CA (2007) Fractal network model for simulating abdominal and lower extremity blood flow during resting and exercise conditions. Comput Methods Biomech Biomed Eng 10: 39–51 |

[75] | Murray CD (1926) The physiological principle of minimum work. I: the vascular system and the cost of blood volume. Proc Natl Acad Sci USA 12: 207–214 |

[76] | Stergiopulos N, Young D, Rogge T (1992) Computer simulation of arterial flow with applications to arterial and aortic stenosis. J Biomech 25: 1477–1488 |

[77] | Zamir M (1999) On fractal properties of arterial trees. J Theor Biol 197: 517–526 · Zbl 0941.70019 |

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