Aorta modeling with the element-based zero-stress state and isogeometric discretization
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Patient-specific arterial fluid–structure interaction computations, including aorta computations, require an estimation of the zero-stress state (ZSS), because the image-based arterial geometries do not come from a ZSS. We have earlier introduced a method for estimation of the element-based ZSS (EBZSS) in the context of finite element discretization of the arterial wall. The method has three main components. 1. An iterative method, which starts with a calculated initial guess, is used for computing the EBZSS such that when a given pressure load is applied, the image-based target shape is matched. 2. A method for straight-tube segments is used for computing the EBZSS so that we match the given diameter and longitudinal stretch in the target configuration and the “opening angle.” 3. An element-based mapping between the artery and straight-tube is extracted from the mapping between the artery and straight-tube segments. This provides the mapping from the arterial configuration to the straight-tube configuration, and from the estimated EBZSS of the straight-tube configuration back to the arterial configuration, to be used as the initial guess for the iterative method that matches the image-based target shape. Here we present the version of the EBZSS estimation method with isogeometric wall discretization. With isogeometric discretization, we can obtain the element-based mapping directly, instead of extracting it from the mapping between the artery and straight-tube segments. That is because all we need for the element-based mapping, including the curvatures, can be obtained within an element. With NURBS basis functions, we may be able to achieve a similar level of accuracy as with the linear basis functions, but using larger-size and much fewer elements. Higher-order NURBS basis functions allow representation of more complex shapes within an element. To show how the new EBZSS estimation method performs, we first present 2D test computations with straight-tube configurations. Then we show how the method can be used in a 3D computation where the target geometry is coming from medical image of a human aorta.
KeywordsPatient-specific arterial FSI Image-based geometry Aorta Zero-stress state Estimated element-based zero-stress state Isogeometric wall discretization
This work was supported in part by JST-CREST; Grant-in-Aid for Scientific Research (S) 26220002 from the Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT); Rice–Waseda research agreement.
- 1.Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2004) Computation of cardiovascular fluid–structure interactions with the DSD/SST method. In: Proceedings of the 6th world congress on computational mechanics (CD-ROM), BeijingGoogle Scholar
- 2.Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2004) Influence of wall elasticity on image-based blood flow simulations. Trans Jpn Soc Mech Eng Ser A 70:1224–1231. doi: 10.1299/kikaia.70.1224 (in Japanese)
- 3.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. doi: 10.1016/j.cma.2005.05.050 MathSciNetCrossRefzbMATHGoogle Scholar
- 12.Bazilevs Y, Gohean JR, Hughes TJR, Moser RD, Zhang Y (2000) 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(2009):3534–3550MathSciNetzbMATHGoogle Scholar
- 28.Hsu M-C, Kamensky D, Xu F, Kiendl J, Wang C, Wu MCH, Mineroff J, Reali A, Bazilevs Y, Sacks MS (2015) Dynamic and fluid–structure interaction simulations of bioprosthetic heart valves using parametric design with T-splines and fung-type material models. Comput Mech 55:1211–1225. doi: 10.1007/s00466-015-1166-x CrossRefzbMATHGoogle Scholar
- 42.Takizawa K, Bazilevs Y, Tezduyar TE, Long CC, Marsden AL, Schjodt K (2014) Patient-specific cardiovascular fluid mechanics analysis with the ST and ALE-VMS methods. In: Idelsohn SR (ed) Numerical simulations of coupled problems in engineering of computational methods in applied sciences. Springer, Basel, pp 71–102CrossRefGoogle Scholar
- 50.Takizawa K, Bazilevs Y, Tezduyar TE, Hsu MC, Øiseth O, Mathisen KM, Kostov N, McIntyre S (2014) Computational engineering analysis and design with ALE-VMS and ST methods. In: Idelsohn SR (ed) Numerical simulations of coupled problems in engineering of computational methods in applied sciences. Springer, BaselGoogle Scholar
- 52.Takizawa K, Tezduyar TE (2016) New directions in space–time computational methods. In: Bazilevs Y, Takizawa K (eds) Advances in computational fluid–structure interaction and flow simulation: new methods and challenging computations, modeling and simulation in science, engineering and technology. Springer, New York, pp 159–178CrossRefGoogle Scholar
- 53.Takizawa K, Bazilevs Y, Tezduyar TE (2012) Space–time and ALE-VMS techniques for patient-specific cardiovascular fluid–structure interaction modeling. Arch Comput Methods Eng 19:171–225. doi: 10.1007/s11831-012-9071-3
- 54.Tezduyar TE, Cragin T, Sathe S, Nanna B (2007) FSI computations in arterial fluid mechanics with estimated zero-pressure arterial geometry. In: Onate E, Garcia J, Bergan P, Kvamsdal T (eds) Marine 2007. CIMNE, BarcelonaGoogle Scholar
- 56.Takizawa K, Tezduyar TE, Sasaki T (2016) Estimation of element-based zero-stress state in arterial FSI computations with isogeometric wall discretization. Springer, New YorkGoogle Scholar