TY - JOUR

T1 - Aorta zero-stress state modeling with T-spline discretization

AU - Sasaki, Takafumi

AU - Takizawa, Kenji

AU - Tezduyar, Tayfun E.

N1 - Funding Information:
Acknowledgements 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); Grant-in-Aid for Scientific Research (A) 18H04100 from Japan Society for the Promotion of Science; and Rice–Waseda research agreement. This work was also supported (first author) in part by Grant-in-Aid for JSPS Research Fellow 18J14680. The mathematical model and computational method parts of the work were also supported (third author) in part by ARO Grant W911NF-17-1-0046 and Top Global University Project of Waseda University.
Publisher Copyright:
© 2018, The Author(s).

PY - 2019/6/15

Y1 - 2019/6/15

N2 - The image-based arterial geometries used in patient-specific arterial fluid–structure interaction (FSI) computations, such as aorta FSI computations, do not come from the zero-stress state (ZSS) of the artery. We propose a method for estimating the ZSS required in the computations. Our estimate is based on T-spline discretization of the arterial wall and is in the form of integration-point-based ZSS (IPBZSS). The method has two main components. (1) An iterative method, which starts with a calculated initial guess, is used for computing the IPBZSS such that when a given pressure load is applied, the image-based target shape is matched. (2) A method, which is based on the shell model of the artery, is used for calculating the initial guess. The T-spline discretization enables dealing with complex arterial geometries, such as an aorta model with branches, while retaining the desirable features of isogeometric discretization. With higher-order basis functions of the isogeometric discretization, 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. In addition, the higher-order basis functions allow representation of more complex shapes within an element. The IPBZSS is a convenient representation of the ZSS because with isogeometric discretization, especially with T-spline discretization, specifying conditions at integration points is more straightforward than imposing conditions on control points. Calculating the initial guess based on the shell model of the artery results in a more realistic initial guess. To show how the new ZSS estimation method performs, we first present 3D test computations with a Y-shaped tube. Then we show a 3D computation where the target geometry is coming from medical image of a human aorta, and we include the branches in our model.

AB - The image-based arterial geometries used in patient-specific arterial fluid–structure interaction (FSI) computations, such as aorta FSI computations, do not come from the zero-stress state (ZSS) of the artery. We propose a method for estimating the ZSS required in the computations. Our estimate is based on T-spline discretization of the arterial wall and is in the form of integration-point-based ZSS (IPBZSS). The method has two main components. (1) An iterative method, which starts with a calculated initial guess, is used for computing the IPBZSS such that when a given pressure load is applied, the image-based target shape is matched. (2) A method, which is based on the shell model of the artery, is used for calculating the initial guess. The T-spline discretization enables dealing with complex arterial geometries, such as an aorta model with branches, while retaining the desirable features of isogeometric discretization. With higher-order basis functions of the isogeometric discretization, 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. In addition, the higher-order basis functions allow representation of more complex shapes within an element. The IPBZSS is a convenient representation of the ZSS because with isogeometric discretization, especially with T-spline discretization, specifying conditions at integration points is more straightforward than imposing conditions on control points. Calculating the initial guess based on the shell model of the artery results in a more realistic initial guess. To show how the new ZSS estimation method performs, we first present 3D test computations with a Y-shaped tube. Then we show a 3D computation where the target geometry is coming from medical image of a human aorta, and we include the branches in our model.

KW - Aorta

KW - Image-based geometry

KW - Integration-point-based zero-stress state

KW - Isogeometric wall discretization

KW - Patient-specific arterial FSI

KW - Shell-model-based initial guess

KW - T-spline basis functions

KW - Zero-stress state

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U2 - 10.1007/s00466-018-1651-0

DO - 10.1007/s00466-018-1651-0

M3 - Article

AN - SCOPUS:85056002056

SN - 0178-7675

VL - 63

SP - 1315

EP - 1331

JO - Computational Mechanics

JF - Computational Mechanics

IS - 6

ER -