### Abstract

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.

Original language | English |
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Journal | Computational Mechanics |

DOIs | |

Publication status | Accepted/In press - 2018 Jan 1 |

### Fingerprint

### Keywords

- Aorta
- Image-based geometry
- Integration-point-based zero-stress state
- Isogeometric wall discretization
- Patient-specific arterial FSI
- Shell-model-based initial guess
- T-spline basis functions
- Zero-stress state

### ASJC Scopus subject areas

- Computational Mechanics
- Ocean Engineering
- Mechanical Engineering
- Computational Theory and Mathematics
- Computational Mathematics
- Applied Mathematics

### Cite this

**Aorta zero-stress state modeling with T-spline discretization.** / Sasaki, Takafumi; Takizawa, Kenji; Tezduyar, Tayfun E.

Research output: Contribution to journal › Article

}

TY - JOUR

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

AU - Sasaki, Takafumi

AU - Takizawa, Kenji

AU - Tezduyar, Tayfun E.

PY - 2018/1/1

Y1 - 2018/1/1

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

UR - http://www.scopus.com/inward/record.url?scp=85056002056&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85056002056&partnerID=8YFLogxK

U2 - 10.1007/s00466-018-1651-0

DO - 10.1007/s00466-018-1651-0

M3 - Article

JO - Computational Mechanics

JF - Computational Mechanics

SN - 0178-7675

ER -