### 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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Pages (from-to) | 1315-1331 |

Number of pages | 17 |

Journal | Computational Mechanics |

Volume | 63 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2019 Jun 15 |

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### 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

*Computational Mechanics*,

*63*(6), 1315-1331. https://doi.org/10.1007/s00466-018-1651-0