### Abstract

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.

Original language | English |
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Pages (from-to) | 1-16 |

Number of pages | 16 |

Journal | Computational Mechanics |

DOIs | |

Publication status | Accepted/In press - 2016 Nov 5 |

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### Keywords

- Aorta
- Estimated element-based zero-stress state
- Image-based geometry
- Isogeometric wall discretization
- Patient-specific arterial FSI
- Zero-stress state

### ASJC Scopus subject areas

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

### Cite this

*Computational Mechanics*, 1-16. https://doi.org/10.1007/s00466-016-1344-5