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Aorta modeling with the element-based zero-stress state and isogeometric discretization

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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.

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Acknowledgments

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.

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Authors and Affiliations

  1. Department of Modern Mechanical Engineering, Waseda University, 1-6-1 Nishi-Waseda, Shinjuku-ku, Tokyo, 169-8050, Japan

    Kenji Takizawa & Takafumi Sasaki

  2. Mechanical Engineering, Rice University – MS 321, 6100 Main Street, Houston, TX, 77005, USA

    Tayfun E. Tezduyar

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  1. Kenji Takizawa
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  2. Tayfun E. Tezduyar
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  3. Takafumi Sasaki
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Correspondence to Tayfun E. Tezduyar.

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Takizawa, K., Tezduyar, T.E. & Sasaki, T. Aorta modeling with the element-based zero-stress state and isogeometric discretization. Comput Mech 59, 265–280 (2017). https://doi.org/10.1007/s00466-016-1344-5

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