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Mechanics of the mitral valve

A critical review, an in vivo parameter identification, and the effect of prestrain

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Abstract

Alterations in mitral valve mechanics are classical indicators of valvular heart disease, such as mitral valve prolapse, mitral regurgitation, and mitral stenosis. Computational modeling is a powerful technique to quantify these alterations, to explore mitral valve physiology and pathology, and to classify the impact of novel treatment strategies. The selection of the appropriate constitutive model and the choice of its material parameters are paramount to the success of these models. However, the in vivo parameters values for these models are unknown. Here, we identify the in vivo material parameters for three common hyperelastic models for mitral valve tissue, an isotropic one and two anisotropic ones, using an inverse finite element approach. We demonstrate that the two anisotropic models provide an excellent fit to the in vivo data, with local displacement errors in the sub-millimeter range. In a complementary sensitivity analysis, we show that the identified parameter values are highly sensitive to prestrain, with some parameters varying up to four orders of magnitude. For the coupled anisotropic model, the stiffness varied from 119,021 kPa at 0 % prestrain via 36 kPa at 30 % prestrain to 9 kPa at 60 % prestrain. These results may, at least in part, explain the discrepancy between previously reported ex vivo and in vivo measurements of mitral leaflet stiffness. We believe that our study provides valuable guidelines for modeling mitral valve mechanics, selecting appropriate constitutive models, and choosing physiologically meaningful parameter values. Future studies will be necessary to experimentally and computationally investigate prestrain, to verify its existence, to quantify its magnitude, and to clarify its role in mitral valve mechanics.

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Acknowledgments

The authors thank Neil B. Ingels for designing the experimental study; John-Peder Escobar Kvitting and Julia C. Swanson for performing the surgical procedures; Paul Chang, Eleazar P. Briones, Lauren R. Davis, and Kathy N. Vo for assisting during the surgery; Maggie Brophy and Sigurd Hartnett for digitizing marker images; and George T. Daughters III for computing four-dimensional marker coordinates data biplane two-dimensional images. This study was supported by the Stanford University BioX Fellowship to Manuel Rausch, by the Deutsche Herzstiftung Research Grant S/06/07 to Wolfgang Bothe, by the US National Institutes of Health grants R01 HL29589 and R01 HL67025 to D. Craig Miller, and by the US National Science Foundation CAREER award CMMI 0952021 and INSPIRE grant 1233054 to Ellen Kuhl.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Stanford University, 496 Lomita Mall, Stanford, CA, 94305, USA

    Manuel K. Rausch & Tyler O’Brien Shultz

  2. Department of Mechanical Engineering, KU Leuven, Celestijnenlaan 300, 3001 , Leuven, Belgium

    Nele Famaey

  3. Department of Cardiothoracic Surgery, Friedrich Schiller University, 07743 , Jena, Germany

    Wolfgang Bothe

  4. Department of Cardiothoracic Surgery, Stanford University, 300 Pasteur Dr, Stanford, CA, 94305, USA

    D. Craig Miller

  5. Departments of Mechanical Engineering, Bioengineering, and Cardiothoracic Surgery, Stanford University, 496 Lomita Mall, Stanford, CA, 94305, USA

    Ellen Kuhl

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  1. Manuel K. Rausch
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  2. Nele Famaey
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Correspondence to Ellen Kuhl.

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Rausch, M.K., Famaey, N., Shultz, T.O. et al. Mechanics of the mitral valve. Biomech Model Mechanobiol 12, 1053–1071 (2013). https://doi.org/10.1007/s10237-012-0462-z

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