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A Hybrid Microstructural-Continuum Multiscale Approach for Modeling Hyperelastic Fibrous Soft Tissue

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Abstract

The heterogeneous, nonlinear, anisotropic material behavior of biological tissues makes precise definition of an accurate constitutive model difficult. One possible solution to this issue would be to define microstructural elements and perform fully coupled multiscale simulation. However, for complex geometries and loading scenarios, the computational costs of such simulations can be prohibitive. Ideally then, we should seek a method that contains microstructural detail, but leverages the speed of classical continuum-based finite-element (FE) modeling. In this work, we demonstrate the use of the Holzapfel-Gasser-Ogden (HGO) model (Holzapfel et al. in J. Elast. 61:1–48, 2000; Gasser et al. in J. R. Soc. Interface 3(6):15–35, 2006) to fit the behavior of microstructural network models. We show that Delaunay microstructural networks can be fit to the HGO strain energy function by calculating fiber network strain energy and average fiber stretch ratio. We then use the HGO constitutive model in a FE framework to improve the speed of our hybrid model, and demonstrate that this method, combined with a material property update scheme, can match a full multiscale simulation. This method gives us flexibility in defining complex FE simulations that would be impossible, or at least prohibitively time consuming, in multiscale simulation, while still accounting for microstructural heterogeneity.

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Data Availability

All raw data are available from the contact author upon request.

Code Availability

The codes, simulations, and models used in this work are available on GitHub.

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Acknowledgements

In this special issue in honor of Gerhard Holzapfel’s remarkable contributions to the field of tissue mechanics, the authors are happy to express their gratitude for his hard work, devotion to high-quality science, and commitment to the biomechanics community. He is both a great scientist and a great person, and we are lucky to have him as a colleague.

Funding

This work was supported by the National Institutes of Health through the grants U01 AT010326, U54 CA210190, T32 AR050938, and U01 HL139471. Ryan R. Mahutga and Lauren M. Bersie-Larson are supported by University of Minnesota Doctoral Dissertation Fellowships. Ryan R. Mahutga was supported by National Science Foundation Graduate Research Fellowship Program (NSF GRFP) under Grant No. 00039202. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the authors(s) and do not necessarily reflect the views of the National Science Foundation.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Minnesota – Twin Cities, Minneapolis, MN, USA

    Maryam Nikpasand

  2. Department of Biomedical Engineering, University of Minnesota – Twin Cities, Minneapolis, MN, USA

    Ryan R. Mahutga, Lauren M. Bersie-Larson, Elizabeth Gacek & Victor H. Barocas

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  1. Maryam Nikpasand
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  2. Ryan R. Mahutga
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  3. Lauren M. Bersie-Larson
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  4. Elizabeth Gacek
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  5. Victor H. Barocas
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Contributions

MN and VHB conceived the initial idea for this work. MN, RRM, LMBL, and EG performed the research. MN, RRM, LMBL, EG, and VHB prepared and edited the manuscript.

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Correspondence to Victor H. Barocas.

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Nikpasand, M., Mahutga, R.R., Bersie-Larson, L.M. et al. A Hybrid Microstructural-Continuum Multiscale Approach for Modeling Hyperelastic Fibrous Soft Tissue. J Elast 145, 295–319 (2021). https://doi.org/10.1007/s10659-021-09843-7

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