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Biomechanics: Trends in Modeling and Simulation pp 1–51Cite as

Mixture Theory for Modeling Biological Tissues: Illustrations from Articular Cartilage

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Part of the book series: Studies in Mechanobiology, Tissue Engineering and Biomaterials ((SMTEB,volume 20))

Abstract

Mixture theory has been used for modeling hydrated biological tissues for several decades. This chapter reviews the basic foundation of mixture theory as applied to biphasic mixtures consisting of a porous-permeable deformable solid matrix and an interstitial fluid. Canonical problems of permeation, confined compression, and unconfined compression are analyzed from theory and compared to prior experimental measurements on articular cartilage, with an emphasis on studies that provide validations of theoretical predictions. A brief overview is also provided of the application of mixture theory to solute transport, reactive kinetics, and growth and remodeling.

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Notes

  1. 1.

    Mow and Lai were this author’s doctoral advisors and mentors, starting in 1986.

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Acknowledgments

I would like to thank the many former and current doctoral students and fellows who labored with me over the years, performing experiments and validating the mixture models used in our investigations of biological tissues: Dr. Huiqun (Laura) Wang, Dr. William H. Warden, Dr. Michael A. Soltz, Prof. Robert L. Mauck, Prof. Chun-Yuh (Charles) Huang, Dr. Changbin Wang, Dr. Ramaswamy Krishnan, Prof. Seonghun Park, Prof. Ines M. Basalo, Prof. Nadeen O. Chahine, Dr. Michael B. Albro, Dr. Matteo M. Caligaris, Dr. Clare Canal-Guterl, Dr. Sevan R. Oungoulian, Dr. Alexander D. Cigan, Mr. Robert J. Nims, Mr. Brian K. Jones, Mr. Chieh Hou, and Ms. Krista M. Durney. I would also like to thank Dr. Albro for providing the experimental data appearing in Fig. 4, and Mr. Brandon K. Zimmerman for re-analyzing older data sets to produce Fig. 13.

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  1. Columbia University, New York, NY, USA

    Gerard A. Ateshian

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  1. Institute of Biomechanics, Graz University of Technology, Graz, Austria

    Gerhard A. Holzapfel

  2. School of Mathematics and Statistics, University of Glasgow, Glasgow, United Kingdom

    Ray W. Ogden

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Ateshian, G.A. (2017). Mixture Theory for Modeling Biological Tissues: Illustrations from Articular Cartilage. In: Holzapfel, G., Ogden, R. (eds) Biomechanics: Trends in Modeling and Simulation. Studies in Mechanobiology, Tissue Engineering and Biomaterials, vol 20. Springer, Cham. https://doi.org/10.1007/978-3-319-41475-1_1

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