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A mathematical model for viscoelastic properties of biological soft tissue

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Abstract

A quaternary viscoelastic structure model with two characteristic times is presented to describe the viscoelastic properties of parallel-fibered collagen tissue. The comparison results of model prediction and experimental data of rabbit medial collateral ligaments show that the model could accurately describe viscoelastic behavior such as stress-relaxation, strain-strengthening and creep of bio-soft-tissue within a small scope of errors. To study the biomechanical mechanism of viscoelasticity that biological soft tissue shows, the influence of model parameters on viscoelastic behavior of bio-soft-tissue is analyzed and researched, which indicated that the major influential elements of stress-relaxation in bio-soft-tissue are elastic modulus, relaxation time and strain rate of proteoglycan-rich matrix. The influence of elastic modulus of collagen fibers on stress-relaxation is not significant. However, the nonlinearity of stress–strain curve and viscoelastic behavior of bio-soft-tissue mostly depends on recruitment and reorientation of collagen fibers under external loading.

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Acknowledgements

This work was supported by National Natural Science Foundation of China, Grant 11072104 and Inner Mongolia natural science foundation of China, Grant 2021MS03018.

Funding

Funding was provided by National Natural Science Foundation of China (11072104) and Natural Science Foundation of Inner Mongolia (2021MS03018).

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Authors and Affiliations

  1. Biomechanics Laboratory of Physical Education Institute, Inner Mongolia Normal University, Hohhot, 010022, People’s Republic of China

    Man Xi & Guohong Yun

  2. College of Physics and Electronic Information, Inner Mongolia Normal University, Hohhot, 010022, People’s Republic of China

    Guohong Yun & B. Narsu

  3. Inner Mongolia Key Lab of Nanoscience and Nanotechnology and School of Physical Science and Technology, Inner Mongolia University, Hohhot, 010022, People’s Republic of China

    Guohong Yun & B. Narsu

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  1. Man Xi
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  2. Guohong Yun
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  3. B. Narsu
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Correspondence to Guohong Yun.

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Xi, M., Yun, G. & Narsu, B. A mathematical model for viscoelastic properties of biological soft tissue. Theory Biosci. 141, 13–25 (2022). https://doi.org/10.1007/s12064-021-00361-7

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  • DOI: https://doi.org/10.1007/s12064-021-00361-7

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