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Research Papers

A Biphasic Transversely Isotropic Poroviscoelastic Model for the Unconfined Compression of Hydrated Soft Tissue

[+] Author and Article Information
H. Hatami-Marbini

Department of Mechanical
and Industrial Engineering,
University of Illinois at Chicago,
Chicago, IL 60607
e-mail: hatami@uic.edu; hamed.hatami@gmail.com

R. Maulik

School of Mechanical
and Aerospace Engineering,
Oklahoma State University,
Stillwater, OK 74075

1Corresponding author.

Manuscript received August 14, 2015; final manuscript received November 8, 2015; published online January 29, 2016. Assoc. Editor: Kristen Billiar.

J Biomech Eng 138(3), 031003 (Jan 29, 2016) (6 pages) Paper No: BIO-15-1407; doi: 10.1115/1.4032059 History: Received August 14, 2015; Revised November 08, 2015

The unconfined compression experiments are commonly used for characterizing the mechanical behavior of hydrated soft tissues such as articular cartilage. Several analytical constitutive models have been proposed over the years to analyze the unconfined compression experimental data and subsequently estimate the material parameters. Nevertheless, new mathematical models are still required to obtain more accurate numerical estimates. The present study aims at developing a linear transversely isotropic poroviscoelastic theory by combining a viscoelastic material law with the transversely isotropic biphasic model. In particular, an integral type viscoelastic model is used to describe the intrinsic viscoelastic properties of a transversely isotropic solid matrix. The proposed constitutive theory incorporates viscoelastic contributions from both the fluid flow and the intrinsic viscoelasticity to the overall stress-relaxation behavior. Moreover, this new material model allows investigating the biomechanical properties of tissues whose extracellular matrix exhibits transverse isotropy. In the present work, a comprehensive parametric study was conducted to determine the influence of various material parameters on the stress–relaxation history. Furthermore, the efficacy of the proposed theory in representing the unconfined compression experiments was assessed by comparing its theoretical predictions with those obtained from other versions of the biphasic theory such as the isotropic, transversely isotropic, and viscoelastic models. The unconfined compression behavior of articular cartilage as well as corneal stroma was used for this purpose. It is concluded that while the proposed model is capable of accurately representing the viscoelastic behavior of any hydrated soft tissue in unconfined compression, it is particularly useful in modeling the behavior of those with a transversely isotropic skeleton.

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Figures

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Fig. 1

A schematic plot of the unconfined compression test. A cylindrical button of tissue with radius r0 is subjected to ramp displacement of Δh over ramp time of t0. The measured reaction force shows a stress-relaxation behavior which reaches a peak value Fmax and relaxes to equilibrium force Feq.

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Fig. 2

The effect of the parameter t0/tg on the unconfined compression stress-relaxation behavior

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Fig. 3

The effect of the parameter Err/Ezz on the unconfined compression stress-relaxation behavior

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Fig. 4

The effect of the Poisson's ratio νrθ on the unconfined compression stress-relaxation behavior

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Fig. 5

The effect of the Poisson's ratio νzr on the unconfined compression stress-relaxation behavior

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Fig. 6

The effect of the parameter c on the unconfined compression stress-relaxation behavior

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Fig. 7

The effect of the parameter τ2 on the unconfined compression stress-relaxation behavior

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Fig. 8

The mechanical behavior of articular cartilage in a typical unconfined compression experiment (Huang et al.) and the theoretical curve-fits obtained from four different biphasic models, i.e., the linear isotropic biphasic, isotropic viscoelastic biphasic, transversely isotropic biphasic, and transversely isotropic viscoelastic (present model) theories. The time is plotted in logarithmic scale in order to highlight the capability of different models in representing the experimental measurements.

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Fig. 9

The mechanical behavior of the cornea in unconfined compression and the theoretical curve-fits obtained from four different biphasic models, i.e., the linear isotropic biphasic, isotropic viscoelastic biphasic, transversely isotropic biphasic, and transversely isotropic viscoelastic (present model) theories. The time is plotted in logarithmic scale in order to highlight the capability of different models in representing the experimental measurements.

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