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TECHNICAL PAPERS: Soft Tissue

Effects of Tension-Compression Nonlinearity on Solute Transport in Charged Hydrated Fibrous Tissues Under Dynamic Unconfined Compression

[+] Author and Article Information
Chun-Yuh Huang

Department of Pediatric Dentistry, Nova Southeastern University, Ft. Lauderdale, FL

Wei Yong Gu1

Tissue Biomechanics Lab, Department of Biomedical Engineering, University of Miami, Coral Gables, FLwgu@miami.edu

1

Corresponding author.

J Biomech Eng 129(3), 423-429 (Nov 06, 2006) (7 pages) doi:10.1115/1.2720920 History: Received March 22, 2006; Revised November 06, 2006

Cartilage is a charged hydrated fibrous tissue exhibiting a high degree of tension-compression nonlinearity (i.e., tissue anisotropy). The effect of tension-compression nonlinearity on solute transport has not been investigated in cartilaginous tissue under dynamic loading conditions. In this study, a new model was developed based on the mechano-electrochemical mixture model [Yao and Gu, 2007, J. Biomech. Model Mechanobiol., 6, pp. 63–72, Lai, 1991, J. Biomech. Eng., 113, pp. 245–258], and conewise linear elasticity model [Soltz and Ateshian, 2000, J. Biomech. Eng., 122, pp. 576–586;Curnier, 1995, J. Elasticity, 37, pp. 1–38]. The solute desorption in cartilage under unconfined dynamic compression was investigated numerically using this new model. Analyses and results demonstrated that a high degree of tissue tension-compression nonlinearity could enhance the transport of large solutes considerably in the cartilage sample under dynamic unconfined compression, whereas it had little effect on the transport of small solutes (at 5% dynamic strain level). The loading-induced convection is an important mechanism for enhancing the transport of large solutes in the cartilage sample with tension-compression nonlinearity. The dynamic compression also promoted diffusion of large solutes in both tissues with and without tension-compression nonlinearity. These findings provide a new insight into the mechanisms of solute transport in hydrated, fibrous soft tissues.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of dynamic unconfined compression test configuration for solute desorption experiment. A ramp compression (u0=20% offset strain) was applied in 100s. After stress relaxation for 800,000s, a dynamic compression (u1=2.5% or 5% dynamic strain) was imposed and the concentration of uncharged solute in the bathing solute was changed to zero.

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Figure 2

Concentration distributions of uncharged solute (hydrodynamic radius: 3nm) within the cartilage samples under two applied dynamic strains. In the simulations, the cartilage samples (H+A∕H−A=16) were subjected to dynamic compressive loading with a frequency of 0.01Hz and strain amplitude of either 2.5 or 5% for 100cycles.

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Figure 3

Effect of tissue tension-compression nonlinearity on desorption of large and small uncharged solutes in tissues under dynamic compression. In the simulations, the cartilage samples were either load-free or subjected to dynamic loading with a frequency of 0.01Hz and strain amplitude of 5% for 5000s(50cycles). The amount of solute desorption (ΔŴ) was calculated for each of the two cases from t̂1=200 to t̂2=201.25, according to Eq. 13. The amount of desorption in a dynamic loading case was normalized by that in a load-free case.

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Figure 4

Profile of convective solute flux at the location r̂=1.45(ẑ=0) during the 50th loading cycle. In the simulations, the cartilage samples (H+A∕H−A=1, 4, and 16) were subjected to dynamic loading with a frequency of 0.01Hz and strain amplitude of 5% for 50cycles. The hydrodynamic radius of uncharged solute was 3nm.

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Figure 5

Effects of convection coefficient and solute size on desorption in the samples with and without tension-compression nonlinearity. The loading conditions are the same as those described in Fig. 3.

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Figure 6

Effects of loading frequency on solute desorption (hydrodynamic radius: 3nm) in the samples with tension-compression nonlinearity (H+A∕H−A=16). In the simulations, the cartilage samples were subjected to dynamic compressive loading with a frequency of either 0.1Hz, 0.01Hz, or 0.001Hz and strain amplitude of 5% for 5000s.

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Figure 7

Ratio of the amount of uncharged solute removed by convection to that by diffusion in the subdomain between r̂=0 and r̂=1.45 during the 50th loading cycle. The loading conditions are the same as those described in Fig. 3.

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