Effects of tension-compression nonlinearity on solute transport in charged hydrated fibrous tissues under dynamic unconfined compression

Abstract

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 et al., 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 et al., 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.

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.

Figure 2

Concentration distributions of uncharged solute (hydrodynamic radius: 3 nm) 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 0.01 Hz and strain amplitude of either 2.5 or 5% for 100 cycles.

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 0.01 Hz and strain amplitude of 5% for 5000 sec (50 cycles). 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.

Figure 4

Profile of convective solute flux at the location r̂ =1.45 (ẑ =0) during the 50^th 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 0.01 Hz and strain amplitude of 5% for 50 cycles. The hydrodynamic radius of uncharged solute was 3 nm.

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 Figure 3.

Figure 6

Effects of loading frequency on solute desorption (hydrodynamic radius: 3 nm) 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 0.1 Hz, 0.01 Hz, or 0.001 Hz and strain amplitude of 5% for 5000 sec.

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 50^th loading cycle. The loading conditions are the same as those described in Figure 3.