Validation of theoretical framework explaining active solute uptake in dynamically loaded porous media

Abstract

Solute transport in biological tissues is a fundamental process necessary for cell metabolism. In connective soft tissues, such as articular cartilage, cells are embedded within a dense extracellular matrix that hinders the transport of solutes. However, according to a recent theoretical study (Mauck et al., 2003, J. Biomech. Eng. 125, 602-614), the convective motion of a dynamically loaded porous solid matrix can also impart momentum to solutes, pumping them into the tissue and giving rise to concentrations which exceed those achived under passive diffusion alone. In this study, the theoretical predictions of this model are verified against experimental measurements. The mechanical and transport properties of an agarose-dextran model system were characterized from independent measurements and substituted into the theory to predict solute uptake or desorption under dynamic mechanical loading for various agarose concentrations and dextran molecular weights, as well as different boundary and initial conditions. In every tested case, agreement was observed between experiments and theoretical predictions as assessed by coefficients of determination ranging from R(2)=0.61 to 0.95. These results provide strong support for the hypothesis that dynamic loading of a deformable porous tissue can produce active transport of solutes via a pumping mechanisms mediated by momentum exchange between the solute and solid matrix.

Fig. 1

Experimentally measured diffusivity of 70 kDa dextran in 7% agarose disks subjected to an initial 48 h of dynamic loading (DL), followed by a free swelling (FS) period of 152 h. Measurements were performed using FRAP, on disks collected at specific time points over the DL or FS periods. The FS period demonstrated that no further significant decrease in diffusivity occurred after loading was terminated (p>0.8 when comparing values at t=100 and 200 h against t=48 h).

Fig. 2

Experimentally measured diffusivity of (A) 70 kDa and (B) 10 kDa dextran in agarose disks subjected to dynamic loading. Dashed curves represent exponential and linear fits to the experimental data, described in Table 2.

Fig. 3

Enhancement of solute uptake in agarose disks subjected to dynamic loading. The experimentally measured ratio $\widehat{c}=c_{\mathit{\text{avg}}}/k{c}_0^{\ast }$ is given for (A) 70 kDa dextran and three agarose gel concentrations (Tests 1, 2 and 4, Table 1); and (B) 7% agarose and two dextran molecular weights (Tests 2 and 3, Table 1). Solid curves represent numerical predictions based on the theoretical framework. Experimental data are from an earlier study (Albro et al., 2008), except for the last time point of 70 kDa dextran in 6% agarose.

Fig. 4

Enhancement ratio of $(\widehat{c}=c_{\mathit{\text{avg}}}/k{c}_0^{\ast })$ 70 kDa dextran in 7% agarose disks subjected to dynamic loading, following a 24-h pre-incubation period in 70 kDa dextran solution (Test 5, Table 1). The solid curve represents the numerical prediction based on the theoretical framework.

Fig. 5

Desorption response of 70 kDa dextran out of 7% agarose disks under static (PD) and dynamic (DL) loading (Test 6, Table 1). Solid curves represent numerical predictions based on the theoretical framework.