Michael B. Albro

Dynamic loading of deformable porous media can induce active solute transport

Active solute transport mediated by molecular motors across porous membranes is a well-recognized mechanism for transport across the cell membrane. In contrast, active transport mediated by mechanical loading of porous media is a non-intuitive mechanism that has only been predicted recently from theory, but not yet observed experimentally. This study uses agarose hydrogel and dextran molecules as a model experimental system to explore this mechanism. Results show that dynamic loading can enhance the uptake of dextran by a factor greater than 15 over passive diffusion, for certain combinations of gel concentration and dextran molecular weight. Upon cessation of loading, the concentration reverts back to that achieved under passive diffusion. Thus, active solute transport in porous media can indeed be mediated by cyclical mechanical loading.

Effect of Dynamic Loading on the Transport of Solutes into Agarose Hydrogels

In functional tissue engineering, the application of dynamic loading has been shown to improve the mechanical properties of chondrocyte-seeded agarose hydrogels relative to unloaded free swelling controls. The goal of this study is to determine the effect of dynamic loading on the transport of nutrients in tissue-engineered constructs. To eliminate confounding effects, such as nutrient consumption in cell-laden disks, this study examines the response of solute transport due to loading using a model system of acellular agarose disks and dextran in phosphate-buffered saline (3 and 70 kDa). An examination of the passive diffusion response of dextran in agarose confirms the applicability of Ficks law of diffusion in describing the behavior of dextran. Under static loading, the application of compressive strain decreased the total interstitial volume available for the 70 kDa dextran, compared to free swelling. Dynamic loading significantly enhanced the rate of solute uptake into agarose disks, relative to static loading. Moreover, the steady-state concentration under dynamic loading was found to be significantly greater than under static loading, for larger-molecular-mass dextran (70 kDa). This experimental finding confirms recent theoretical predictions that mechanical pumping of a porous tissue may actively transport solutes into the disk against their concentration gradient. The results of this study support the hypothesis that the application of dynamic loading in the presence of growth factors of large molecular weight may result in both a mechanically and chemically stimulating environment for tissue growth.

Synthesis rates and binding kinetics of matrix products in engineered cartilage constructs using chondrocyte-seeded agarose gels

Large-sized cartilage constructs suffer from inhomogeneous extracellular matrix deposition due to insufficient nutrient availability. Computational models of nutrient consumption and tissue growth can be utilized as an efficient alternative to experimental trials to optimize the culture of large constructs; models require system-specific growth and consumption parameters. To inform models of the [bovine chondrocyte]-[agarose gel] system, total synthesis rate (matrix accumulation rate+matrix release rate) and matrix retention fractions of glycosaminoglycans (GAG), collagen, and cartilage oligomeric matrix protein (COMP) were measured either in the presence (continuous or transient) or absence of TGF-β3 supplementation. TGF-β3s influences on pyridinoline content and mechanical properties were also measured. Reversible binding kinetic parameters were characterized using computational models. Based on our recent nutrient supplementation work, we measured glucose consumption and critical glucose concentration for tissue growth to computationally simulate the culture of a human patella-sized tissue construct, reproducing the experiment of Hung et al. (2003). Transient TGF-β3 produced the highest GAG synthesis rate, highest GAG retention ratio, and the highest binding affinity; collagen synthesis was elevated in TGF-β3 supplementation groups over control, with the highest binding affinity observed in the transient supplementation group; both COMP synthesis and retention were lower than those for GAG and collagen. These results informed the modeling of GAG deposition within a large patella construct; this computational example was similar to the previous experimental results without further adjustments to modeling parameters. These results suggest that these nutrient consumption and matrix synthesis models are an attractive alternative for optimizing the culture of large-sized constructs.

Accumulation of Exogenous Activated TGF-β in the Superficial Zone of Articular Cartilage

It was recently demonstrated that mechanical shearing of synovial fluid (SF), induced during joint motion, rapidly activates latent transforming growth factor β (TGF-β). This discovery raised the possibility of a physiological process consisting of latent TGF-β supply to SF, activation via shearing, and transport of TGF-β into the cartilage matrix. Therefore, the two primary objectives of this investigation were to characterize the secretion rate of latent TGF-β into SF, and the transport of active TGF-β across the articular surface and into the cartilage layer. Experiments on tissue explants demonstrate that high levels of latent TGF-β1 are secreted from both the synovium and all three articular cartilage zones (superficial, middle, and deep), suggesting that these tissues are capable of continuously replenishing latent TGF-β to SF. Furthermore, upon exposure of cartilage to active TGF-β1, the peptide accumulates in the superficial zone (SZ) due to the presence of an overwhelming concentration of nonspecific TGF-β binding sites in the extracellular matrix. Although this response leads to high levels of active TGF-β in the SZ, the active peptide is unable to penetrate deeper into the middle and deep zones of cartilage. These results provide strong evidence for a sequential physiologic mechanism through which SZ chondrocytes gain access to active TGF-β: the synovium and articular cartilage secrete latent TGF-β into the SF and, upon activation, TGF-β transports back into the cartilage layer, binding exclusively to the SZ.

Finite Element Implementation of Mechanochemical Phenomena in Neutral Deformable Porous Media Under Finite Deformation

Biological soft tissues and cells may be subjected to mechanical as well as chemical (osmotic) loading under their natural physiological environment or various experimental conditions. The interaction of mechanical and chemical effects may be very significant under some of these conditions, yet the highly nonlinear nature of the set of governing equations describing these mechanisms poses a challenge for the modeling of such phenomena. This study formulated and implemented a finite element algorithm for analyzing mechanochemical events in neutral deformable porous media under finite deformation. The algorithm employed the framework of mixture theory to model the porous permeable solid matrix and interstitial fluid, where the fluid consists of a mixture of solvent and solute. A special emphasis was placed on solute-solid matrix interactions, such as solute exclusion from a fraction of the matrix pore space (solubility) and frictional momentum exchange that produces solute hindrance and pumping under certain dynamic loading conditions. The finite element formulation implemented full coupling of mechanical and chemical effects, providing a framework where material properties and response functions may depend on solid matrix strain as well as solute concentration. The implementation was validated using selected canonical problems for which analytical or alternative numerical solutions exist. This finite element code includes a number of unique features that enhance the modeling of mechanochemical phenomena in biological tissues. The code is available in the public domain, open source finite element program FEBio (http:∕∕mrl.sci.utah.edu∕software).

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

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.

Osmotic Loading of Spherical Gels: A Biomimetic Study of Hindered Transport in the Cell Protoplasm

Osmotic loading of cells has been used to investigate their physicochemical properties as well as their biosynthetic activities. The classical Kedem-Katchalsky framework for analyzing cell response to osmotic loading, which models the cell as a fluid-filled membrane, does not generally account for the possibility of partial volume recovery in response to loading with a permeating osmolyte, as observed in some experiments. The cell may be more accurately represented as a hydrated gel surrounded by a semi-permeable membrane, with the gel and membrane potentially exhibiting different properties. To help assess whether this more elaborate model of the cell is justified, this study investigates the response of spherical gels to osmotic loading, both from experiments and theory. The spherical gel is described using the framework of mixture theory. In the experimental component of the study alginate is used as the model gel, and is osmotically loaded with dextran solutions of various concentrations and molecular weight, to verify the predictions from the theoretical analysis. Results show that the mixture framework can accurately predict the transient and equilibrium response of alginate gels to osmotic loading with dextran solutions. It is found that the partition coefficient of dextran in alginate regulates the equilibrium volume response and can explain partial volume recovery based on passive transport mechanisms. The validation of this theoretical framework facilitates future investigations of the role of the protoplasm in the response of cells to osmotic loading.

Dynamic Loading of Immature Epiphyseal Cartilage Pumps Nutrients out of Vascular Canals

The potential influence of mechanical loading on transvascular transport in vascularized soft tissues has not been explored extensively. This experimental investigation introduced and explored the hypothesis that dynamic mechanical loading can pump solutes out of blood vessels and into the surrounding tissue, leading to faster uptake and higher solute concentrations than could otherwise be achieved under unloaded conditions. Immature epiphyseal cartilage was used as a model tissue system, with fluorescein (332 Da), dextran (3, 10, and 70 kDa) and transferrin (80 kDa) as model solutes. Cartilage disks were either dynamically loaded (± 10% compression over a 10% static offset strain, at 0.2 Hz) or maintained unloaded in solution for up to 20 h. Results demonstrated statistically significant solute uptake in dynamically loaded (DL) explants relative to passive diffusion (PD) controls for all solutes except unbound fluorescein, as evidenced by the DL:PD concentration ratios after 20 h (1.0 ± 0.2, 2.4 ± 1.1, 6.1 ± 3.3, 9.0 ± 4.0, and 5.5 ± 1.6 for fluorescein, 3, 10, and 70 kDa dextran, and transferrin). Significant uptake enhancements were also observed within the first 30s of loading. Termination of dynamic loading produced dissipation of enhanced solute uptake back to PD control values. Confocal images confirmed that solute uptake occurred from cartilage canals into their surrounding extracellular matrix. The incidence of this loading-induced transvascular solute pumping mechanism may significantly alter our understanding of the interaction of mechanical loading and tissue metabolism.

Dynamic mechanical compression of devitalized articular cartilage does not activate latent TGF-β.

A growing body of research has highlighted the role that mechanical forces play in the activation of latent TGF-β in biological tissues. In synovial joints, it has recently been demonstrated that the mechanical shearing of synovial fluid, induced during joint motion, rapidly activates a large fraction of its soluble latent TGF-β content. Based on this observation, the primary hypothesis of the current study is that the mechanical deformation of articular cartilage, induced by dynamic joint motion, can similarly activate the large stores of latent TGF-β bound to the tissue extracellular matrix (ECM). Here, devitalized deep zone articular cartilage cylindrical explants (n=84) were subjected to continuous dynamic mechanical loading (low strain: ±2% or high strain: ±7.5% at 0.5Hz) for up to 15h or maintained unloaded. TGF-β activation was measured in these samples over time while accounting for the active TGF-β that remains bound to the cartilage ECM. Results indicate that TGF-β1 is present in cartilage at high levels (68.5±20.6ng/mL) and resides predominantly in the latent form (>98% of total). Under dynamic loading, active TGF-β1 levels did not statistically increase from the initial value nor the corresponding unloaded control values for any test, indicating that physiologic dynamic compression of cartilage is unable to directly activate ECM-bound latent TGF-β via purely mechanical pathways and leading us to reject the hypothesis of this study. These results suggest that deep zone articular chondrocytes must alternatively obtain access to active TGF-β through chemical-mediated activation and further suggest that mechanical deformation is unlikely to directly activate the ECM-bound latent TGF-β of various other tissues, such as muscle, ligament, and tendon.

Influence of the Partitioning of Osmolytes by the Cytoplasm on the Passive Response of Cells to Osmotic Loading

Due to the dense organization of organelles, cytoskeletal elements, and protein complexes that make up the intracellular environment, it is likely that membrane-permeant solutes may be excluded from a fraction of the interstitial space of the cytoplasm via steric restrictions, electrostatic interactions, and other long-range intermolecular forces. This study investigates the hypothesis that the intracellular partitioning of membrane-permeant solutes manifests itself as a partial volume recovery in response to hyperosmotic loading, based on prior theoretical and biomimetic experimental studies. Osmotic loading experiments are performed on immature bovine chondrocytes using culture conditions where regulatory volume responses are shown to be insignificant. Osmotic loading with membrane-permeant glycerol (92 Da) and urea (60 Da) are observed to produce partial volume recoveries consistent with the proposed hypothesis, whereas loading with 1,2-propanediol (76 Da) produces complete volume recovery. Combining these experimental results with the previous theoretical framework produces a measure for the intracellular partition coefficient of each of these solutes. At 1000 mOsm, 1,2-propanediol is the only osmolyte to yield a partition coefficient not statistically different from unity, kappa(p)(i) = 1.00 +/- 0.02. For glycerol, the partition coefficient increases with osmolarity from kappa(p)(i) = 0.48 +/- 0.19 at 200 mOsm to kappa(p)(i) = 0.80 +/- 0.07 at 1000 mOsm; urea exhibits no such dependence, with an average value of kappa(p)(i) = 0.87 +/- 0.07 for all osmolarities from 200 to 1000 mOsm. The finding that intracellular partitioning of membrane-permeant solutes manifests itself as a partial volume recovery under osmotic loading offers a simple method for characterizing the partition coefficient. These measurements suggest that significant partitioning may occur even for small membrane-permeant osmolytes. Furthermore, a positive correlation is observed, suggesting that a solutes cytoplasmic partition coefficient increases with increasing hydrophobicity.