Eliot H. Frank

Cartilage electromechanics—II. A continuum model of cartilage electrokinetics and correlation with experiments

We have formulated a continuum model for linear electrokinetic transduction in cartilage. Expressions are derived for the streaming potential and streaming current induced by oscillatory, uniaxial confined compression of the tissue, as well as the mechanical stress generated by a current density or potential difference applied to the tissue. The experimentally observed streaming potential and current-generated stress response, measured on the same specimens, are compared with the predictions of the theory over a wide frequency range. The theory compares well with the data for reasonable values of cartilage intrinsic mechanical parameters and electrokinetic coupling coefficients. Experiments also show a linear relationship between the stimulus amplitude and the transduction response amplitude, within the range of stimulus amplitudes of interest. This observation is shown to be consistent with the predictions of the linear theory.

The effect of dynamic compression on the response of articular cartilage to insulin-like growth factor-I

Articular cartilage is routinely subjected to mechanical forces and to cell‐regulatory molecules. Previous studies have shown that mechanical stimuli can influence articular chondrocyte metabolic activity, and biochemical studies have shown that growth factors and cytokines control many of the same cell functions. Little is known, however, of the relationships or interplay, if any, between these two key components of the articular environment. This study investigated the comparative and interactive effects of low amplitude, sinusoidal, dynamic compression and insulin‐like growth factor‐I (IGF‐I), a polypeptide in synovial fluid that is anabolic for cartilage. In bovine patellofemoral cartilage explants, IGF‐I increased protein and proteoglycan synthesis 90% and 120%, respectively while dynamic compression increased protein and proteoglycan synthesis 40% and 90%, respectively. Stimulation by IGF‐I was significantly greater than by dynamic compression for both protein and proteoglycan synthesis. When applied together, the two stimuli enhanced protein and proteoglycan synthesis by 180% and 290%, respectively, a degree greater than that achieved by either stimulus alone. IGF‐I augmented protein synthesis with a time constant of 12.2 h. Dynamic compression increased protein synthesis with a time constant of 2.9 h, a rate significantly faster than that of IGF‐I, suggesting that these signals act via distinct cell activation pathways. When used together, dynamic compression and IGF‐I acted with a time constant of 5.6 h. Thus, dynamic compression accelerated the biosynthetic response to IGF‐I and increased transport of IGF‐I into the articular cartilage matrix, suggesting that, in addition to independently stimulating articular chondrocytes, cyclic compression may improve the access of soluble growth factors to these relatively isolated cells.

A versatile shear and compression apparatus for mechanical stimulation of tissue culture explants

We have developed an incubator housed, biaxial-tissue-loading device capable of applying axial deformations as small as 1 microm and sinusoidal rotations as small as 0.01 degrees. Axial resolution is 50 nm for applying sinewaves as low as 10 microm (or 1% based on a 1 mm thickness) or as large as 100 microm. Rotational resolution is 0.0005 degrees. The machine is small enough (30 cm high x 25 cm x 20 cm) to be placed in a standard incubator for long-term tissue culture loading studies. In metabolic studies described here, application of sinusoidal macroscopic shear deformation to articular cartilage explants resulted in a significant increase in the synthesis of proteoglycan and proteins (uptake of (35)S-sulfate and (3)H-proline) over controls held at the same static offset compression.

Transport and binding of insulin-like growth factor I through articular cartilage.

This study focused on the role of insulin-like growth factor (IGF) binding proteins (IGFBPs) in cartilage on the transport and binding of IGF-I within the tissue. We have developed experimental and theoretical modeling techniques to quantify and contrast the roles of diffusion, binding, fluid convection, and electrical migration on the transport of IGF-I within cartilage tissue. Bovine articular cartilage disks were equilibrated in buffer containing 125I-IGF-I and graded levels of unlabeled IGF-I. Equilibrium binding, as measured by the uptake ratio of 125I-IGF-I in the tissue (free plus bound) to the concentration of labeled species in the buffer, was found to be consistent with a first-order reversible binding model involving one dominant family of binding sites within the matrix. Western ligand blots revealed a major IGF binding doublet around 23 kDa, which has been previously shown to coincide with IGFBP-6. Diffusive transport of 125I-IGF-I through cartilage was measured and found to be consistent with a diffusion-limited reaction theoretical model incorporating first-order reversible binding. Addition of excess amounts of unlabeled IGF-I during steady state transport of 125I-IGF-I resulted in release of bound 125I-IGF-I from the tissue, as predicted by the diffusion-reaction model. In contrast, addition of the low-affinity Des(1-3)IGF-I analog did not result in release of bound 125I-IGF-I. Application of electric current was used to augment transport of IGF-I through cartilage via electroosmosis and electrophoresis. Taken together, our results suggest that a single dominant substrate family, the high-affinity IGFBPs, is responsible for much of the observed binding of IGF-I within cartilage. The data suggest that intratissue fluid flow, such as that induced by mechanical loading of cartilage in vivo may be expected to enhance IGF transport by an order of magnitude and that this increment may help to counterbalance the restrictions encountered by the immobilization of IGFs by the binding proteins.

Variationally derived 3-field finite element formulations for quasistatic poroelastic analysis of hydrated biological tissues

Hydrated biological tissues are often modeled mechanically as poroelastic media with intrinsically incompressible solid and fluid constituents. Unlike many engineering materials, these tissues may typically experience finite deformations during normal, physiological activities. Accurate and efficient finite element formulations are required to solve large problems of experimental and clinical relevance. This manuscript describes two new 3-field (u-p-W) mixed finite element formulations based on Lagrange multiplier and Augmented Lagrangian representations of the saturation/incompressibility constraint. As a precursor, the continuum mixture theory for finite deformation, quasistatic poroelasticity with constituent incompressibility is first reformulated within the variational framework of the principal of virtual power. In doing so, the equivalence of the continuum mixture theory and Biot formulations for this problem is established. The improved performance of the mixed formulations over an analogous 2-field (u-W) penalty formulation is demonstrated using axisymmetric numerical examples.

Avidin as a model for charge driven transport into cartilage and drug delivery for treating early stage post-traumatic osteoarthritis.

Local drug delivery into cartilage remains a challenge due to its dense extracellular matrix of negatively charged proteoglycans enmeshed within a collagen fibril network. The high negative fixed charge density of cartilage offers the unique opportunity to utilize electrostatic interactions to augment transport, binding and retention of drug carriers. With the goal of developing particle-based drug delivery mechanisms for treating post-traumatic osteoarthritis, our objectives were, first, to determine the size range of a variety of solutes that could penetrate and diffuse through normal cartilage and enzymatically treated cartilage to mimic early stages of OA, and second, to investigate the effects of electrostatic interactions on particle partitioning, uptake and binding within cartilage using the highly positively charged protein, Avidin, as a model. Results showed that solutes having a hydrodynamic diameter ≤10 nm can penetrate into the full thickness of cartilage explants while larger sized solutes were trapped in the tissues superficial zone. Avidin had a 400-fold higher uptake than its neutral same-sized counterpart, NeutrAvidin, and >90% of the absorbed Avidin remained within cartilage explants for at least 15 days. We report reversible, weak binding (K(D) ~ 150 μM) of Avidin to intratissue sites in cartilage. The large effective binding site density (N(T) ~ 2920 μM) within cartilage matrix facilitates Avidins retention, making its structure suitable for particle based drug delivery into cartilage.

The effects of glycosaminoglycan content on the compressive modulus of cartilage engineered in type II collagen scaffolds

OBJECTIVE The current study determined the unconfined compressive modulus of tissue-engineered constructs with varying sulfated glycosaminoglycan (GAG) density produced by goat articular chondrocytes in type II collagen scaffolds prepared with a range of cross-link densities and various times in culture. The purpose of this work is to establish a basis for future studies employing constructs of selected maturity (e.g., 25%, 50%, or 75% normal GAG content) for cartilage repair in vivo. METHODS Porous scaffolds (8 mm diameter by 2 mm thick) were fabricated from porcine type II collagen by freeze-drying, followed by dehydrothermal treatment and carbodiimide cross-linking. In a pilot study, passage 3 adult caprine articular chondrocytes isolated from one goat were grown in scaffolds with six cross-link densities for 2, 3, 4, and 6 weeks (n=3). The goal was to select scaffold cross-link densities and times in culture that would produce constructs with approximately 25%, 50% and 75% the GAG density of native articular cartilage. Based on the results of the pilot study, chondrocytes from three goats were grown in scaffolds with two cross-link densities for three time periods: 3, 5, and 9 weeks (n=6; one of the cross-link groups was run in quadruplicate). The equilibrium modulus from unconfined compression testing of these samples was correlated with GAG content. RESULTS There was a notable increase in GAG density with decreasing cross-link density. Histological analysis verified a chondrogenic phenotype and revealed various amounts of GAG and type II collagen-containing cartilage. The correlation between modulus and GAG density had a linear coefficient of determination of 0.60. One group with a mean GAG density of 22 microg/mm(3), which was 140% the GAG density of normal caprine articular cartilage, averaged a compressive modulus of 31.5 kPa, which was 10% of caprine articular cartilage tested in this study. CONCLUSIONS The GAG density and modulus of tissue-engineered constructs can be controlled by the degree of cross-linking of type II collagen scaffolds and time in culture.

Moderate dynamic compression inhibits pro-catabolic response of cartilage to mechanical injury, tumor necrosis factor-α and interleukin-6, but accentuates degradation above a strain threshold.

OBJECTIVE Traumatic joint injury can initiate early cartilage degeneration in the presence of elevated inflammatory cytokines (e.g., tumor necrosis factor (TNF)-α and interleukin (IL)-6). The positive/negative effects of post-injury dynamic loading on cartilage degradation and repair in vivo are not well-understood. This study examined the effects of dynamic strain on immature bovine cartilage in vitro challenged with TNF-α + IL-6 and its soluble receptor (sIL-6R) with/without initial mechanical injury. METHODS Groups of mechanically injured or non-injured explants were cultured in TNF-α + IL-6/sIL-6R for 8 days. Intermittent dynamic compression was applied concurrently at 10%, 20%, or 30% strain amplitude. Outcome measures included sulfated glycosaminoglycan (sGAG) loss (dimethylmethylene blue (DMMB)), aggrecan biosynthesis ((35)S-incorporation), aggrecanase activity (Western blot), chondrocyte viability (fluorescence staining) and apoptosis (nuclear blebbing via light microscopy), and gene expression (qPCR). RESULTS In bovine explants, cytokine alone and injury-plus-cytokine treatments markedly increased sGAG loss and aggrecanase activity, and induced chondrocyte apoptosis. These effects were abolished by moderate 10% and 20% strains. However, 30% strain amplitude greatly increased apoptosis and had no inhibitory effect on aggrecanase activity. TNF + IL-6/sIL-6R downregulated matrix gene expression and upregulated expression of inflammatory genes, effects that were rescued by moderate dynamic strains but not by 30% strain. CONCLUSIONS Moderate dynamic compression inhibits the pro-catabolic response of cartilage to mechanical injury and cytokine challenge, but there is a threshold strain amplitude above which loading becomes detrimental to cartilage. Our findings support the concept of appropriate loading for post-injury rehabilitation.

Nondestructive detection of cartilage degeneration using electromechanical surface spectroscopy

We have constructed an electrokinetic surface probe capable of applying small sinusoidal currents to the surface of articular cartilage and measuring the resulting current-generated stress with a piezoelectric sensor. Using the probe, we have characterized the electromechanical response of excised discs of normal and chemically modified adult bovine femoropatellar groove cartilage. The measured stress amplitude was proportional to the applied current density and inversely proportional to the excitation frequency, consistent with a poroelastic model. As a function of bath pH, the stress amplitude exhibited a minimum in the range pH 2.4-2.8 and the phase underwent an abrupt 180 degrees transition in the same range, consistent with an electrokinetic mechanism as the origin of the current-generated mechanical stress. Digestion of the tissue with trypsin resulted in a progressive loss of highly charged proteoglycan molecules from the tissue, with a concomitant decrease in the measured stress amplitude. These results support the feasibility of surface measurements as a means of assessing electromechanical transduction in cartilage and of detecting subtle molecular-level degradative changes in the extracellular matrix. This technique of surface spectroscopy provides a new means of nondestructively measuring the material properties of cartilage on intact joints and detecting degradative changes such as those seen in the earliest stages of osteoarthritis.

Solute transport in cartilage undergoing cyclic deformation

There are no blood vessels in cartilage to transport nutrients and growth factors to chondrocytes dispersed throughout the cartilage matrix. Insulin-like growth factor-I (IGF-I) is a large molecule with an important role in cartilage growth and metabolism, however, it first must reach the chondrocytes to exert its effect. While diffusion of IGF-I through cartilage is possible, it has been speculated that cyclic loading can enhance the rate of solute transport within cartilage. To better understand this process, here a one-dimensional axisymmetric mathematical model is developed to examine the transport of solutes through a cylindrical plug of cartilage undergoing cyclic axial deformation in the range of 10− 3–1 Hz. This study has revealed the role of timescales in interpreting transport results in cartilage. It is shown that dynamic strains can either enhance or inhibit IGF-I transport at small timescales ( < 20 min after onset of loading), depending on loading frequency. However, on longer timescales it is found that dynamic loading has negligible effect on IGF-I transport. Most importantly, in all cases examined the steady state IGF-I concentration did not exceed the fixed boundary value, in contrast to the predictions of Mauk et al. (2003).