The nonlinear relationship between speed of sound and compression in articular cartilage: Measurements and modeling.

We measured speed of sound in bovine articular cartilage as a function of compressive strain. Using techniques we developed, it was possible to apply strain starting from the unstrained, full height of a sample. Our measurements showed that speed of sound was not a monotonic function of strain as reported in earlier investigations. Speed increased with increasing strain over a range of lower strains. It reached a maximum, and then decreased as the strain increased further. These results were corroborated using a model of wave propagation in deformable porous materials. Using this model, we also established conditions under which a maximum in the speed would exist for samples in compression. Our measurements and analysis resolve the conflicting results reported in previous studies.

Apparatus and Method for Rapid Detection of Acoustic Anisotropy in Cartilage.

PURPOSE: Articular cartilage is known to be mechanically anisotropic. In this paper, the acoustic anisotropy of bovine articular cartilage and the effects of freeze-thaw cycling on acoustic anisotropy were investigated. METHODS: We developed apparatus and methods that use a magnetic L-shaped sample holder, which allowed minimal handling of a tissue, reduced the number of measurements compared to previous studies, and produced highly reproducible results. RESULTS: SOS was greater in the direction perpendicular to the articular surface compared to the direction parallel to the articular surface (N=17, P = 0.00001). Average SOS was 1,758 ± 107 m/s perpendicular to the surface, and 1,617 ± 55 m/s parallel to it. The average percentage difference in SOS between the perpendicular and parallel directions was 8.2% (95% CI: 5.4% to 11%). Freeze-thaw cycling did not have a significant effect on SOS (P>0.4). CONCLUSION: Acoustic measurement of tissue properties is particularly attractive for work in our laboratory since it has the potential for nondestructive characterization of the properties of developing engineered cartilage. Our approach allowed us to observe acoustic anisotropy of articular cartilage rapidly and reproducibly. This property was not significantly affected by freeze-thawing of the tissue samples, making cryopreservation practical for these assays.

Rapid Detection of Shear-Induced Damage in Tissue-Engineered Cartilage Using Ultrasound.

Previous investigations have shown that tissue-engineered articular cartilage can be damaged under a combination of compression and sliding shear. In these cases, damage was identified in histological sections after a test was completed. This approach is limited, in that it does not identify when damage occurred. This especially limits the utility of an assay for evaluating damage when comparing modifications to a tissue-engineering protocol. In this investigation, the feasibility of using ultrasound (US) to detect damage as it occurs was investigated. US signals were acquired before, during, and after sliding shear, as were stereomicroscope images of the cartilage surface. Histology was used as the standard for showing if a sample was damaged. We showed that US reflections from the surface of the cartilage were attenuated due to roughening following sliding shear. Furthermore, it was shown that by scanning the transducer across a sample, surface roughness and erosion following sliding shear could be identified. Internal delamination could be identified by the appearance of new echoes between those from the front and back of the sample. Thus, it is feasible to detect damage in engineered cartilage using US.

Dynamics of Intrinsic Glucose Uptake Kinetics in Human Mesenchymal Stem Cells During Chondrogenesis.

Chondrogenesis of human mesenchymal stem cells (hMSCs) is an important biological process in many applications including cartilage tissue engineering. We investigated the glucose uptake characteristics of aggregates of hMSCs undergoing chondrogenesis over a 3-week period both experimentally and by using a mathematical model. Initial concentrations of glucose in the medium were varied from 1 to 4.5 g/L to mimic limiting conditions and glucose uptake profiles were obtained. A reaction-diffusion mathematical model was implemented and solved to estimate kinetic parameters. Experimental glucose uptake rates increased with culture time for aggregates treated with higher initial glucose concentrations (3 and 4.5 g/L), whereas they decreased or remained constant for those treated with lower initial glucose concentrations (1 and 2 g/L). Lactate production rate increased by as much as 40% for aggregates treated with higher initial glucose concentrations (2, 3 and 4.5 g/L), whereas it remained constant for those treated with 1 g/L initial glucose concentration. The estimated DNA-normalized maximum glucose uptake rate decreased by a factor of 9 from day 0-2 (12.5 mmol/s/g DNA) to day 6-8 (1.5 mmol/s/g DNA), after which it started to increase. On day 18-20, its value (17.5 mmol/s/g DNA) was about 11 times greater than its lowest value. Further, the extracellular matrix levels of aggregates at day 14 and day 21 correlated with their overall glucose uptake and lactate production. The results suggest that during chondrogenesis, for optimal results, cells require increasing amounts of glucose. Our results also suggest that diffusion limitations play an important role in glucose uptake even in the smaller size aggregate model of chondrogenesis. Further, the results indicate that glucose uptake or lactate production can be a tool for predicting the end quality of tissue during the process of chondrogenesis. The estimated kinetic parameters can be used to model glucose requirements in cartilage tissue engineering applications.

Depth-dependent shear behavior of bovine articular cartilage: relationship to structure.

The mechanical behavior of bovine articular cartilage in shear was measured and related to its structure through the depth of the tissue. To make these measurements, we designed an apparatus that could apply controlled shear displacement and measure the resulting shear force on cartilage specimens. Shear displacement and shear strain were obtained from confocal images of photobleached lines on fluorescently stained deformed samples. Depth-dependent collagen structure was obtained using compensated polarized light microscopy. Depth-dependent shear behavior and structure of samples from two animals were measured (group A and B). Both animals were 18-24 months old, which is the range in which they are expected reach skeletal maturity. In mature samples (group A), the stiffest region was located beneath the superficial zone, and the most compliant region was found in the radial zone. In contrast, in samples that were in the process of maturing (group B) the most compliant region was located in the superficial zone. Compensated polarized light microscopy suggested that the animal from which the group A samples were obtained was skeletally mature, whereas the animal yielding the group B samples was in the process of maturing. Compensated polarized light microscopy was an important adjunct to the mechanical shear behavior in that it provided a means to reconcile differences in observed shear behavior in mature and immature cartilage. Although samples were harvested from two animals, there were clear differences in structure and shear mechanical behavior. Differences in the depth-dependent shear strain were consistent with previous studies on mature and immature samples and, based on the structural variation between mature and immature articular cartilage, their mechanical behavior differences can be tenable. These results suggest that age, as well as species and anatomic location, need to be considered when reporting mechanical behavior results.

Investigating a continuous shear strain function for depth-dependent properties of native and tissue engineering cartilage using pixel-size data.

A previously developed novel imaging technique for determining the depth dependent properties of cartilage in simple shear is implemented. Shear displacement is determined from images of deformed lines photobleached on a sample, and shear strain is obtained from the derivative of the displacement. We investigated the feasibility of an alternative systematic approach to numerical differentiation for computing the shear strain that is based on fitting a continuous function to the shear displacement. Three models for a continuous shear displacement function are evaluated: polynomials, cubic splines, and non-parametric locally weighted scatter plot curves. Four independent approaches are then applied to identify the best-fit model and the accuracy of the first derivative. One approach is based on the Akaiki Information Criteria, and the Bayesian Information Criteria. The second is based on a method developed to smooth and differentiate digitized data from human motion. The third method is based on photobleaching a predefined circular area with a specific radius. Finally, we integrate the shear strain and compare it with the total shear deflection of the sample measured experimentally. Results show that 6th and 7th order polynomials are the best models for the shear displacement and its first derivative. In addition, failure of tissue-engineered cartilage, consistent with previous results, demonstrates the qualitative value of this imaging approach.