Influence of the pericellular and extracellular matrix structural properties on chondrocyte mechanics.

Understanding the mechanical factors that drive the biological responses of chondrocytes is central to our interpretation of the cascade of events that lead to osteoarthritic changes in articular cartilage. Chondrocyte mechanics is complicated by changes in tissue properties that can occur as osteoarthritis (OA) progresses and by the interaction between macro-scale, tissue level, properties, and micro-scale pericellular matrix (PCM) and local extracellular matrix (ECM) properties, both of which cannot be easily studied using in vitro systems. Our objective was to study the influence of macro- and micro-scale OA-associated structural changes on chondrocyte strains. We developed a multi-scale finite element model of articular cartilage subjected to unconfined loading, for the following three conditions: (i) normal articular cartilage, (ii) OA cartilage (where macro and micro-scale changes in collagen content, matrix modulus, and permeability were modeled), and (iii) early-stage OA cartilage (where only micro-scale changes in matrix modulus were modeled). In the macro-scale model, we found that a depth-dependent strain field was induced in both healthy and OA cartilage and that the middle and superficial zones of OA cartilage had increased tensile and compressive strains. At the micro-scale, chondrocyte shear strains were sensitive to PCM and local ECM properties. In the early-OA model, micro-scale spatial softening of PCM and ECM resulted in a substantial increase (30%) of chondrocyte shear strain, even with no structural changes in macro-scale tissue properties. Our study provides evidence that micromechanical changes at the cellular level may affect chondrocyte activities before macro-scale degradations at the tissue level become apparent. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 36:721-729, 2018.

A comparison between dynamic implicit and explicit finite element simulations of the native knee joint.

The finite element (FE) method has been widely used to investigate knee biomechanics. Time integration algorithms for dynamic problems in finite element analysis can be classified as either implicit or explicit. Although previously both static/dynamic implicit and dynamic explicit method have been used, a comparative study on the outcomes of both methods is of high interest for the knee modeling community. The aim of this study is to compare static, dynamic implicit and dynamic explicit solutions in analyses of the knee joint to assess the prediction of dynamic effects, potential convergence problems, the accuracy and stability of the calculations, the difference in computational time, and the influence of mass-scaling in the explicit formulation. The heel-strike phase of fast, normal and slow gait was simulated for two different body masses in a model of the native knee. Our results indicate that ignoring the dynamic effect can alter joint motion. Explicit analyses are suitable to simulate dynamic loading of the knee joint in high-speed simulations, as this method offers a substantial reduction of the computational time with a similar prediction of cartilage stresses and meniscus strains. Although mass-scaling can provide even more gain in computational time, it is not recommended for high-speed activities, in which inertial forces play a significant role.

The influence of cell-matrix attachment and matrix development on the micromechanical environment of the chondrocyte in tissue-engineered cartilage.

Insufficiency of mechanical properties of tissue-engineered (TE) cartilage grafts is still a limiting factor for their clinical application. It has been shown that mechanostimulation of chondrocytes enhances synthesis of extracellular matrix (ECM) and thereby improves the mechanical properties of the grafts. However, the optimal mechanical loading required to stimulate chondrocytes for sufficient matrix synthesis is still unknown. The properties of the pericellular matrix (PCM) and the ability of the chondrocytes to attach to its adjacent matrix may importantly determine the stimulation of the cell in loaded tissue. The aim of the present study is to numerically investigate the influence of tissue development and cell-matrix attachment on the mechanical environment of a chondrocyte embedded in agarose. Mechanical environment inside TE constructs is evaluated and compared with that in native cartilage under 10% unconfined compression. A multiscale finite element modeling approach in conjunction with a validated nonlinear fiber-reinforced poroviscoelastic swelling cartilage model is used. Results indicate that without cell attachment, excessive local strains may be induced in the cell. With PCM development and the establishment of focal adhesions at the cell surface, the cell is strained more homogenously upon external loading. However, compared with chondrocytes in native cartilage, the transmission of the external compression to the cells in TE constructs is less. This suggests that, over time, the loading magnitude may be increased to continue stimulation of chondrocytes at the physiological or even higher levels to possibly enhance matrix synthesis. These findings improve our insights into the micromechanical environment of cells in tissue engineering cultures.

Influence of the temporal deposition of extracellular matrix on the mechanical properties of tissue-engineered cartilage.

Enhancement of the load-bearing capacity of tissue-engineered (TE) cartilage is expected to improve the clinical outcome of implantations. Generally, cartilage TE studies aim to increase the total extracellular matrix (ECM) content to improve implant mechanical properties. Besides the ECM content, however, temporal variations in deposition rate of ECM components during culture may also have an effect. Using a computational approach, the present study aims to quantify possible effects of temporal variations in the deposition of glycosaminoglycan (GAG) at given collagen synthesis rates on the mechanical stiffness of cartilage TE constructs. Maturation of a cylindrical cartilage TE construct over 42 days of culture was simulated using a composition-based finite element model that accounted for the transient deposition of GAG and collagen. Results showed an effect of GAG deposition rate on the swelling behavior and the collagen network strain, which resulted in significant changes in the compressive stiffness of cartilage TE constructs. When collagen deposition was first allowed in the constructs while the GAG deposition was delayed for the first 2 or 4 weeks, the collagen more effectively restricted tissue swelling later during the culture. Consequently, while the ultimate amount of ECM at day 42 was identical between the constructs, those with delayed GAG deposition contained elevated internal osmotic swelling pressure (up to 48%). This increased the compressive stiffness (up to 60%) of cartilage TE constructs at day 42. These findings clarify similar, yet unexplained, experimental observations. By providing further insights into mechanical effects inside cartilage TE constructs, these analyses are expected to help in designing culture regimes for engineering TE cartilage with improved load-bearing properties.

The effects of matrix inhomogeneities on the cellular mechanical environment in tissue-engineered cartilage: an in silico investigation.

Mechanical stimulation during cartilage tissue-engineering enhances extracellular matrix (ECM) synthesis and thereby improves the mechanical properties of tissue engineered (TE) cartilage. Generally, these mechanical stimuli are of a fixed magnitude. However, as a result of ECM synthesis and spatial variations thereof at both the macroscopic and microscopic scales, the internal mechanical conditions in the constructs change with time. Consequently, the physical signals in the environment of the cells will vary spatially and temporally, even though macroscopically the same loading is applied to the construct. The purpose of the present study was to numerically quantify such effects and thereby reveal the importance of adjusting loading regimes during cartilage tissue-engineering. A validated nonlinear fiber-reinforced poroviscoelastic swelling cartilage model that can accommodate for effects of collagen reinforcement and swelling by proteoglycans was used. At the microscopic scale, ECM was gradually varied from localized in the pericellular area, toward equally distributed throughout the surrounding interterritorial matrix. At the macroscopic tissue scale, ECM was gradually varied from predominantly localized in the periphery of the TE construct toward homogeneously distributed. Both concentration of ECM in the pericellular area and concentration of ECM in the periphery of a construct alter the physical signals up to an order of magnitude compared to those at the onset of the culture. Of particular interest, is the effect of elevated osmotic swelling pressure in the pericellular area, which shields not only the cells from receiving external mechanical compression, but also directly induces tension on the cells. Based on the present computational simulations, it is therefore, proposed that cartilage TE studies should consider ECM distribution as an important factor when developing loading protocols for cartilage culturing process. For instance, the level of mechanical compression should gradually increase to sufficiently deform chondrocytes over time, in case there is matrix accumulation in the pericellular area.

The effect of tissue-engineered cartilage biomechanical and biochemical properties on its post-implantation mechanical behavior.

The insufficient load-bearing capacity of today's tissue-engineered (TE) cartilage limits its clinical application. Focus has been on engineering cartilage with enhanced mechanical stiffness by reproducing native biochemical compositions. More recently, depth dependency of the biochemical content and the collagen network architecture has gained interest. However, it is unknown whether the mechanical performance of TE cartilage would benefit more from higher content of biochemical compositions or from achieving an appropriate collagen organization. Furthermore, the relative synthesis rate of collagen and proteoglycans during the TE process may affect implant performance. Such insights would assist tissue engineers to focus on those aspects that are most important. The aim of the present study is therefore to elucidate the relative importance of implant ground substance stiffness, collagen content, and collagen architecture of the implant, as well as the synthesis rate of the biochemical constituents for the post-implantation mechanical behavior of the implant. We approach this by computing the post-implantation mechanical conditions using a composition-based fibril-reinforced poro-viscoelastic swelling model of the medial tibia plateau. Results show that adverse implant composition and ultrastructure may lead to post-implantation excessive mechanical loads, with collagen orientation being the most critical variable. In addition, we predict that a faster synthesis rate of proteoglycans compared to that of collagen during TE culture may result in excessive loads on collagen fibers post-implantation. This indicates that even with similar final contents, constructs may behave differently depending on their development. Considering these aspects may help to engineer TE cartilage implants with improved survival rates.

Influence of tissue- and cell-scale extracellular matrix distribution on the mechanical properties of tissue-engineered cartilage.

The insufficient load-bearing capacity of today's tissue- engineered (TE) cartilage limits its clinical application. Generally, cartilage TE studies aim to increase the extracellular matrix (ECM) content, as this is thought to determine the load-bearing properties of the cartilage. However, there are apparent inconsistencies in the literature regarding the correlation between ECM content and mechanical properties of TE constructs. In addition to the amount of ECM, the spatial inhomogeneities in ECM distribution at the tissue scale as well as at the cell scale may affect the mechanical properties of TE cartilage. The relative importance of such structural inhomogeneities on mechanical behavior of TE cartilage is unknown. The aim of the present study was, therefore, to theoretically elucidate the influence of these inhomogeneities on the mechanical behavior of chondrocyte-agarose TE constructs. A validated non-linear fiber-reinforced poro-elastic swelling cartilage model that can accommodate for effects of collagen reinforcement and swelling by proteoglycans was used. At the tissue scale, ECM was gradually varied from predominantly localized in the periphery of the TE construct toward an ECM-rich inner core. The effect of these inhomogeneities in relation to the total amount of ECM was also evaluated. At the cell scale, ECM was gradually varied from localized in the pericellular area, toward equally distributed throughout the interterritorial area. Results from the tissue-scale model indicated that localization of ECM in either the construct periphery or in the inner core may reduce construct stiffness compared with that of constructs with homogeneous ECM. Such effects are more significant at high ECM amounts. At the cell scale, localization of ECM around the cells significantly reduced the overall stiffness, even at low ECM amounts. The compressive stiffness gradually increased when ECM distribution became more homogeneous and the osmotic swelling pressure in the interterritorial area increased. We conclude that for the same amount of ECM content in TE cartilage constructs, superior mechanical properties can be achieved with more homogeneous ECM distribution at both tissue and cell scale. Inhomogeneities at the cell scale are more important than those at the tissue scale.

Mechanical stimulation to stimulate formation of a physiological collagen architecture in tissue-engineered cartilage: a numerical study.

The load-bearing capacity of today's tissue-engineered (TE) cartilage is insufficient. The arcade-like collagen network in native cartilage plays an important role in its load-bearing properties. Inducing the formation of such collagen architecture in engineered cartilage can, therefore, enhance mechanical properties of TE cartilage. Considering the well-defined relationship between tensile strains and collagen alignment in the literature, we assume that cues for inducing this orientation should come from mechanical loading. In this study, strain fields prescribed by loading conditions of unconfined compression, sliding indentation and a novel loading regime of compression-sliding indentation are numerically evaluated to assess the probability that these would trigger a physiological collagen architecture. Results suggest that sliding indentation is likely to stimulate the formation of an appropriate superficial zone with parallel fibres. Adding lateral compression may stimulate the formation of a deep zone with perpendicularly aligned fibres. These insights may be used to improve loading conditions for cartilage tissue engineering.