Analysis of the mechanical behavior of chondrocytes in unconfined compression tests for cyclic loading

Experimental evidence indicates that the biosynthetic activity of chondrocytes is associated with the mechanical environment. For example, excessive, repetitive loading has been found to induce cell death, morphological and cellular damage, as seen in degenerative joint disease, while cyclic, physiological-like loading has been found to trigger a partial recovery of morphological and ultrastructural aspects in osteoarthritic human articular chondrocytes. Mechanical stimuli are believed to influence the biosynthetic activity via the deformation of cells. However, the in situ deformation of chondrocytes for cyclic loading conditions has not been investigated experimentally or theoretically. The purpose of the present study was to simulate the mechanical response of chondrocytes to cyclic loading in unconfined compression tests using a finite element model. The material properties of chondrocytes and extracellular matrix were considered to be biphasic. The time-histories of the shape and volume variations of chondrocytes at three locations (i.e., surface, center, and bottom) within the cartilage were predicted for static and cyclic loading conditions at two frequencies (0.02 and 0.1 Hz) and two amplitudes (0.1 and 0.2 MPa). Our results show that cells at different depths within the cartilage deform differently during cyclic loading, and that the depth dependence of cell deformation is influenced by the amplitude of the cyclic loading. Cell deformations under cyclic loading of 0.02 Hz were found to be similar to those at 0.1 Hz. We conclude from the simulation results that, in homogeneous cartilage layers, cell deformations are location-dependent, and further are affected by load magnitude. In physiological conditions, the mechanical environment of cells are even more complex due to the anisotropy, depth-dependent inhomogeneity, and tension-compression non-linearity of the cartilage matrix. Therefore, it is feasible to speculate that biosynthetic responses of chondrocytes to cyclic loading depend on cell location and load magnitude.     

Determination of the Poisson's ratio of the cell: recovery properties of chondrocytes after release from complete micropipette aspiration

Chondrocytes in articular cartilage are regularly subjected to compression and recovery due to dynamic loading of the joint. Previous studies have investigated the elastic and viscoelastic properties of chondrocytes using micropipette aspiration techniques, but in order to calculate cell properties, these studies have generally assumed that cells are incompressible with a Poisson's ratio of 0.5. The goal of this study was to measure the Poisson's ratio and recovery properties of the chondrocyte by combining theoretical modeling with experimental measures of complete cellular aspiration and release from a micropipette. Chondrocytes isolated from non-osteoarthritic and osteoarthritic cartilage were fully aspirated into a micropipette and allowed to reach mechanical equilibrium. Cells were then extruded from the micropipette and cell volume and morphology were measured throughout the experiment. This experimental procedure was simulated with finite element analysis, modeling the chondrocyte as either a compressible two-mode viscoelastic solid, or as a biphasic viscoelastic material. By fitting the experimental data to the theoretically predicted cell response, the Poisson's ratio and the viscoelastic recovery properties of the cell were determined. The Poisson's ratio of chondrocytes was found to be 0.38 for non-osteoarthritic cartilage and 0.36 for osteoarthritic chondrocytes (no significant difference). Osteoarthritic chondrocytes showed an increased recovery time following full aspiration. In contrast to previous assumptions, these findings suggest that chondrocytes are compressible, consistent with previous studies showing cell volume changes with compression of the extracellular matrix.     

In situ chondrocyte deformation with physiological compression of the feline patellofemoral joint

The mechanical environment is an important factor affecting the maintenance and adaptation of articular cartilage, and thus the function of the joint and the progression of joint degeneration. Recent evidence suggests that cartilage deformation caused by mechanical loading is directly associated with deformation and volume changes of chondrocytes. Furthermore, in vitro experiments have shown that these changes in the mechanical states of chondrocytes correlate with a change in the biosynthetic activity of cartilage cells. The purpose of this study was to apply our knowledge of contact forces within the feline patellofemoral joint to quantify chondrocyte deformation in situ under loads of physiological magnitude. A uniform, static load of physiological magnitude was applied to healthy articular cartilage still fully intact and attached to its native bone. The compressed cartilage was then chemically fixed to enable the evaluation of cartilage strain, chondrocyte deformation and chondrocyte volumetric fraction. Patella and femoral groove articular cartilages differ in thickness, chondrocyte aspect ratio, and chondrocyte volumetric fraction in both magnitude and depth distribution. Furthermore, when subjected to the same compressive loads, changes to all of these parameters differ in magnitude and depth distribution between patellar and femoral groove articular cartilage. This evidence suggests that significant chondrocyte deformation likely occurs during in vivo joint loading, and may influence chondrocyte biosynthetic activity. Furthermore, we hypothesise that the contrasts between patella and femoral groove cartilages may explain, in part, the site-specific progression of osteoarthritis in the patellofemoral joint of the feline anterior cruciate ligament transected knee.     

Rapid regulation of collagen but not metalloproteinase 1, 3, 13, 14 and tissue inhibitor of metalloproteinase 1, 2, 3 expression in response to mechanical loading of cartilage explants in vitro

This study analyzes the molecular response of articular chondrocytes to short-term mechanical loading with a special focus on gene expression of molecules relevant for matrix turnover. Porcine cartilage explants were exposed to static and dynamic unconfined compression and viability of chondrocytes was assessed to define physiologic loading conditions. Cell death in the superficial layer correlated with mechanical loading and occurred at peak stresses >or=6 MPa and a cartilage compression above 45%. Chondrocytes in native cartilage matrix responded to dynamic loading by rapid and highly specific suppression of collagen expression. mRNA levels dropped 11-fold (collagen 2; 6 MPa, P=0.009) or 14-fold (collagen 1; 3 and 6 MPa, P=0.009) while levels of aggrecan, tenascin-c, matrix metalloproteinases (MMP1, 3, 13, 14), and their inhibitors (TIMP1-3) did not change significantly. Thus, dynamic mechanical loading rapidly shifted the balance between collagen and aggrecan/tenascin/MMP/TIMP expression. A better knowledge of the chondrocyte response to mechanical stress may improve our understanding of mechanically induced osteoarthrits.     

The Mechanical Behaviour of Chondrocytes Predicted with a Micro-structural Model of Articular Cartilage

The integrity of articular cartilage depends on the proper functioning and mechanical stimulation of chondrocytes, the cells that synthesize extracellular matrix and maintain tissue health. The biosynthetic activity of chondrocytes is influenced by genetic factors, environmental influences, extracellular matrix composition, and mechanical factors. The mechanical environment of chondrocytes is believed to be an important determinant for joint health, and chondrocyte deformation in response to mechanical loading is speculated to be an important regulator of metabolic activity. In previous studies of chondrocyte deformation, articular cartilage was described as a biphasic material consisting of a homogeneous, isotropic, linearly elastic solid phase, and an inviscid fluid phase. However, articular cartilage is known to be anisotropic and inhomogeneous across its depth. Therefore, isotropic and homogeneous models cannot make appropriate predictions for tissue and cell stresses and strains. Here, we modelled articular cartilage as a transversely isotropic, inhomogeneous (TI) material in which the anisotropy and inhomogeneity arose naturally from the microstructure of the depth-dependent collagen fibril orientation and volumetric fraction, as well as the chondrocyte shape and volumetric fraction. The purpose of this study was to analyse the deformation behaviour of chondrocytes using the TI model of articular cartilage. In order to evaluate our model against experimental results, we simulated indentation and unconfined compression tests for nominal compressions of 15%. Chondrocyte deformations were analysed as a function of location within the tissue. The TI model predicted a non-uniform behaviour across tissue depth: in indentation testing, cell height decreased by 43% in the superficial zone and between 11 and 29% in the deep zone. In unconfined compression testing, cell height decreased by 32% in the superficial zone, 25% in the middle, and 18% in the deep zones. This predicted non-uniformity is in agreement with experimental studies. The novelty of this study is the use of a cartilage material model accounting for the intrinsic inhomogeneity and anisotropy of cartilage caused by its microstructure.     

Effects of shear stress on articular chondrocyte metabolism

The articular cartilage of diarthrodial joints experiences a variety of stresses, strains and pressures that result from normal activities of daily living. In normal cartilage, the extracellular matrix exists as a highly organized composite of specialized macromolecules that distributes loads at the bony ends. The chondrocyte response to mechanical loading is recognized as an integral component in the maintenance of articular cartilage matrix homeostasis. With inappropriate mechanical loading of the joint, as occurs with traumatic injury, ligament instability, bony malalignment or excessive weight bearing, the cartilage exhibits manifestations characteristic of osteoarthritis. Breakdown of cartilage in osteoarthritis involves degradation of the extracellular matrix macromolecules and decreased expression of chondrocyte proteins necessary for normal joint function. Osteoarthritic cartilage often exhibits increased amounts of type I collagen and synthesis of proteoglycans characteristic of immature cartilage. The shift in cartilage phenotype in response to altered load yields a matrix that fails to support normal joint function. Mathematical modeling and experimental studies in animal models confirm an association between altered loading of diarthrotic joints and arthritic changes. Both types of studies implicate shear forces as a critical component in the destructive profile. The severity of cartilage destruction in response to altered loads appears linked to expression of biological factors influencing matrix integrity and cellular metabolism. Determining how shear stress alters chondrocyte metabolism is fundamental to understanding how to limit matrix destruction and stimulate cartilage repair and regeneration. At present, the precise biochemical and molecular mechanisms by which shear forces alter chondrocyte metabolism from a normal to a degenerative phenotype remain unclear. The results presented here address the hypothesis that articular chondrocyte metabolism is modulated by direct effects of shear forces that act on the cell through mechanotransduction processes. The purpose of this work is to develop critical knowledge regarding the basic mechanisms by which mechanical loading modulates cartilage metabolism in health and disease. This presentation will describe the effects of using fluid induced shear stress as a model system for stimulation of articular chondrocytes in vitro. The fluid induced shear stress was applied using a cone viscometer system to stimulate all the cells uniformly under conditions of minimal turbulence. The experiments were carried using high-density primary monolayer cultures of normal and osteoarthritic human and normal bovine articular chondrocytes. The analysis of the cellular response included quantification of cytokine release, matrix metalloproteinase expression and activation of intracellular signaling pathways. The data presented here show that articular chondrocytes exhibit a dose- and time-dependent response to shear stress that results in the release of soluble mediators and extracellular matrix macromolecules. The data suggest that the chondrocyte response to mechanical stimulation contributes to the maintenance of articular cartilage homeostasis in vivo.     

Chondrocyte extracellular matrix synthesis and turnover are influenced by static compression in a new alginate disk culture system

The goal of this study was to examine the effects of mechanical compression on chondrocyte biosynthesis of extracellular matrix (ECM) components during culture in a new alginate disk culture system. Specifically, we have examined chondrocyte biosynthesis rates, and the structure of aggrecan core protein species present in the cell-associated matrix (CM), in the further removed matrix (FRM) and in the surrounding culture medium. In this alginate disk culture system, chondrocytes can be subjected to mechanical deformations similar to those experienced in vivo. Our results show that over an 8-week culture period, chondrocytes synthesize a functional ECM and can respond to mechanical forces similarly to chondrocytes maintained in native cartilage. In the alginate disk system, static compression was shown to decrease and dynamic compression to increase synthesis of aggrecan of bovine chondrocytes. Western blot analysis of the core proteins of aggrecan molecules identified a number of different species that were present in different relative amounts in the CM, FRM, and medium. Over 21 days of culture, the predominant form of aggrecan found in the ECM was a full-length link-stabilized species. In addition, our data show that the application of 40 h of static compression caused an increase in the proportion of newly synthesized aggrecan molecules released into the medium. However, this was not accompanied by a significant change in the size and composition of aggrecan and aggrecan fragments in the different compartments, suggesting that mechanical compression did not alter the catabolic pathways. Together, these data show that chondrocyte function is maintained in an alginate disk culture system and that this culture system is a useful model to examine chondrocyte ECM assembly and some aspects of catabolism normally found in vivo.     

Chondrocyte intracellular calcium, cytoskeletal organization, and gene expression responses to dynamic osmotic loading

While chondrocytes in articular cartilage experience dynamic stimuli from joint loading activities, few studies have examined the effects of dynamic osmotic loading on their signaling and biosynthetic activities. We hypothesize that dynamic osmotic loading modulates chondrocyte signaling and gene expression differently than static osmotic loading. With the use of a novel microfluidic device developed in our laboratory, dynamic hypotonic loading (–200 mosM) was applied up to 0.1 Hz and chondrocyte calcium signaling, cytoskeleton organization, and gene expression responses were examined. Chondrocytes exhibited decreasing volume and calcium responses with increasing loading frequency. Phalloidin staining showed osmotic loading-induced changes to the actin cytoskeleton in chondrocytes. Real-time PCR analysis revealed a stimulatory effect of dynamic osmotic loading compared with static osmotic loading. These studies illustrate the utility of the microfluidic device in cell signaling investigations, and their potential role in helping to elucidate mechanisms that mediate chondrocyte mechanotransduction to dynamic stimuli. cartilage; calcium signaling; actin cytoskeleton; aggrecan     

Immobilized fibrinogen in PEG hydrogels does not improve chondrocyte-mediated matrix deposition in response to mechanical stimulation

The present investigation aims to explore the role of cell-scaffold interactions and whole cell compression in chondrocyte mechanotransduction using encapsulating poly(ethylene glycol) (PEG) hydrogel scaffolds and primary bovine chondrocytes. Scaffolds made from PEG hydrogels with immobilized fibrinogen molecules were seeded with chondrocytes and subjected to 15% dynamic compressive strain at 1-Hz frequency. Dynamic strain stimulation resulted in a 37% increase in the levels of sulfated glycosaminoglycan (sGAG) after 2 weeks of stimulation, when compared to static controls. Comparing results of the PEG-fibrinogen scaffolds with their respective PEG control group did not show significant differences between the two, even following 2 weeks of dynamic mechanical stimulation. Accordingly, these findings indicate that while cell deformations cause metabolic changes in chondrocytes seeded in PEG hydrogels, it is difficult to ascertain the role of matrix bioactivity in enhancing chondrocyte mechanotransduction in encapsulating scaffolds subjected to physical deformations. This study shows how interactions between mechanical stimulation and scaffold composition are evaluated using an experimental approach and customized biomaterial scaffolds.     

The deformation behavior and viscoelastic properties of chondrocytes in articular cartilage

Chondrocytes in articular cartilage utilize mechanical signals in conjunction with other environmental factors to regulate their metabolic activity. However, the sequence of biomechanical and biochemical events involved in the process of mechanical signal transduction has not been fully deciphered. A fundamental step in determining the role of various factors in regulating chondrocyte activity is to characterize accurately the biophysical environment within the tissue under physiological conditions of mechanical loading. Microscopic imaging studies have revealed that chondrocytes as well as their nuclei undergo shape and volume changes in a coordinated manner with deformation of the tissue matrix. Through micromechanical experiments, it has been shown that the chondrocyte behaves as a viscoelastic solid material with a mechanical stiffness that is several orders of magnitude lower than that of the cartilage extracellular matrix. These properties seem to be due to the structure of the chondrocyte cytoskeleton, and in part, the viscoelastic properties of the cell nucleus. The mechanical properties of the pericellular matrix that immediately surrounds the chondrocyte significantly differ from those of the chondrocyte and the extracellular matrix, suggesting that the pericellular matrix plays an important role in defining the mechanical environment of the chondrocyte. These experimentally measured values for chondrocyte and cartilage mechanical properties have been used in combination with theoretical constitutive modeling of the chondrocyte within articular cartilage to predict the non-uniform and time-varying stress-strain and fluid flow environment of the cell. The ultimate goal of these studies has been to elucidate the sequence of biomechanical and biochemical events through which mechanical stress influences chondrocyte activity in both health and in disease.     

In Vivo Dynamic Deformation of Articular Cartilage in Intact Joints Loaded by Controlled Muscular Contractions

When synovial joints are loaded, the articular cartilage and the cells residing in it deform. Cartilage deformation has been related to structural tissue damage, and cell deformation has been associated with cell signalling and corresponding anabolic and catabolic responses. Despite the acknowledged importance of cartilage and cell deformation, there are no dynamic data on these measures from joints of live animals using muscular load application. Research in this area has typically been done using confined and unconfined loading configurations and indentation testing. These loading conditions can be well controlled and allow for accurate measurements of cartilage and cell deformations, but they have little to do with the contact mechanics occurring in a joint where non-congruent cartilage surfaces with different material and functional properties are pressed against each other by muscular forces. The aim of this study was to measure in vivo, real time articular cartilage deformations for precisely controlled static and dynamic muscular loading conditions in the knees of mice. Fifty and 80% of the maximal knee extensor muscular force (equivalent to approximately 0.4N and 0.6N) produced average peak articular cartilage strains of 10.5±1.0% and 18.3±1.3% (Mean ± SD), respectively, during 8s contractions. A sequence of 15 repeat, isometric muscular contractions (0.5s on, 3.5s off) of 50% and 80% of maximal muscular force produced cartilage strains of 3.0±1.1% and 9.6±1.5% (Mean ± SD) on the femoral condyles of the mouse knee. Cartilage thickness recovery following mechanical compression was highly viscoelastic and took almost 50s following force removal in the static tests.     

Alterations in the Young's modulus and volumetric properties of chondrocytes isolated from normal and osteoarthritic human cartilage

The mechanical environment of the chondrocyte is an important factor that influences the maintenance of the articular cartilage extracellular matrix. Previous studies have utilized theoretical models of chondrocytes within articular cartilage to predict the stress-strain and fluid flow environments around the cell, but little is currently known regarding the cellular properties which are required for implementation of these models. The objectives of this study were to characterize the mechanical behavior of primary human chondrocytes and to determine the Young's modulus of chondrocytes from non-osteoarthritic ('normal') and osteoarthritic cartilage. A second goal was to quantify changes in the volume of isolated chondrocytes in response to mechanical deformation. The micropipette aspiration technique was used to measure the deformation of a single chondrocyte into a glass micropipette in response to a prescribed pressure. The results of this study indicate that the human chondrocyte behaves as a viscoelastic solid. No differences were found between the Young's moduli of normal (0.65+/-0.63 kPa, n = 44) and osteoarthritic chondrocytes (0.67+/-0.86 kPa, n = 69, p = 0.93). A significant difference in cell volume was observed immediately and 600 s after complete aspiration of the cell into the pipette (p < 0.001), and the magnitude of this volume change between normal (11+/-11%, n = 40) and osteoarthritic (20+/-11%, n = 41) chondroctyes was significantly different at both time points (p < 0.002). This finding suggests that chondrocytes from osteoarthritic cartilage may have altered volume regulation capabilities in response to mechanical deformation. The mechanical and volumetric properties determined in this study will be of use in analytical and finite element models of chondrocyte-matrix interactions in order to better predict the mechanical environment of the cell in vivo.     

Strain-dependent viscoelastic behaviour and rupture force of single chondrocytes and chondrons under compression

The chondron in articular cartilage includes the chondrocyte and its surrounding pericellular matrix (PCM). Single chondrocytes and chondrons were compressed between two parallel surfaces by a micromanipulation technique to investigate their biomechanical properties and to discover the mechanical significance of the PCM. The force imposed on the cells was measured directly during deformation at various compression speeds and deformations up to cell rupture. When the deformation at the end of compression was 50%, relaxation showed that the cells were viscoelastic, but this viscoelasticity was generally insignificant at 30% deformation or lower. When the deformation was 70%, the cells had deformed plastically. Chondrons ruptured at a mean deformation of 85 ± 1%, whilst chondrocytes ruptured at a mean deformation of 78 ± 1%. Chondrons were generally stiffer than chondrocytes and showed less viscoelastic behaviour than chondrocytes. Thus, the PCM significantly influences the mechanical properties of the cells.     

Competing regulation of matrix biosynthesis by mechanical and IGF-1 signalling in elderly human articular cartilage in vitro

This study investigates the separate and combined effects of IGF-1 and mechanical loads on chondrocytes in elderly human femoral head articular cartilage. Full depth biopsies of articular cartilage were subjected to either no load, static or cyclic (2 s on/2 s off) loading in unconfined compression at a stress of 1 MPa for 48 h with or without IGF-1 (300 ng ml(-1)). Chondrocyte biosynthetic activity was measured using 35S-sulphate and 3H-leucine during the last 24 h of loading. IGF-1 alone increased the rates of isotope incorporation, by 80% for 35S-SO4 and 40% for 3H-leucine, whereas loading alone reduced matrix biosynthesis. Applying load (cyclic or static) in the presence of IGF-1 returned the incorporation rates to their unstimulated levels. This study suggests elderly human articular cartilage is responsive to stimulation by IGF-1 but mechanical factors seem to act sufficiently strongly in the opposite direction to cancel this response.     

A biphasic multiscale study of the mechanical microenvironment of chondrocytes within articular cartilage under unconfined compression

Computational analyses have been used to study the biomechanical microenvironment of the chondrocyte that cannot be assessed by in vitro experimental studies; yet all computational studies thus far have focused on the effect of zonal location (superficial, middle, and deep) on the mechanical microenvironment of chondrocytes. The aim of this paper was to study the effect of both zonal and radial locations on the biomechanical microenvironment of chondrocytes in inhomogeneous cartilage under unconfined stress relaxation. A biphasic multiscale approach was employed and nine chondrocytes in different locations were studied. Hyperelastic biphasic theory and depth-dependent aggregate modulus and permeability of articular cartilage were included in the models. It was found that both zonal and radial locations affected the biomechanical stresses and strains of the chondrocytes. Chondrocytes in the mid-radial location had increased volume during the early stage of the loading process. Maximum principal shear stress at the interface between the chondrocyte and the extracellular matrix (ECM) increased with depth, yet that at the ECM–pericellular matrix (PCM) interface had an inverse trend. Fluid pressure decreased with depth, while the fluid pressure difference between the top and bottom boundaries of the microscale model increased with depth. Regardless of location, fluid was exchanged between the chondrocyte, PCM, and ECM. These findings suggested that even under simple compressive loading conditions, the biomechanical microenvironment of the chondrocytes, PCM and ECM was spatially dependent. The current study provides new insight on chondrocyte biomechanics.     

The mechanical microenvironment of high concentration agarose for applying deformation to primary chondrocytes

Cartilage and chondrocytes experience loading that causes alterations in chondrocyte biological activity. In vivo chondrocytes are surrounded by a pericellular matrix with a stiffness of ~25–200 kPa. Understanding the mechanical loading environment of the chondrocyte is of substantial interest for understanding chondrocyte mechanotransduction. The first objective of this study was to analyze the spatial variability of applied mechanical deformations in physiologically stiff agarose on cellular and sub-cellular length scales. Fluorescent microspheres were embedded in physiologically stiff agarose hydrogels. Microsphere positions were measured via confocal microscopy and used to calculate displacement and strain fields as a function of spatial position. The second objective was to assess the feasibility of encapsulating primary human chondrocytes in physiologically stiff agarose. The third objective was to determine if primary human chondrocytes could deform in high-stiffness agarose gels. Primary human chondrocyte viability was assessed using live–dead imaging following 24 and 72 h in tissue culture. Chondrocyte shape was measured before and after application of 10% compression. These data indicate that (1) displacement and strain precision are ~1% and 6.5% respectively, (2) high-stiffness agarose gels can maintain primary human chondrocyte viability of >95%, and (3) compression of chondrocytes in 4.5% agarose can induce shape changes indicative of cellular compression. Overall, these results demonstrate the feasibility of using high-concentration agarose for applying in vitro compression to chondrocytes as a model for understanding how chondrocytes respond to in vivo loading.     

Chondrocyte deformations as a function of tibiofemoral joint loading predicted by a generalized high-throughput pipeline of multi-scale simulations

Cells of the musculoskeletal system are known to respond to mechanical loading and chondrocytes within the cartilage are not an exception. However, understanding how joint level loads relate to cell level deformations, e.g. in the cartilage, is not a straightforward task. In this study, a multi-scale analysis pipeline was implemented to post-process the results of a macro-scale finite element (FE) tibiofemoral joint model to provide joint mechanics based displacement boundary conditions to micro-scale cellular FE models of the cartilage, for the purpose of characterizing chondrocyte deformations in relation to tibiofemoral joint loading. It was possible to identify the load distribution within the knee among its tissue structures and ultimately within the cartilage among its extracellular matrix, pericellular environment and resident chondrocytes. Various cellular deformation metrics (aspect ratio change, volumetric strain, cellular effective strain and maximum shear strain) were calculated. To illustrate further utility of this multi-scale modeling pipeline, two micro-scale cartilage constructs were considered: an idealized single cell at the centroid of a 100×100×100 μm block commonly used in past research studies, and an anatomically based (11 cell model of the same volume) representation of the middle zone of tibiofemoral cartilage. In both cases, chondrocytes experienced amplified deformations compared to those at the macro-scale, predicted by simulating one body weight compressive loading on the tibiofemoral joint. In the 11 cell case, all cells experienced less deformation than the single cell case, and also exhibited a larger variance in deformation compared to other cells residing in the same block. The coupling method proved to be highly scalable due to micro-scale model independence that allowed for exploitation of distributed memory computing architecture. The method's generalized nature also allows for substitution of any macro-scale and/or micro-scale model providing application for other multi-scale continuum mechanics problems.     

Scaffold-free cartilage by rotational culture for tissue engineering

Our objective was to investigate the hypothesis that tissue-engineered cartilage with promising biochemical, mechanical properties can be formed by loading mechanical stress under existing cell-cell interactions analogous to those that occur in condensation during embryonic development. By loading dedifferentiated chondrocytes with mechanical stress under existing cell-cell interactions, we could first form a scaffold-free cartilage tissue with arbitrary shapes and a large size with promising biological, mechanical properties. The cartilage tissue which constituted of chondrocytes and ECM produced by inoculated dedifferentiated chondrocytes to a high porous simple mold has arbitrary shapes, and did not need any biodegradable scaffold to control the shape. In contrast, scaffold-free cartilage tissue cultured under static conditions could not keep their shapes; it was fragile tissue. The possibility of scaffold-free organ design was suggested because the cartilage tissue increases steadily in size with culture time; indeed, the growth of cartilage tissue starting from an arbitrary shape might be predictable by mathematical expression. For tissue-engineered cartilage formation with arbitrary shapes, biochemical and mechanical properties, loading dedifferentiated chondrocytes with mechanical stress under existing cell-cell interactions has prominent effects. Therefore, our scaffold-free cartilage model loaded mechanical stress based on a simple mold system may be applicable for tissue-engineered cartilage.