Internal strains and stresses measured in cortical bone via high-energy X-ray diffraction

High-energy synchrotron X-ray diffraction was used to study internal stresses in bone under in situ compressive loading. A transverse cross-section of a 12-14 year old beagle fibula was studied with 80.7 keV radiation, and the transmission geometry was used to quantify internal strains and corresponding stresses in the mineral phase, carbonated hydroxyapatite. The diffraction patterns agreed with tabulated patterns, and the distribution of diffracted intensity around 00.2/00.4 and 22.2 diffraction rings was consistent with the imperfect 00.1 fiber texture expected along the axis of a long bone. Residual compressive stress along the bone's longitudinal axis was observed in the specimen prior to testing: for 22.2 this stress equaled -95 MPa and for 00.2/00.4 was between -160 and -240 MPa. Diffraction patterns were collected for applied compressive stresses up to -110 MPa, and, up to about -100 MPa, internal stresses rose proportionally with applied stress but at a higher rate, corresponding to stress concentration in the mineral of 2.8 times the stress applied. The widths of the 00.2 and 00.4 diffraction peaks indicated that crystallite size perpendicular to the 00.1 planes increased from t=41 nm before stress was applied to t=44 nm at -118 MPa applied stress and that rms strain epsilon(rms) rose from 2200 muepsilon before loading to 4600 muepsilon at the maximum applied stress. Small angle X-ray scattering of the unloaded sample, recorded after deformation was complete, showed a collagen D-period of 66.4 nm (along the bone axis).     

Predicting fracture of the femoral neck

A prediction of the probability of safe loading of the femoral neck, based on queueing theory, is presented. The following methods have been applied: (I) criterion of bone fracture was formulated, taking into consideration the complex state of stress-strain in the porosity zones of the bone; (II) tensile stresses around pores in the stretched zone of the bone were evaluated; (III) the influence of random events of the critical regimes of loading was modeled. The evaluation of the probability of safe loading of bones was obtained based on the levels of the tensile stresses, Young's moduli and ultimate tensile stresses which are affected by the increase in bone porosity and the distribution of the pores. Examples of analysis involving typical mechanical properties of bone in areas of vascular and lacunar-canalicular porosity are demonstrated. The ranges of initial average values of effective Young's moduli and ultimate tensile strengths were taken as 15.8-17.5GPa and 83-95MPa, respectively. The present analysis discovers the existence of three levels of safe loading: (1) a relatively safe level of the nominal tensile stresses (smaller than (2.8-3.2)MPa) where the probability of safe loading is of the order of 0.95 for the bone porosity which is less than 0.15; (2) an intermediate level of safety where the nominal tensile stresses are below (4.2-4.8)MPa and the probability of safe loading is 0.89 or higher, for the same level of bone porosity; (3) a critical level of safe loading where the nominal tensile stresses are about (8.3-9.5)MPa; they lead to sharp drop of probabilities of safe loading to 0.85-0.8 if the porosity is about 0.10 and to probabilities of 0.41-0.4 if the porosity is about 0.15.     

Post-yield nanomechanics of human cortical bone in compression using synchrotron X-ray scattering techniques

The ultrastructural response to applied loads governs the post-yield deformation and failure behavior of bone, and is correlated with bone fragility fractures. Combining a novel progressive loading protocol and synchrotron X-ray scattering techniques, this study investigated the correlation of the local deformation (i.e., internal strains of the mineral and collagen phases) with the bulk mechanical behavior of bone. The results indicated that the internal strains of the longitudinally oriented collagen fibrils and mineral crystals increased almost linearly with respect to the macroscopic strain prior to yielding, but markedly decreased first and then gradually leveled off after yielding. Similar changes were also observed in the applied stress before and after yielding of bone. However, the collagen to mineral strain ratio remained nearly constant throughout the loading process. In addition, the internal strains of longitudinal mineral and collagen phases did not exhibit a linear relationship with either the modulus loss or the plastic deformation of bulk bone tissue. Finally, the time-dependent response of local deformation in the mineral phase was observed after yielding. Based on the results, we speculate that the mineral crystals and collagen fibrils aligned with the loading axis only partially explain the post-yield deformation, suggesting that shear deformation involving obliquely oriented crystals and fibrils (off axis) is dominant mechanism of yielding for human cortical bone in compression.     

Tensile experiments and SEM fractography on bovine subchondral bone

Subchondral bone undecalcified samples, extracted from bovine femoral heads, are subjected to a direct tensile load. The Young's modulus of each sample is determined from repeated tests within the elastic limit. In a last test, the tensile load is increased up to the specimen failure, determining the ultimate tensile strength. The investigation is performed on both dry and wet specimens. The measured Young's modulus for dry samples is 10.3+/-2.5GPa, while that of wet samples is 3.5+/-1.2GPa. The ultimate tensile strengths are 36+/-10 and 30+/-7.5MPa for dry and wet specimens, respectively. SEM micrographs of failure surfaces show characteristic lamellar bone structures, with lamellae composed of calcified collagen fibers. Rudimentary osteon-like structures are also observed. Failure surfaces of wet samples show a marked fiber pull-out, while delamination predominates in dry samples. The obtained results are interpreted on the basis of the deformation mechanisms typical of fiber-reinforced laminated composite materials.     

Collagen synthesis of articular cartilage explants in response to frequency of cyclic mechanical loading

Articular cartilage in vivo experiences the effects of both cell-regulatory proteins and mechanical forces. This study has addressed the hypothesis that the frequency of intermittently or continuously applied mechanical loads is a critical parameter in the regulation of chondrocyte collagen biosynthesis. Cyclic compressive pressure was applied intermittently to bovine articular cartilage explants by using a sinusoidal waveform of 0.1–1.0 Hz frequency with a peak stress of 0.5 MPa for a period of 5–20 s followed by a load-free period of 10–1,000 s. These loading protocols were repeated for a total duration of 6 days. In separate experiments, cyclic loading was continuously applied by using a sinusoidal waveform of 0.001–0.5 Hz frequency and a peak stress of 1.0 MPa for a period of 3 days. Unloaded cartilage discs of the same condyle were cultured in identically constructed loading chambers and served as controls. We report quantitative data showing that (1) no correlation exists between the relative rate of collagen synthesis expressed as the proportion of newly synthesized collagen among newly made proteins and either the frequency of intermittently or continuously applied loads or the overall time cartilage is actively loaded, and (2) individual protocols of intermittently applied loads can reduce the relative rate of collagen synthesis and increase the water content, whereas (3) continuously applied cyclic loads always suppress the relative rate of collagen synthesis compared with that of unloaded control specimens. The results provide further experimental evidence that collagen metabolism is difficult to manipulate by mechanical stimuli. This is physiologically important for the maintainance of the material properties of collagen in view of the heavy mechanical demands made upon it. Moreover, the unaltered or reduced collagen synthesis of cartilage explants might reflect more closely the metabolism of normal or early human osteoarthritic cartilage.This work was supported by the Federal Ministry of Education and Research (BMBF no. 0311058) and by the foundation S.E.T.     

Effects of cyclic stress on the mechanical properties of cultured collagen fascicles from the rabbit patellar tendon

Effects of cyclic stress on the mechanical properties of collagen fascicles were studied by in vitro tissue culture experiments. Collagen fascicles (approximately 300 microns in diameter) obtained from the rabbit patellar tendon were applied cyclic load at 4 Hz for one hour per day during culture period for one or two weeks, and then their mechanical properties were determined using a micro-tensile tester. There was a statistically significant correlation between tensile strength and applied peak stress in the range of 0 to 5 MPa, and the relation was expressed by a quadratic function. The maximum strength (19.4 MPa) was obtained at the applied peak stress of 1.8 MPa. The tensile strength of fascicles were within a range of control values, if they were cultured under peak stresses between 1.1 and 2.6 MPa. Similar results were also observed in the tangent modulus, which was maintained at control level under applied peak stresses between 0.9 and 2.8 MPa. The stress of 0.9 to 1.1 MPa is equivalent to approximately 40% of the in vivo peak stress which is developed in the intact rabbit patellar tendon by running, whereas that of 2.6 to 2.8 MPa corresponds to approximately 120% of the in vivo peak stress. Therefore, the fascicles cultured under applied peak stresses of lower than 40% and higher than 120% of the in vivo peak stress do not keep the original strength and modulus. These results indicate that the mechanical properties of cultured collagen fascicles strongly depend upon the magnitude of the stress applied during culture, which are similar to our previous results observed in stress-shielded and overstressed patellar tendons in vivo.     

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.     

Mechanical properties of native and cross-linked type I collagen fibrils

Micromechanical bending experiments using atomic force microscopy were performed to study the mechanical properties of native and carbodiimide-cross-linked single collagen fibrils. Fibrils obtained from a suspension of insoluble collagen type I isolated from bovine Achilles tendon were deposited on a glass substrate containing microchannels. Force-displacement curves recorded at multiple positions along the collagen fibril were used to assess the bending modulus. By fitting the slope of the force-displacement curves recorded at ambient conditions to a model describing the bending of a rod, bending moduli ranging from 1.0 GPa to 3.9 GPa were determined. From a model for anisotropic materials, the shear modulus of the fibril is calculated to be 33 ± 2 MPa at ambient conditions. When fibrils are immersed in phosphate-buffered saline, their bending and shear modulus decrease to 0.07-0.17 GPa and 2.9 ± 0.3 MPa, respectively. The two orders of magnitude lower shear modulus compared with the Young's modulus confirms the mechanical anisotropy of the collagen single fibrils. Cross-linking the collagen fibrils with a water-soluble carbodiimide did not significantly affect the bending modulus. The shear modulus of these fibrils, however, changed to 74 ± 7 MPa at ambient conditions and to 3.4 ± 0.2 MPa in phosphate-buffered saline.     

Effects of static stress on the mechanical properties of cultured collagen fascicles from the rabbit patellar tendon

In-vitro tissue culture experiments were performed to study the effects of static stress on the mechanical properties of collagen fascicles obtained from the rabbit patellar tendon. After collagen fascicles having the diameter of approximately 300 microm were cultured for 1 and 2 wk under static stress between 0 and 3 MPa, their mechanical properties and crimp morphology were determined using a micro-tensile tester and a light microscope, respectively. The tensile strength and tangent modulus of the fascicles were significantly decreased by culture under no load compared to control fascicles. A statistically significant correlation, which was described by a quadratic curve, was observed between applied stress and tensile strength. The maximum tensile strength (16.7 MPa) was obtained at the applied stress of 1.2 MPa; the strength was within a range of control values. There was a similar correlation between applied stress and tangent modulus, and the modulus was maintained at control level under 1.3 MPa stress. The stress of 1.2 to 1.3 MPa is equivalent to approximately 50 percent of the peak stress developed in the intact rabbit patellar tendon by running. Strain at failure of cultured collagen fascicles was negatively correlated with applied stress, and that at 1.2 to 1.3 MPa stress was almost the same as the control value. Crimp morphology in the fascicles cultured under about 1.2 MPa stress was similar to that in control fascicles. These results indicate that cultured collagen fascicles change the mechanical properties and structure in response to static tensile stress. In addition, their mechanical properties and structure are maintained at control level if the static stress of 50 percent of in-vivo peak stress is applied.     

The relation between collagen fibril kinematics and mechanical properties in the mitral valve anterior leaflet

We have recently demonstrated that the mitral valve anterior leaflet (MVAL) exhibited minimal hysteresis, no strain rate sensitivity, stress relaxation but not creep (Grashow et al., 2006, Ann Biomed Eng., 34(2), pp. 315-325; Grashow et al., 2006, Ann Biomed. Eng., 34(10), pp. 1509-1518). However, the underlying structural basis for this unique quasi-elastic mechanical behavior is presently unknown. As collagen is the major structural component of the MVAL, we investigated the relation between collagen fibril kinematics (rotation and stretch) and tissue-level mechanical properties in the MVAL under biaxial loading using small angle X-ray scattering. A novel device was developed and utilized to perform simultaneous measurements of tissue level forces and strain under a planar biaxial loading state. Collagen fibril D-period strain (epsilonD) and the fibrillar angular distribution were measured under equibiaxial tension, creep, and stress relaxation to a peak tension of 90 N/m. Results indicated that, under equibiaxial tension, collagen fibril straining did not initiate until the end of the nonlinear region of the tissue-level stress-strain curve. At higher tissue tension levels, epsilonD increased linearly with increasing tension. Changes in the angular distribution of the collagen fibrils mainly occurred in the tissue toe region. Using epsilonD, the tangent modulus of collagen fibrils was estimated to be 95.5+/-25.5 MPa, which was approximately 27 times higher than the tissue tensile tangent modulus of 3.58+/-1.83 MPa. In creep tests performed at 90 N/m equibiaxial tension for 60 min, both tissue strain and epsilonD remained constant with no observable changes over the test length. In contrast, in stress relaxation tests performed for 90 min epsilonD was found to rapidly decrease in the first 10 min followed by a slower decay rate for the remainder of the test. Using a single exponential model, the time constant for the reduction in collagen fibril strain was 8.3 min, which was smaller than the tissue-level stress relaxation time constants of 22.0 and 16.9 min in the circumferential and radial directions, respectively. Moreover, there was no change in the fibril angular distribution under both creep and stress relaxation over the test period. Our results suggest that (1) the MVAL collagen fibrils do not exhibit intrinsic viscoelastic behavior, (2) tissue relaxation results from the removal of stress from the fibrils, possibly by a slipping mechanism modulated by noncollagenous components (e.g. proteoglycans), and (3) the lack of creep but the occurrence of stress relaxation suggests a "load-locking" behavior under maintained loading conditions. These unique mechanical characteristics are likely necessary for normal valvular function.     

Determination of mechanical properties of human femoral cortical bone by the Hopkinson bar stress technique

The Hopkinson bar stress technique and a universal testing machine (Instron 1125) have been used to investigate the dynamic and static mechanical properties of cortical bone taken from a human femur respectively. We found that the average dynamic Young's modulus value (Ed = 19.9 GPa) to be 23% higher than the average static Young's modulus value (Ed = 16.2 GPa). Furthermore, the Poisson's ratio did not exhibit any significant variation for the two different types of loading. No difference was observed between the values of the dynamic Young's modulus in tension and those found in compression. A comparison was made of the results of this study with those found by other researchers using different techniques, such as ultrasonics, and it was found that they agree well with most of the results of previous studies. Finally, the viscosity for cortical bone found in this study correlates with viscosity reported by Tennyson et al. [Expl Mech. 12, 502-507 (1972)] for ten days post mortem age specimens.     

Design and mechanical properties of insect cuticle

Since nearly all adult insects fly, the cuticle has to provide a very efficient and lightweight skeleton. Information is available about the mechanical properties of cuticle-Young's modulus of resilin is about 1 MPa, of soft cuticles about 1 kPa to 50 MPa, of sclerotised cuticles 1-20 GPa; Vicker's Hardness of sclerotised cuticle ranges between 25 and 80 kgf mm(-2); density is 1-1.3 kg m(-3)-and one of its components, chitin nanofibres, the Young's modulus of which is more than 150 GPa. Experiments based on fracture mechanics have not been performed although the layered structure probably provides some toughening. The structural performance of wings and legs has been measured, but our understanding of the importance of buckling is lacking: it can stiffen the structure (by elastic postbuckling in wings, for example) or be a failure mode. We know nothing of fatigue properties (yet, for instance, the insect wing must undergo millions of cycles, flexing or buckling on each cycle). The remarkable mechanical performance and efficiency of cuticle can be analysed and compared with those of other materials using material property charts and material indices. Presented in this paper are four: Young's modulus-density (stiffness per unit weight), specific Young's modulus-specific strength (elastic hinges, elastic energy storage per unit weight), toughness-Young's modulus (fracture resistance under various loading conditions), and hardness (wear resistance). In conjunction with a structural analysis of cuticle these charts help to understand the relevance of microstructure (fibre orientation effects in tendons, joints and sense organs, for example) and shape (including surface structure) of this fibrous composite for a given function. With modern techniques for analysis of structure and material, and emphasis on nanocomposites and self-assembly, insect cuticle should be the archetype for composites at all levels of scale.     

Mechanical properties of physiological and pathological models of collagen peptides investigated via steered molecular dynamics simulations

In this work we used molecular simulations to investigate the elastic properties of collagen single chain and triple helix with the aim of understanding its features starting from first principles. We analysed ideal collagen peptides, homotrimeric and heterotrimeric collagen type I and pathological models of collagen. Triple helices were found much more rigid than single chains, thus enlightening the important role of interchain stabilizing forces, like hydrophobic interaction and hydrogen bonds. We obtained Young's moduli close to 4.5GPa for the ideal model of collagen and for the physiological heterotrimer, while the physiological homotrimer presented a Young's modulus of 2.51GPa, that can be related to a mild form of Osteogenesis Imperfecta in which only the homotrimeric form of collagen type I is produced. Otherwise, the pathological model (presenting a glycine to alanine substitution) showed an elastic modulus of 4.32GPa, thus only slightly lower than the ideal model. This suggests that this mutation only slightly affects the mechanical properties of the collagen molecule, but possibly acts on an higher scale, such as the packing of collagen fibrils.     

Material properties of the human lumbar facet joint capsule

The human facet joint capsule is one of the structures in the lumbar spine that constrains motions of vertebrae during global spine loading (e.g., physiological flexion). Computational models of the spine have not been able to include accurate nonlinear and viscoelastic material properties, as they have not previously been measured. Capsules were tested using a uniaxial ramp-hold protocol or a haversine displacement protocol using a commercially available materials testing device. Plane strain was measured optically. Capsules were tested both parallel and perpendicular to the dominant orientation of the collagen fibers in the capsules. Viscoelastic material properties were determined. Parallel to the dominant orientation of the collagen fibers, the complex modulus of elasticity was E*=1.63MPa, with a storage modulus of E'=1.25MPa and a loss modulus of: E" =0.39MPa. The mean stress relaxation rates for static and dynamic loading were best fit with first-order polynomials: B(epsilon) = 0.1110epsilon-0.0733 and B(epsilon)= -0.1249epsilon + 0.0190, respectively. Perpendicular to the collagen fiber orientation, the viscous and elastic secant moduli were 1.81 and 1.00 MPa, respectively. The mean stress relaxation rate for static loading was best fit with a first-order polynomial: B (epsilon) = -0.04epsilon - 0.06. Capsule strength parallel and perpendicular to collagen fiber orientation was 1.90 and 0.95 MPa, respectively, and extensibility was 0.65 and 0.60, respectively. Poisson's ratio parallel and perpendicular to fiber orientation was 0.299 and 0.488, respectively. The elasticity moduli were nonlinear and anisotropic, and capsule strength was larger aligned parallel to the collagen fibers. The phase lag between stress and strain increased with haversine frequency, but the storage modulus remained large relative to the complex modulus. The stress relaxation rate was strain dependent parallel to the collagen fibers, but was strain independent perpendicularly.     

Evaluation of threshold stress for bone resorption around screws based on in vivo strain measurement of miniplate

The purpose of this study is to investigate the critical threshold stress causing bone resorption evaluated from strain measurement in vivo, comparing the various finite element models. In this study strains of miniplates used for mandibular fractures were measured once a week until the strains reduced. The maximum bite force for each patient was applied in the incisal, right molar and left molar region. The strains increased and reached a peak level at 2-4 weeks, whereas the bite forces increased during the period of measurements. A 3-D osteosynthesis model using finite element method showed that the compressive stresses of the bone surrounding screws ranged within approximately -40 MPa under the condition generating the same amounts of strains measured in the miniplates. Furthermore, various finite element models simulating mandibular reconstruction using the fibular graft were constructed. The models for reconstruction using single strut fibula showed distinct stress concentration in the cortical bone surrounding screws, and the peak stress levels were 2 to 3 times as strong as that of the fracture model. We conclude that critical threshold for bone resorption should be approximately -50 MPa (3600 micro strain).     

Mechanical aspects of the development of artificial heart valves

The development of an antithrombogenic coating permits a hybrid design for artificial heart valves. A substrate material optimized for its application is coated to meet the electrochemical requirements of improved hemocompatibility. But future progress in artificial heart valves requires an improvement in design as well as of the material. The basis of both aspects is the determination of such fundamental mechanical properties as the elasticity and plasticity of the valve ring and the deformation and fraction behaviour of the occluder. Analytical and numerical calculations of various different models result in different requirements for the substrate of ring and occluder. A combination of high elastic temper and low resistance to flow requires a ring material with a Young's modulus of 40 GPa or more, and a 0.2% proof stress to (Young's modulus)2/3 ratio of 0.3 MPa1/3. The best occluder materials should have a Young's modulus of more than 50 GPa and a flexural strength of at least 800 MPa. On the basis of these criteria, a heart valve consisting of a TiA15Fe2,5 ring and occluders made partially stabilized zirconia is introduced.     

Internal strain gradients quantified in bone under load using high-energy X-ray scattering

High-energy synchrotron X-ray scattering (>60 keV) allows noninvasive quantification of internal strains within bone. In this proof-of-principle study, wide angle X-ray scattering maps internal strain vs position in cortical bone (murine tibia, bovine femur) under compression, specifically using the response of the mineral phase of carbonated hydroxyapatite. The technique relies on the response of the carbonated hydroxyapatite unit cells and their Debye cones (from nanocrystals correctly oriented for diffraction) to applied stress. Unstressed, the Debye cones produce circular rings on the two-dimensional X-ray detector while applied stress deforms the rings to ellipses centered on the transmitted beam. Ring ellipticity is then converted to strain via standard methods. Strain is measured repeatedly, at each specimen location for each applied stress. Experimental strains from wide angle X-ray scattering and an attached strain gage show bending of the rat tibia and agree qualitatively with results of a simplified finite element model. At their greatest, the apatite-derived strains approach 2500 με on one side of the tibia and are near zero on the other. Strains maps around a hole in the femoral bone block demonstrate the effect of the stress concentrator as loading increased and agree qualitatively with the finite element model. Experimentally, residual strains of approximately 2000 με are present initially, and strain rises to approximately 4500 με at 95 MPa applied stress (about 1000 με above the strain in the surrounding material). The experimental data suggest uneven loading which is reproduced qualitatively with finite element modeling.     

Intrinsic mechanical properties of trabecular calcaneus determined by finite-element models using 3D synchrotron microtomography

To determine intrinsic mechanical properties (elastic and failure) of trabecular calcaneus bone, chosen as a good predictor of hip fracture, we looked for the influence of image's size on a numerical simulation. One cubic sample of cancellous bone (9 x 9 x 9 mm(3)) was removed from the body of the calcaneus (6 females, 6 males, 79+/-9 yr). These samples were tested under compressive loading. Before compressive testing, these samples were imaged at 10.13 microm resolution using a 3D microcomputed tomography (muCT) (ESRF, France). The muCT images were converted to finite-element models. Depending on the bone density values (BV/TV), we compared two different finite element models: a linear hexahedral and a linear beam finite element models. Apparent experimental Young's modulus (E(app)(exp)) and maximum apparent experimental compressive stress (sigma(max)(exp)) were significantly correlated with bone density obtained by Archimedes's test (E(app)(exp)=236+/-231 MPa [19-742 MPa], sigma(max)(exp)=2.61+/-1.97 MPa [0.28-5.81 MPa], r>0.80, p<0.001). Under threshold at 40 microm, the size of the numerical samples (5.18(3) and 6.68(3)mm(3)) seems to be an important parameter on the accuracy of the results. The numerical trabecular Young's modulus was widely higher (E(trabecular)(num)=34,182+/-22,830 MPa [9700-87,211 MPa]) for the larger numerical samples and high BV/TV than those found classically by other techniques (4700-15,000 MPa). For rod-like bone samples (BV/TV<12%, n=7), Young's modulus, using linear beam element (E(trabecular)(num-skeleton): 10,305+/-5500 MPa), were closer to the Young's modulus found by other techniques. Those results show the limitation of hexahedral finite elements at 40 microm, mostly used, for thin trabecular structures.     

Influence of stress rate on water loss, matrix deformation and chondrocyte viability in impacted articular cartilage

The biomechanical response of articular cartilage to a wide range of impact loading rates was investigated for stress magnitudes that exist during joint trauma. Viable, intact bovine cartilage explants were impacted in confined compression with stress rates of 25, 50, 130 and 1000 MPa/s and stress magnitudes of 10, 20, 30 and 40 MPa. Water loss, cell viability, dynamic impact modulus (DIM) and matrix deformation were measured. Under all loading conditions the water loss was small (approximately 15%); water loss increased linearly with increasing peak stress and decreased exponentially with increasing stress rate. Cell death was localized within the superficial zone (< or =12% of total tissue thickness); the depth of cell death from the articular surface increased with peak stress and decreased with increasing stress rate. The DIM increased (200-700 MPa) and matrix deformation decreased with increasing stress rate. Initial water and proteoglycan (PG) content had a weak, yet significant influence on water loss, cell death and DIM. However, the significance of the inhomogeneous structure and composition of the cartilage matrix was accentuated when explants impacted on the deep zone had less water loss and matrix deformation, higher DIM, and no cell death compared to explants impacted on the articular surface. The mechano-biological response of articular cartilage depended on magnitude and rate of impact loading.     

IL-1beta decreases the elastic modulus of human tenocytes.

Cellular responses to mechanical stimuli are regulated by interactions with the extracellular matrix, which, in turn, are strongly influenced by the degree of cell stiffness (Young's modulus). It was hypothesized that a more elastic cell could better withstand the rigors of remodeling and mechanical loading. It was further hypothesized that interleukin-1beta (IL-1beta) would modulate intracellular cytoskeleton polymerization and regulate cell stiffness. The purpose of this study was to investigate the utility of IL-1beta to alter the Young's modulus of human tenocytes. Young's modulus is the ratio of the stress to the strain, E = stress/strain = (F/A)/(deltaL/L0), where L0 is the equilibrium length, deltaL is the length change under the applied stress, F is the force applied, and A is the area over which the force is applied. Human tenocytes were incubated with 100 pM recombinant human IL-1beta for 5 days. The Young's modulus was reduced by 27-63%. Actin filaments were disrupted in >75% of IL-1beta-treated cells, resulting in a stellate shape. In contrast, immunostaining of alpha-tubulin showed increased intensity in IL-1beta-treated tenocytes. Human tenocytes in IL-1beta-treated bioartificial tendons were more tolerant to mechanical loading than were untreated counterparts. These results indicate that IL-1beta reduced the Young's modulus of human tenocytes by disrupting the cytoskeleton and/or downregulating the expression of actin and upregulating the expression of tubulins. The reduction in cell modulus may help cells to survive excessive mechanical loading that may occur in damaged or healing tendons.