Effect of fiber orientation and strain rate on the nonlinear uniaxial tensile material properties of tendon

Tendons are exposed to complex loading scenarios that can only be quantified by mathematical models, requiring a full knowledge of tendon mechanical properties. This study measured the anisotropic, nonlinear, elastic material properties of tendon. Previous studies have primarily used constant strain-rate tensile tests to determine elastic modulus in the fiber direction. Data for Poisson's ratio aligned with the fiber direction and all material properties transverse to the fiber direction are sparse. Additionally, it is not known whether quasi-static constant strain-rate tests represent equilibrium elastic tissue behavior. Incremental stress-relaxation and constant strain-rate tensile tests were performed on sheep flexor tendon samples aligned with the tendon fiber direction or transverse to the fiber direction to determine the anisotropic properties of toe-region modulus (E0), linear-region modulus (E), and Poisson's ratio (v). Among the modulus values calculated, only fiber-aligned linear-region modulus (E1) was found to be strain-rate dependent. The E1 calculated from the constant strain-rate tests were significantly greater than the value calculated from incremental stress-relaxation testing. Fiber-aligned toe-region modulus (E(1)0 = 10.5 +/- 4.7 MPa) and linear-region modulus (E1 = 34.0 +/- 15.5 MPa) were consistently 2 orders of magnitude greater than transverse moduli (E(2)0 = 0.055 +/- 0.044 MPa, E2 = 0.157 +/- 0.154 MPa). Poisson's ratio values were not found to be rate-dependent in either the fiber-aligned (v12 = 2.98 +/- 2.59, n = 24) or transverse (v21 = 0.488 +/- 0.653, n = 22) directions, and average Poisson's ratio values in the fiber-aligned direction were six times greater than in the transverse direction. The lack of strain-rate dependence of transverse properties demonstrates that slow constant strain-rate tests represent elastic properties in the transverse direction. However, the strain-rate dependence demonstrated by the fiber-aligned linear-region modulus suggests that incremental stress-relaxation tests are necessary to determine the equilibrium elastic properties of tendon, and may be more appropriate for determining the properties to be used in elastic mathematical models.     

Bi-directional mechanical properties of the axillary pouch of the glenohumeral capsule: implications for modeling and surgical repair

The objective of this study was to determine the mechanical properties of the axillary pouch of the inferior glenohumeral ligament in the directions perpendicular (transverse) and parallel (longitudinal) to the longitudinal axis of the anterior band of the inferior glenohumeral ligament. A punch was used to excise one transverse and one longitudinal tissue sample from the axillary pouch of each cadaveric shoulder (n = 10). Each tissue sample was preconditioned and then a load-to-failure test was performed. All tissue samples exhibited the typical nonlinear behavior reported for ligaments and tendons. Significant differences (p < 0.05) were detected between the transverse and longitudinal tissue samples for ultimate stress (0.8 +/- 0.4 MPa and 2.0 +/- 1.0 MPa, respectively) and tangent modulus (5.4 +/- 2.9 MPa and 14.8 +/- 13.1 MPa, respectively). No significant differences (p > 0.05) were observed between the ultimate strain (transverse: 23.5 +/- 11.5%, longitudinal: 33.3 +/- 23.6%) and strain energy density (transverse: 10.8 +/- 8.5 MPa, longitudinal: 21.1 +/- 15.4 MPa) of the transverse and longitudinal tissue samples. The ultimate stress determined for the longitudinal axillary pouch tissue samples was comparable to a previous study that reported it to be 5.5 +/- 2.0 MPa. The ratio of the longitudinal to transverse moduli (3.3 +/- 2.8) is considerably less than that of the medial collateral ligament of the knee (30) and interosseous ligament of the forearm (385), suggesting that the axillary pouch functions to stabilize the joint in more than just one direction. Future models of the glenohumeral joint and surgical repair procedures should consider the properties of the axillary pouch in its transverse and longitudinal directions to fully describe the behavior of the inferior glenohumeral ligament.     

Bi-directional mechanical properties of the posterior region of the glenohumeral capsule

The objective of this study was to determine the mechanical properties of the posterior region of the glenohumeral capsule in the directions perpendicular (transverse) and parallel (longitudinal) to the longitudinal axis of the posterior band of the inferior glenohumeral ligament. A punch was used to excise one transverse and one longitudinal tissue sample from the posterior capsule of 11 cadaveric shoulders. All tissue samples exhibited the typical nonlinear behavior reported for ligaments and tendons. Significant differences (p < 0.05) were detected between the transverse and longitudinal tissue samples for ultimate stress (1.5+/-1.4 and 4.9+/-2.9 MPa, respectively) and tangent modulus (10.3+/-6.6 and 31.5+/-12.7 MPa, respectively). No significant differences (p > 0.05) were observed between the ultimate strain (transverse: 22.3+/-12.5%, longitudinal: 22.8+/-11.1%) and strain energy density (transverse: 27.2+/-52.8 MPa, longitudinal: 67.5+/-88.2 MPa) of the transverse and longitudinal tissue samples. The ratio of the longitudinal to transverse moduli (4.8+/-4.2) was similar to that found for the axillary pouch (3.3+/-2.8) in a previous study. Thus, both the axillary pouch and the posterior capsule function to stabilize the joint multi-axially. Future analytical models of the glenohumeral joint should consider the properties of the posterior capsule in its transverse and longitudinal directions to fully describe the behavior of the glenohumeral capsule. These models will be clinically important by providing a more accurate representation of the intact capsule as well as simulated capsular injuries and surgical repair procedures.     

Material characterization of human medial collateral ligament.

The objectives of this study were to determine the longitudinal and transverse material properties of the human medial collateral ligament (MCL) and to evaluate the ability of three existing constitutive models to describe the material behavior of MCL. Uniaxial test specimens were punched from ten human cadaveric MCLs and tensile tested along and transverse to the collagen fiber direction. Using load and optical strain analysis information, the tangent modulus, tensile strength and ultimate strain were determined. The material coefficients for each constitutive model were determined using nonlinear regression. All specimens failed within the substance of the tissue. Specimens tested along the collagen fiber direction exhibited the typical nonlinear behavior reported for ligaments. This behavior was absent from the stress-strain curves of the transverse specimens. The average tensile strength, ultimate strain, and tangent modulus for the longitudinal specimens was 38.6 +/- 4.8 MPa, 17.1 +/- 1.5 percent, and 332.2 +/- 58.3 MPa, respectively. The average tensile strength, ultimate strain, and tangent modulus for the transverse specimens was 1.7 +/- 0.5 MPa, 11.7 +/- 0.9 percent, and 11.0 +/- 3.6 MPa, respectively. All three constitutive models described the longitudinal behavior of the ligament equally well. However, the ability of the models to describe the transverse behavior of the ligament varied.     

The dependence of transversely isotropic elasticity of human femoral cortical bone on porosity

The objective of this study was to examine the dependence of the elastic properties of cortical bone as a transversely isotropic material on its porosity. The longitudinal Young's modulus, transverse Young's modulus, longitudinal shear modulus, transverse shear modulus, and longitudinal Poisson's ratio of cortical bone were determined from eighteen groups of longitudinal and transverse specimens using tensile and torsional tests on a servo-hydraulic material testing system. These cylindrical waisted specimens of cortical bone were harvested from the middle diaphysis of three pairs of human femora. The porosity of these specimens was assessed by means of histology. Our study demonstrated that the longitudinal Young's and shear moduli of human femoral cortical bone were significantly (p<0.01) negatively correlated with the porosity of cortical bone. Conversely, the elastic properties in the transverse direction did not have statistically significant correlations with the porosity of cortical bone. As a result, the transverse elastic properties of cortical bone were less sensitive to changes in porosity than those in the longitudinal direction. Additionally, the anisotropic ratios of cortical bone elasticity were found to be significantly (p<0.01) negatively correlated with its porosity, indicating that cortical bone tended to become more isotropic when its porosity increased. These results may help a number of researchers develop more accurate micromechanics models of cortical bone.     

Comparison of the elastic and yield properties of human femoral trabecular and cortical bone tissue

The ability to determine trabecular bone tissue elastic and failure properties has biological and clinical importance. To date, trabecular tissue yield strains remain unknown due to experimental difficulties, and elastic moduli studies have reported controversial results. We hypothesized that the elastic and tensile and compressive yield properties of trabecular tissue are similar to those of cortical tissue. Effective tissue modulus and yield strains were calibrated for cadaveric human femoral neck specimens taken from 11 donors, using a combination of apparent-level mechanical testing and specimen-specific, high-resolution, nonlinear finite element modeling. The trabecular tissue properties were then compared to measured elastic modulus and tensile yield strain of human femoral diaphyseal cortical bone specimens obtained from a similar cohort of 34 donors. Cortical tissue properties were obtained by statistically eliminating the effects of vascular porosity. Results indicated that mean elastic modulus was 10% lower (p<0.05) for the trabecular tissue (18.0+/-2.8 GPa) than for the cortical tissue (19.9+/-1.8 GPa), and the 0.2% offset tensile yield strain was 15% lower for the trabecular tissue (0.62+/-0.04% vs. 0.73+/-0.05%, p<0.001). The tensile-compressive yield strength asymmetry for the trabecular tissue, 0.62 on average, was similar to values reported in the literature for cortical bone. We conclude that while the elastic modulus and yield strains for trabecular tissue are just slightly lower than those of cortical tissue, because of the cumulative effect of these differences, tissue strength is about 25% greater for cortical bone.     

Development and growth of long bones in European water frogs (Amphibia: Anura: Ranidae), with remarks on age determination

Differentiation and development of long bones were studied in European water frogs: Rana lessonae, R. ridibunda, and R. esculenta. The study included premetamorphic larvae (Gosner Stage 40) to frogs that were 5 years old. Femora, metatarsal bones, and proximal phalanges of the hindlimb exhibit the same pattern of periosteal bone differentiation and the same pattern of growth. Longitudinal and radial growth of these bones was studied by examination of the diaphyses and epiphyses, particularly where the edge of periosteal bone is inserted into the epiphysis. The periosteum seems to be responsible for both longitudinal and radial growth. Investigation of the formation, length, and arrangement of lines of arrested growth reveals that the first line is present only in the middle 25-35% of the length of the diaphysis of an adult bone; therefore, only the central portion of the diaphysis should be used for age estimation in skeletochronological studies. Comparison of the shapes and histological structures of epiphyses in the femur, metatarsal bones, and phalanges revealed that epiphyseal cartilages are composed of an inner and outer part. The inner metaphyseal cartilage has distinct zones and plugs the end of the periosteal bone cylinder; its role in longitudinal growth is questioned. The outer epiphyseal cartilage is composed of articular cartilages proper, in addition to lateral articular cartilages. Differences in the symmetry of the lateral articular cartilages of distal epiphyses of the femur and toes may reflect adaptations to different kinds of movements at the knee and in the foot.     

Anatomical variation of orthotropic elastic moduli of the proximal human tibia

The anatomical variation of orthotropic elastic moduli of the cancellous bone from three human proximal tibiae was investigated using an ultrasonic technique. With this technique, it was possible to measure three orthogonal elastic moduli and three shear moduli from cubic specimens of cancellous bone as small as 8 mm per side. Correlation with mechanical tensile testing has shown this technique to offer a precise measure of cancellous modulus (Eten = 0.94Eult + 144.6 MPa, r2 = 0.96, n = 34). The cancellous bone of the proximal tibia was found to be very inhomogeneous, with the axial modulus ranging between 340 and 3350 MPa. A course map is presented, showing measured Young's moduli as a function of anatomical position. The anisotropy of the cancellous bone, determined by the relative differences between the three orthogonal moduli, was shown to be relatively constant over the entire range of cancellous densities tested. The relationship between the axial elastic modulus and the apparent density was found to be approximately linear, as reported by others for proximal tibial cancellous bone.     

How is the indentation modulus of bone tissue related to its macroscopic elastic response? A validation study

This work consists of the validation of a novel approach to estimate the local anisotropic elastic constants of the bone extracellular matrix using nanoindentation. For this purpose, nanoindentation on two planes of material symmetry were analyzed and the resulting longitudinal elastic moduli compared to the moduli measured with a macroscopic tensile test. A combined lathe and tensile system was designed that allows machining and testing of cylindrical microspecimens of approximately 4mm in length and 300 microm in diameter. Three bovine specimens were tested in tension and their outer geometry and porosity assessed by synchrotron radiation microtomography. Based on the results of the traction test and the precise outer geometry, an apparent longitudinal Young's modulus was calculated. Results between 20.3 and 27.6 GPa were found that match with previously reported values for bovine compact bone. The same specimens were then characterized by nanoindentation on a transverse and longitudinal plane. A longitudinal Young's modulus for the bone matrix was then derived using the numerical scheme proposed by Swadener and Pharr and the fabric-elasticity relationship by Zysset and Curnier. Based on the matrix modulus and a power law effective volume fraction, an apparent longitudinal Young's modulus was predicted for each microspecimen. This alternative approach provided values between 19.9 and 30.0 GPa, demonstrating differences between 2% and 13% to the values provided by the initial tensile test. This study therefore raises confidence in our nanoindentation protocol of the bone extracellular matrix and supports the underlying hypotheses used to extract the anisotropic elastic constants.     

The physical and mechanical effects of suspension-induced osteopenia on mouse long bones.

The present investigation addresses the extent of tail-suspension effects on the long bones of mice. The effects are explored in both sexes, in both forelimb and hindlimb bones, and in both diaphyseal and metaphyseal/epiphyseal bones. Two weeks of suspension provided unloading of the femora and tibiae and an altered loading of the humeri. Whole-bone effects included lower mass (approximately 10%) and length (approximately 4%) in the bones of suspended mice compared to controls. The geometric and material properties of the femora were considered along the entire length of the diaphysis and in the metaphysis/epiphysis portions as a unit. Geometric effects included lower cross-sectional cortical area (16%), cortical thickness (25%) and moment of inertia (21%) in the femora of suspended mice; these differences were observed in both distal and proximal portions of the femur diaphysis. The relative amount of bone comprising the middle 8 mm of the diaphysis was greater (3%) in the control mice than in the suspended mice. Significant mass differences between the group in the metaphysis/epiphysis were not observed. Material effects included lower %ash (approximately 2%) in the femora and tibiae as well as in the humeri of suspended mice compared to controls. With respect to the measured physical and material properties, suspension produced similar bone responses in male and female mice. The effects of suspension are manifested largely through geometric rather than through material changes.     

Elastic modulus and hardness of cortical and trabecular bone lamellae measured by nanoindentation in the human femur.

The mechanical properties of bone tissue are determined by composition as well as structural, microstructural and nanostructural organization. The aim of this study was to quantify the elastic properties of bone at the lamellar level and compare these properties among osteonal, interstitial and trabecular microstructures from the diaphysis and the neck of the human femur. A nanoindentation technique with a custom irrigation system was used for simultaneously measuring force and displacement of a diamond tip pressed 500 nm into the moist bone tissue. An isotropic elastic modulus was calculated from the unloading curve with an assumed Poisson ratio of 0.3, while hardness was defined as the maximal force divided by the corresponding contact area. The elastic moduli ranged from 6.9 +/- 4.3 GPa in trabecular tissue from the femoral neck of a 74 yr old female up to 25.0 +/- 4.3 GPa in interstitial tissue from the diaphyseal cortex of a 69 yr old female. The mean elastic modulus was found to be significantly influenced by the type of lamella (p < 10(-6)) and by donor (p < 10(-6)). The interaction between the type of lamella and the donor was also highly significant (p < 10(-6)). Hardness followed a similar distribution as elastic modulus among types of lamellae and donor, but with lower statistical contrast. It is concluded that the nanostructure of bone tissue must differ substantially among lamellar types, anatomical sites and individuals and suggests that tissue heterogeneity is of potential importance in bone fragility and adaptation.     

Forces and deformations of the abdominal wall--a mechanical and geometrical approach to the linea alba

Force-elongation responses of the human abdominal wall in the linea alba region were determined by tensile tests in which the linea alba was seen to exhibit a nonlinear elastic, anisotropic behavior as is frequently observed in soft biological tissues. In addition, the geometry of the abdominal wall was determined, based on MRI data. The geometry can be specified by principal radii of curvature in longitudinal of approximately 470 mm and in the transverse direction of about 200 mm. The determined radii agree with values found in other studies. Mechanical stresses, deformations and abdominal pressures for load cases above 6% elongation can be related using Laplace's formula and our constitutive and geometrical findings. Results from uni- and biaxial tensile tests can thus be compared using this model. Calculations confirm that abdominal pressures of approximately 20 kPa correspond to related biaxial forces of about 3.4N/mm in the transverse and 1.5 N/mm in the longitudinal direction. Young's moduli can be calculated with respect to the uniaxial as well as the biaxial loading. At these physiological loadings, a compliance ratio of about 2:1 between the longitudinal and transversal directions is found. Young's moduli of about 50 kPa occur in transversal direction and of about 20 kPa in longitudinal direction at transverse and longitudinal strains both in the order of 6%. These findings coincide with results from other investigations in which the properties of the abdominal wall have been examined.     

Anatomic variation in the elastic inhomogeneity and anisotropy of human femoral cortical bone tissue is consistent across multiple donors

Numerical models commonly account for elastic inhomogeneity in cortical bone using power-law scaling relationships with various measures of tissue density, but limited experimental data exists for anatomic variation in elastic anisotropy. A recent study revealed anatomic variation in the magnitude and anisotropy of elastic constants along the entire femoral diaphysis of a single human femur (Espinoza Orías et al., 2009). The objective of this study was to confirm these trends across multiple donors while also considering possible confounding effects of the anatomic quadrant, apparent tissue density, donor age, and gender. Cortical bone specimens were sampled from the whole femora of 9 human donors at 20%, 50%, and 80% of the total femur length. Elastic constants from the main diagonal of the reduced fourth-order tensor were measured on hydrated specimens using ultrasonic wave propagation. The tissue exhibited orthotropy overall and at each location along the length of the diaphysis (p < 0.0001). Elastic anisotropy increased from the mid-diaphysis toward the epiphyses (p < 0.05). The increased elastic anisotropy was primarily caused by a decreased radial elastic constant (C(11)) from the mid-diaphysis toward the epiphyses (p < 0.05), since differences in the circumferential (C(22)) and longitudinal (C(33)) elastic constants were not statistically significant (p > 0.29). Anatomic variation in intracortical porosity may account for these trends, but requires further investigation. The apparent tissue density was positively correlated with the magnitude of each elastic constant (p < 0.0001, R(2) > 0.46), as expected, but was only weakly correlated with C(33)/C(11) (p < 0.05, R(2) = 0.04) and not significantly correlated with C(33)/C(22) and C(11)/C(22).     

Analysis of the passive mechanical properties of rat carotid arteries

The passive mechanical properties of rat carotid arteries were studied in vitro. Using a tensile testing machine and a piston pump, intact segments of carotid arteries were subjected to large deformations both in the longitudinal and circumferential directions. Internal pressure, external diameter, length and longitudinal force were measured during the experiment and compared with the in vivo dimensions of the segments prior to excision. The anisotropic mechanical properties of the vessel wall material were analyzed using incremental elastic moduli and incremental Poisson's ratios. The results suggest that there is a characteristic deformation pattern common to all vessels investigated which is highly correlated with the conditions of loading that occur in vivo. That is, under average physiological deformation of the vessel, the longitudinal force is nearly independent of internal pressure. In this range of loading the circumferential incremental elastic modulus is nearly independent of longitudinal strain. However, the longitudinal and radial incremental elastic moduli vary significantly with deformation in this direction. The values of the moduli in all three directions increase with raising internal pressure. The weak coupling between circumferential and longitudinal direction in the wall material of carotid arteries is shown by the small value of the corresponding incremental Poisson's ratios.     

Elastic moduli, yield stress, and ultimate stress of cancellous bone in the canine proximal femur

Elastic moduli, yield stress and ultimate compressive stress were determined for cancellous bone from the femoral head and neck regions of the canine femur. Unconfined compression tests were performed on 5 mm cubic samples which were cut from two femurs. Elastic moduli were measured in three orthogonal directions, and the yield stress and ultimate stress were measured along the proximal-distal axis. The results from this investigation support previous assumptions that the mechanical behavior of canine cancellous bone is qualitatively similar to human cancellous bone. The canine cancellous bone was observed to be anisotropic in elastic modulus. For two thirds of the cubic specimens tested, the elastic modulus was largest in the load-bearing, proximal-distal direction. A linear relationship between yield stress and elastic modulus was observed for canine bone, as is typical of human bone. A similar linear relationship between ultimate stress and elastic modulus was observed. Thus, for canine bone as well as for human bone, failure appears to be governed by a strain level which is position independent. The yield strain of 0.0259 and ultimate strain of 0.0288 for canine bone were both less than the yield strain of 0.0395 reported for human bone.     

The elastic moduli of human subchondral, trabecular, and cortical bone tissue and the size-dependency of cortical bone modulus

The elastic moduli of human subchondral, trabecular, and cortical bone tissue from a proximal tibia were experimentally determined using three-point bending tests on a microstructural level. The mean modulus of subchondral specimens was 1.15 GPa, and those of trabecular and cortical specimens was 4.59 GPa and 5.44 GPa respectively. Significant differences were found in the modulus values between bone tissues, which may have mainly resulted from the differences in the microstructures of each bone tissue rather than in the mineral density. Furthermore, the size-dependency of the modulus was examined using eight different sizes of cortical specimens (heights h = 100-1000 microns). While the modulus values for relatively large specimens (h greater than 500 microns) remained fairly constant (approximately 15 GPa), the values decreased as the specimens became smaller. A significant correlation was found between the modulus and specimen size. The surface area to volume ratio proved to be a key variable to explain the size-dependency.     

Growth and shaping of metacarpal and carpal cartilage anlagen: application of morphometry to the development of short and long bone. A study of human hand anlagen in the fetal period

A histological and morphometric analysis of human metacarpal and carpal anlagen between the 16th and 22nd embryonic weeks was carried out with the aim of studying the establishment of the respective anlage architecture. No differences in the pattern of growth were documented between the peripheral and central zones of the metacarpal epiphyses and those of the carpals. The regulation of longitudinal growth in long bone anlagen occurred in the transition zone between the epiphysis and the diaphysis (homologous to the metaphyseal growth plate cartilage in more advanced developmental stage of the bone). Comparative zonal analysis was conducted to assess the chondrocyte density, the mean chondrocyte lacunar area, the paired chondrocyte polarity in the orthogonal longitudinal and transverse planes, and the lacunar shape transformation in the metacarpal. In transition from epiphysis to diaphysis chondrocyte density decreased and mean lacunar area increased. No significant differences in the chondrocyte maturation cycle were observed between proximal/distal metacarpal epiphyses and the carpal anlagen. The number of paired chondrocyte oriented along the growth vector was significantly higher in both proximal/distal transition zones between epiphysis and diaphysis. Human metacarpals shared with experimental models (like mice and nonmammal tetrapods) an early common chondrocyte maturation cycle but with a different timing due to the slower embryonic and fetal developmental rate of human anlagen.     

Anisotropic and inhomogeneous tensile behavior of the human anulus fibrosus: experimental measurement and material model predictions

The anulus fibrosus (AF) of the intervertebral disc exhibits spatial variations in structure and composition that give rise to both anisotropy and inhomogeneity in its material behaviors in tension. In this study, the tensile moduli and Poisson's ratios were measured in samples of human AF along circumferential, axial, and radial directions at inner and outer sites. There was evidence of significant inhomogeneity in the linear-region circumferential tensile modulus (17.4+/-14.3 MPa versus 5.6+/-4.7 MPa, outer versus inner sites) and the Poisson's ratio v21 (0.67+/-0.22 versus 1.6+/-0.7, outer versus inner), but not in the axial modulus (0.8+/-0.9 MPa) or the Poisson's ratios V12 (1.8+/-1.4) or v13 (0.6+/-0.7). These properties were implemented in a linear an isotropic material model of the AF to determine a complete set of model properties and to predict material behaviors for the AF under idealized kinematic states. These predictions demonstrate that interactions between fiber populations in the multilamellae AF significantly contribute to the material behavior, suggesting that a model for th     

Anisotropic strain-dependent material properties of bovine articular cartilage in the transitional range from tension to compression

Articular cartilage exhibits complex mechanical properties such as anisotropy, inhomogeneity and tension-compression nonlinearity. This study proposes and demonstrates that the application of compressive loading in the presence of osmotic swelling can be used to acquire a spectrum of incremental cartilage moduli (EYi) and Poisson's ratios (upsilon ij) from tension to compression. Furthermore, the anisotropy of the tissue can be characterized in both tension and compression by conducting these experiments along three mutually perpendicular loading directions: parallel to split-line (1-direction), perpendicular to split-line (2-direction) and along the depth direction (3-direction, perpendicular to articular surface), accounting for tissue inhomogeneity between the surface and deep layers in the latter direction. Tensile moduli were found to be strain-dependent while compressive moduli were nearly constant. The peak tensile (+) Young's moduli in 0.15M NaCl were E+Y1=3.1+/-2.3, E+Y2=1.3+/-0.3, E+Y3(Surface)=0.65+/-0.29 and E+Y3(Deep)=2.1+/-1.2 MPa. The corresponding compressive (-) Young's moduli were E-Y1=0.23+/-0.07, E-Y2=0.22+/-0.07, E-Y3(Surface)=0.18+/-0.07 and E-Y3(Deep)=0.35+/-0.11 MPa. Peak tensile Poisson's ratios were upsilon+12=0.22+/-0.06, upsilon+21=0.13+/-0.07, upsilon+31(Surface)=0.10+/-0.03 and upsilon+31(Deep)=0.20+/-0.05 while compressive Poisson's ratios were upsilon-12=0.027+/-0.012, upsilon-21=0.017+/-0.07, upsilon-31(Surface)=0.034+/-0.009 and upsilon-31(Deep)=0.065+/-0.024. Similar measurements were also performed at 0.015 M and 2 M NaCl, showing strong variations with ionic strength. Results indicate that (a) a smooth transition occurs in the stress-strain and modulus-strain responses between the tensile and compressive regimes, and (b) cartilage exhibits orthotropic symmetry within the framework of tension-compression nonlinearity. The strain-softening behavior of cartilage (the initial decrease in EYi with increasing compressive strain) can be interpreted in the context of osmotic swelling and tension-compression nonlinearity.     

Structural properties of fourth-generation composite femurs and tibias

The purpose of this study was to measure the structural properties of the latest design (fourth-generation) of composite femurs and tibias from Pacific Research Laboratories, Inc. Fourth-generation composite bones have the same geometries as the third-generation bones, but the cortical bone analogue material was changed to one with increased fracture and fatigue resistance, tensile and compressive properties, thermal stability, and moisture resistance. The stiffnesses of the femurs and tibias were tested under bending, axial, and torsional loading, and the longitudinal strain distribution along the proximal-medial diaphysis of the femur was also determined. The fourth-generation composite bones had average stiffnesses and strains that were for the most part closer to corresponding values measured for natural bones, than was the case for third-generation composite bones; all measurements were taken by the same investigator in separate studies using identical methodology. For the stiffness tests, variability between the specimens was less than 10% for all cases, and setup variability was less than 6%.