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.     

Region-specific mechanical properties of the human patella tendon.

The present study investigated the mechanical properties of tendon fascicles from the anterior and posterior human patellar tendon. Collagen fascicles from the anterior and posterior human patellar tendon in healthy young men (mean +/- SD, 29.0 +/- 4.6 yr, n = 6) were tested in a mechanical rig. A stereoscopic microscope equipped with a digital camera recorded elongation. The fascicles were preconditioned five cycles before the failure test based on pilot data on rat tendon fascicle. Human fascicle length increased with repeated cycles (P < 0.05); cycle 5 differed from cycle 1 (P < 0.05), but not cycles 2-4. Peak stress and yield stress were greater for anterior (76.0 +/- 9.5 and 56.6 +/- 10.4 MPa, respectively) than posterior fascicles (38.5 +/- 3.9 and 31.6 +/- 2.9 MPa, respectively), P < 0.05, while yield strain was similar (anterior 6.8 +/- 1.0%, posterior 8.7 +/- 1.4%). Tangent modulus was greater for the anterior (1,231 +/- 188 MPa) than the posterior (583 +/- 122 MPa) fascicles, P < 0.05. In conclusion, tendon fascicles from the anterior portion of the human patellar tendon in young men displayed considerably greater peak and yield stress and tangent modulus compared with the posterior portion of the tendon, indicating region-specific material properties.     

Evidence against proteoglycan mediated collagen fibril load transmission and dynamic viscoelasticity in tendon

The glycosaminoglycan (GAG) dermatan sulfate and chondroitin sulfate side-chains of small leucine-rich proteoglycans have been increasingly posited to act as molecular cross links between adjacent collagen fibrils and to directly contribute to tendon elasticity. GAGs have also been implicated in tendon viscoelasticity, supposedly affecting frictional loss during elongation or fluid flow through the extra cellular matrix. The current study sought to systematically test these theories of tendon structure–function by investigating the mechanical repercussions of enzymatic depletion of GAG complexes by chondroitinase ABC in a reproducible tendon structure–function model (rat tail tendon fascicles). The extent of GAG removal (at least 93%) was verified by relevant spectrophotometric assays and transmission electron microscopy. Dynamic viscoelastic tensile tests on GAG depleted rat tail tendon fascicle were not mechanically different from controls in storage modulus (elastic behavior) over a wide range of strain-rates (0.05, 0.5, and 5% change in length per second) in either the linear or nonlinear regions of the material curve. Loss modulus (viscoelastic behavior) was only affected in the nonlinear region at the highest strain-rate, and even this effect was marginal (19% increased loss modulus, p = 0.035). Thus glycosaminoglycan chains of small leucine-rich proteoglycans do not appear to mediate dynamic elastic behavior nor do they appear to regulate the dynamic viscoelastic properties in rat tail tendon fascicles.     

Experimental and biphasic FEM determinations of the material properties and hydraulic permeability of the meniscus in tension

Tensile tests and biphasic finite element modeling were used to determine a set of transversely isotropic properties for the meniscus, including the hydraulic permeability coefficients and solid matrix properties. Stress-relaxation tests were conducted on planar samples of canine meniscus samples of different orientations, and the solid matrix properties were determined from equilibrium data. A 3-D linear biphasic and tranversely isotropic finite element model was developed to model the stress-relaxation behavior of the samples in tension, and optimization was used to determine the permeability coefficients, k1 and k2, governing fluid flow parallel and perpendicular to the collagen fibers, respectively. The collagen fibrillar orientation was observed to have an effect on the Young's moduli (E1=67.8 MPa, E2=11.1 MPa) and Poisson's ratios (v12=2.13, v21 =1.50, v23=1.02). However, a significant effect of anisotropy on permeability was not detected (k1 =0.09x10(-16) m4/Ns, k2=0.10x10(-16) m4/Ns). The low permeability values determined in this study provide insight into the extent of fluid pressurization in the meniscus and will impact modeling predictions of load support in the meniscus.     

Direct measurement of the Poisson's ratio of human patella cartilage in tension

Articular cartilage has been shown to exhibit large transverse contractions when loaded in tension, suggesting the existence of large values for the Poisson's ratio. Previous studies have suggested that this effect is dependent on amplitude of applied strain, so that a single Poisson's ratio may not be sufficient to describe cartilage behavior. In this study, the Poisson's ratio (v), toe region modulus (Eo), and linear region modulus (E) of human patellar articular cartilage were calculated in simple tension tests from optical analysis of the two-dimensional strain fields at equilibrium. The Poisson's ratio was found to be independent of strain due to the absence of viscoelastic effects during testing. The Poisson's ratio was found to be significantly higher in the surface zone (1.87 +/- 1.11, p<0.01) than in the middle zone (0.62 +/- 0.23), with no significant correlation of v with age of the cartilage. In general, values for Poisson's ratio were greater than 0.5, suggesting cartilage behavior in tension deviates from isotropy. Reported values for the Poisson's ratio of cartilage in compression have been much lower than values measured here in tension, reflecting a mechanical contribution of the collagen fibers to anisotropy in tension but not compression. The toe-region modulus (Eo) was significantly higher in the surface zone (4.51 +/- 2.78 MPa, n=8) compared to the middle zone (2.51 +/- 1.93 MPa, n=10). In addition, the linear-region modulus (E) in the surface zone, but not middle zone (3.42 +/- 2.17 MPa, n=10), was found to correlate with age (R=0.97, p<0.02) with values of surface zone E equal to 23.92 +/- 12.29 MPa (n=5) for subjects under 70 yr of age, and 4.27 +/- 2.89 MPa (n=3) for subjects over 70 yr. Moduli values and trends with depth were consistent with previous studies of human and animal cartilage. From direct measures of two independent material properties, v and E, we calculated a shear modulus, G, which had not been previously reported for cartilage from tensile testing. Calculated values for surface zone G were 3.64 +/- 1.80 MPa for subjects under 70 yr old and 0.96 +/- 0.69 MPa for subjects over 70 yr old, and were significantly higher in the surface zone than in the middle zone (1.10 +/- 0.78 MPa). This study provides an intrinsic measure for the Poisson's ratio of articular cartilage and its dependence on depth which will be important in understanding the nonlinear tension-compression and anisotropic behaviors of articular cartilage.     

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.     

Comparison of the equilibrium response of articular cartilage in unconfined compression,confined compression and indentation

At mechanical equilibrium, articular cartilage is usually characterized as an isotropic elastic material with no interstitial fluid flow. In this study, the equilibrium properties (Young's modulus, aggregate modulus and Poisson's ratio) of bovine humeral, patellar and femoral cartilage specimens (n=26) were investigated using unconfined compression, confined compression, and indentation tests. Optical measurements of the Poisson's ratio of cartilage were also carried out. Mean values of the Young's modulus (assessed from the unconfined compression test) were 0.80+/-0.33, 0.57+/-0.17 and 0.31+/-0.18MPa and of the Poisson's ratio (assessed from the optical test) 0.15+/-0.06, 0.16+/-0.05 and 0.21+/-0.05 for humeral, patellar, and femoral cartilages, respectively. The indentation tests showed 30-79% (p<0.01) higher Young's modulus values than the unconfined compression tests. In indentation, values of the Young's modulus were independent of the indenter diameter only in the humeral cartilage. The mean values of the Poisson's ratio, obtained indirectly using the mathematical relation between the Young's modulus and the aggregate modulus in isotropic material, were 0.16+/-0.06, 0.21+/-0.05, and 0.26+/-0.08 for humeral, patellar, and femoral cartilages, respectively. We conclude that the values of the elastic parameters of the cartilage are dependent on the measurement technique in use. Based on the similar values of Poisson's ratios, as determined directly or indirectly, the equilibrium response of articular cartilage under unconfined and confined compression is satisfactorily described by the isotropic elastic model. However, values of the isotropic Young's modulus obtained from the in situ indentation tests are higher than those obtained from the in vitro unconfined or confined compression tests and may depend on the indenter size in use.     

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     

A micromechanical model of skeletal muscle to explore the effects of fiber and fascicle geometry

Computational models of muscle generally lump the material properties of connective tissue, muscle fibers, and muscle fascicles together into one constitutive relationship that assumes a transversely isotropic microstructure. These models do not take into account how variations in the microstructure of muscle affect its macroscopic material properties. The goal of this work was to develop micromechanical models of muscle to determine the effects of variations in muscle microstructure on the macroscopic constitutive behavior. We created micromechanical models at the fiber and fascicle levels based on histological cross-sections of two rabbit muscles, the rectus femoris (RF) and the soleus, to determine the effects of microstructure geometry (fiber and fascicle shapes) on the along-fiber shear modulus of muscle. The two fiber-level models predicted similar macroscopic shear moduli (within 13.5% difference); however, the two fascicle-level models predicted very different macroscopic shear moduli (up to 161% difference). We also used the micromechanical models to test the assumption that the macroscopic properties of muscle are transversely isotropic about the fiber (or fascicle) direction. The fiber-level models exhibited behavior consistent with the transverse isotropy assumption; however, the fascicle-level models exhibited transversely anisotropic behavior. Micromechanical models, combined with fiber and fiber bundle mechanical experiments, are needed to understand how normal or pathological variations in microstructure give rise to the observed macroscopic behavior of muscle.     

Strain-rate sensitive mechanical properties of tendon fascicles from mice with genetically engineered alterations in collagen and decorin

Tendons have complex mechanical behaviors that are nonlinear and time dependent. It is widely held that these behaviors are provided by the tissue composition and structure. It is generally thought that type I collagen provides the primary elastic strength to tendon while proteoglycans, such as decorin, play a role in failure and viscoelastic properties. This study sought to quantify such structure-function relationships by comparing tendon mechanical properties between normal mice and mice genetically engineered for altered type I collagen content and absence of decorin. Uniaxial tensile ramp to failure experiments were performed on tail tendon fascicles at two strain rates, 0.5%/s and 50%/s. Mutations in type I collagen led to reduced failure load and stiffness with no changes in failure stress, modulus or strain rate sensitivity. Fascicles without decorin had similar elastic properties to normal fascicles, but reduced strain rate sensitivity. Fascicles from immature mice, with increased decorin content compared to adult fascicles, had inferior elastic properties but higher strain rate sensitivity. These results showed that tendon viscoelasticity is affected by decorin content but not by collagen alterations. This study provides quantitative evidence for structure-function relationships in tendon, including the role of proteoglycan in viscoelasticity.     

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.     

A quantitative investigation of structure-function relationships in a tendon fascicle model

These studies sought to investigate quantitative relationships between the complex composite structure and mechanical properties of tendon. The isolated mouse tail tendon fascicle was chosen as an appropriate model for these so-called "structure-function" investigations. Specifically, collagen fibril diameters and mechanical properties were measured in fascicles from immature (3 week) control, adult (8 week) control, and adult (8 week) MovI3 transgenic mice. Results demonstrated a moderate correlation between mean fibril diameter and fascicle stiffness (r = 0.73, p = 0.001) and maximum load (r = 0.75, p < 0.001), whereas a weak correlation with fascicle modulus (r = 0.39, p = 0.11) and maximum stress (r = 0.48, p = 0.04). An analysis of pooled within-group correlations revealed no strong structure-function trends evidenced at the local or group level, indicating that correlations observed in the general structure-function analyses were due primarily to having three different experimental groups, rather than significant correlations of parameters within the groups.     

Comparison of nonlinear mechanical properties of bovine articular cartilage and meniscus

Nonlinear, linear and failure properties of articular cartilage and meniscus in opposing contact surfaces are poorly known in tension. Relationships between the tensile properties of articular cartilage and meniscus in contact with each other within knee joints are also not known. In the present study, rectangular samples were prepared from the superficial lateral femoral condyle cartilage and lateral meniscus of bovine knee joints. Tensile tests were carried out with a loading rate of 5 mm/min until the tissue rupture. Nonlinear properties of the toe region, linear properties in larger strains, and failure properties of both tissues were analysed. The strain-dependent tensile modulus of the toe region, Young's modulus of the linear region, ultimate tensile stress and toughness were on average 98.2, 8.3, 4.0 and 1.9 times greater (p<0.05) for meniscus than for articular cartilage. In contrast, the toe region strain, yield strain and failure strain were on average 9.4, 3.1 and 2.3 times greater (p<0.05) for cartilage than for meniscus. There was a significant negative correlation between the strain-dependent tensile moduli of meniscus and articular cartilage samples within the same joints (r=−0.690, p=0.014). In conclusion, the meniscus possesses higher nonlinear and linear elastic stiffness and energy absorption capability before rupture than contacting articular cartilage, while cartilage has longer nonlinear region and can withstand greater strains before failure. These findings point out different load carrying demands that both articular cartilage and meniscus have to fulfil during normal physiological loading activities of knee joints.     

Biphasic indentation of articular cartilage--II. A numerical algorithm and an experimental study

Part I (Mak et al., 1987, J. Biomechanics 20, 703-714) presented the theoretical solutions for the biphasic indentation of articular cartilage under creep and stress-relaxation conditions. In this study, using the creep solution, we developed an efficient numerical algorithm to compute all three material coefficients of cartilage in situ on the joint surface from the indentation creep experiment. With this method we determined the average values of the aggregate modulus. Poisson's ratio and permeability for young bovine femoral condylar cartilage in situ to be HA = 0.90 MPa, vs = 0.39 and k = 0.44 x 10(-15) m4/Ns respectively, and those for patellar groove cartilage to be HA = 0.47 MPa, vs = 0.24, k = 1.42 x 10(-15) m4/Ns. One surprising finding from this study is that the in situ Poisson's ratio of cartilage (0.13-0.45) may be much less than those determined from measurements performed on excised osteochondral plugs (0.40-0.49) reported in the literature. We also found the permeability of patellar groove cartilage to be several times higher than femoral condyle cartilage. These findings may have important implications on understanding the functional behavior of cartilage in situ and on methods used to determine the elastic moduli of cartilage using the indentation experiments.     

The mechanical properties of tail tendon fascicles from lubricin knockout, wild type and heterozygous mice

The purpose of this study was to analyze the effects of lubricin on tendon stiffness and viscoelasticity.A total of 36 mice were tested with 12 mice in each of the following groups: lubricin knock-out (−/−), heterozygous (+/−) and wild-type (+/+). A ramp test was used to determine the elastic modulus by pulling the fascicles to 2.5% strain amplitude at a rate of 0.05 mm/s. Then, followed by a relaxation test that pulled the fascicles to 5% strain amplitude at a rate of 2 mm/s. The fascicles were allowed to relax for 2 min at the maximum strain and a single-cycle relaxation ratio was used to characterize viscoelastic properties.There was no significant difference in the Young’s modulus between the three groups (p > 0.05), but the knockout mice had a significantly (p < 0.05) lower relaxation ratio than the wild type mice.Based on these data, we concluded that lubricin expression has an effect on the viscoelastic properties of tendon fascicles. The clinical significance of this finding, if any, remains to be demonstrated.     

Investigation into the biphasic properties of a hydrogel for use in a cushion form replacement joint.

A hydrogel with potential applications in the role of a cushion form replacement joint bearing surface material has been investigated. The material properties are required for further development and design studies and have not previously been quantified. Creep indentation experiments were therefore performed on samples of the hydrogel. The biphasic model developed by Mow and co-workers (Mak et al., 1987; Mow et al., 1989a) was used to curve-fit the experimental data to theoretical solutions in order to extract the three intrinsic biphasic material properties of the hydrogel (aggregate modulus, HA, Poisson's ratio, Vs, and permeability, k). Ranges of material properties were determined: aggregate modulus was calculated to be between 18.4 and 27.5 MPa, Poisson's ratio 0.0-0.307, and permeability 0.012-7.27 x 10(-17) m4/Ns. The hydrogel thus had a higher aggregate modulus than values published for natural normal articular cartilage, the Poisson's ratios were similar to articular cartilage, and finally the hydrogel was found to be less permeable than articular cartilage. The determination of these values will facilitate further numerical analysis of the stress distribution in a cushion form replacement joint.     

Tendon tissue microdamage and the limits of intrinsic repair

The transmission of mechanical muscle force to bone for musculoskeletal stability and movement is one of the most important functions of tendon. The load-bearing tendon core is composed of highly aligned collagen-rich fascicles interspersed with stromal cells (tenocytes). Despite being built to bear very high mechanical stresses, supra-physiological/repetitive mechanical overloading leads to tendon microdamage in fascicles, and potentially to tendon disease and rupture. To date, it is unclear to what extent intrinsic healing mechanisms of the tendon core compartment can repair microdamage. In the present study, we investigated the healing capacity of the tendon core compartment in an ex vivo tissue explant model. To do so, we isolated rat tail tendon fascicles, damaged them by applying a single stretch to various degrees of sub-rupture damage and longitudinally assessed downstream functional and structural changes over a period of several days. Functional damage was assessed by changes in the elastic modulus of the material stress-strain curves, and biological viability of the resident tenocytes. Structural damage was quantified using a fluorescent collagen hybridizing peptide (CHP) to label mechanically disrupted collagen structures. While we observed functional mechanical damage for strains above 2% of the initial fascicle length, structural collagen damage was only detectable for 6% strain and beyond. Minimally loaded/damaged fascicles (2–4% strain) progressively lost elastic modulus over the course of tissue culture, despite their collagen structures remaining intact with high degree of maintained cell viability. In contrast, more severely overloaded fascicles (6–8% strain) with damage at the molecular/collagen level showed no further loss of the elastic modulus but markedly decreased cell viability. Surprisingly, in these heavily damaged fascicles the elastic modulus partially recovered, an effect also seen in further experiments on devitalized fascicles, implying the possibility of a non-cellular but matrix-driven mechanism of molecular repair. Overall, our findings indicate that the tendon core has very little capacity for self-repair of microdamage. We conclude that stromal tenocytes likely do not play a major role in anabolic repair of tendon matrix microdamage, but rather mediate catabolic matrix breakdown and communication with extrinsic cells that are able to effect tissue repair.     

Determination of Poisson's ratio of articular cartilage by indentation using different-sized indenters

Articular cartilage is often characterized as an isotropic elastic material with no interstitial fluid flow during instantaneous and equilibrium conditions, and indentation testing commonly used to deduce material properties of Young's modulus and Poisson's ratio. Since only one elastic parameter can be deduced from a single indentation test, some other test method is often used to allow separate measurement of both parameters. In this study, a new method is introduced by which the two material parameters can be obtained using indentation tests alone, without requiring a secondary different type of test. This feature makes the method more suitable for testing small samples in situ. The method takes advantages of the finite layer effect. By indenting the sample twice with different-sized indenters, a nonlinear equation with the Poisson's ratio as the only unknown can be formed and Poisson's ratio obtained by solving the nonlinear equation. The method was validated by comparing the predicted Poisson's ratio for urethane rubber with the manufacturer's supplied value, and comparing the predicted Young's modulus for urethane rubber and an elastic foam material with modulii measured by unconfined compression. Anisotropic and nonhomogeneous finite-element (FE) models of the indentation were developed to aid in data interpretation. Applying the method to bovine patellar cartilage, the tissue Young's modulus was found to be 1.79 +/- 0.59 MPa in instantaneous response and 0.45 +/- 0.26 MPa in equilibrium, and the Poisson's ratio 0.503 +/- 0.028 and 0.463 +/- 0.073 in instantaneous and equilibrium, respectively. The equilibrium Poisson's ratio obtained in our work was substantially higher than those derived from biphasic indentation theory and those optically measured in an unconfined compression test. The finite element model results and examination of viscoelastic-biphasic models suggest this could be due to viscoelastic, inhomogeneity, and anisotropy effects.     

Changes of calf muscle-tendon biomechanical properties induced by passive-stretching and active-movement training in children with cerebral palsy

Biomechanical properties of calf muscles and Achilles tendon may be altered considerably in children with cerebral palsy (CP), contributing to childhood disability. It is unclear how muscle fascicles and tendon respond to rehabilitation and contribute to improvement of ankle-joint properties. Biomechanical properties of the calf muscle fascicles of both gastrocnemius medialis (GM) and soleus (SOL), including the fascicle length and pennation angle in seven children with CP, were evaluated using ultrasonography combined with biomechanical measurements before and after a 6-wk treatment of passive-stretching and active-movement training. The passive force contributions from the GM and SOL muscles were separated using flexed and extended knee positions, and fascicular stiffness was calculated based on the fascicular force-length relation. Biomechanical properties of the Achilles tendon, including resting length, cross-sectional area, and stiffness, were also evaluated. The 6-wk training induced elongation of muscle fascicles (SOL: 8%, P = 0.018; GM: 3%, P = 0.018), reduced pennation angle (SOL: 10%, P = 0.028; GM: 5%, P = 0.028), reduced fascicular stiffness (SOL: 17%, P = 0.128; GM: 21%, P = 0.018), decreased tendon length (6%, P = 0.018), increased Achilles tendon stiffness (32%, P = 0.018), and increased Young's modulus (20%, P = 0.018). In vivo characterizations of calf muscles and Achilles tendon mechanical properties help us better understand treatment-induced changes of calf muscle-tendon and facilitate development of more effective treatments.     

The role of viscoelasticity of collagen fibers in articular cartilage: theory and numerical formulation

The relative importance of fluid-dependent and fluid-independent transient mechanical behavior in articular cartilage was examined for tensile and unconfined compression testing using a fibril reinforced model. The collagen matrix of articular cartilage was modeled as viscoelastic using a quasi-linear viscoelastic formulation with strain-dependent elastic modulus, while the proteoglycan matrix was considered as linearly elastic. The collagen viscoelastic properties were obtained by fitting experimental data from a tensile test. These properties were used to investigate unconfined compression testing, and the sensitivity of the properties was also explored. It was predicted that the stress relaxation observed in tensile tests was not caused by fluid pressurization at the macroscopic level. A multi-step tensile stress relaxation test could be approximated using a hereditary integral in which the elastic fibrillar modulus was taken to be a linear function of the fibrillar strain. Applying the same formulation to the radial fibers in unconfined compression, stress relaxation could not be simulated if fluid pressurization were absent. Collagen viscoelasticity was found to slightly weaken fluid pressurization in unconfined compression, and this effect was relatively more significant at moderate strain rates. Therefore, collagen viscoelasticity appears to play an import role in articular cartilage in tensile testing, while fluid pressurization dominates the transient mechanical behavior in compression. Collagen viscoelasticity plays a minor role in the mechanical response of cartilage in unconfined compression if significant fluid flow is present.