Mechanical properties of anterior malleolar ligament from experimental measurement and material modeling analysis

In this paper, mechanical properties of the anterior malleolar ligament (AML) of human middle ear were studied through the uniaxial tensile, stress relaxation and failure tests. The digital image correlation (DIC) method was used to assess the boundary effect in experiments and calculate the strain on specimens. The constitutive behavior of the AML was described by a transversely isotropic hyperelastic model which consists of a first-order Ogden model augmented by a I (4)-type reinforcing term. The material parameters of the model were estimated and the viscoelasticity of the AML was illustrated by hysteresis phenomena and stress relaxation function. The mechanical strength of the AML was obtained through the failure test and the mean ultimate stress and stretch ratio were measured as 1.05 MPa and 1.51, respectively. Finally, a linear Young's modulus-stress relationship of the AML was derived based on constitutive equation of the AML within a stress range of 0-0.5 MPa.     

The tensile and stress relaxation responses of human patellar tendon varies with specimen cross-sectional area.

In order to provide insight into the mechanical response of the collagen fascicle structures in tendon, a series of constant strain rate and constant displacement, stress relaxation mechanical tests were performed on sequentially sectioned human patellar tendon specimens (protocol 1) and specimens with both small (approximately 1 mm2) and large (approximately 20 mm2) cross-sectional areas (protocol 2). These data described the stress relaxation and constant strain rate tensile responses as a function of cross-sectional area and water content. The experimental data suggested that small portions of tendon exhibit a higher tensile modulus, a slower rate of relaxation and a lower amount of relaxation in comparison to larger specimens from the same location in the same tendon. The decrease in relaxation response and the increase in tensile modulus with decreasing cross-sectional area was nonlinear. These data suggest that there may be structures other than the subfascicle, such as the epitenon and other connective tissue components, which influence the tensile and stress relaxation responses in tendon.     

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.     

Time-resolved X-ray diffraction from tendon collagen during creep using synchrotron radiation

In order to understand the molecular mechanism of relaxation phenomena in collagenous tissue, time-resolved, small-angle X-ray diffraction measurements were performed on bovine Achilles tendon collagen under creep. A tension-induced increase in the 67 nm period (D-period) was observed, and the strain in the D-period, epsilon D, was found to be almost proportional to the external force per unit cross-sectional area (average stress) of the specimen. With an increase in epsilon D, a change in the ratio of intensities of the third-order reflection peak of the D-period to that of the second-order peak was also observed. The increase in epsilon D was decomposed into three elementary processes of D-period deformation, which are presented on the basis of the Hodge-Petruska model: (1) molecular elongation, (2) increase in gap region, and (3) relative slippage of lateral adjoining molecules. Up to 8 MPa of average stress, the contribution to epsilon D originated mostly from only mode (1). At more than 10 MPa of average stress, modes (2) and (3) also contributed to fibril elongation. For epsilon D by molecular elongation (mode (1)), the time dependence of the D-period change in the immediate response region is a sharply shaped step function, while the contribution to epsilon D by molecular rearranging modes gives a slight creep nature at the immediate response region in the time dependence of epsilon D. Because this creep nature is observed at the immediate response, it is related qualitatively to the KWW function in a stress-relaxation modulus of collagenous tissue observed in an immediate response region (Sasaki et al. (1993). Journal of Biomechanics 26, 1369-1376). The elementary process of KWW-type relaxation is concluded to be related to the tension-induced molecular rearrangement within a D-period.     

A biphasic and transversely isotropic mechanical model for tendon: application to mouse tail fascicles in uniaxial tension

A transversely isotropic biphasic mixture model was applied to tendon in uniaxial tension. Parametric analyses were performed and the sensitivity in predicting material parameters was evaluated. Our results provide quantitative evidence for fluid flow as a mechanism that contributes to tendon viscoelasticity. Transversely isotropic material properties were calculated for mouse tail tendon fascicles. The average transverse modulus (E(1)) was 0.046 MPa, the fiber-aligned Poisson's ratio (v(31)) was 2.73, and the transverse Poisson's ratio [(v(21)) was 0.96; these properties were not strain-dependent. The fiber-aligned modulus (E(s)) was strain-dependent and was 20.7 MPa in the toe region and 86.1 MPa in the linear region. These solid matrix properties were consistent with previously published tendon tissue and fascicle data. The fascicle permeability was strain-dependent and was 5.5 x 10(-18)m(4)/Ns in the toe region and 0.32 x 10(-18)m(4)/Ns in the linear region, similar to previously reported meniscus permeability in tension. The similar permeabilities of both fascicle and tissue-level samples suggest that fluid flow from individual fascicles, not the packing of multiple fascicles together, may be the primary barrier to fluid flow in tendon and thus the primary mechanism for viscoelasticity.     

Why are mammalian tendons so thick?

The maximum stresses to which a wide range of mammalian limb tendons could be subjected in life were estimated by considering the relative cross-sectional areas of each tendon and of the fibres of its muscle. These cross-sectional areas were derived from mass and length measurements on tendons and muscles assuming published values for the respective densities. The majority of the stresses are low. The distribution has a broad peak with maximum frequency at a stress of about 13 MPa, whereas the fracture stress for tendon in tension is about 100 MPa. Thus, the majority of tendons are far thicker than is necessary for adequate strength. Much higher stresses are found among those tendons which act as springs to store energy during locomotion. The acceptability of low safety factors in these tendons has been explained previously (Alexander, 1981). A new theory explains the thickness of the majority of tendons. The muscle with its tendon is considered as a combined system which delivers mechanical energy: the thickness of the tendon is optimized by minimizing the combined mass. A thinner tendon would stretch more. To take up this stretch, the muscle would require longer muscle fibres, which would increase the combined mass. The predicted maximum stress in a tendon of optimum thickness is about 10 MPa, which is within the main peak of the observed stress distribution. Individual variations from this value are to be expected and can be understood in terms of the functions of the various muscles.     

Stress relaxation of human ankles is only minimally affected by knee and ankle angle

Comprehensive characterization of stress relaxation in musculotendinous structures is needed to create robust models of viscoelastic behavior. The commonly used quasi-linear viscoelastic (QLV) theory requires that the relaxation response be independent of tissue strain (length). This study aims to characterize stress relaxation in the musculotendinous and ligamentous structures crossing the human ankle (ankle-only structures and the gastrocnemius muscle–tendon unit, which crosses the ankle and knee), and to determine whether stress relaxation is independent of the length of these structures. Two experiments were conducted on 8 healthy subjects. The first experiment compared stress relaxation over 10 min at different gastrocnemius muscle–tendon unit lengths keeping the length of ankle-joint only structures fixed. The second experiment compared stress relaxation at different lengths of ankle-joint only structures keeping gastrocnemius muscle–tendon unit length fixed. Stress relaxation data were fitted with a two-term exponential function (T=G₀+G₁e^?λ₁t+G₂e^?λ₂t). The first experiment demonstrated a significant effect of gastrocnemius muscle–tendon unit length on G₁, and the second experiment demonstrated an effect of the length of ankle-joint only structures on G₂, λ₁ and λ₂ (p<0.05). Nonetheless, the size of effects on stress relaxation was small (ΔG/G<10%), similar to experimental variability. We conclude that stress relaxation in the relaxed human ankle is minimally affected by changing gastrocnemius muscle–tendon unit length or by changing the lengths of ankle-joint only structures. Consequently quasi-linear viscoelastic models of the relaxed human ankle can use a common stress relaxation modulus at different knee and ankle angles with minimal error.     

A three-dimensional constitutive model for the stress relaxation of articular ligaments

A new nonlinear constitutive model for the three-dimensional stress relaxation of articular ligaments is proposed. The model accounts for finite strains, anisotropy, and strain-dependent stress relaxation behavior exhibited by these ligaments. The model parameters are identified using published uniaxial stress–stretch and stress relaxation data on human medial collateral ligaments (MCLs) subjected to tensile tests in the fiber and transverse to the fiber directions (Quapp and Weiss in J Biomech Eng Trans ASME 120:757–763, 1998; Bonifasi-Lista et al. in J Orthop Res 23(1):67–76, 2005). The constitutive equation is then used to predict the nonlinear elastic and stress relaxation response of ligaments subjected to shear deformations in the fiber direction and transverse to the fiber direction, and an equibiaxial extension. A direct comparison with stress relaxation data collected by subjecting human MCLs to shear deformation in the fiber direction is presented in order to demonstrate the predictive capabilities of the model.     

Studies of fibrin film. I. Stress relaxation and birefringence

Measurements of stress relaxation in uniaxial extension and associated time-dependent birefringence have been made on bovine fibrin film, prepared by gentle compaction of coarse fibrin clots, containing 13–22% fibrin plasticized with either aqueous buffer or glycerol. Both unligated and ligated (i.e., with α-α and γ-γ ligation by fibrinoligase, factor XIIIa) films were studied. Both types showed two stages of stress relaxation, with time scales of approximately 10 and 10³–10⁴ s, respectively, with a plateau region between. In the plateau, the nominal (engineering) stress for ligated glycerol-plasticized film is proportional to In λ, where λ is the stretch ratio, up to λ ? 2, and it decreases with increasing temperature. For unligated glycerol-plasticized film, the stresses are smaller by a factor of one-half to one-third. For ligated film, the second stage of relaxation is relatively slight, and recovery after release of stress is often nearly complete. For unligated film, the second stage involves a substantial drop in stress, and after recovery there is a significant permanent set. A second relaxation for ligated film reproduces the first, but for unligated film it reproduces the first only if the initial relaxation is terminated before the second stage; otherwise, the second relaxation shows a weaker structure. The behavior of water-plasticized film is similar to that of glycerol-plasticized except that the second stage of relaxation occurs at shorter times. During the first stage of stress relaxation, up to about 100 s, the birefringence and the stress-optical coefficient increase; during the plateau zone of stress relaxation, the birefringence of ligated films is approximately constant and is proportional to 2λ²/(λ² + 1) ? 1, where λ is the stretch ratio. This dependence is predicted by a two-dimensional model in which rodlike elements in the plane of the film are oriented with independent alignment. During the final stage of stress relaxation, the birefringence of ligated films decreases slightly; that of unligated films decreases substantially, but less rapidly than the stress, corresponding to a further increase in the stress-optical coefficient. With additional information from small-angle x-ray scattering reported in an accompanying paper, the first stage of relaxation is attributed to partial release of bending forces in the fibers by orientation, accompanied by increased birefringence. The second stage is attributed, for ligated films, to an internal transition in the fibrin units accompanied by elongation of some of the fibers; and in the unligated films, to a combination of the latter transition with slippage of protofibrils lengthwise within the fiber bundles that causes some loss of orientation, which diminishes the birefringence.     

Tensile properties of the in vivo human gastrocnemius tendon

In the present experiment we obtained the tensile properties of the human gastrocnemius tendon, a high-stressed tendon suitable for spring-like action during locomotion. Measurements were taken in vivo in six men. The gastrocnemius tendon elongation during tendon loading−unloading induced by muscle contraction−relaxation was measured using real-time ultrasonography. Tendon forces were calculated from the moment generated during isometric plantarflexion contraction, using tendon moment arm length data obtained in vivo with the tendon travel method. Tendon stiffness data were calculated from the slope of the tendon force−elongation curve, and were then normalized to the tendon's original dimensions, obtained from morphometric analysis of sonographs, to estimate the tendon Young's modulus. Mechanical hysteresis values were obtained from area calculations by numerical integration. The elongation of the tendon increased curvilinearly with the force acting upon it, from 1.7±1 mm (0.8±0.3% strain) at 87.5±8.5 N to 11.1±3.1 mm (4.9±1% strain) at 875±85 N. The tendon Young's modulus and mechanical hysteresis were 1.16±0.15 GPa and 18±3%, respectively. These values fall within the range of values obtained from in vitro experiments and are very similar to the respective values recently obtained from in vivo measurements in the less highly stressed human tibialis anterior tendon (1.2 GPa and 19%), thus indicating that the material properties of tendon are independent of physiological loading and function. Combining the present tendon force−elongation data with previously reported Achilles tendon force data recorded during walking indicates that the gastrocnemius tendon would provide 6% of the total external work produced by the locomotor system. This estimate illustrates the contribution of passive elastic mechanisms on the economy and efficiency of walking. The contributions would be greater in more active exercise such as running.     

Determining the mechanical properties of yeast cell walls

The intrinsic cell wall mechanical properties of Baker's yeast (Saccharomyces cerevisiae) cells were determined. Force-deformation data from compression of individual cells up to failure were recorded, and these data were fitted by an analytical model to extract the elastic modulus of the cell wall and the initial stretch ratio of the cell. The cell wall was assumed to be homogeneous, isotropic, and incompressible. A linear elastic constitutive equation was assumed based on Hencky strains to accommodate the large stretches of the cell wall. Because of the high compression speed, water loss during compression could be assumed to be negligible. It was then possible to treat the initial stretch ratio and elastic modulus as adjustable parameters within the analytical model. As the experimental data fitted numerical simulations well up to the point of cell rupture, it was also possible to extract cell wall failure criteria. The mean cell wall properties for resuspended dried Baker's yeast were as follows: elastic modulus 185 ± 15 MPa, initial stretch ratio 1.039 ± 0.006, circumferential stress at failure 115 ± 5 MPa, circumferential strain at failure 0.46 ± 0.03, and strain energy per unit volume at failure 30 ± 3 MPa. Data on yeast cells obtained by this method and model should be useful in the design and optimization of cell disruption equipment for yeast cell processing.     

Mechanical characterisation of porcine rectus sheath under uniaxial and biaxial tension

Incisional hernia development is a significant complication after laparoscopic abdominal surgery. Intra-abdominal pressure (IAP) is known to initiate the extrusion of intestines through the abdominal wall, but there is limited data on the mechanics of IAP generation and the structural properties of rectus sheath. This paper presents an explanation of the mechanics of IAP development, a study of the uniaxial and biaxial tensile properties of porcine rectus sheath, and a simple computational investigation of the tissue. Analysis using Laplace?s law showed a circumferential stress in the abdominal wall of approx. 1.1 MPa due to an IAP of 11 kPa, commonly seen during coughing. Uniaxial and biaxial tensile tests were conducted on samples of porcine rectus sheath to characterise the stress–stretch responses of the tissue. Under uniaxial tension, fibre direction samples failed on average at a stress of 4.5 MPa at a stretch of 1.07 while cross-fibre samples failed at a stress of 1.6 MPa under a stretch of 1.29. Under equi-biaxial tension, failure occurred at 1.6 MPa with the fibre direction stretching to only 1.02 while the cross-fibre direction stretched to 1.13. Uniaxial and biaxial stress–stretch plots are presented allowing detailed modelling of the tissue either in silico or in a surrogate material. An FeBio computational model of the tissue is presented using a combination of an Ogden and an exponential power law model to represent the matrix and fibres respectively. The structural properties of porcine rectus sheath have been characterised and add to the small set of human data in the literature with which it may be possible to develop methods to reduce the incidence of incisional hernia development.     

Comparison of viscoelastic, structural, and material properties of double-looped anterior cruciate ligament grafts made from bovine digital extensor and human hamstring tendons

Due to ready availability, decreased cost, and freedom from transmissible diseases in humans such as hepatitis and AIDS, it would be advantageous to use tendon grafts from farm animals as a substitute for human tendon grafts in in vitro experiments aimed at improving the outcome of anterior cruciate ligament (ACL) reconstructive surgery. Thus the objective of this study was to determine whether an anterior cruciate ligament (ACL) graft composed of two loops of bovine common digital extensor tendon has the same viscoelastic, structural, and material properties as a graft composed of a double loop of semitendinosus and gracilis tendons from humans. To satisfy this objective, grafts were constructed from each tissue source. The cross-sectional area was measured using an area micrometer, and each graft was then pulled using a materials testing system while submerged in a saline bath. Using two groups of tendon grafts (n = 10), viscoelastic tests were conducted over a three-day period during which a constant displacement load relaxation test was followed by a constant amplitude, cyclic load creep test (first day), a constant load creep test (second day), and an incremental cyclic load creep test (third day). Load-to-failure tests were performed on two different groups of grafts (n = 8). When the viscoelastic behavior was compared, there were no significant differences in the rate of load decay or the final load (relaxation test) and rates of displacement increase or final displacements (creep tests) (p > 0.115). To compare both the structural and material properties in the toe region (i.e., < 250 N) of the load-elongation curve, the tangent stiffness and modulus functions were computed from parameters used in an exponential model fit to the load (stress)-elongation (strain) data. Although one of the two parameters in the functions was different statistically, this difference translated into a difference of only 0.03 mm in displacement at 250 N of load. In the linear region (i.e., 50-75 percent of ultimate load) of the load-elongation curve, the linear stiffness of the two graft types compared closely (444 N/mm for bovine and 418 N/mm for human) (p = 0.341). At failure, the ultimate loads (2901 N and 2914 N for bovine and human, respectively) and the ultimate stresses (71.8 MPa and 65.6 MPa for bovine and human, respectively) were not significantly different (p > 0.261). The theoretical effect of any differences in properties between these two grafts on the results of two types of in vitro experiments (i.e., effect of surgical variables on knee laxity and structural properties of fixation devices) are discussed. Despite some statistical differences in the properties evaluated, these differences do not translate into important effects on the dependent variables of interest in the experiments. Thus the bovine tendon graft can be substituted for the human tendon graft in both types of experiments.     

Trabeculated embryonic myocardium shows rapid stress relaxation and non-quasi-linear viscoelastic behavior

Passive viscoelastic behavior is important in embryonic cardiovascular function, influencing the rate and magnitude of contraction and relaxation. We hypothesized that if viscoelastic behavior is influenced by interstitial fluid flow, then the stage-21 (312d) and stage-24 (4d) chick myocardium with large intertrabecular spaces will exhibit much different viscoelastic behavior than stage-16 (212d) and stage-18 (3d) compact myocardium and a non-quasi-linear response. Excised left ventricular sections were tested with ramp-and-hold stress relaxation tests at axial stretch ratios of 1.05:1.1:1.2:1.3. The measured stress relaxation was much more rapid than previously observed in the compact, non-trabeculated myocardium. The reduced relaxation curves depended significantly on the stretch level. A continuous-spectrum quasi-linear relaxation function described their shape well but the model-fit parameters also depended on the stretch level. Sinusoidal stretching of ventricular sections at rates from 0.2 to 25Hz showed that the steepening of stress-strain curves with increasing strain rate was half as much as predicted by a quasi-linear model. Hysteresis ranged from 25-35%, varied little with loading rate from 0.2 to 8Hz, and was twice that predicted from a quasi-linear model. Doubling the viscosity of the perfusate in stress-relaxation tests produced increased stiffness and decreased relaxation rate. These results demonstrate that the passive viscoelastic behavior of the trabeculated embryonic myocardium is markedly different from that of younger, compact myocardium and is not quasi-linear.     

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.     

A comparison of biomechanical properties between human and porcine cornea

Due to the difficulty in obtaining human corneas, pig corneas are often substituted as models for cornea research. The purpose of this study is to find the similarities and differences in the biomechanical properties between human and porcine corneas. Uniaxial tests were conducted using an Instron apparatus to determine their tensile strength, stress-strain relationship, and stress-relaxation properties. The tensile strength and stress-strain relation were very similar but significant differences between the two tissues were observed in the stress-relaxation relationship. Under the same stretch ratio lambda=1.5, porcine cornea relaxed much more than human cornea. If tensile strength and the stress-strain relation are the only mechanical factors to be investigated, porcine cornea can be used as a substitute model for human cornea research. However, when stress relaxation is a factor, porcine corneas cannot be used as an appropriate model for human corneas in mechanical property studies. It is very difficult to get enough specimens of human cornea, so we did the experiments for stress-strain relationship at a specific value of strain rate (corresponding to the velocity of loading 10mm/min), and for stress relaxation at a specific stretch ratio lambda=1.5.     

Hysteresis measurements in intact human tendon

Mechanical hysteresis in tendons has traditionally been quantified from tensile testing of isolated specimens. Limitations associated with tendon displacement measurement and clamping, and uncertainties as to whether in vitro material represents intact tendon function necessitate measuring hysteresis under in vivo conditions. In the present study such measurements were taken in the human tibialis anterior (TA) tendon. Having the foot fixed on a dynamometer footplate, the displacement of the TA tendon during stimulation and relaxation of the TA muscle was recorded by means of ultrasonography in six men. Combining moment data corresponding to 0, 20, 40, 60, 80 and 100% of maximum voltage moment and the respective tendon-displacement data, a hysteresis loop was obtained between the load–displacement curves during contraction and relaxation. Measurement of the hysteresis loop area yielded a value of 19%. This value agrees with results from in vitro tensile tests of low-stress tendons, suitable for tensile force transmission and joint displacement control. In fact, the human TA tendon has such functional characteristics. The methodology presented allows design of longitudinal and cross-sectional experimental protocols, and in vivo assessment of tendon function and propensity to overheat.     

The biomechanical effects of limb lengthening and botulinum toxin type A on rabbit tendon

Numerous studies have examined the effects of distraction osteogenesis (DO) on bone, but relatively fewer have explored muscle adaptation, and even less have addressed the concomitant alterations that occur in the tendon. The purpose herein was to characterize the biomechanical properties of normal and elongated rabbit (N=20) tendons with and without prophylactic botulinum toxin type A (BTX-A) treatment. Elastic and viscoelastic properties of Achilles and Tibialis anterior (TA) tendons were evaluated through pull to failure and stress relaxation tests.All TA tendons displayed nonlinear viscoelastic responses that were strain dependent. A power law formulation was used to model tendon viscoelastic responses and tendon elastic responses were fit with a microstructural model. Distraction-elongated tendons displayed increases in compliance and stress relaxation rates over undistracted tendons; BTX-A administration offset this result. The elastic moduli of distraction-lengthened TA tendons were diminished (p=0.010) when distraction was combined with gastrocnemius (GA) BTX-A administration, elastic moduli were further decreased (p=0.004) and distraction following TA BTX-A administration resulted in TA tendons with moduli not different from contralateral control (p>0.05). Compared to contralateral control, distraction and GA BTX-A administration displayed shortened toe regions, (p=0.031 and 0.038, respectively), while tendons receiving BTX-A in the TA had no differences in the toe region (p>0.05). Ultimate tensile stress was unaltered by DO, but stress at the transition from the toe to the linear region of the stress–stretch curve was diminished in all distraction-elongated TA tendons (p<0.05). The data suggest that prophylactic BTX-A treatment to the TA protects some tendon biomechanical properties.     

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.     

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.