Chiral behavior in rat tail tendon fascicles.

Ex vivo tendon mechanical behavior has been well described under rotationally constrained uniaxial tensile testing. During standard loading of rat tail tendon (RTT) fascicles, apparent axial twist has been observed. To quantify this behavior, we designed a custom testing setup, utilizing magnetic suspension, to allow unconstrained axial rotation during tensile loading. We characterized the rotational behavior of single and paired RTT fascicles under cyclic loading. We also measured stress relaxation across loading cycles as well as "rotational relaxation". Single fascicle nonlinear stretch-twist coupling is well described by the asymptotic function Δθ=A(1-e-Bε) in which fascicles rotated a mean ±51.1° within about 1% applied axial strain. On average, paired fascicles rotated just over 10° less. Specimen cross-sectional diameter had a noticeable effect on the measured mechanical properties, particularly effective elastic modulus. Such stretch-twist coupling and size dependence cannot be understood via classical elasticity but is predicted by Cosserat (micropolar) elasticity. The current study demonstrates RTT fascicles are chiral based on observed axial load-induced twist. Additionally, our findings support existing research that suggests a helical fascicle structure. Potential consequences of helical substructures, mechanical and biological, merit further investigation.

Shear loads induce cellular damage in tendon fascicles.

Tendon is vital to musculoskeletal function, transferring loads from muscle to bone for joint motion and stability. It is an anisotropic, highly organized, fibrous structure containing primarily type I collagen in addition to tenocytes and other extracellular matrix components contributing to maintenance and function. Tendon is generally loaded via normal stress in a longitudinal direction. However, certain situations, including fiber breakage, enzymatic remodeling, or tendon pathology may introduce various degrees of other loading modalities, such as shear-lag at the fiber level, potentially affecting cellular response and subsequent function. Fascicles from rat tail tendon were dissected and placed in one of three paired groups: intact, single laceration, or double laceration. Each pair had a mechanically tested and control specimen. Single laceration fascicles contained one transverse laceration to mimic a partial tear. Double laceration fascicles had overlapping, longitudinally separated lacerations on opposite sides to cause intra-fascicular shear transfer to be the primary mechanism of loading. Elastic properties of the fascicle, e.g. peak load, steady state load, and stiffness, decreased from intact to single laceration to double laceration groups. Surprisingly, 45% of the intact strength was maintained when shear was the primary internal load transfer mechanism. Cellular viability decreased after mechanical testing in both laceration groups; cell death appeared primarily in a longitudinal plane where high shear load transfer occurred. This cell death extended far from the injury site and may further compromise an already damaged tendon via enzymatic factors and subsequent remodeling associated with cell necrosis.

Shear load transfer in high and low stress tendons.

BACKGROUND: Tendon is an integral part of joint movement and stability, as it functions to transmit load from muscle to bone. It has an anisotropic, fibrous hierarchical structure that is generally loaded in the direction of its fibers/fascicles. Internal load distributions are altered when joint motion rotates an insertion site or when local damage disrupts fibers/fascicles, potentially causing inter-fiber (or inter-fascicular) shear. Tendons with different microstructures (helical versus linear) may redistribute loads differently. METHOD OF APPROACH: This study explored how shear redistributes axial loads in rat tail tendon (low stress tendons with linear microstructure) and porcine flexor tendon (high stress with helical microstructure) by creating lacerations on opposite sides of the tendon, ranging from about 20% to 60% of the tendon width, to create various magnitudes of shear. Differences in fascicular orientation were quantified using polarized light microscopy. RESULTS AND CONCLUSIONS: Unexpectedly, both tendon types maintained about 20% of pre-laceration stress values after overlapping cuts of 60% of tendon width (no intact fibers end to end) suggesting that shear stress transfer can contribute more to overall tendon strength and stiffness than previously reported. All structural parameters for both tendon types decreased linearly with increasing laceration depth. The tail tendon had a more rapid decline in post-laceration elastic stress and modulus parameters as well as a more linear and less tightly packed fascicular structure, suggesting that positional tendons may be less well suited to redistribute loads via a shear mechanism.

Evaluation of global load sharing and shear-lag models to describe mechanical behavior in partially lacerated tendons.

The mechanical effect of a partial thickness tear or laceration of a tendon is analytically modeled under various assumptions and results are compared with previous experimental data from porcine flexor tendons. Among several fibril-level models considered, a shear-lag model that incorporates fibril-matrix interaction and a fibril-fibril interaction defined by the contact area of the interposed matrix best matched published data for tendons with shallow cuts (less than 50% of the cross-sectional area). Application of this model to the case of many disrupted fibrils is based on linear superposition and is most successful when more fibrils are incorporated into the model. An equally distributed load sharing model for the fraction of remaining intact fibrils was inadequate in that it overestimates the strength for a cut less than half of the tendon's cross-sectional area. In a broader sense, results imply that shear-lag contributes significantly to the general mechanical behavior of tendons when axial loads are nonuniformly distributed over a cross section, although the predominant hierarchical level and microstructural mediators for this behavior require further inquiry.

Changes in large pulmonary arterial viscoelasticity in chronic pulmonary hypertension.

Conduit pulmonary artery (PA) stiffening is characteristic of pulmonary arterial hypertension (PAH) and is an excellent predictor of mortality due to right ventricular (RV) overload. To better understand the impact of conduit PA stiffening on RV afterload, it is critical to examine the arterial viscoelastic properties, which require measurements of elasticity (energy storage behavior) and viscosity (energy dissipation behavior). Here we hypothesize that PAH leads to frequency-dependent changes in arterial stiffness (related to elasticity) and damping ratio (related to viscosity) in large PAs. To test our hypothesis, PAH was induced by the combination of chronic hypoxia and an antiangiogenic compound (SU5416) treatment in mice. Static and sinusoidal pressure-inflation tests were performed on isolated conduit PAs at various frequencies (0.01-20 Hz) to obtain the mechanical properties in the absence of smooth muscle contraction. Static mechanical tests showed significant stiffening of large PAs with PAH, as expected. In dynamic mechanical tests, structural stiffness (κ) increased and damping ratio (D) decreased at a physiologically relevant frequency (10 Hz) in hypertensive PAs. The dynamic elastic modulus (E), a material stiffness, did not increase significantly with PAH. All dynamic mechanical properties were strong functions of frequency. In particular, κ, E and D increased with increasing frequency in control PAs. While this behavior remained for D in hypertensive PAs, it reversed for κ and E. Since these novel dynamic mechanical property changes were found in the absence of changes in smooth muscle cell content or contraction, changes in collagen and proteoglycans and their interactions are likely critical to arterial viscoelasticity in a way that has not been previously described. The impact of these changes in PA viscoelasticity on RV afterload in PAH awaits further investigation.

Comparison of approaches to quantify arterial damping capacity from pressurization tests on mouse conduit arteries.

Large conduit arteries are not purely elastic, but viscoelastic, which affects not only the mechanical behavior but also the ventricular afterload. Different hysteresis loops such as pressure-diameter, pressure-luminal cross-sectional area (LCSA), and stress-strain have been used to estimate damping capacity, which is associated with the ratio of the dissipated energy to the stored energy. Typically, linearized methods are used to calculate the damping capacity of arteries despite the fact that arteries are nonlinearly viscoelastic. The differences in the calculated damping capacity between these hysteresis loops and the most common linear and correct nonlinear methods have not been fully examined. The purpose of this study was thus to examine these differences and to determine a preferred approach for arterial damping capacity estimation. Pressurization tests were performed on mouse extralobar pulmonary and carotid arteries in their physiological pressure ranges with pressure (P) and outer diameter (OD) measured. The P-inner diameter (ID), P-stretch, P-Almansi strain, P-Green strain, P-LCSA, and stress-strain loops (including the Cauchy and Piola-Kirchhoff stresses and Almansi and Green strains) were calculated using the P-OD data and arterial geometry. Then, the damping capacity was calculated from these loops with both linear and nonlinear methods. Our results demonstrate that the linear approach provides a reasonable approximation of damping capacity for all of the loops except the Cauchy stress-Almansi strain, for which the estimate of damping capacity was significantly smaller (22 ± 8% with the nonlinear method and 31 ± 10% with the linear method). Between healthy and diseased extralobar pulmonary arteries, both methods detected significant differences. However, the estimate of damping capacity provided by the linear method was significantly smaller (27 ± 11%) than that of the nonlinear method. We conclude that all loops except the Cauchy stress-Almansi strain loop can be used to estimate artery wall damping capacity in the physiological pressure range and the nonlinear method is recommended over the linear method.

Effect of age and exercise on the viscoelastic properties of rat tail tendon.

Tendon mechanical properties are thought to degrade during aging but improve with exercise. A remaining question is whether exercise in aged animals provides sufficient regenerative, systemic stimulus to restore younger mechanical behaviors. Herein we address that question with tail tendons from aged and exercised rats, which would be subject to systemic effects but not direct loading from the exercise regimen. Twenty-four month old rats underwent one of three treadmill exercise training protocols for 12 months: sedentary (walking at 0° incline for 5 min/day), moderate (running at 0° incline for 30 min/day), or high (running at 4° incline for 30 min/day). A group of 9 month old rats were used to provide an adult control, while a group of 3 month old rats provided a young control. Tendons were harvested at sacrifice and mechanically tested. Results show significant age-dependent differences in modulus, ultimate stress, relaxation rate, and percent relaxation. Relaxation rate was strain-dependent, consistent with nonlinear superposition or Schapery models but not with quasilinear viscoelasticity (QLV). Trends in exercise data suggest that with exercise, tendons assume the elastic character of younger rats (lower elastic modulus and ultimate stress).

Relationship between tendon stiffness and failure: a metaanalysis.

Tendon is a highly specialized, hierarchical tissue designed to transfer forces from muscle to bone; complex viscoelastic and anisotropic behaviors have been extensively characterized for specific subsets of tendons. Reported mechanical data consistently show a pseudoelastic, stress-vs.-strain behavior with a linear slope after an initial toe region. Many studies report a linear, elastic modulus, or Young's modulus (hereafter called elastic modulus) and ultimate stress for their tendon specimens. Individually, these studies are unable to provide a broader, interstudy understanding of tendon mechanical behavior. Herein we present a metaanalysis of pooled mechanical data from a representative sample of tendons from different species. These data include healthy tendons and those altered by injury and healing, genetic modification, allograft preparation, mechanical environment, and age. Fifty studies were selected and analyzed. Despite a wide range of mechanical properties between and within species, elastic modulus and ultimate stress are highly correlated (R(2) = 0.785), suggesting that tendon failure is highly strain-dependent. Furthermore, this relationship was observed to be predictable over controlled ranges of elastic moduli, as would be typical of any individual species. With the knowledge gained through this metaanalysis, noninvasive tools could measure elastic modulus in vivo and reasonably predict ultimate stress (or structural compromise) for diseased or injured tendon.

Mechanical compromise of partially lacerated flexor tendons.

Tendons function to transmit loads from muscle to move and stabilize joints and absorb impacts. Functionality of lacerated tendons is diminished, however clinical practice often considers surgical repair only after 50% or more of the tendon is lacerated, the "50% rule." Few studies provide mechanical insight into the 50% rule. In this study cyclic and static stress relaxation tests were performed on porcine flexor tendons before and after a 0.5, 1.0, 2.0, or 2.75 mm deep transverse, midsubstance laceration. Elastic and viscoelastic properties, such as maximum stress, change in stress throughout each test, and stiffness, were measured and compared pre- and post-laceration. Nominal stress and stiffness parameters decreased, albeit disproportionately in magnitude, with increasing percent loss of cross-sectional area. Conversely, mean stress at the residual area (determined using remaining intact area at the laceration cross section) exhibited a marked increase in stress concentration beginning at 47.2% laceration using both specified load and constant strain analyses. The marked increase in stress concentration beginning near 50% laceration provides mechanical insight into the 50% rule. Additionally, a drastic decrease in viscoelastic stress parameters after only an 8.2% laceration suggests that time-dependent mechanisms protecting tissues during impact loadings are highly compromised regardless of laceration size.

Effects of collagen deposition on passive and active mechanical properties of large pulmonary arteries in hypoxic pulmonary hypertension.

Proximal pulmonary artery (PA) stiffening is a strong predictor of mortality in pulmonary hypertension. Collagen accumulation is mainly responsible for PA stiffening in hypoxia-induced pulmonary hypertension (HPH) in mouse models. We hypothesized that collagen cross-linking and the type I isoform are the main determinants of large PA mechanical changes during HPH, which we tested by exposing mice that resist type I collagen degradation (Col1a1[Formula: see text] and littermate controls (Col1a1[Formula: see text] to hypoxia for 10 days with or without [Formula: see text]-aminopropionitrile (BAPN) treatment to prevent cross-link formation. Static and dynamic mechanical tests were performed on isolated PAs with smooth muscle cells (SMC) in passive and active states. Percentages of type I and III collagen were quantified by histology; total collagen content and cross-linking were measured biochemically. In the SMC passive state, for both genotypes, hypoxia tended to increase PA stiffness and damping capacity, and BAPN treatment limited these increases. These changes were correlated with collagen cross-linking ([Formula: see text]). In the SMC active state, hypoxia increased PA dynamic stiffness and BAPN had no effect in Col1a1[Formula: see text] mice ([Formula: see text]). PA stiffness did not change in Col1a1[Formula: see text] mice. Similarly, damping capacity did not change for either genotype. Type I collagen accumulated more in Col1a1[Formula: see text] mice, whereas type III collagen increased more in Col1a1[Formula: see text] mice during HPH. In summary, PA passive mechanical properties (both static and dynamic) are related to collagen cross-linking. Type I collagen turnover is critical to large PA remodeling during HPH when collagen metabolism is not mutated and type III collagen may serve as a reserve.

Resonant ultrasound spectroscopy of cubes over the full range of Poisson's ratio.

Methods are developed for study of isotropic cubes via resonant ultrasound spectroscopy. To that end, mode structure maps are determined for freely vibrating isotropic cubes via finite element method over the full range of Poisson's ratio ν (-1 to +0.5). The fundamental torsional mode has the lowest frequency provided ν is between about -0.31 and +0.5. Experimental measurements for the mode structures of materials with Poisson's ratio +0.33, +0.3, +0.15, -0.15, and -0.72 are performed using resonant ultrasound spectroscopy and interpreted. Methods are developed to identify pertinent modes. The experimental results match well with the analysis with the exception of some splitting of some modes because of slight material anisotropy. The effects of slight imperfection of specimen shape on the first 10 modes are analyzed for various Poisson's ratios.

Strain-induced damage reduces echo intensity changes in tendon during loading.

Tendon functionality is related to its mechanical properties. Tendon damage leads to a reduction in mechanical strength and altered biomechanical behavior, and therefore leads to compromised ability to carry out normal functions such as joint movement and stabilization. Damage can also accumulate in the tissue and lead to failure. A noninvasive method with which to measure such damage potentially could quantify structural compromise from tendon injury and track improvement over time. In this study, tendon mechanics are measured before and after damage is induced by "overstretch" (strain exceeding the elastic limit of the tissue) using a traditional mechanical test system while ultrasonic echo intensity (average gray scale brightness in a B-mode image) is recorded using clinical ultrasound. The diffuse damage caused by overstretch lowered the stress at a given strain in the tissue and decreased viscoelastic response. Overstretch also lowered echo intensity changes during stress relaxation and cyclic testing. As the input strain during overstretch increased, stress levels and echo intensity changes decreased. Also, viscoelastic parameters and time-dependent echo intensity changes were reduced.

Damage mechanics of porcine flexor tendon: mechanical evaluation and modeling.

Porcine flexor tendons underwent cyclic and stress relaxation testing before and after strain exceeding elastic limit ("overstretch") to examine which mechanical parameters undergo changes following subfailure damage. From these data, we developed an "effective strain" damage model (in which the tendon is modeled as if being pulled to a lower strain). Damage was induced at three strain levels to determine the extent to which post-damage parameter changes were affected by overstretch strain level. We found that diffuse damage induced by overstretch decreased elastic and viscoelastic parameters obtained during testing. The stress response of tendon to strain is therefore altered following damage. We next compared the strain-dependent parameter behavior to damage-dependent behavior to determine the effective strain for each parameter. Effects of damage became more pronounced as strain during overstretch increased; following overstretch to 6.5, 9, or 13% strain, effective strain was 2.43 ± 0.33, 1.98 ± 0.3, or 0.88 ± 0.43% strain, respectively. By determining the effective strain and using it to calculate predicted values of post-damage mechanical parameters, it was possible to predict the stress relaxation behavior of tendons with Schapery's nonlinear viscoelastic model. Using this approach, a single parameter predicts both elastic and viscoelastic compromise from known, strain-dependent behaviors.

Quantification of collagen organization using fractal dimensions and Fourier transforms.

Collagen fibers and fibrils that comprise tendons and ligaments are disrupted or damaged during injury. Fibrillogenesis during healing produces a matrix that is initially quite disorganized, but remodels over time to resemble, but not replicate, the original roughly parallel microstructure. Quantification of these changes is traditionally a laborious and subjective task. In this work we applied two automated techniques, fast Fourier transformation (FFT) and fractal dimension analysis (FA) to quantify the organization of collagen fibers or fibrils. Using multi-photon images of collagen fibers obtained from rat ligament we showed that for healing ligaments, FA differentiates more clearly between the different time-points during healing. Using scanning electron microscopy images of overstretched porcine flexor tendon, we showed that combining FFT and FA measures distinguishes the damaged and undamaged groups more clearly than either method separately.

Effect of storage time on the viscoelastic properties of elastomeric impression materials.

PURPOSE: The aim of this study was to evaluate creep and viscoelastic properties of dental impression materials after different storage times. METHODS: Six commercially available impression materials (one polyether and five silicones) were tested after being stored for 30 min to 2 weeks under both static and dynamic testing. Shear and Young's moduli, dynamic viscosity, loss tangent and other viscoelastic parameters were calculated. Four of the materials were tested 1 h after setting under creep for three hours and recovery was recorder for 50 h. RESULTS: The tested materials showed differences among them, while storage time had significant influence on their properties. Young's modulus E ranged from 1.81 to 12.99 MPa with the polyether material being the stiffest. All of the materials showed linear viscoelastic behavior exhibiting permanent deformation after 50h of creep recovery. CONCLUSION: As storage time affects the materials' properties, pouring time should be limited in the first 48 h after impression.

Time-dependent ultrasound echo changes occur in tendon during viscoelastic testing.

The viscoelastic behavior of tendons has been extensively studied in vitro. A noninvasive method by which to acquire mechanical data would be highly beneficial, as it could lead to the collection of viscoelastic data in vivo. Our lab has previously presented acoustoelasticity as an alternative ultrasound-based method of measuring tendon stress and strain by reporting a relationship between ultrasonic echo intensity (B mode ultrasound image brightness) and mechanical behavior of tendon under pseudoelastic in vitro conditions [Duenwald, S., Kobayashi, H., Frisch, K., Lakes, R., and Vanderby Jr, R., 2011, "Ultrasound Echo is Related to Stress and Strain in Tendon," J. Biomech., 44(3), pp. 424-429]. Viscoelastic properties of the tendons were not examined in that study, so the presence of time-dependent echo intensity changes has not been verified. In this study, porcine flexor tendons were subjected to relaxation and cyclic testing while ultrasonic echo response was recorded. We report that time- and strain history-dependent mechanical properties during viscoelastic testing are manifested in ultrasonic echo intensity changes. We also report that the patterns of the echo intensity changes do not directly mimic the patterns of viscoelastic load changes, but the intensity changed in a repeatable (and therefore predictable) fashion. Although mechanisms need further elucidation, viscoelastic behavior can be anticipated from echo intensity changes. This phenomenon could potentially lead to a more extensive characterization of in vivo tissue behavior.

Viscoelastic properties of low-shrinking composite resins compared to packable composite resins.

The aim of this study was to evaluate the viscoelastic properties of novel low-shrinking composites and compare them to those of packable composites. Six materials were tested: Clearfil Majesty Posterior (CM), ELS Extra Low Shrinkage (EL), Filtek P60 (FP), Filtek Silorane (FS), Prodigy (PR) and Surefil (SU). Static and dynamic testing was performed and materials were tested dry and wet at different temperatures (21°C to 50°C). Shear and flexural modulus, loss tangent, dynamic viscosity, Poisson's ratio and creep recovery were calculated among others. Significant differences were found both between the two groups and between materials belonging to the same group. CM presented the highest shear and flexural modulus and EL the lowest. All materials were softened by an increase of temperature, while FS was the least affected by water and PR showed to be the most susceptible. Different approaches used to overcome polymerization shrinkage lead to materials with different properties.

Resonant ultrasound spectroscopy of cylinders over the full range of Poisson's ratio.

Mode structure maps for freely vibrating cylinders over a range of Poisson's ratio, ν, are desirable for the design and interpretation of experiments using resonant ultrasound spectroscopy (RUS). The full range of isotropic ν (-1 to +0.5) is analyzed here using a finite element method to accommodate materials with a negative Poisson's ratio. The fundamental torsional mode has the lowest frequency provided ν is between about -0.24 and +0.5. For any ν, the torsional mode can be identified utilizing the polarization sensitivity of the shear transducers. RUS experimental results for materials with Poisson's ratio +0.3, +0.16, and -0.3 and a previous numerical study for ν = 0.33 are compared with the present analysis. Interpretation of results is easiest if the length∕diameter ratio of the cylinder is close to 1. Slight material anisotropy leads to splitting of the higher modes but not of the fundamental torsion mode.

Ultrasound echo is related to stress and strain in tendon.

The mechanical behavior of tendons has been well studied in vitro. A noninvasive method to acquire mechanical data would be highly beneficial. Elastography has been a promising method of gathering in vivo tissue mechanical behavior, but it has inherent limitations. This study presents acoustoelasticity as an alternative ultrasound-based method of measuring tendon stress and strain by reporting a relationship between ultrasonic echo intensity (B-mode ultrasound image brightness) and mechanical behavior of tendon in vitro. Porcine digital flexor tendons were cyclically loaded in a mechanical testing system while an ultrasonic echo response was recorded. We report that echo intensity closely follows the applied cyclic strain pattern in time with higher strain protocols resulting in larger echo intensity changes. We also report that echo intensity is related nonlinearly to stress and nearly linearly to strain. This indicates that ultrasonic echo intensity is related to the mechanical behavior in a loaded tissue by an acoustoelastic response, as previously described in homogeneous, nearly incompressible materials. Acoustoelasticity is therefore able to relate strain-dependent stiffness and stress to the reflected echo, even in the processed B-mode signals reflected from viscoelastic and inhomogeneous material such as tendon, and is a promising metric to acquire in vivo mechanical data noninvasively.

Stress relaxation and recovery in tendon and ligament: experiment and modeling.

Accurate joint models require the ability to predict soft tissue behavior. This study evaluates the ability of constitutive equations to predict the nonlinear and viscoelastic behavior of tendon and ligament during stress relaxation testing in a porcine model. Three constitutive equations are compared in their ability to model relaxation, recovery and reloading of tissues. Quasi-linear viscoelasticity (QLV) can fit a single stress relaxation curve, but fails to account for the strain-dependence in relaxation. Nonlinear superposition can fit the single relaxation curve and will account for the strain-dependent relaxation behavior, but fails to accurately predict recovery behavior. Schapery's nonlinear viscoelastic model successfully fits a single relaxation curve, accounts for strain-dependent relaxation behavior, and accurately predicts recovery and reloading behavior. Comparing Schapery's model to QLV and nonlinear superposition, Schapery's method was uniquely capable of fitting the different nonlinearities that arise in stress relaxation curves from different tissues, e.g. the porcine digital flexor tendon and the porcine medial collateral ligament (MCL), as well as predicting subsequent recovery and relaxation curves after initial loads.