Effects of stress shielding on the transverse mechanical properties of rabbit patellar tendons

With the aim of studying mechanisms of the remodeling of tendons and ligaments, the effects of stress shielding on the rabbit patellar tendon were studied by performing tensile and stress relaxation tests in the transverse direction. The tangent modulus, tensile strength, and strain at failure of non-treated, control patellar tendons in the transverse direction were 1272 kPa, 370 kPa, and 40.5 percent, respectively, whereas those of the tendons stress-shielded for 1 week were 299 kPa, 108 kPa, and 40.4 percent, respectively. Stress shielding markedly decreased tangent modulus and tensile strength in the transverse direction, and the decreases were larger than those in the longitudinal direction, which were determined in our previous study. For example, tensile strength in the transverse and longitudinal direction decreased to 29 and 50 percent of each control value, respectively, after 1 week stress shielding. In addition, the stress relaxation in the transverse direction of stress-shielded patellar tendons was much larger than that of nontreated, control ones. In contrast to longitudinal tensile tests for the behavior of collagen, transverse tests reflect the contributions of ground substances such as proteoglycans and mechanical interactions between collagen fibers. Ground substances provide lubrication and spacing between fibers, and also confer viscoelastic properties. Therefore, the results obtained from the present study suggest that ground substance matrix, and interfiber and fiber-matrix interactions have important roles in the remodeling response of tendons to stress.     

Continuum description of the Poisson׳s ratio of ligament and tendon under finite deformation

Ligaments and tendons undergo volume loss when stretched along the primary fiber axis, which is evident by the large, strain-dependent Poisson?s ratios measured during quasi-static tensile tests. Continuum constitutive models that have been used to describe ligament material behavior generally assume incompressibility, which does not reflect the volumetric material behavior seen experimentally. We developed a strain energy equation that describes large, strain dependent Poisson?s ratios and nonlinear, transversely isotropic behavior using a novel method to numerically enforce the desired volumetric behavior. The Cauchy stress and spatial elasticity tensors for this strain energy equation were derived and implemented in the FEBio finite element software (www.febio.org). As part of this objective, we derived the Cauchy stress and spatial elasticity tensors for a compressible transversely isotropic material, which to our knowledge have not appeared previously in the literature. Elastic simulations demonstrated that the model predicted the nonlinear, upwardly concave uniaxial stress–strain behavior while also predicting a strain-dependent Poisson?s ratio. Biphasic simulations of stress relaxation predicted a large outward fluid flux and substantial relaxation of the peak stress. Thus, the results of this study demonstrate that the viscoelastic behavior of ligaments and tendons can be predicted by modeling fluid movement when combined with a large Poisson?s ratio. Further, the constitutive framework provides the means for accurate simulations of ligament volumetric material behavior without the need to resort to micromechanical or homogenization methods, thus facilitating its use in large scale, whole joint models.     

Mechanical characteristics of biological soft tissue]

In a detailed study mechanical properties of tendons, muscles, nerves, blood-vessels and skin of just slaughtered pigs have been investigated in nearly stationary stress tests. Tensile tests have produced tensile strength, ultimate stress and their appropriate strains, Young's modulus and the work up to fatigue of samples. In hysteresis tests the deformation work has been determined as a function of numbers of stress cycles. The hysteresis decrease with the number of stress cycles and approaches asymptotically to cero. By preconditioning of tendons, nerves and blood-vessels to steady state significant differences of strain at tensile strength and of Young's modulus have been established. Moreover for nerves the tests have revealed significant deviations of tensile strength. Bruise tests have been carried out with muscle tissue. For the described setup the limit force can be specified, at which pathological changes appear. Subsequently conducted histological investigations have demonstrated this. In dynamical bruise tests there appeared no pathological changes in muscle tissue in spite of higher transmitted energy.     

Elastic energy storage in tendons: mechanical differences related to function and age

We investigated the possibility that tendons that normally experience relatively high stresses and function as springs during locomotion, such as digital flexors, might develop different mechanical properties from those that experience only relatively low stresses, such as digital extensors. At birth the digital flexor and extensor tendons of pigs have identical mechanical properties, exhibiting higher extensibility and mechanical hysteresis and lower elastic modulus, tensile strength, and elastic energy storage capability than adult tendons. With growth and aging these tendons become much stronger, stiffer, less extensible, and more resilient than at birth. Furthermore, these alterations in elastic properties occur to a significantly greater degree in the high-load-bearing flexors than in the low-stress extensors. At maturity the pig digital flexor tendons have twice the tensile strength and elastic modulus but only half the strain energy dissipation of the corresponding extensor tendons. A morphometric analysis of the digital muscles provides an estimate of maximal in vivo tendon stresses and suggests that the muscle-tendon unit of the digital flexor is designed to function as an elastic energy storage element whereas that of the digital extensor is not. Thus the differences in material properties between mature flexor and extensor tendons are correlated with their physiological functions, i.e., the flexor is much better suited to act as an effective biological spring than is the extensor.     

Tensile properties of calcified and uncalcified avian tendons

The mechanical properties of turkey and heron leg tendons have been investigated in dynamic tensile tests. Heron tendons have properties similar to those found for various mammalian tendons. The Young's modulus and the density of turkey tendons increase with increasing calcification. Ultimate tensile stresses are similar to those found for uncalcified tendon, but Young's modulus may reach about 16 GPa, a value normally associated with bone. Calcification lowers the amount of strain energy that can be stored temporarily in the tendons of the legs. The contribution made by elastic strain energy storage to lowering the cost of running is reduced.     

Fatigue damage of human tendons

The study was designed to examine the effects of partial fatigue on specific mechanical parameters which characterise human tendons in vitro. Specimens prepared from 12 intact Extensor digitorum longus tendons of the foot were subjected to partial fatigue, equivalent to 25% of the median fatigue life, by a cyclic square tension-tension stress waveform at the physiological frequency of 4 Hz. The maximum stress was set at a value corresponding to 20% of the calculated ultimate tensile strength (UTS) of 100 MPa. The minimum stress was set at 1% of the UTS. Dynamic characterisation was performed at stress levels of 10% and 20% of the UTS prior to and following partial mechanical fatigue. Subsequent quasi-static tests were performed on some of the specimens. Comparative analysis of the damage ratios (DRs) of quasi-static and dynamic mechanical parameters suggested the use of the DR for dynamic tensile modulus as a good indicator of damage inflicted by mechanical fatigue. Such an approach might be used for an in vivo assessment of tendon damage.     

Water movement in tendon in response to a repeated static tensile load using one-dimensional magnetic resonance imaging

Rabbit Achilles tendons (N = 8) were subjected to tensile loading while internal water movements were followed using NMR. The distribution of the internal water in tendons was measured using a one-dimensional proton-density map that was collected along a radial line oriented transverse to the tendon's long axis. The proton density map was created from fits to T2 relaxation data. The experimental design included two cycles of loading (7.5 N tensile load) and relaxation. The first load application was for 42.67 min: unloaded for 21.33 min, reloaded for 21.33 min, and then unloaded for 21.33 min. Water was redistributed in a time-dependent fashion upon loading: proton density decreased in the core region and increased in the rim region. In addition there was evidence that tensile loading caused water to become NMR visible. In separate, parallel experiments, we studied the mechanical behavior of tendons using identical conditions of uniaxial loading (N = 7). The time constants of water movements were very different from the time constants of mechanical relaxation, indicating that water redistribution is not the sole determining factor of mechanical behavior.     

Confocal microscopy-based three-dimensional cell-specific modeling for large deformation analyses in cellular mechanics

This study introduces a new confocal microscopy-based three-dimensional cell-specific finite element (FE) modeling methodology for simulating cellular mechanics experiments involving large cell deformations. Three-dimensional FE models of undifferentiated skeletal muscle cells were developed by scanning C2C12 myoblasts using a confocal microscope, and then building FE model geometries from the z-stack images. Strain magnitudes and distributions in two cells were studied when the cells were subjected to compression and stretching, which are used in pressure ulcer and deep tissue injury research to induce large cell deformations. Localized plasma membrane and nuclear surface area (NSA) stretches were observed for both the cell compression and stretching simulation configurations. It was found that in order to induce large tensile strains (>5%) in the plasma membrane and NSA, one needs to apply more than ～15% of global cell deformation in cell compression tests, or more than ～3% of tensile strains in the elastic plate substrate in cell stretching experiments. Utilization of our modeling can substantially enrich experimental cellular mechanics studies in classic cell loading designs that typically involve large cell deformations, such as static and cyclic stretching, cell compression, micropipette aspiration, shear flow and hydrostatic pressure, by providing magnitudes and distributions of the localized cellular strains specific to each setup and cell type, which could then be associated with the applied stimuli.     

Local strain measurement reveals a varied regional dependence of tensile tendon mechanics on glycosaminoglycan content

Proteoglycans (PG) and their associated glycosaminoglycan (GAG) side chains are known to play a key role in the bearing of compressive loads in cartilage and other skeletal connective tissues. In tendons and connective tissues that are primarily loaded in tension, the influence of proteoglycans on mechanical behavior is debated due to conflicting experimental evidence that alternately supports or controverts a functional role of proteoglycans in bearing tensile load. In this study we sought to better reconcile these conflicting data by investigating the possibility that GAG content is differentially related to tensile tendon mechanics depending upon the anatomical subregion one considers. To test this hypothesis, we quantified the mechanical consequences of proteoglycan disruption within specific tendon anatomical subregions using an optical–mechanical measurement approach.Achilles tendons from adult mice were treated with chondroitinase ABC to obtain two groups consisting of native tendons and GAG-depleted tendons. All the tendons were mechanically tested and imaged with high-resolution digital video in order to optically quantify tendon strains. Tendon surface strains were locally analyzed in three main subregions: the central midsubstance, and the proximal and distal midsubstance near the muscle and bone insertions, respectively. Upon GAG digestion, the tendon midsubstance softened appreciably near the bone insertion, while elastic modulus in the central and proximal thirds was unchanged. Thus the contribution of PGs to tensile tendon mechanics is not straightforward and points to a heterogeneous and complex structure–function relationship in tendon. This study further highlights the importance of performing local strain analysis with regard to tensile tendon mechanics.     

Micromechanical models of helical superstructures in ligament and tendon fibers predict large Poisson's ratios

Experimental measurements of the Poisson's ratio in tendon and ligament tissue greatly exceed the isotropic limit of 0.5. This is indicative of volume loss during tensile loading. The microstructural origin of the large Poisson's ratios is unknown. It was hypothesized that a helical organization of fibrils within a fiber would result in a large Poisson's ratio in ligaments and tendons, and that this helical organization would be compatible with the crimped nature of these tissues, thus modeling their classic nonlinear stress–strain behavior. Micromechanical finite element models were constructed to represent crimped fibers with a super-helical organization, composed of fibrils embedded within a matrix material. A homogenization procedure was performed to determine both the effective Poisson's ratio and the Poisson function. The results showed that helical fibril organization within a crimped fiber was capable of simultaneously predicting large Poisson's ratios and the nonlinear stress–strain behavior seen experimentally. Parametric studies revealed that the predicted Poisson's ratio was strongly dependent on the helical pitch, crimp angle and the material coefficients. The results indicated that, for physiologically relevant parameters, the models were capable of predicting the large Poisson's ratios seen experimentally. It was concluded that helical organization within a crimped fiber can produce both the characteristic nonlinear stress–strain behavior and large Poisson's ratios, while fiber crimp alone could only account for the nonlinear stress–strain behavior.     

Mechanical characterization of anisotropic planar biological soft tissues using large indentation: a computational feasibility study

Traditionally, the complex mechanical behavior of planar soft biological tissues is characterized by (multi)axial tensile testing. While uniaxial tests do not provide sufficient information for a full characterization of the material anisotropy, biaxial tensile tests are difficult to perform and tethering effects limit the analyses to a small central portion of the test sample. In both cases, determination of local mechanical properties is not trivial. Local mechanical characterization may be performed by indentation testing. Conventional indentation tests, however, often assume linear elastic and isotropic material properties, and therefore these tests are of limited use in characterizing the nonlinear, anisotropic material behavior typical for planar soft biological tissues. In this study, a spherical indentation experiment assuming large deformations is proposed. A finite element model of the aortic valve leaflet demonstrates that combining force and deformation gradient data, one single indentation test provides sufficient information to characterize the local material behavior. Parameter estimation is used to fit the computational model to simulated experimental data. The aortic valve leaflet is chosen as a typical example. However, the proposed method is expected to apply for the mechanical characterization of planar soft biological materials in general.     

Different regions of bovine deep digital flexor tendon exhibit distinct elastic,but not viscous,mechanical properties under both compression and shear loading

Tendons in different locations function in unique, and at times complex, invivo loading environments. Specifically, some tendons are subjected to compression, shear and/or torsion in addition to tensile loading, which play an important role in regulating tendon properties. To date, there have been few studies evaluating tendon mechanics when loaded in compression and shear, which are particularly relevant for understanding tendon regions that experience such non-tensile loading during normal physiologic function. The objective of this study was to evaluate mechanical responses of different regions of bovine deep digital flexor tendons (DDFT) under compressive and shear loading, and correlate structural characteristics to functional mechanical properties. Distal and proximal regions of DDFT were evaluated in a custom-made loading system via three-step incremental stress-relaxation tests. A two-relaxation-time solid linear model was used to describe the viscoelastic response. Results showed large differences in the elastic behavior between regions: distal region stresses were 4–5 times larger than proximal region stresses during compression and 2–3 times larger during shear. Surprisingly, the viscous (i.e., relaxation) behavior was not different between regions for either compression or shear. Histological analysis showed that collagen and proteoglycan in the distal region distributed differently from the proximal region. Results demonstrate mechanical differences between two regions of DDFT under compression and shear loading, which are attributed to variations of composition and microstructural organization. These findings deepen our understanding of structure–function relationships of tendon, particularly for tissues adapted to supporting combinations of tension, compression, and shear in physiological loading environments.     

Site specific inelasticity of arterial tissue

Understanding the mechanical behaviour of arterial tissue is vital to the development and analysis of medical devices targeting diseased vessels. During angioplasty and stenting, stress softening and permanent deformation of the vessel wall occur during implantation of the device, however little data exists on the inelastic behaviour of cardiovascular tissue and how this varies through the arterial tree. The aim of this study was to characterise the magnitude of stress softening and inelastic deformations due to loading throughout the arterial tree and to investigate the anisotropic inelastic behaviour of the tissue. Cyclic compression tests were used to investigate the differences in inelastic behaviour for carotid, aorta, femoral and coronary arteries harvested from 3-4 month old female pigs, while the anisotropic behaviour of aortic and carotid tissue was determined using cyclic tensile tests in the longitudinal and circumferential directions. The differences in inelastic behaviour were correlated to the ratio of collagen to elastin content of the arteries. It was found that larger inelastic deformations occurred in muscular arteries (coronary), which had a higher collagen to elastin ratio than elastic arteries (aorta), where the smallest inelastic deformations were observed. Lower magnitude inelastic deformations were observed in the circumferential tensile direction than in the longitudinal tensile direction or due to radial compression. This may be as a result of non-collagenous components in the artery becoming more easily damaged than the collagen fibres during loading. Stress softening was also found to be dependent on artery type. In the future, computational models should consider such site dependant, anisotropic inelastic behaviour in order to better predict the outcomes of interventional procedures such as angioplasty and stenting.     

A geometric theory of the equilibrium mechanics of fibers in ligaments and tendons.

This paper presents a theoretical analysis of the equilibrium mechanics of bending and twisting fiber geometries in ligaments and tendons. The theory predicts that the bending of loaded fibers is necessarily accompanied by large transverse pressures and pressure gradients. The predicted pressures are especially large at the bone tunnel entries of ligament grafts, where they can equal or exceed the applied tensile loads. Experimental measurements of internal pressures confirm these predictions.     

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

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

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.     

Cell-to-cell variability in deformations across compressed myoblasts

Many biological consequences of external mechanical loads applied to cells depend on localized cell deformations rather than on average whole-cell-body deformations. Such localized intracellular deformations are likely to depend, in turn, on the individual geometrical features of each cell, e.g., the local surface curvatures or the size of the nucleus, which always vary from one cell to another, even within the same culture. Our goal here was to characterize cell-to-cell variabilities in magnitudes and distribution patterns of localized tensile strains that develop in the plasma membrane (PM) and nuclear surface area (NSA) of compressed myoblasts, in order to identify resemblance or differences in mechanical performances across the cells. For this purpose, we utilized our previously developed confocal microscopy-based three-dimensional cell-specific finite element modeling methodology. Five different C2C12 undifferentiated cells belonging to the same culture were scanned confocally and modeled, and were then subjected to compression in the simulation setting. We calculated the average and peak tensile strains in the PM and NSA, the percentage of PM area subjected to tensile strains above certain thresholds and the coefficient of variation (COV) in average and peak strains. We found considerable COV values in tensile strains developing at the PM and NSA (up to ~35%) but small external compressive deformations induced greater variabilities in intracellular strains across cells compared to large deformations. Interestingly, the external deformations needed to cause localized PM or NSA strains exceeding each threshold were very close across the different cells. Better understanding of variabilities in mechanical performances of cells-either of the same type or of different types-is important for interpreting experimental data in any experiments involving delivery of mechanical loads to cells.     

Mechanical properties of the gastrocnemius aponeurosis in wild turkeys

In many muscles, the tendinous structures include both an extramuscular free tendon as well as a sheet-like aponeurosis. In both free tendons and aponeuroses the collagen fascicles are oriented primarily longitudinally, along the muscle's line of action. It is generally assumed that this axis represents the direction of loading for these structures. This assumption is well founded for free tendons, but aponeuroses undergo a more complex loading regime. Unlike free tendons, aponeuroses surround a substantial portion of the muscle belly and are therefore loaded both parallel (longitudinal) and perpendicular (transverse) to a muscle's line of action when contracting muscles bulge to maintain a constant volume. Given this biaxial loading pattern, it is critical to understand the mechanical properties of aponeuroses in both the longitudinal and transverse directions. In this study, we use uniaxial testing of isolated tissue samples from the aponeurosis of the lateral gastrocnemius of wild turkeys to determine mechanical properties of samples loaded longitudinally (along the muscle's line of action) and transversely (orthogonal to the line of action). We find that the aponeurosis has a significantly higher Young's modulus in the longitudinal than in the transverse direction. Our results also show that aponeuroses can behave as efficient springs in both the longitudinal and transverse directions, losing little energy to hysteresis. We also test the failure properties of aponeuroses to quantify the likely safety factor with which these structures operate during muscular force production. These results provide an essential foundation for understanding the mechanical function of aponeuroses as biaxially loaded biological springs.     

Evaluation of four methods of flexor tendon repair for postoperative active mobilization

Active mobilization of repaired flexor tendons requires sufficient suture strength. This study was designed to investigate the suitability of four newly developed and comparatively strong tendon sutures for flexor tendon repair with active digital mobilization. Fifty fresh flexor digitorum profundus tendons were randomly assigned to five groups and repaired using the Tang, cruciate, Robertson, Silfverskiold, and modified Kessler suture methods. The repaired tendons were subjected to mechanical testing in an Instron tensile machine to determine the 2-mm gap formation force, ultimate strength, elastic modulus, and energy to failure of the sutures. The 2-mm gap formation forces of the sutures were 43.0 N for the Tang, 37.4 N for the cruciate, 25.0 N for the Robertson, 32.3 N for the Silfverskiold, and 21.2 N for the modified Kessler methods. The ultimate strength of the sutures was 53.6 N for the Tang, 46.3 N for the cruciate, 41.6 N for the Robertson, 41.0 N for the Silfverskiold, and 24.7 N for the modified Kessler methods. Statistically, the gap formation force and ultimate strength were the highest in the Tang, higher in the cruciate, and the lowest for the Robertson and the modified Kessler methods. The elastic modulus of the repaired tendons, as represented by the linear slope of the force-displacement curve, was also statistically the largest in the Tang, larger in the cruciate, and lowest for the Robertson and modified Kessler methods. Energy to failure was statistically the largest in the Tang, higher in the cruciate, lower in the Silfverskiold and the Robertson, and the lowest for the modified Kessler methods. It was concluded that significant differences exist in mechanical properties of the newly developed tendon suture methods. Among the methods for tendon repair that were tested, the Tang and the cruciate sutures were the best candidates for flexor tendon repair in the hand with postoperative active mobilization because of their superior tensile strength, elastic properties, energy to failure, and reasonable operation time.