Search

Collagen XI is ubiquitous in tissues such as joint cartilage, cancellous bone, muscles, and tendons and is an important contributor during a crucial part in fibrillogenesis. The COL11A1 gene encodes one of three alpha chains of collagen XI. The present study elucidates the role of collagen XI in the establishment of mechanical properties of tendons and ligaments. We investigated the mechanical response of three tendons and one ligament tissues from wild type and a targeted mouse model null for collagen XI: Achilles tendon (ACH), the flexor digitorum longus tendon (FDL), the supraspinatus tendon (SST), and the anterior cruciate ligament (ACL). Area was substantially lower in Col11a1ΔTen/ΔTen ACH, FDL, and SST. Maximum load and maximum stress were significantly lower in Col11a1ΔTen/ΔTen ACH and FDL. Stiffness was lower in Col11a1ΔTen/ΔTen ACH, FDL, and SST. Modulus was reduced in Col11a1ΔTen/ΔTen FDL and SST (both insertion site and midsubstance). Collagen fiber distributions were more aligned under load in both wild type group and Col11a1ΔTen/ΔTen groups. Results also revealed that the effect of collagen XI knockout on collagen fiber realignment is tendon-dependent and location-dependent (insertion versus midsubstance). In summary, this study clearly shows that the regulatory role of collagen XI on tendon and ligament is tissue specific and that joint hypermobility in type II Stickler's Syndrome may in part be due to suboptimal mechanical response of the soft tissues surrounding joints., (Copyright © 2025 by ASME.)

Aging is a primary risk factor for degenerative tendon injuries, yet the etiology and progression of this degeneration are poorly understood. While aged tendons have innate cellular differences that support a reduced ability to maintain mechanical tissue homeostasis, the response of aged tendons to altered levels of mechanical loading has not yet been studied. To address this question, we subjected young and aged murine flexor tendon explants to various levels of in vitro tensile strain. We first compared the effect of static and cyclic strain on matrix remodeling in young tendons, finding that cyclic strain is optimal for studying remodeling in vitro. We then investigated the remodeling response of young and aged tendon explants after 7 days of varied mechanical stimulus (stress deprivation, 1%, 3%, 5%, or 7% cyclic strain) via assessment of tissue composition, biosynthetic capacity, and degradation profiles. We hypothesized that aged tendons would show muted adaptive responses to changes in tensile strain and exhibit a shifted mechanical setpoint, at which the remodeling balance is optimal. Interestingly, we found that 1% cyclic strain best maintains native physiology while promoting extracellular matrix (ECM) turnover for both age groups. However, aged tendons display fewer strain-dependent changes, suggesting a reduced ability to adapt to altered levels of mechanical loading. This work has a significant impact on understanding the regulation of tissue homeostasis in aged tendons, which can inform clinical rehabilitation strategies for treating elderly patients., (Copyright © 2024 by ASME.)

Tendon, ligament, and skeletal muscle are highly organized tissues that largely rely on a hierarchical collagenous matrix to withstand high tensile loads experienced in activities of daily life. This critical biomechanical role predisposes these tissues to injury, and current treatments fail to recapitulate the biomechanical function of native tissue. This has prompted researchers to pursue engineering functional tissue replacements, or dysfunction/disease/development models, by emulating in vivo stimuli within in vitro tissue engineering platforms-specifically mechanical stimulation, as well as active contraction in skeletal muscle. Mechanical loading is critical for matrix production and organization in the development, maturation, and maintenance of native tendon, ligament, and skeletal muscle, as well as their interfaces. Tissue engineers seek to harness these mechanobiological benefits using bioreactors to apply both static and dynamic mechanical stimulation to tissue constructs, and induce active contraction in engineered skeletal muscle. The vast majority of engineering approaches in these tissues are scaffold-based, providing interim structure and support to engineered constructs, and sufficient integrity to withstand mechanical loading. Alternatively, some recent studies have employed developmentally inspired scaffold-free techniques, relying on cellular self-assembly and matrix production to form tissue constructs. Whether utilizing a scaffold or not, incorporation of mechanobiological stimuli has been shown to improve the composition, structure, and biomechanical function of engineered tendon, ligament, and skeletal muscle. Together, these findings highlight the importance of mechanobiology and suggest how it can be leveraged to engineer these tissues and their interfaces, and to create functional multitissue constructs., (Copyright © 2021 by ASME.)

Pregnant women experience weight gain, gait changes, and biochemical fluctuations that impair joint function and alter the maternal skeleton. Hormonal changes increase pelvic ligament laxity in preparation for childbirth and affect peripheral joint laxity. Calcium demands also rise during pregnancy and lactation, resulting in reduced bone mineral density (BMD) and maternal bone loss. Altered tendon properties and bone loss during pregnancy and lactation may impact tendon insertion sites, such as rotator cuff tendons where insertion site ruptures are common. However, the effects of pregnancy and lactation at the tendon-to-bone interface have not been investigated. Therefore, the objective of this study was to evaluate supraspinatus tendon mechanical properties and insertion site microstructure during pregnancy, lactation, and postweaning recovery in female rats. We hypothesized that pregnancy and lactation would compromise supraspinatus tendon mechanical properties and subchondral bone microstructure. Female rats were divided into virgin, pregnancy, lactation, and recovery groups, and supraspinatus tendons were mechanically evaluated. Surprisingly, tendon mechanics was unaffected by pregnancy and lactation. However, tendon modulus decreased two-weeks postweaning. Additionally, tendons failed by bony avulsion at the insertion site, and the lactation group exhibited reduced failure properties corresponding to decreased subchondral bone mineralization. Lactation also resulted in dramatic bone loss at the epiphysis, but trabecular bone microarchitecture recovered postweaning. In conclusion, lactation following pregnancy impaired trabecular bone microstructure and subchondral bone mineralization, leading to reduced supraspinatus tendon-to-bone insertion site failure properties. These findings will contribute toward understanding the pathogenesis of tendon-to-bone disorders., (Copyright © 2020 by ASME.)

Sex differences in the mechanical properties of different musculoskeletal tissues and their impact on tendon function and disease are becoming increasingly recognized. Tendon mechanical properties are influenced by the presence or absence of sex hormones and these effects appear to be tendon- or ligament-specific. The objective of this study was to determine how sex and hormone differences in rats affect supraspinatus tendon and muscle properties. We hypothesized that male supraspinatus tendons would have increased cross-sectional area but no differences in tendon material properties or muscle composition when compared to supraspinatus tendons from female or ovariectomized (OVX) female rats. Uninjured supraspinatus tendons and muscles from male, female, and OVX female rats were collected and mechanical and histological properties were determined. Our analysis demonstrated decreased dynamic modulus and increased hysteresis and cross-sectional area in male tendons. We found that male tendons exhibited decreased dynamic modulus (during low strain frequency sweep and high strain fatigue loading), increased hysteresis, and increased cross-sectional area compared to female and OVX female tendons. Despite robust mechanical differences, tendon cell density and shape, and muscle composition remained unchanged between groups. Interestingly, these differences were unique compared to previously reported sex differences in rat Achilles tendons, which further supports the concept that the effect of sex on tendon varies anatomically. These differences may partially provide a mechanistic explanation for the increased rate of acute supraspinatus tendon ruptures seen in young males.

Advancements in computational musculoskeletal biomechanics are constrained by a lack of experimental measurement under real-time physiological loading conditions. This paper presents the design, configuration, capabilities, accuracy, and repeatability of The University of Texas at El Paso Joint Load Simulator (UTJLS) by testing four cadaver knee specimens with 47 real-time tests including heel and toe squat maneuvers with and without musculotendon forces. The UTJLS is a musculoskeletal simulator consisting of two robotic manipulators and eight musculotendon actuators. Sensors include eight tension load cells, two force/torque systems, nine absolute encoders, and eight incremental encoders. A custom control system determines command output for position, force, and hybrid control and collects data at 2000 Hz. Controller configuration performed forward-dynamic control for all knee degrees-of-freedom (DOFs) except knee flexion. Actuator placement and specimen potting techniques uniquely replicate muscle paths. Accuracy and repeatability standard deviations across specimen during squat simulations were equal or less than 8 N and 5 N for musculotendon actuators, 30 N and 13 N for ground reaction forces (GRFs), and 4.4 N·m and 1.9 N·m for ground reaction moments. The UTJLS is the first of its design type. Controller flexibility and physical design support axis constraints to match traditional testing rigs, absolute motion, and synchronous real-time simulation of multiplanar kinematics, GRFs, and musculotendon forces. System DOFs, range of motion, and speed support future testing of faster maneuvers, various joints, and kinetic chains of two connected joints.

Proteoglycans (PGs) are broadly distributed within many soft tissues and, among other roles, often contribute to mechanical properties. Although PGs, consisting of a core protein and glycosaminoglycan (GAG) sidechains, were once hypothesized to regulate stress/strain transfer between collagen fibrils and help support load in tendon, several studies have reported no changes to tensile mechanics after GAG depletion. Since GAGs are known to help sustain nontensile loading in other tissues, we hypothesized that GAGs might help support shear loading in human supraspinatus tendon (SST), a commonly injured tendon which functions in a complex multiaxial loading environment. Therefore, the objective of this study was to determine whether GAGs contribute to the response of SST to shear, specifically in terms of multiscale mechanical properties and mechanisms of microscale matrix deformation. Results showed that chondroitinase ABC (ChABC) treatment digested GAGs in SST while not disrupting collagen fibers. Peak and equilibrium shear stresses decreased only slightly after ChABC treatment and were not significantly different from pretreatment values. Reduced stress ratios were computed and shown to be slightly greater after ChABC treatment compared to phosphate-buffered saline (PBS) incubation without enzyme, suggesting that these relatively small changes in stress values were not due strictly to tissue swelling. Microscale deformations were also not different after ChABC treatment. This study demonstrates that GAGs possibly play a minor role in contributing to the mechanical behavior of SST in shear, but are not a key tissue constituent to regulate shear mechanics.

Tendons are highly anisotropic and also viscoelastic. For understanding and modeling their 3D deformation, information is needed on their viscoelastic response under off-axis loading. A study was made, therefore, of creep and recovery of bovine digital extensor tendons when subjected to transverse compressive stress of up to ca. 100 kPa. Preconditioned tendons were compression tested between glass plates at increasing creep loads. The creep response was anomalous: the relative rate of creep reduced with the increasing stress. Over each ca. 100 s creep period, the transverse creep deformation of each tendon obeyed a power law dependence on time, with the power law exponent falling from ca. 0.18 to an asymptote of ca. 0.058 with the increasing stress. A possible explanation is stress-driven dehydration, as suggested previously for the similar anomalous behavior of ligaments. Recovery after removal of each creep load was also anomalous. Relative residual strain reduced with the increasing creep stress, but this is explicable in terms of the reducing relative rate of creep. When allowance was made for some adhesion occurring naturally between tendon and the glass plates, the results for a given load were consistent with creep and recovery being related through the Boltzmann superposition principle (BSP). The tendon tissue acted as a pressure-sensitive adhesive (PSA) in contact with the glass plates: explicable in terms of the low transverse shear modulus of the tendons.

Several features of the tendon-to-bone attachment were examined allometrically to determine load transfer mechanisms. The humeral head diameter increased geometrically with animal mass. Area of the attachment site exhibited a near isometric increase with muscle physiological cross section. In contrast, the interfacial roughness as well as the mineral gradient width demonstrated a hypoallometric relationship with physiologic cross-sectional area (PCSA). The isometric increase in attachment area indicates that as muscle forces increase, the attachment area increases accordingly, thus maintaining a constant interfacial stress. Due to the presence of constant stresses at the attachment, the micrometer-scale features may not need to vary with increasing load.

Computational modeling and simulation of neuromusculoskeletal (NMS) systems enables researchers and clinicians to study the complex dynamics underlying human and animal movement. NMS models use equations derived from physical laws and biology to help solve challenging real-world problems, from designing prosthetics that maximize running speed to developing exoskeletal devices that enable walking after a stroke. NMS modeling and simulation has proliferated in the biomechanics research community over the past 25 years, but the lack of verification and validation standards remains a major barrier to wider adoption and impact. The goal of this paper is to establish practical guidelines for verification and validation of NMS models and simulations that researchers, clinicians, reviewers, and others can adopt to evaluate the accuracy and credibility of modeling studies. In particular, we review a general process for verification and validation applied to NMS models and simulations, including careful formulation of a research question and methods, traditional verification and validation steps, and documentation and sharing of results for use and testing by other researchers. Modeling the NMS system and simulating its motion involves methods to represent neural control, musculoskeletal geometry, muscle-tendon dynamics, contact forces, and multibody dynamics. For each of these components, we review modeling choices and software verification guidelines; discuss variability, errors, uncertainty, and sensitivity relationships; and provide recommendations for verification and validation by comparing experimental data and testing robustness. We present a series of case studies to illustrate key principles. In closing, we discuss challenges the community must overcome to ensure that modeling and simulation are successfully used to solve the broad spectrum of problems that limit human mobility.

A relationship between tendon stress and strain and ultrasonic echo intensity has previously been defined in tendons, demonstrating a correlation between tissue stiffness and echo intensity. An analogous relationship between volume-dependent pressure changes and echo intensity changes in inflating lungs would indicate a correlation between lung compliance and echo intensity. Lung compliance is an important metric to diagnose pathologies which affect lung tissue mechanics, such as emphysema and cystic fibrosis. The goal of this study is to demonstrate a correlation between ultrasound echo intensity and lung tissue mechanics in an ex vivo model using a fluid-filled negative pressure bath design which provides a controlled environment for ultrasonic and mechanical measurements. Lungs from 4 male Sprague-Dawley rats were removed and mechanically tested via inflation and deflation in a negative pressure chamber filled with hetastarch. Specific volumes (1, 2, 3, and 4 mL) were removed from the chamber using a syringe to create negative pressure, which resulted in lung inflation. A pressure transducer recorded the pressure around the lungs. From these data, lung compliance was calculated. Ultrasound images were captured through the chamber wall to determine echo intensity (grayscale brightness in the ultrasound image), which was then related to mechanical parameters. Ultrasound images of the lung were successfully captured through the chamber wall with sufficient resolution to deduce echo intensity changes in the lung tissue. Echo intensity (0-255 scale) increased with volumetric changes (18.4 ± 5.5, 22.6 ± 5.1, 26.1 ± 7.5, and 42.9 ± 19.5 for volumetric changes of 1, 2, 3, and 4 mL) in a pattern similar to pressure (-6.8 ± 1.7, -6.8 ± 1.4, -9.4 ± 0.7, and -16.9 ± 6.8 cm H2O for 1, 2, 3, and 4 mL), reflecting changes in lung compliance. Measured rat lung tissue compliance was comparable to reported values from ex vivo lungs (0.178 ± 0.067, 0.378 ± 0.051, 0.427 ± 0.062, and 0.350 ± 0.160 mL/cm H20 for 1, 2, 3, and 4 mL), supporting proof of concept for the experimental method. Changes in echo intensity reflected changes in lung compliance in this ex vivo model, thus, supporting our hypothesis that the stiffness-related changes in echo intensity originally seen in tendon can be similarly detected in lung tissue. The presented ultrasound-based methods allowed measurement of local lung tissue compliance in a controlled environment, however, the methods could be expanded to facilitate both ex vivo and in vivo studies.

Experimental results presented in the literature suggest that humans use a position control strategy to indirectly control force rather than direct force control. Modeling the muscle-tendon system as a third-order linear model, we provide an explanation of why an indirect force control strategy is preferred. We analyzed a third-order muscle system and verified that it is required for a faithful representation of muscle-tendon mechanics, especially when investigating critical damping conditions. We provided numerical examples using biomechanical properties of muscles and tendons reported in the literature. We demonstrated that at maximum isotonic contraction, for muscle and tendon stiffness within physiologically compatible ranges, a third-order muscle-tendon system can be under-damped. Over-damping occurs for values of the damping coefficient included within a finite interval defined by two separate critical limits (such interval is a semi-infinite region in second-order models). An increase in damping beyond the larger critical value would lead the system to mechanical instability. We proved the existence of a theoretical threshold for the ratio between tendon and muscle stiffness above which critical damping can never be achieved; thus resulting in an oscillatory free response of the system, independently of the value of the damping. Under such condition, combined with high muscle activation, oscillation of the system can be compensated only by active control.

Collagen fiber realignment is one mechanism by which tendon responds to load. Re-alignment is altered when the structure of tendon is altered, such as in the natural process of aging or with alterations of matrix proteins, such as proteoglycan expression. While changes in re-alignment and mechanical properties have been investigated recently during development, they have not been studied in (1) aged tendons, or (2) in the absence of key proteoglycans. Collagen fiber re-alignment and the corresponding mechanical properties are quantified throughout tensile mechanical testing in both the insertion site and the midsubstance of mouse supraspinatus tendons in wild type (WT), decorin-null (Dcn(-/-)), and biglycan-null (Bgn(-/-)) mice at three different ages (90 days, 300 days, and 570 days). Percent relaxation was significantly decreased with age in the WT and Dcn(-/-) tendons, but not in the Bgn(-/-) tendons. Changes with age were found in the linear modulus at the insertion site where the 300 day group was greater than the 90 day and 570 day group in the Bgn(-/-) tendons and the 90 day group was smaller than the 300 day and 570 day groups in the Dcn(-/-) tendons. However, no changes in modulus were found across age in WT tendons were found. The midsubstance fibers of the WT and Bgn(-/-) tendons were initially less aligned with increasing age. The re-alignment was significantly altered with age in the WT tendons, with older groups responding to load later in the mechanical test. This was also seen in the Dcn(-/-) midsubstance and the Bgn(-/-) insertion, but not in the other locations. Although some studies have found changes in the WT mechanical properties with age, this study did not support those findings. However, it did show fiber re-alignment changes at both locations with age, suggesting a breakdown of tendon's ability to respond to load in later ages. In the proteoglycan-null tendons however, there were changes in the mechanical properties, accompanied only by location-dependent re-alignment changes, suggesting a site-specific role for these molecules in loading. Finally, changes in the mechanical properties did not occur in concert with changes in re-alignment, suggesting that typical mechanical property measurements alone are insufficient to describe how structural alterations affect tendon's response to load.

Muscle-driven simulations of human and animal motion are widely used to complement physical experiments for studying movement dynamics. Musculotendon models are an essential component of muscle-driven simulations, yet neither the computational speed nor the biological accuracy of the simulated forces has been adequately evaluated. Here we compare the speed and accuracy of three musculotendon models: two with an elastic tendon (an equilibrium model and a damped equilibrium model) and one with a rigid tendon. Our simulation benchmarks demonstrate that the equilibrium and damped equilibrium models produce similar force profiles but have different computational speeds. At low activation, the damped equilibrium model is 29 times faster than the equilibrium model when using an explicit integrator and 3 times faster when using an implicit integrator; at high activation, the two models have similar simulation speeds. In the special case of simulating a muscle with a short tendon, the rigid-tendon model produces forces that match those generated by the elastic-tendon models, but simulates 2-54 times faster when an explicit integrator is used and 6-31 times faster when an implicit integrator is used. The equilibrium, damped equilibrium, and rigid-tendon models reproduce forces generated by maximally-activated biological muscle with mean absolute errors less than 8.9%, 8.9%, and 20.9% of the maximum isometric muscle force, respectively. When compared to forces generated by submaximally-activated biological muscle, the forces produced by the equilibrium, damped equilibrium, and rigid-tendon models have mean absolute errors less than 16.2%, 16.4%, and 18.5%, respectively. To encourage further development of musculotendon models, we provide implementations of each of these models in OpenSim version 3.1 and benchmark data online, enabling others to reproduce our results and test their models of musculotendon dynamics.

Inverse dynamics combined with a constrained static optimization analysis has often been proposed to solve the muscular redundancy problem. Typically, the optimization problem consists in a cost function to be minimized and some equality and inequality constraints to be fulfilled. Penalty-based and Lagrange multipliers methods are common optimization methods for the equality constraints management. More recently, the pseudo-inverse method has been introduced in the field of biomechanics. The purpose of this paper is to evaluate the ability and the efficiency of this new method to solve the muscular redundancy problem, by comparing respectively the musculo-tendon forces prediction and its cost-effectiveness against common optimization methods. Since algorithm efficiency and equality constraints fulfillment highly belong to the optimization method, a two-phase procedure is proposed in order to identify and compare the complexity of the cost function, the number of iterations needed to find a solution and the computational time of the penalty-based method, the Lagrange multipliers method and pseudo-inverse method. Using a 2D knee musculo-skeletal model in an isometric context, the study of the cost functions isovalue curves shows that the solution space is 2D with the penalty-based method, 3D with the Lagrange multipliers method and 1D with the pseudo-inverse method. The minimal cost function area (defined as the area corresponding to 5% over the minimal cost) obtained for the pseudo-inverse method is very limited and along the solution space line, whereas the minimal cost function area obtained for other methods are larger or more complex. Moreover, when using a 3D lower limb musculo-skeletal model during a gait cycle simulation, the pseudo-inverse method provides the lowest number of iterations while Lagrange multipliers and pseudo-inverse method have almost the same computational time. The pseudo-inverse method, by providing a better suited cost function and an efficient computational framework, seems to be adapted to the muscular redundancy problem resolution in case of linear equality constraints. Moreover, by reducing the solution space, this method could be a unique opportunity to introduce optimization methods for a posteriori articulation of preference in order to provide a palette of solutions rather than a unique solution based on a lot of hypotheses.

Numerical simulation of soft tissue mechanical properties is a critical step in developing valuable biomechanical models of live organisms. A cubic Hermitian spline optimization routine is proposed in this paper to model nonlinear experimental force-elongation curves of soft tissues, in particular when modeled as lumped elements. Boundary conditions are introduced to account for the positive definiteness and the particular curvature of the experimental curve to be fitted. The constrained least-square routine minimizes user intervention and optimizes fitting of the experimental data across the whole fitting range. The routine provides coefficients of a Hermitian spline or corresponding knots that are compatible with a number of constraints that are suitable for modeling soft tissue tensile curves. These coefficients or knots may become inputs to user-defined component properties of various modeling software. Splines are particularly advantageous over the well-known exponential model to account for the traction curve flatness at low elongations and to allow for more flexibility in the fitting process. This is desirable as soft tissue models begin to include more complex physical phenomena.

Developing appropriate mathematical models for biological soft tissues such as ligaments, tendons, and menisci is challenging. Stress-strain behavior of these tissues is known to be continuous and characterized by an exponential toe region followed by a linear elastic region. The conventional curve-fitting technique applies a linear curve to the elastic region followed by a separate exponential curve to the toe region. However, this technique does not enforce continuity at the transition between the two regions leading to inaccuracies in the material model. In this work, a Continuous Method is developed to fit both the exponential and linear regions simultaneously, which ensures continuity between regions. Using both methods, three cases were evaluated: idealized data generated mathematically, noisy idealized data produced by adding random noise to the idealized data, and measured data obtained experimentally. In all three cases, the Continuous Method performed superiorly to the conventional technique, producing smaller errors between the model and data and also eliminating discontinuities at the transition between regions. Improved material models may lead to better predictions of nonlinear biological tissues' behavior resulting in improved the accuracy for a large array of models and computational analyses used to predict clinical outcomes.

Measure of the cross-sectional area (CSA) of biological specimens is a primary concern for many biomechanical tests. Different procedures are presented in literature but besides the fact that noncontact techniques are required during mechanical testing, most of these procedures lack accuracy or speed. Moreover, they often require a precise positioning of the specimen, which is not always feasible, and do not enable the measure of the same section during tension. The objective of this study was to design a noncontact, fast, and accurate device capable of acquiring CSA of specimens mounted on a testing machine. A system based on the horizontal linear displacement of two charge-coupled device reflectance laser devices next to the specimen, one for each side, was chosen. The whole measuring block is mounted on a vertical linear guide to allow following the measured zone during sample tension (or compression). The device was validated by measuring the CSA of metallic rods machined with geometrical shapes (circular, hexagonal, semicircular, and triangular) as well as an equine superficial digital flexor tendon (SDFT) in static condition. We also performed measurements during mechanical testing of three SDFTs, obtaining the CSA variations until tendon rupture. The system was revealed to be very fast with acquisition times in the order of 0.1 s and interacquisition time of about 1.5 s. Measurements of the geometrical shapes yielded mean errors lower than 1.4% (n=20 for each shape) while the tendon CSA at rest was 90.29 ± 1.69 mm(2) (n=20). As for the tendons that underwent tension, a mean of 60 measures were performed for each test, which lasted about 2 min until rupture (at 20 mm/min), finding CSA variations linear with stress (R(2)>0.85). The proposed device was revealed to be accurate and repeatable. It is easy to assemble and operate and capable of moving to follow a defined zone on the specimen during testing. The system does not need precise centering of the sample and can perform noncontact measures during mechanical testing; therefore, it can be used to measure variations of the specimen CSA during a tension (or compression) test in order to determine, for instance, the true stress and transverse deformations.

Disk herniation is often considered a cumulative injury in that repetitive stress on the posterior annulus can result in the nucleus pulposus penetrating the annulus fibrosus and eventually extruding posteriorly. Further, it has been documented that the nucleus pulposus works its way through the annulus through clefts, which form as a result of repetitive tensile strain. The annulus fibrosus is viscoelastic in nature and therefore could express different mechanical responses to applied strain at varying rates. Other viscoelastic tissues, including tendons and ligaments, have shown altered mechanical responses to different rates of applied strain, but the response of the annulus to varying rates of strain is largely unknown. The present study examined the mechanical properties of 20 two-layered samples of porcine annulus fibrosus tissue at three distinct rates of applied 20% biaxial strain (20% strain over 20 s (slow), over 10 s (medium), and over 5 s (fast)); these three rates are considered applicable to nontraumatic loading. No differences in the stiffness or maximum stress in each of the two directions of applied strain were observed between the three strain rates. Specifically, the average (standard deviation) moduli calculated at the fast, medium, and slow rates, respectively, in the axial direction were 7.42 MPa (6.06), 7.77 MPa (6.61), and 7.63 MPa (6.67) and 8.22 MPa (8.4), 8.63 MPa (9.00), and 8.49 MPa (8.69) in the circumferential direction. The maximum stress values reached during the fast, medium, and slow rates, respectively, in the axial direction were 0.40 (0.36) MPa, 0.40 (0.36) MPa, and 0.39 (0.35) MPa and 0.45 (0.47) MPa, 0.44 (0.46) MPa, and 0.43 (0.46) MPa in the circumferential direction. At submaximal strain magnitudes over a range of nontraumatic rates likely to result in clefts in the annulus and potentially leading to disk herniation, any strain rate dependence is not significant.

While modeling the trapeziometacarpal (TMC) joint for determination of tendon forces, the TMC has been considered frictionless and passive moments created by soft tissues neglected. This, however, becomes inaccurate when reaching the joint end range of motion and considering that the TMC is entirely crossed by a complex network of skin, ligaments, soft tissues, and tendons. The objective of this study was to evaluate the passive moments with respect to joint posture in order to further include this relationship in biomechanical modeling. An experimental method was proposed to estimate in vivo a global passive moment including the sum of the actions of each passive anatomical structure. An external force was applied at the level of the metacarpophalangeal joint in various directions ranging from neutral position to full extension and full adduction to full abduction. The passive moment was computed and expressed as a function of the adopted joint angles. An exponential regression was then developed to fit the experimental data and to propose a generic passive moment model. Results showed a good agreement between the proposed exponential regression model and the experimental measures. Moreover, it was shown that joint stiffness could represent more than 60% of the net joint moment during a typical pulp grip task. These results showed the necessity to include the data in biomechanical modeling. The results may help predict more realistic tendons force especially in abduction/adduction muscles.

Soft tissue injuries are poorly understood at the molecular level. Previous work using differential scanning calorimetry (DSC) has shown that tendon collagen becomes less thermally stable with rupture. However, most soft tissue injuries do not result in complete tissue rupture but in damaging fiber overextension. Covalent crosslinking, which increases with animal maturity and age, plays an important role in collagenous fiber mechanics. It is also a determinant of tissue strength and is hypothesized to inhibit the loss of thermal stability of collagen due to mechanical damage. Controlled overextension without rupture was investigated to determine if overextension was sufficient to reduce the thermal stability of collagen in the bovine tail tendon (BTT) model and to examine the effects of aging on the phenomenon. Baseline data from DSC and hydrothermal isometric tension (HIT) techniques were compared between two groups: steers aged 24-30 months (young group), and skeletally mature bulls and oxen aged greater than five years (old group). Covalent crosslinks were quantified by ion exchange chromatography. Overextension resulted in reduced collagen thermal stability in the BTT model. The Young specimens, showing detectably lower tissue thermomechanical competence, lost more thermal stability with overextension than did the old specimens. The effect on old specimens, while smaller, was detectable. Multiple overextension cycles increased the loss of stability in the young group. Compositional differences in covalent crosslinking corresponded with tissue thermomechanical competence and therefore inversely with the loss of thermal stability. HIT testing gave thermal denaturation temperatures similar to those measured with DSC. The thermal stability of collagen was reduced by overextension of the tendon--without tissue rupture--and this effect was amplified by increased cycles of overextension. Increased tissue thermomechanical competence with aging seemed to mitigate the loss of collagen stability due to mechanical overextension. Surprisingly, the higher tissue thermomechanical competence did not directly correlate with the concentration of endogenous enzymatically derived covalent crosslinking on a mole per mole of collagen basis. It did, however, correlate with the percentage of mature and thermally stable crosslinks. Compositional changes in fibrous collagens that occur with aging affect fibrous collagen mechanics and partially determine the nature of mechanical damage at the intermolecular level. As techniques develop and improve, this new information may lead to important future studies concerning improved detection, prediction, and modeling of mechanical damage at much finer levels of tissue hierarchy than currently possible.

Orthopaedic research on in vitro forces applied to bones, tendons, and ligaments during joint loading has been difficult to perform because of limitations with existing robotic simulators in applying full-physiological loading to the joint under investigation in real time. The objectives of the current work are as follows: (1) describe the design of a musculoskeletal simulator developed to support in vitro testing of cadaveric joint systems, (2) provide component and system-level validation results, and (3) demonstrate the simulator's usefulness for specific applications of the foot-ankle complex and knee. The musculoskeletal simulator allows researchers to simulate a variety of loading conditions on cadaver joints via motorized actuators that simulate muscle forces while simultaneously contacting the joint with an external load applied by a specialized robot. Multiple foot and knee studies have been completed at the Cleveland Clinic to demonstrate the simulator's capabilities. Using a variety of general-use components, experiments can be designed to test other musculoskeletal joints as well (e.g., hip, shoulder, facet joints of the spine). The accuracy of the tendon actuators to generate a target force profile during simulated walking was found to be highly variable and dependent on stance position. Repeatability (the ability of the system to generate the same tendon forces when the same experimental conditions are repeated) results showed that repeat forces were within the measurement accuracy of the system. It was determined that synchronization system accuracy was 6.7+/-2.0 ms and was based on timing measurements from the robot and tendon actuators. The positioning error of the robot ranged from 10 microm to 359 microm, depending on measurement condition (e.g., loaded or unloaded, quasistatic or dynamic motion, centralized movements or extremes of travel, maximum value, or root-mean-square, and x-, y- or z-axis motion). Algorithms and methods for controlling specimen interactions with the robot (with and without muscle forces) to duplicate physiological loading of the joints through iterative pseudo-fuzzy logic and real-time hybrid control are described. Results from the tests of the musculoskeletal simulator have demonstrated that the speed and accuracy of the components, the synchronization timing, the force and position control methods, and the system software can adequately replicate the biomechanics of human motion required to conduct meaningful cadaveric joint investigations.

Since the direction of the quadriceps force and location of the patellofemoral contact point likely differ between axial and multiplane loadings, the force and moment balance solutions for a multiplane loading condition may not yield the same patella ligament force/quadriceps force ratio (F(PL)/F(Q) ratio) when compared with an axial loading condition. The purpose of this study was to compare the effects of an axial loading condition and an anatomical, multiplane loading condition on the F(PL)/F(Q) ratio at various knee flexion angles. Ten cadaver knees were used in this investigation. Each was mounted on a custom jig that was fixed to an Instron frame. Quadriceps muscle loads were applied with same resultant force magnitudes under two force directions, as follows: (1) axial loading (central quadriceps tendon loading parallel to the femoral axis), and (2) an anatomically based, multiplane loading condition (individual vasti loaded, taking into consideration physiologic muscle fiber orientation). Patellar ligament tension was measured using a buckle transducer. The patellar ligament force/quadriceps force ratio (F(PL)/F(Q) ratio) was calculated for both loading conditions at 0 deg, 20 deg, 40 deg, and 60 deg of knee flexion. Across the range of knee motion evaluated, the F(PL)/F(Q) ratio for the axial loading condition was significantly greater than the F(PL)/F(Q) ratio for the multiplane loading condition. Our results suggest that loading orientation affects the transfer of forces from the quadriceps tendon to the patellar ligament.

Although the overall bulk properties of the Achilles tendon have been measured, there is little information detailing the properties of individual fascicles or their interactions. The knowledge of biomechanical properties at the fascicle-scale is critical in understanding the biomechanical behavior of tendons and for the construction of accurate and detailed computational models. Seven tissue samples (approximately 15x4x1 mm(3)) harvested from four freshly thawed human (all male) tendons, each sample having four to six fascicles, were tested in uniaxial tension. A sequential sectioning protocol was used to isolate interaction effects between adjacent fascicles and to obtain the loading response for a single fascicle. The specimen deformation was measured directly using a novel polarized light imaging system with digital image correlation (DIC) for marker-free deformation measurement. The modulus of the single fascicle was significantly higher compared with the intact fascicle group (single: 226 MPa (SD 179), group: 68 MPa (SD 33)). The interaction effect between the adjacent fascicles was less than 10% of the applied load and evidence of sub- and postfailure fascicle sliding was clearly visible. The DIC direct deformation measurements revealed that the modulus of single fascicles could be as much as three to four times the intact specimen. The consistently higher moduli values of the single (strongest) fascicle indicate that the overall response of the tendon may be dominated by a subset of "strongest" fascicles. Also, fascicle-to-fascicle interactions were small, which was <10% of the overall response. This knowledge is useful for developing computational models representing single fascicle and/or fascicle group mechanical behavior and provides valuable insights into fascicle-scale Achilles tendon material properties.

There is still no agreement on the nature of tissues' viscoelasticity and on its reliable modeling. We speculate that disagreements between previous observations stem from difficulties of separating between viscoelastic and preconditioning effects, since both are manifested by similar response features. Here, this and related issues were studied in the tendon as a prototype for other soft tissues. Sheep digital tendons were preconditioned under strain that was higher by 1% than the one used in subsequent testing. Each specimen was then subjected to stress relaxation, and quick release or creep. A stochastic microstructural viscoelastic theory was developed based on the collagen fibers' properties and on their gradual recruitment with stretch. Model parameters were estimated from stress relaxation data and predictions were compared with the creep data. Following its validation, the new recruitment viscoelasticity (RVE) model was compared, both theoretically and experimentally, with the quasilinear viscoelastic (QLV) theory. The applied preconditioning protocol produced subsequent pure viscoelastic response. The proposed RVE model provided excellent fit to both stress relaxation and creep data. Both analytical and numerical comparisons showed that the new RVE theory and the popular QLV one are equivalent under deformation schemes at which no fibers buckle. Otherwise, the equivalence breaks down; QLV may predict negative stress, in contrast to data of the quick release tests, while RVE predicts no such negative stress. The results are consistent with the following conclusions: (1) fully preconditioned tendon exhibits pure viscoelastic response, (2) nonlinearity of the tendon viscoelasticity is induced by gradual recruitment of its fibers, (3) a new structure-based RVE theory is a reliable representation of the tendon viscoelastic properties under both stress relaxation and creep tests, and (4) the QLV theory is equivalent to the RVE one (and valid) only under deformations in which no fibers buckle. The results also suggest that the collagen fibers themselves are linear viscoelastic.

Determination of the biomechanical properties of soft tissues such as tendons and ligaments is dependent on the accurate measurement of their cross-sectional area (CSA). Measurement methods, which involve contact with the specimen, are problematic because soft tissues are easily deformed. Noncontact measurement methods are preferable in this regard, but may experience difficulty in dealing with the complex cross-sectional shapes and glistening surfaces seen in soft tissues. Additionally, existing CSA measurement systems are separated from the materials testing machine, resulting in the inability to measure CSA during testing. Furthermore, CSA measurements are usually made in a different orientation, and with a different preload, prior to testing. To overcome these problems, a noncontact laser reflectance system (LRS) was developed. Designed to fit in an Instron 8872 servohydraulic test machine, the system measures CSA by orbiting a laser transducer in a circular path around a soft tissue specimen held by tissue clamps. CSA measurements can be conducted before and during tensile testing. The system was validated using machined metallic specimens of various shapes and sizes, as well as different sizes of bovine tendons. The metallic specimens could be measured to within 4% accuracy, and the tendons to within an average error of 4.3%. Statistical analyses showed no significant differences between the measurements of the LRS and those of the casting method, an established measurement technique. The LRS was successfully used to measure the changing CSA of bovine tendons during uniaxial tensile testing. The LRS developed in this work represents a simple, quick, and accurate way of reconstructing complex cross-sectional profiles and calculating cross-sectional areas. In addition, the LRS represents the first system capable of automatically measuring changing CSA of soft tissues during tensile testing, facilitating the calculation of more accurate biomechanical properties.

Collagen is a key structural protein in the extracellular matrix of many tissues. It provides biological tissues with tensile mechanical strength and is enzymatically cleaved by a class of matrix metalloproteinases known as collagenases. Collagen enzymatic kinetics has been well characterized in solubilized, gel, and reconstituted forms. However, limited information exists on enzyme degradation of structurally intact collagen fibers and, more importantly, on the effect of mechanical deformation on collagen cleavage. We studied the degradation of native rat tail tendon fibers by collagenase after the fibers were mechanically elongated to strains of epsilon=1-10%. After the fibers were elongated and the stress was allowed to relax, the fiber was immersed in Clostridium histolyticum collagenase and the decrease in stress (sigma) was monitored as a means of calculating the rate of enzyme cleavage of the fiber. An enzyme mechanokinetic (EMK) relaxation function T(E)(epsilon) in s(-1) was calculated from the linear stress-time response during fiber cleavage, where T(E)(epsilon) corresponds to the zero order Michaelis-Menten enzyme-substrate kinetic response. The EMK relaxation function T(E)(epsilon) was found to decrease with applied strain at a rate of approximately 9% per percent strain, with complete inhibition of collagen cleavage predicted to occur at a strain of approximately 11%. However, comparison of the EMK response (T(E) versus epsilon) to collagen's stress-strain response (sigma versus epsilon) suggested the possibility of three different EMK responses: (1) constant T(E)(epsilon) within the toe region (epsilon<3%), (2) a rapid decrease ( approximately 50%) in the transition of the toe-to-heel region (epsilon congruent with3%) followed by (3) a constant value throughout the heel (epsilon=3-5%) and linear (epsilon=5-10%) regions. This observation suggests that the mechanism for the strain-dependent inhibition of enzyme cleavage of the collagen triple helix may be by a conformational change in the triple helix since the decrease in T(E)(epsilon) appeared concomitant with stretching of the collagen molecule.

The effects of location of aponeurotomy on the muscular mechanics of extramuscularly connected muscle were assessed. Using finite element modeling, extensor digitorum longus muscle of the rat was studied for the effects of aponeurotomy performed in each of three locations on the proximal aponeurosis: (1) a proximal location (case P), (2) an intermediate location (case I), and (3) a distal location (case D). Proximo-distal force differences were more pronounced for more proximal aponeurotomy. The location also affected proximally and distally assessed muscle length-force characteristics: (1) Muscle optimum length and active slack length shifted differentially to higher lengths, increasing slack to optimum length range (for D to P: distally by 15-44%; proximally by 2-6%). (2) Muscle forces decreased at all lengths (e.g., for D to P distal optimal force=88-68% and proximal optimal force=87-60% of intact values, respectively). Increased length range and force decreases were highest for case P, as were effects on muscle geometry: gap length within the proximal aponeurosis; decreased proximal fiber population pennation angle. Parallel, but not serial, heterogeneity of sarcomere length was highest in case P: (a) For the distal fiber population, sarcomere shortening was highest; (b) for the proximal population, sarcomeres were longer. It is concluded that if aponeurotomy is performed closer to the tendon, intended surgical effects are more pronounced. For bi-articular muscle, mechanics of both proximal and distal joints will be affected, which should be considered in selecting the location of aponeurotomy for optimal results at both joints.

Understanding the transformation of tendon forces into joint torques would greatly aid in the investigation of the complex temporal and spatial coordination of multiple muscles in finger movements. In this study, the effects of the finger posture on the tendon force transmission within the finger extensor apparatus were investigated. In five cadaver specimens, a constant force was applied sequentially to the two extrinsic extensor tendons in the index finger, extensor digitorum communis and extensor indicis proprius. The responses to this loading, i.e., fingertip force/moment and regional strains of the extensor apparatus, were measured and analyzed to estimate the tendon force transmission into the terminal and central slips of the extensor hood. Repeated measures analysis of variance revealed that the amount of tendon force transmitted to each tendon slip was significantly affected by finger posture, specifically by the interphalangeal (IP) joint angles (p<0.01). Tendon force transmitted to each of the tendon slips was found to decrease with the IP flexion. The main effect of the metacarpophalangeal (MCP) joint angle was not as consistent as the IP angle, but there was a strong interaction effect for which MCP flexion led to large decreases in the slip forces (>30%) when the IP joints were extended. The ratio of terminal slip force:central slip force remained relatively constant across postures at approximately 1.7:1. Force dissipation into surrounding structures was found to be largely responsible for the observed force-posture relationship. Due to the significance of posture in the force transmission to the tendon slips, the impact of finger posture should be carefully considered when studying finger motor control or examining injury mechanisms in the extensor apparatus.

Connective tissues are biological composites comprising of collagen fibrils embedded in (and reinforcing) the hydrated proteoglycan-rich (PG) gel within the extracellular matrices (ECMs). Age-related changes to the mechanical properties of tissues are often associated with changes to the structure of the ECM, namely, fibril diameter. However, quantitative attempts to correlate fibril diameter to mechanical properties have yielded inconclusive evidence. Here, we described a novel approach that was based on the rule of mixtures for fiber composites to evaluate the dependence of age-related changes in tendon tensile strength (sigma) and stiffness (E) on the collagen fibril cross-sectional area fraction (rho), which is related to the fibril volume fraction. Tail tendons from C57BL6 mice from age groups 1.6-35.3 months old were stretched to failure to determine sigma and E. Parallel measurements of rho as a function of age were made using transmission electron microscopy. Mathematical models (rule of mixtures) of fibrils reinforcing a PG gel in tendons were used to investigate the influence of rho on ageing changes in sigma and E. The magnitudes of sigma, E, and rho increased rapidly from 1.6 months to 4.0 months (P-values <0.05) before reaching a constant (age independent) from 4.0 months to 29.0 months (P-values >0.05); this trend continued for E and rho (P-values >0.05) from 29.0 months to 35.3 months, but not for sigma, which decreased gradually (P-values <0.05). Linear regression analysis revealed that age-related changes in sigma and E correlated positively to rho (P-values <0.05). Collagen fibril cross-sectional area fraction rho is a significant predictor of ageing changes in sigma and E in the tail tendons of C57BL6 mice.

The objective of the present study was to investigate the age-related effects of submaximal static and cyclic loading on the mechanical properties of the vastus lateralis (VL) tendon and aponeurosis in vivo. Fourteen old and 12 young male subjects performed maximal voluntary isometric knee extensions (MVC) on a dynamometer before and after (a) a sustained isometric contraction at 25% MVC and (b) isokinetic contractions at 50% isokinetic MVC, both until task failure. The elongation of the VL tendon and aponeurosis was examined using ultrasonography. To calculate the resultant knee joint moment, the kinematics of the leg were recorded with eight cameras (120 Hz). The old adults displayed significantly lower maximal moments but higher strain values at any given tendon force from 400 N and up in all tested conditions. Neither of the loading protocols influenced the strain-force relationship of the VL tendon and aponeurosis in either the old or young adults. Consequently, the capacity of the tendon and aponeurosis to resist force remained unaffected in both groups. It can be concluded that in vivo tendons are capable of resisting long-lasting static (~4.6 min) or cyclic (~18.5 min) mechanical loading at the attained strain levels (4-5%) without significantly altering their mechanical properties regardless of age. This implies that as the muscle becomes unable to generate the required force due to fatigue, the loading of the tendon is terminated prior to provoking any significant changes in tendon mechanical properties.

Measurement on mechanical properties of the stapedial tendon in human middle ear has not been reported in the literature. In this paper, we used the material testing system to conduct uniaxial tensile, stress relaxation, and failure tests on stapedial tendon specimens harvested from human temporal bones. The digital image correlation method was employed to assess the boundary effect on experimental data. The stress-strain relationship of the tendon obtained from experiments was analyzed using the hyperelastic Ogden model. The results presented include (1) the constitutive equation of the tendon for stretch ratio of 1-1.4 or stress range of 0-1.45 MPa, (2) the mean ultimate stress and stretch ratio of the tendon at 4.04 MPa and 1.65, respectively, and (3) the hysteresis and normalized stress relaxation function of the tendon. The data reported in this paper contribute to ear mechanics, especially for theoretical analysis of human ear function.

Rotator cuff tears frequently occur and can lead to pain and decreased shoulder function. Repair of the torn tendon back to bone is often successful in relieving pain, but failure of the repair commonly occurs. Post-operative activity level is an important treatment component that has received minimal attention for the shoulder, but may have the potential to enhance tendon to bone healing. The objective of this study was to investigate the effect of short and long durations of various activity levels on the healing supraspinatus tendon to bone insertion site. Rotator cuff tears were surgically created in Sprague-Dawley rats by detaching the supraspinatus tendon from its insertion on the humerus and these tears were immediately repaired back to the insertion site. The post-operative activity level was controlled through shoulder immobilization (IM), cage activity (CA), or moderate exercise (EX) for durations of 4 or 16 weeks. The healing tissue was evaluated utilizing biomechanical testing and a quantitative polarized light microscopy method. We found that activity level had no effect on the elastic properties (stiffness, modulus) of the insertion site at four weeks post injury and repair, and a decreased activity level had a positive effect on these properties at 16 weeks (IM>CA=EX). Furthermore, a decreased activity level had the greatest positive effect on these properties over time (IM>CA=EX). The angular deviation of the collagen, a measure of disorganization, was decreased with a decrease in activity level at 4 weeks (IM

Although single-loop tibialis tendon allografts have increased in popularity owing to their many advantages over patellar tendon and double-loop hamstring tendon autografts, some percentage of the patient population do not have clinically stable knees following anterior cruciate ligament reconstruction with single-loop tibialis tendon allografts. Therefore, it would be advantageous to determine the causes of increased anterior laxity which ultimately must be traced to lengthening of the graft construct. One objective of this study was to demonstrate the feasibility of using Roentgen stereophotogrammetric analysis (RSA) to determine the causes of lengthening of a single-loop graft construct subjected to cyclic loading. A second objective was to determine which cause(s) contributes most to an increase in length of this graft construct. Radio-opaque markers were inserted into ten grafts to measure the lengthening at the sites of the tibial and femoral fixations and between the sites of fixation. Each graft was passed through a tibial tunnel in a calf tibia, looped around a rigid cross-pin, and fixed to the tibia with a Washerloc fixation device. The grafts were cyclically loaded for 225,000 cycles from 20 to 170 N. Prior to and at intervals during the cyclic loading, simultaneous radiographs were taken. RSA was used to determine the three-dimensional coordinates of the markers from which the lengthening at the sites of fixation and between the sites of fixation was computed at each interval. The sites of the femoral and tibial fixations were the largest contributors to the increase in length of the graft construct, with maximum average values of 0.68 and 0.55 mm, respectively, after 225,000 cycles. The graft substance between the sites of fixation contributed least to lengthening of the graft, with a maximum average value of 0.31 mm. Ninety percent of the maximum average values occurred before 100,000 cycles of loading for the largest contributors. RSA proved to be a useful method for measuring lengthening due to all three causes. Lengthening of the graft construct at the sites of both fixations is sufficiently large that the combined contributions may manifest as a clinically important increase in anterior laxity.

The effects of frequency or duration of cyclic stress on the mechanical properties of collagen fascicles were studied by means of in vitro tissue culture experiments. Collagen fascicles of approximately 300 microm in diameter were obtained from rabbit patellar tendons. During culture, cyclic stress having the peak stress of approximately 2 MPa was applied to the fascicles at 1 Hz for 1 hour/day (1 Hz-1 h group), at 1 Hz for 4 hours/day (1 Hz-4 h group), or at 4 Hz for 1 hour/day (4 Hz-1 h group). The frequency of 4 Hz and the duration of 1 hour/day are considered to be similar to those of the in vivo stress applied to fascicles in the intact rabbit patellar tendon. After culture for 1 or 2 weeks, the mechanical properties of the fascicles were determined using a microtensile tester, and were compared to the properties of non-cultured, fresh fascicles (control group) and the fascicles cultured under no load condition (non-loaded group). The tangent modulus and tensile strength of fascicles in the 4 Hz-1 h group were similar to those in the control group; however, the fascicles of the 1 Hz-1 h and 1 Hz-4 h groups had significantly lower values than those of the control group. There was no significant difference in the tensile strength between the 1 Hz-1 h and non-loaded groups, although the strength in the 1 Hz-4 h group was significantly higher than that of the non-loaded group. It was concluded that the frequency and duration of cyclic stress significantly affect the mechanical properties of cultured collagen fascicles. If we apply cyclic stress having the frequency and duration which are experienced in vivo, the biomechanical properties are maintained at control, normal level. Lower frequencies or less cycles of applied force induce adverse effects.

The objective of this study was to develop a nonlinear and anisotropic three-dimensional mathematical model of tendon behavior in which the structural components of fibers, matrix, and fiber-matrix interactions are explicitly incorporated and to use this model to infer the contributions of these structures to tendon mechanical behavior. We hypothesized that this model would show that: (i) tendon mechanical behavior is not solely governed by the isotropic matrix and fiber stretch, but is also influenced by fiber-matrix interactions; and (ii) shear fiber-matrix interaction terms will better describe tendon mechanical behavior than bulk fiber-matrix interaction terms. Model versions that did and did not include fiber-matrix interaction terms were applied to experimental tendon stress-strain data in longitudinal and transverse orientations, and the R2 goodness-of-fit was evaluated. This study showed that models that included fiber-matrix interaction terms improved the fit to longitudinal data (R2(toe) = 0.88, R2(Lin) = 0.94) over models that only included isotropic matrix and fiber stretch terms (R2(Toe) = 0.36, R2(Lin) = 0.84). Shear fiber-matrix interaction terms proved to be responsible for the best fit to data and to contribute to stress-strain nonlinearity. The mathematical model of tendon behavior developed in this study showed that fiber-matrix interactions are an important contributor to tendon behavior The more complete characterization of mechanical behavior afforded by this mathematical model can lead to an improved understanding of structure-function relationships in soft tissues and, ultimately, to the development of tissue-engineered therapies for injury or degeneration.

Because thoroughbred racehorses have a high incidence of forelimb musculoskeletal injuries, a model was desired to screen potential risk factors for injuries. This paper describes the development of a musculoskeletal model of the thoroughbred forelimb and a dynamic simulation of the motion of the distal segments during the stance phase of high-speed (18 m/s) gallop. The musculoskeletal model is comprised of segment, joint, muscle-tendon, and ligament information. The dynamic simulation incorporates a proximal forward-driving force, a distal ground reaction force model, muscle activations, and initial positions and velocities. A simulation of the gallop after transection of an accessory ligament demonstrated increased soft tissue strains in the remaining support structures of the distal forelimb. These data were consistent with those previously reported from in vitro experimental data and supported usefulness of the model for the study of distal forelimb soft tissue mechanics during the stance phase of the gallop.

Evaluations of tendon mechanical behavior based on biochemical and structural arrangement have implications for designing tendon specific treatment modalities or replacement strategies. In addition to the well studied type I collagen, other important constituents of tendon are the small proteoglycans (PGs). PGs have been shown to vary in concentration within differently loaded areas of tendon, implicating them in specific tendon function. This study measured the mechanical properties of multiple tendon tissues from normal mice and from mice with knock-outs of the PGs decorin or biglycan. Tail tendon fascicles, patellar tendons (PT), and flexor digitorum longus tendons (FDL), three tissues representing different in vivo loading environments, were characterized from the three groups of mice. It was hypothesized that the absence of decorin or biglycan would have individual effects on each type of tendon tissue. Surprisingly, no change in mechanical properties was observed for the tail tendon fascicles due to the PG knockouts. The loss of decorin affected the PT causing an increase in modulus and stress relaxation, but had little effect on the FDL. Conversely, the loss of biglycan did not significantly affect the PT, but caused a reduction in both the maximum stress and modulus of the FDL. These results give mechanical support to previous biochemical data that tendons likely are uniquely tailored to their specific location and function. Variances such as those presented here need to be further characterized and taken into account when designing therapies or replacements for any one particular tendon.

Background: Tendon's mechanical behaviors have frequently been quantified using the quasi-linear viscoelastic (QLV) model. The QLV parameters are typically estimated by fitting the model to a single-step stress relaxation experiment. Unfortunately, overshoot of the target strain occurs to some degree in most experiments. This has never been formally investigated even though failing to measure, minimize, or compensate for overshoot may cause large errors in the estimation of parameters. Therefore, the objective of this study was to investigate the effect of overshoot on the estimation of QLV parameters., Method of Approach: A simulated experiment was first performed to quantify the effect of different amounts of overshoot on the estimated QLV parameters. Experimental data from tendon was then used to determine if the errors associated with overshoot could be reduced when a direct fit is used (i.e., the actual strain history was used in the curve fit)., Results: We found that both the elastic and viscous QLV parameters were incorrectly estimated if overshoot was not properly accounted for in the fit. Furthermore, the errors associated with overshoot were partially reduced when overshoot was accounted for using a direct fit., Conclusions: A slow ramp rate is recommended to limit the amount of overshoot and a direct fit is recommended to limit the errors associated with overshoot, although other approaches such as adjusting the control system to limit overshoot could also be utilized.

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

Effects of cyclic stress on the mechanical properties of collagen fascicles were studied by in vitro tissue culture experiments. Collagen fascicles (approximately 300 microns in diameter) obtained from the rabbit patellar tendon were applied cyclic load at 4 Hz for one hour per day during culture period for one or two weeks, and then their mechanical properties were determined using a micro-tensile tester. There was a statistically significant correlation between tensile strength and applied peak stress in the range of 0 to 5 MPa, and the relation was expressed by a quadratic function. The maximum strength (19.4 MPa) was obtained at the applied peak stress of 1.8 MPa. The tensile strength of fascicles were within a range of control values, if they were cultured under peak stresses between 1.1 and 2.6 MPa. Similar results were also observed in the tangent modulus, which was maintained at control level under applied peak stresses between 0.9 and 2.8 MPa. The stress of 0.9 to 1.1 MPa is equivalent to approximately 40% of the in vivo peak stress which is developed in the intact rabbit patellar tendon by running, whereas that of 2.6 to 2.8 MPa corresponds to approximately 120% of the in vivo peak stress. Therefore, the fascicles cultured under applied peak stresses of lower than 40% and higher than 120% of the in vivo peak stress do not keep the original strength and modulus. These results indicate that the mechanical properties of cultured collagen fascicles strongly depend upon the magnitude of the stress applied during culture, which are similar to our previous results observed in stress-shielded and overstressed patellar tendons in vivo.

The quasi-linear viscoelastic (QLV) model was applied to incremental stress-relaxation tests and an expression for the stress was derived for each step. This expression was used to compare two methods for normalizing stress data prior to estimating QLV parameters. The first and commonly used normalization method was shown to be strain-dependent. Thus, a second normalization method was proposed and shown to be strain-independent and more sensitive to QLV time constants. These analytical results agreed with representative tendon data. Therefore, this method for normalizing stress data was proposed for future studies of incremental stress-relaxation, or whenever comparing stress-relaxation at different strains.

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 present study deals with the stiffness and damping profiles of the leg joints during the ground-contact phase of hopping. A two-dimensional (sagittal plane) jumping model, consisting of four linked rigid segments and including the paired feet, shanks, thighs, and the head-arms-trunk segment, was developed. The segments were interconnected by damped torsional springs, representing the action of the muscles, tendons and ligaments across the joint and of the other joint tissues. A regressive function was used to express stiffness and damping, and included second-order dependence on angle and first-order dependence on angular velocity. By eliminating redundancies in the numerical solution using multicollinearity diagnostic algorithms, the model results revealed that the correct and sufficient nonlinearity for the joint stiffness is of the first order. Damping was found negligible. The stiffness profiles obtained were bell-shaped with a maximum near midstance and nonzero edge values. In predicting the joint moments, the obtained variable joint stiffnesses provided a closer agreement compared to a constant stiffness model. The maximal stiffness was found to be in linear correlation with the initial stiffness in each joint, providing support to the of muscles' preactivation strategy during the flight phase of hopping. All stiffnesses increased with increasing hopping frequency. The model presented provides an effective tool for future designing of artificial legs and robots and for the development of more accurate control strategies.

This study shows how a probabilistic microstructural model for fibrous connective tissue behavior can be used to objectively describe soft tissue low-load behavior. More specifically, methods to determine tissue reference length and the transition from the strain-stiffening "toe-region" to the more linear region of the stress-strain curve of fibrous connective tissues are presented. According to a microstructural model for uniaxially loaded collagenous tissues, increasingly more fibers are recruited and bear load with increased tissue elongation. Fiber recruitment is represented statistically according to a Weibull probability density function (PDF). The Weibull PDF location parameter in this formulation corresponds to the stretch at which the first fibers begin to bear load and provides a convenient method of determining reference length. The toe-to-linear region transition is defined by utilizing the Weibull cumulative distribution function (CDF) which relates the fraction of loaded fibers to the tissue elongation. These techniques are illustrated using representative tendon and ligament data from the literature, and are shown to be applicable retrospectively to data from specimens that are not heavily preloaded. The reference length resulting from this technique provides an objective datum from which to calculate stretch, strain, and tangent modulus, while the Weibull CDF provides an objective parameter with which to characterize the limits of low-load behavior.

A biomechanical model of the foot is developed and analyzed to determine the distribution of support under the metatarsal heads, the tension in the plantar aponeurosis, and the bending moment at each of the joints of the foot. This model is an extension of our earlier work to include the role of muscles, tendons, and ligaments. Two cases are presented: in the first the center of gravity of the body is over the mid foot, and in the second, the center of gravity is anterior, over the metatarsals, and no support is provided by the heel. The model shows the extent to which the muscles reduce the force in the supporting ligaments at each of the joints and decrease the tension in the plantar aponeurosis, and that this effect is more pronounced when the center of gravity of the body is moved forward.

The tensile stress-strain behavior of ligaments and tendons begins with a toe region that is believed to result from the straightening of crimped collagen fibrils. The in situ mechanical function is mostly confined to this toe region and changes in crimp morphology are believed to be associated with pathological conditions. A relatively new imaging technique, optical coherence tomography (OCT), provides a comparatively inexpensive method for nondestructive investigation of tissue ultrastructure with resolution on the order of 15 microm and the potential for use in a clinical setting. The objectives of this work were to assess the utility of OCT for visualizing crimp period, and to use OCT to determine how crimp period changed as a function of applied tensile strain in rat tail tendon fascicles. Fascicles from rat tail tendons were subjected to 0.5 percent strain increments up to 5 percent and imaged at each increment using OCT. A comparison between OCT images and optical microscopy images taken between crossed polarizing lenses showed a visual correspondence between features indicative of crimp pattern. Crimp pattern always disappeared completely before 3 percent axial strain was reached. Average crimp period increased as strain increased, but both elongation and shortening occurred within single crimp periods during the application of increasing strain to the fascicle.

The time-dependent mechanical properties of sheep digital extensor tendons were studied by sequences of stress-relaxation tests. The results exhibited irreversible preconditioning and reversible viscoelasticity. Preconditioning effects were manifested by stress decay during consecutive stretch cycles to the same strain level, accompanied by elongation of the tendon's reference length. They intensified with increased strain level, and were reduced or became negligible as the strain decreased. The significance of intrinsic response mechanisms was studied via a structural model that includes viscoelasticity, preconditioning, and morphology of the tendon's collagen fibers. Model/data comparisons showed good agreement and good predictive power, suggesting that preconditioning can be integrated into comprehensive material characterization of tendons.

In-vitro tissue culture experiments were performed to study the effects of static stress on the mechanical properties of collagen fascicles obtained from the rabbit patellar tendon. After collagen fascicles having the diameter of approximately 300 microm were cultured for 1 and 2 wk under static stress between 0 and 3 MPa, their mechanical properties and crimp morphology were determined using a micro-tensile tester and a light microscope, respectively. The tensile strength and tangent modulus of the fascicles were significantly decreased by culture under no load compared to control fascicles. A statistically significant correlation, which was described by a quadratic curve, was observed between applied stress and tensile strength. The maximum tensile strength (16.7 MPa) was obtained at the applied stress of 1.2 MPa; the strength was within a range of control values. There was a similar correlation between applied stress and tangent modulus, and the modulus was maintained at control level under 1.3 MPa stress. The stress of 1.2 to 1.3 MPa is equivalent to approximately 50 percent of the peak stress developed in the intact rabbit patellar tendon by running. Strain at failure of cultured collagen fascicles was negatively correlated with applied stress, and that at 1.2 to 1.3 MPa stress was almost the same as the control value. Crimp morphology in the fascicles cultured under about 1.2 MPa stress was similar to that in control fascicles. These results indicate that cultured collagen fascicles change the mechanical properties and structure in response to static tensile stress. In addition, their mechanical properties and structure are maintained at control level if the static stress of 50 percent of in-vivo peak stress is applied.