Viscoelastic relaxation and recovery of tendon

Comparative mechanical and elastic properties of the dorsal and ventral tendons in the peduncle of harbor porpoise (Phocoena phocoena)

Cetaceans swim via vertical movements of the tail. The tendons located in the caudal peduncle are attached to the caudal vertebrae to generate propulsive oscillations. Arguments have centered on whether the upstrokes and downstrokes of the tail and propulsive flukes are symmetrical or asymmetrical in time. Previous research from kinematics of swimming animals, muscle architecture and histology has supported both conditions. However, the composition and structure of the tendons suggest a potential mechanism to evaluate this disparity. In this study, the tendons of the caudal peduncle of the harbor porpoise (Phocoena phocoena) - specifically, the extensor caudae medialis (ECM) and the extensor caudae lateralis (ECL) from the epaxial muscle, and the medial hypaxialis lumborum (MHL) from the hypaxial muscle - were mechanically tested. Ramp to failure was performed on isolated tendon fascicles. Stress relaxation tests to 3% strain were also performed on fascicles. Polarized light microscopy was used to visualize the fibril crimp as tensile forces were applied to fascicles. Uncrimping of isolated fascicles was visualized at mean strain values between 0.031% and 0.048%. The maximum elastic moduli of fascicles taken to failure were between 1039.5 and 1185.8 MPa. No differences were found in the mechanical performance of the fascicles of the epaxial and hypaxial tendons. The mechanical properties of peduncle fascicles suggest a symmetrical stroke cycle for swimming by the porpoise.

Ultrasound quantitative characterization of tendinopathy with shear wave elastography in an ex vivo porcine tendon model

BACKGROUND

Early detection and treatment of tendinopathy may prevent progression to partial tears or complete rupture. Shear wave elastography (SWE) may help address the need for better tendon pathology characterization. This study aimed to quantify the effect of structural damage in an ex vivo animal tendinopathy model using SWE.

METHODS

Forty-two porcine flexor tendons were injected with a 0.05-mL bolus of 1.5% collagenase solution to induce focal structural damage without surface tears. Control tendons were injected with saline (n = 42). Twenty-one tendons from each group were incubated at 37 °C for 3.5 h, while the remaining 21 from each group were incubated for 7 h. Each group was then divided into three groups of seven, and tendon incisions were made at 25%, 50%, and 75% of the tendon thickness. Tendons were mechanically stretched axially during simultaneous collection of SWE at the injection site.

RESULTS

There were significant differences in shear wave speed (SWS) (saline > collagenase) at 3.5-h incubation (p < 0.001) and 7-h incubation (p < 0.001). Additionally, there was a significant difference in SWS between tendons cut at 25% and tendons cut at 50% and 75% (p = 0.040 and p = 0.001, respectively). Collagenase-treated tendons ruptured at a lower force than saline-treated tendons at both incubation times (both p < 0.001) when controlling for cut depth. Tendons treated with collagenase ruptured at a lower force than the saline control group at each cut thickness (all p < 0.001) controlling for incubation time.

CONCLUSION

In a controlled ex vivo porcine model, SWE can be used to detect structural damage associated with tendinopathy.

RELEVANCE STATEMENT

Shear wave elastography can be used to show differences in abnormal tendons that may be translatable to clinical use as an adjunctive measure of tendon elasticity and injury.

KEY POINTS

Tendon abnormality was quantitatively characterized using shear wave elastography in an ex vivo porcine experimental model. Shear wave speed was an accurate imaging biomarker for tendon health. Shear wave elastography was effective at detecting the extent of tendon damage. Tendons with decreased shear wave speed measurements rupture at smaller applied mechanical force.

Nonlinear time-dependent mechanical behavior of mammalian collagen fibrils

The viscoelastic mechanical behavior of collagenous tissues has been studied extensively at the macroscale, yet a thorough quantitative understanding of the time-dependent mechanics of the basic building blocks of tissues, the collagen fibrils, is still missing. In order to address this knowledge gap, stress relaxation and creep tests at various stress (5-35 MPa) and strain (5-20%) levels were performed with individual collagen fibrils (average diameter of fully hydrated fibrils: 253 ± 21 nm) in phosphate buffered saline (PBS). The experimental results showed that the time-dependent mechanical behavior of fully hydrated individual collagen fibrils reconstituted from Type I calf skin collagen, is described by strain-dependent stress relaxation and stress-dependent creep functions in both the heel-toe and the linear regimes of deformation in monotonic stress-strain curves. The adaptive quasilinear viscoelastic (QLV) model, originally developed to capture the nonlinear viscoelastic response of collagenous tissues, provided a very good description of the nonlinear stress relaxation and creep behavior of the collagen fibrils. On the other hand, the nonlinear superposition (NSP) model fitted well the creep but not the stress relaxation data. The time constants and rates extracted from the adaptive QLV and the NSP models, respectively, pointed to a faster rate for stress relaxation than creep. This nonlinear viscoelastic behavior of individual collagen fibrils agrees with prior studies of macroscale collagenous tissues, thus demonstrating consistent time-dependent behavior across length scales and tissue hierarchies. STATEMENT OF SIGNIFICANCE: Pure stress relaxation and creep experiments were conducted for the first time with fully hydrated individual collagen fibrils. It is shown that collagen nanofibrils have a nonlinear time-dependent behavior which agrees with prior studies on macroscale collagenous tissues, thus demonstrating consistent time-dependent behavior across length scales and tissue hierarchies. This new insight into the non-linear viscoelastic behavior of the building blocks of mammalian collagenous tissues may serve as the foundation for improved macroscale tissue models that capture the mechanical behavior across length scales.

Structural damping renders the hawkmoth exoskeleton mechanically insensitive to non-sinusoidal deformations

Muscles act through elastic and dissipative elements to mediate movement, which can introduce dissipation and filtering which are important for energetics and control. The high power requirements of flapping flight can be reduced by an insect's exoskeleton, which acts as a spring with frequency-independent material properties under purely sinusoidal deformation. However, this purely sinusoidal dynamic regime does not encompass the asymmetric wing strokes of many insects or non-periodic deformations induced by external perturbations. As such, it remains unknown whether a frequency-independent model applies broadly and what implications it has for control. We used a vibration testing system to measure the mechanical properties of isolated Manduca sexta thoraces under symmetric, asymmetric and band-limited white noise deformations. The asymmetric and white noise conditions represent two types of generalized, multi-frequency deformations that may be encountered during steady-state and perturbed flight. Power savings and dissipation were indistinguishable between symmetric and asymmetric conditions, demonstrating that no additional energy is required to deform the thorax non-sinusoidally. Under white noise conditions, stiffness and damping were invariant with frequency, suggesting that the thorax has no frequency-dependent filtering properties. A simple flat frequency response function fits our measured frequency response. This work demonstrates the potential of materials with frequency-independent damping to simplify motor control by eliminating any velocity-dependent filtering that viscoelastic elements usually impose between muscle and wing.

Biomechanical Properties of Knee Medial Collateral Ligament Compared to Palmaris Longus for Ulnar Collateral Ligament Reconstruction

Ulnar collateral ligament reconstruction (UCLR) is frequently performed among injured overhead-throwing athletes. One of the most common graft choices when performing a UCLR is the ipsilateral palmaris longus tendon (PL). The purpose of this study was to investigate the material properties of aseptically processed cadaveric knee collateral ligaments (kMCL) as a potential graft source for UCLR and compare them to the gold standard PL autograft. Each PL and kMCL cadaveric sample was subjected to cyclic preconditioning, stress relaxation, and load-to-failure testing, and the mechanical properties were recorded. PL samples exhibited a greater average decrease in stress compared to the kMCL samples during the stress-relaxation test (p < 0.0001). PL samples also demonstrated a greater average Young's modulus in the linear region of the stress-strain curve compared to the kMCL samples (p < 0.01). The average yield strain and maximum strain of kMCL samples were significantly greater than the PL, p = 0.03 and 0.02, respectively. Both graft materials had comparable maximum toughness and demonstrated a similar ability to deform plastically without rupture. The clinical significance of our result is that prepared knee medial collateral ligament allografts may provide a viable graft material for use in the reconstruction of elbow ligaments.

A Numerical Scheme for Anisotropic Reactive Nonlinear Viscoelasticity

Reactive viscoelasticity is a theoretical framework based on the theory of reactive constrained mixtures that encompasses nonlinear viscoelastic responses. It models a viscoelastic solid as a mixture of strong and weak bonds that maintain the cohesiveness of the molecular constituents of the solid matter. Strong bonds impart the elastic response while weak bonds break and reform into a stress-free state in response to loading. The process of bonds breaking and reforming is modeled as a reaction where loaded bonds are the reactants and bonds reformed into a stress-free state are the products of a reaction. The reaction is triggered by the evolving state of loading. The state of stress in strong bonds is a function of the total strain in the material, whereas the state of stress in weak bonds is based on the state of strain relative to the time that these bonds were reformed. This study introduces two important practical contributions to the reactive nonlinear viscoelasticity framework: (1) normally, the evaluation of the stress tensor involves taking a summation over a continually increasing number of weak bond generations, which is poorly suited for a computational scheme. Therefore, this study presents an effective numerical scheme for evaluating the strain energy density, the Cauchy stress, and spatial elasticity tensors of reactive viscoelastic materials. (2) We provide the conditions for satisfying frame indifference for anisotropic nonlinear viscoelasticity, including for tension-bearing fiber models. Code verifications and model validations against experimental data provide evidence in support of this updated formulation.

Effects of tendon viscoelasticity on the distribution of forces across sutures in a model tendon-to-bone repair

Tears to the rotator cuff often require surgical repair. These repairs often culminate in re-tearing when sutures break through the tendon in the weeks following repair. Although numerous studies have been performed to identify suturing strategies that reduce this risk by balancing forces across sutures, none have accounted for how the viscoelastic nature of tendon influences load sharing. With the aim of providing insight into this problem, we studied how tendon viscoelasticity, tendon stiffness, and suture anchor spacing affect this balancing of forces across sutures. Results from a model of a three-row sutured re-attachment demonstrated that optimized distributions of suture stiffnesses and of the spacing of suture anchors can balance the forces across sutures to within a few percent, even when accounting for tendon viscoelasticity. Non-optimized distributions resulted in concentrated force, typically in the outermost sutures. Results underscore the importance of accounting for viscoelastic effects in the design of tendon to bone repairs.

Exploring the Mechanical Properties and Performance of Type-I Collagen at Various Length Scales: A Progress Report

Collagen is the basic protein of animal tissues and has a complex hierarchical structure. It plays a crucial role in maintaining the mechanical and structural stability of biological tissues. Over the years, it has become a material of interest in the biomedical industries thanks to its excellent biocompatibility and biodegradability and low antigenicity. Despite its significance, the mechanical properties and performance of pure collagen have been never reviewed. In this work, the emphasis is on the mechanics of collagen at different hierarchical levels and its long-term mechanical performance. In addition, the effect of hydration, important for various applications, was considered throughout the study because of its dramatic influence on the mechanics of collagen. Furthermore, the discrepancies in reports of the mechanical properties of collagenous tissues (basically composed of 20-30% collagen fibres) and those of pure collagen are discussed.

Mechanics Of Ultrasonic Neuromodulation In A Mouse Subject

Ultrasound neuromodulation (UNM), where a region in the brain is targeted by focused ultrasound (FUS), which, in turn, causes excitation or inhibition of neural activity, has recently received considerable attention as a promising tool for neuroscience. Despite its great potential, several aspects of UNM are still unknown. An important question pertains to the off-target sensory effects of UNM and their dependence on stimulation frequency. To understand these effects, we have developed a finite-element model of a mouse, including elasticity and viscoelasticity, and used it to interrogate the response of mouse models to focused ultrasound (FUS). We find that, while some degree of focusing and magnification of the signal is achieved within the brain, the induced pressure-wave pattern is complex and delocalized. In addition, we find that the brain is largely insulated, or 'cloaked', from shear waves by the cranium and that the shear waves are largely carried away from the skull by the vertebral column, which acts as a waveguide. We find that, as expected, this waveguide mechanism is strongly frequency dependent, which may contribute to the frequency dependence of UNM effects. Our calculations further suggest that off-target skin locations experience displacements and stresses at levels that, while greatly attenuated from the source, could nevertheless induce sensory responses in the subject.

The Development of a Gracilis and Quadriceps Tendons Calibration Device for Uniaxial Tensile Tests

To determine the biomechanical properties of the distal tendon of the gracilis muscle and the upper third of the quadriceps femoris muscle used for reconstruction of the medial patellofemoral ligament (MPFL), it is necessary to develop a calibration device for specimen preparation for uniaxial tensile tests. The need to develop this device also stems from the fact that there is currently no suitable regulatory or accurate protocol by which soft tissues such as tendons should be tested. In recent studies, various methods have been used to prepare test specimens, such as the use of different ratios of gauge lengths, different gripping techniques, etc., with the aim of obtaining measurable and comparable biomechanical tissue properties. Since tendons, as anisotropic materials, have viscoelastic properties, the guideline for manufacturing calibrator devices was the ISO 527-1:1993 standard, used for testing polymers, since they also have viscoelastic behaviour. The functionality of a calibrator device was investigated by preparing gracilis and quadriceps tendon samples. Fused deposition modeling (FDM) technology was used for the manufacturing of parts with complex geometry. The proposed calibrator could operate in two positions, horizontal and vertical. The maximum gauge length to be achieved was 60 mm, with the maximum tendon length of 120 mm. The average preparation time was 3 min per tendon. It was experimentally proven that it is possible to use a calibrator to prepare tendons for tensile tests. This research can help in the further development of soft tissue testing devices and also in the establishment of standards and exact protocols for their testing.

A hyperelastic model to capture the mechanical behaviour and histological aspects of the soft tissues

It is well established that the soft connective tissues show a nonlinear elastic response that comes from their microstructural arrangement. Tissues' microstructure alters with various physiological conditions and may affect their mechanical responses. Therefore, the accurate prediction of tissue's mechanical response is crucial for clinical diagnosis and treatments. Thus, a physically motivated and mathematically simplified model is required for the accurate prediction of tissues' mechanical and structural responses. This study explored the 'Exp-Ln' hyperelastic model (Khajehsaeid et al., 2013) to capture soft tissues' mechanical and histological behaviour. In this work, uniaxial tensile test data for the belly and back pig skin were extracted from the experiments performed in our laboratory, whereas uniaxial test data for other soft tissues (human skin, tendon, ligament, and aorta) were extracted from the literature. The 'Exp-Ln; and other hyperelastic models (e.g. Money Rivlin, Ogden, Yeoh, and Gent models) were fitted with these experimental data, and obtained results were compared between the models. These results show that the 'Exp-Ln' model could capture the mechanical behaviour of soft tissues more accurately than other hyperelastic models. This model was also found numerically stable for all modes and ranges of deformation. This study also investigated the link between 'Exp-Ln' material parameters and tissue's histological parameters. The histological parameters such as collagen content, fibre free length, crosslink density, and collagen arrangement were measured using staining and ATR-FTIR techniques. The material parameters were found statistically correlated with the histological parameters. Further, 'Exp-Ln' model was implemented in ABAQUS through the VUMAT subroutine, where the mechanical behaviour of various soft tissues was simulated for different modes of deformation. The finite element analysis results obtained using the 'Exp-Ln' model agreed with the experiments and were more accurate than other hyperelastic models. Overall, these results demonstrate the capability of 'Exp-Ln' model to predict the mechanical and structural responses of the soft tissues.

Different Passive Viscoelastic Properties Between the Left and Right Ventricles in Healthy Adult Ovine

Ventricle dysfunction is the most common cause of heart failure, which leads to high mortality and morbidity. The mechanical behavior of the ventricle is critical to its physiological function. It is known that the ventricle is anisotropic and viscoelastic. However, the understanding of ventricular viscoelasticity is much less than that of its elasticity. Moreover, the left and right ventricles (LV&RV) are different in embryologic origin, anatomy, and function, but whether they distinguish in viscoelastic properties is unclear. We hypothesized that passive viscoelasticity is different between healthy LVs and RVs. Ex vivo cyclic biaxial tensile mechanical tests (1, 0.1, 0.01 Hz) and stress relaxation (strain of 3, 6, 9, 12, 15%) were performed for ventricles from healthy adult sheep. Outflow track direction was defined as the longitudinal direction. Hysteresis stress-strain loops and stress relaxation curves were obtained to quantify the viscoelastic properties. We found that the RV had more pronounced frequency-dependent viscoelastic changes than the LV. Under the physiological frequency (1 Hz), the LV was more anisotropic in the elasticity and stiffer than the RV in both directions, whereas the RV was more anisotropic in the viscosity and more viscous than the LV in the longitudinal direction. The LV was quasi-linear viscoelastic in the longitudinal but not circumferential direction, and the RV was nonlinear viscoelastic in both directions. This study is the first to investigate passive viscoelastic differences in healthy LVs and RVs, and the findings will deepen the understanding of biomechanical mechanisms of ventricular function.

Biomechanical, biochemical, and near infrared spectral data of bovine knee ligaments and patellar tendon

Knee joint ligaments and patellar tendon are rope-like tissues that enable the proper function of the knee by connecting the bones that form the joint. A better understanding of ligament structure-function relationships is needed to develop objective and reliable diagnostic methods for ligaments. Recently, arthroscopic near infrared spectroscopy (NIR) has shown the potential to quantitatively evaluate the health of the cartilages and menisci of the knee. In this dataset, we present a unique combination of NIR spectral data, biomechanical properties, and biochemical composition of bovine primary knee ligaments and patellar tendon (10 knees, 50 tissue samples). NIR spectral data were measured at 5 locations in each sample, biomechanical properties were obtained with tensile testing, and biochemical composition was quantified using colorimetric biochemical methods. The data can be reused for investigations of structure-function relationships of knee ligaments and patellar tendon, for the development of NIR spectroscopic methods to quantify the health of these tissues, and to develop new computational models to describe ligament and tendon biomechanics.

Microdamage in the equine superficial digital flexor tendon

The forelimb superficial digital flexor tendon (SDFT) is an energy-storing tendon that is highly susceptible to injury during activities such as galloping and jumping, such that it is one of the most commonly reported causes of lameness in the performance horse. This review outlines the biomechanical and biothermal effects of strain on the SDFT and how these contribute to the accumulation of microdamage. The effect of age-related alterations on strain response and subsequent injury risk is also considered. Given that tendon is a slowly healing and poorly regenerative tissue, prompt detection of early stages of pathology in vivo and timely adaptations to training protocols are likely to have a greater outcome than advances in treatment. Early screening tools and detection protocols could subsequently be of benefit in identifying subclinical signs of degeneration during the training programme. This provides an opportunity for preventative strategies to be implemented to minimise incidences of SDFT injury and reduce recovery periods in elite performance horses. Therefore, this review will focus on the modalities available to implement early screening and prevention protocols as opposed to methods to diagnose and treat injuries.

Biomimetic Tough Gels with Weak Bonds Unravel the Role of Collagen from Fibril to Suprafibrillar Self-Assembly

Biological tissues rich in type I collagen exhibit specific hierarchical fibrillar structures together with remarkable mechanical toughness. However, the role of collagen alone in their mechanical response at different structural levels is not fully understood. Here, it is proposed to rationalize such challenging interplay from a materials science perspective through the subtle control of this protein self-assembly in vitro. It is relied on a spray-processing approach to readily use the collagen phase diagram and set a palette of biomimetic self-assembled collagen gels in terms of suprafibrillar organization. Their mechanical responses unveil the involvement of mechanisms occurring either at fibrillar or suprafibrillar scales. Noticeably, both modulus at early stage of deformations and tensile toughness probe the suprafibrillar organization, while durability under cyclic loading and stress relaxation reflect mechanisms at the fibril level. By changing the physicochemical environment, the interfibrillar interactions are modified toward more biomimetic mechanical responses. The possibility of making tissue-like materials with versatile compositions and toughness opens perspectives in tissue engineering.

Biaxial softening of isolated cerebral arteries following axial overstretch

Arteries play a critical role in carrying essential nutrients and oxygen throughout the brain; however, vessels can become damaged in traumatic brain injury (TBI), putting neural tissue at risk. Even in the absence of hemorrhage, large deformations can disrupt both the physiological and mechanical behavior of the cerebral vessels. Our group recently reported the effect of vessel overstretch on axial mechanics; however, that work did not address possible changes in circumferential mechanics that are critical to the regulation of blood flow. In order to address this in the present work, ovine middle cerebral arteries were isolated and overstretched axially to 10, 20, or 40% beyond the in vivo configuration. Results showed a statistically significant decrease in circumferential stiffness and strain energy, as well as an increase in vessel diameter following 40% overstretch (p < 0.05). These passive changes would lead to a decrease in vascular resistance and likely play a role in previous reports of cellular dysfunction. We anticipate that our findings will both increase understanding of vessel softening phenomena and also promote improved modeling of cerebrovascular mechanics following head trauma.

Nonlinear viscoelastic properties of human dentin under uniaxial tension

OBJECTIVE

Dentin is a viscoelastic tissue that contributes to the load distribution in human teeth and leads to their fracture resistance. Despite previous researches on the time-dependent behavior of dentin, it is not very clear whether the viscoelastic behavior of this tissue is linear or nonlinear, and what viscoelastic constitutive equations mechanically characterize it. Therefore, the aim of this study was to describe the viscoelastic behavior of human dentin and determine the best-fitting viscoelastic model for this tissue.

METHODS

After preparation of human dentin specimens from 50 subjects, tensile stress relaxation tests were performed at 1%, 3%, 5% and 7% strain amplitudes. We first evaluated the viscoelastic linearity of this tissue and then fitted the experimental data using different constitutive models, namely, 2-, 3- and 4-term Prony series for linear viscoelasticity, Fung's quasilinear viscoelastic model, and also Schapery and modified superposition models for nonlinear viscoelasticity.

RESULTS

Despite an almost linear trend at small strains up to 5%, the relaxation rate generally depended on strain amplitude, indicating some degree of nonlinearity in dentine viscoelasticity. According to the results of data fitting using different models, the modified superposition formulation could best capture the viscoelastic behavior of human dentin.

SIGNIFICANCE

In this study, we have quantitatively examined the viscoelastic behavior of human dentin, using a large number of samples. We have obtained the coefficients of various viscoelastic formulations, which can be utilized in subsequent researches on human dentin assuming linear, quasilinear or nonlinear viscoelasticity for this tissue.

Transient Effects of Applying and Removing Strain on the Mechanical Behavior of Rubber

For viscoelastic materials, the relationship between stress and strain depends on time, where the applied strain (or stress) can be expressed as a step function of time. In the present work, we investigated two temporary effects in the response of viscoelastic materials when a given strain is applied and then removed. The application of strain causes a stress response over time, also known as relaxation. By contrast, recovery is the response that occurs following the removal of an applied stress or strain. Both stress and relaxation constitute transient stages of a viscoelastic material exposed to a permanent force. In the current work, we performed several experimental tests to record the recovery in response to the total or partial removal of the strain. By observing and analyzing the mechanical response of the material to strain, we deduced that recovery is a procedure not only related to creep but also to relaxation. Hence, we created a model that simulates the behavior of viscoelastic materials, contributing to the prediction of relevant results concerning different conditions.

A Recruitment Model of Tendon Viscoelasticity That Incorporates Fibril Creep and Explains Strain-Dependent Relaxation

Soft tissues exhibit complex viscoelastic behavior, including strain-rate dependence, hysteresis, and strain-dependent relaxation. In this paper, a model for soft tissue viscoelasticity is developed that captures all of these features and is based upon collagen recruitment, whereby fibrils contribute to tissue stiffness only when taut. We build upon existing recruitment models by additionally accounting for fibril creep and by explicitly modeling the contribution of the matrix to the overall tissue viscoelasticity. The fibrils and matrix are modeled as linear viscoelastic and each fibril has an associated critical strain (corresponding to its length) at which it becomes taut. The model is used to fit relaxation tests on three rat tail tendon fascicles and predict their response to cyclic loading. It is shown that all of these mechanical tests can be reproduced accurately with a single set of constitutive parameters, the only difference between each fascicle being the distribution of their fibril crimp lengths. By accounting for fibril creep, we are able to predict how the fibril length distribution of a fascicle changes over time under a given deformation. Furthermore, the phenomenon of strain-dependent relaxation is explained as arising from the competition between the fibril and matrix relaxation functions.

Non-minimum phase viscoelastic properties of soft biological tissues

Understanding the viscoelastic properties of biological tissues is important because they can reveal tissue structure. This study analyzes the viscoelastic properties of soft biological tissues using a fractional dynamics model. We conducted a dynamic viscoelastic test on several porcine samples, i.e., liver, breast, and skeletal muscle tissues, using a plate-plate rheometer. We found that some soft biological tissues have non-minimum phase properties, i.e., the relationship between compliance and phase delay is not uniquely related to the non-integer derivative order in the fractional dynamics model. The experimental results show that the actual phase delay is larger than that estimated from compliance. We propose an empirical model to represent these non-minimum phase properties; a fractional Maxwell model with the fractional Hilbert transform term is proposed. The model and experimental results were highly correlated in terms of compliance and phase diagrams, and complex mechanical impedance. We also show that the amount of additional phase delay, defined as the increase in actual phase delay compared to that estimated from compliance, differs with tissue type.

Biomechanical pathways of dentoalveolar fibrous joints in health and disease

Spatial and temporal adaptations within periodontal tissues and their interfaces result from functional loads. Functional loads can be physiologic and/or pathologic in nature. The prolonged effect of these loads can alter the overall biomechanics of a dentoalveolar fibrous joint (dentoalveolar joint) by changing the form of the tooth root and its socket. This "sculpting" of the tooth root and alveolar bony socket is a consequence of several mechano-biological changes that occur within the periodontal complex of a load-bearing dentoalveolar joint. These include changes in biochemical expressions, structure, elemental composition, and mechanical properties of alveolar bone, the underlying tissues of the roots of teeth, and their interfaces. These physicochemical changes in tissues continue to prompt mechano-responsive biochemical activities at the attachment sites of periodontal ligament (soft) with bone (hard), and ligament with cementum (hard), which are the entheses of a load-bearing dentoalveolar joint. Forces at soft-hard tissue attachment sites between disparate materials with different stiffness values theoretically generate strain singularities or discontinuities. These discontinuities under prolonged functional loading increase the probability for failure to occur specifically at the enthesial zones. However, in a normal dentoalveolar joint, gradual stiffness gradients exist from ligament to bone, and from ligament to cementum. The gradual transitions in stiffness from softer ligament (lower stiffness) to harder bone or cementum (higher stiffness) or vice versa optimize tissue and interfacial strains. Optimization of tissue and ligament-enthesial physical and chemical properties facilitates transmission of cyclic forces of varying magnitudes and frequencies that collectively maintain the overall biomechanics of a dentoalveolar joint. The objectives of this review are 3-fold: (i) to illustrate physicochemical adaptations at the periodontal ligament entheses of a human periodontal complex affected by subgingival calculus; (ii) to demonstrate how to "program" the hallmarks of periodontitis in small-scale vertebrates in vivo to generate spatiotemporal maps of physicochemical adaptations in a diseased dentoalveolar joint; and (iii) to correlate dentoalveolar joint biomechanics in healthy and diseased states to spatiotemporal maps of physicochemical adaptations within respective periodontal tissues. This interdisciplinary approach demonstrates that physicochemical adaptations within periodontal tissues using the mechanics of materials (tissue mechanics), materials science (tissue composition), and mechano-biology (matrix molecules) can help explain the mechano-adaptation of dentoalveolar joints in normal and diseased functional states. Multiscale biomechanics and mechano-biology approaches can provide insights into the functional competence of a diseased relative to a normal dentoalveolar joint. Insights gathered from interdisciplinary and multiscale biomechanics approaches include the following: (i) physiologic loads related to chewing maintain a balance between mineral-forming and-resorbing biochemical cellular events, resulting in gradual stiffness gradients at the periodontal ligament entheses, and, in turn, sustain the overall biomechanics of a normal "healthy" dentoalveolar joint; (ii) pathologic loads resulting from tissue degradation and physical changes to the periodontal complex promote an abrupt stiffness gradient at the periodontal ligament entheses. The shift from gradual to an abrupt stiffness gradient could prompt a shift in the biochemical cascades, exacerbate mechano-responsive biochemical expressions at periodontal ligament entheses farther away from the site of insult, and culminate in joint degradation; (iii) sustained pathologic function on periodontally diseased joints exacerbates degradation of periodontal ligament entheses providing insights into "rescue therapy", such as the use of an adequate "mechanocal dose" to regain joint function; and (iv) spatiotemporal maps of changes in biochemical expressions, and physicochemical properties of strain-dominated affected sites, including the periodontal ligament entheses, can guide anatomy-specific therapeutics for tissue regeneration and/or disease control with the purpose of regaining dentoalveolar joint function. Modulation of occlusal loads could minimize disease progression and potentially assist in regaining functional attachment of ligament to bone and/or ligament to cementum of the dentoalveolar joint. Elucidating mechanisms that drive the breakdown of the functionally active periodontal complex burdened with microbes will provide the required critical insights into regenerative medicine and/or biomimetic approaches that would facilitate rescue/regain of dentoalveolar joint function.

Loading Rate Has Little Influence on Tendon Fascicle Mechanics

Mechanically, tendons behave like springs and store energy by stretching in proportion to applied stress. This relationship is potentially modified by the rate at which stress is applied, a phenomenon known as viscosity. Viscoelasticity, the combined effects of elasticity and viscosity, can affect maximum strain, the amount of stored energy, and the proportion of energy recovered (resilience). Previous studies of tendons have investigated the functional effects of viscoelasticity, but not at the intermediate durations of loading that are known to occur in fast locomotor events. In this study, we isolated tendon fascicles from rat tails and performed force-controlled tensile tests at rates between ∼10 MPa s^–1 to ∼80 MPa s^–1. At high rates of applied stress, we found that tendon fascicles strained less, stored less energy, and were more resilient than at low rates of stress (p = 0.007, p = 0.040, and p = 0.004, respectively). The measured changes, however, were very small across the range of strain rates studied. For example, the average strain for the slowest loading rate was 0.637% while it was 0.614% for the fastest loading. We conclude that although there is a measurable effect of loading rate on tendon mechanics, the effect is small and can be largely ignored in the context of muscle-actuated locomotion, with the possible exception of extreme muscle-tendon morphologies.

Objective assessment of stiffness in the gastrocnemius muscle in patients with symptomatic Achilles tendons

OBJECTIVES

To establish quantitative values of stiffness for the gastrocnemius muscle in patients diagnosed with Achilles tendinopathy.

DESIGN

Case-control study with a single (cross sectional) time point of patients diagnosed with unilateral Achilles tendinopathy and an asymptomatic group.

METHODS

Sample of 50 participants: 25 participants with symptomatic unilateral Achilles tendinopathy (symptomatic group) with the asymptomatic side of this group used as a control (control group 1). A third group of 25 participants with asymptomatic Achilles tendons (control group 2). Mechanical stiffness parameters, including natural oscillation frequency (F), dynamic stiffness (S), mechanical stress relaxation time (R), logarithmic decrement (D) and creep (C), were assessed using the MyotonPRO. Measurements at the medial and lateral gastrocnemii were taken as non-weight bearing (NWB) and weight bearing (WB).

RESULTS

Significant (p<0.05) differences were observed between the mean symptomatic group and control groups 1 and 2 in the WB and NWB conditions for natural oscillation frequency (F), dynamic stiffness (S), and creep (C). There was a significant reduction in S WB and conversely a significant increase in S of the symptomatic group NWB. Creep (C) and mechanical stress relaxation time (R) were significantly (p<0.05) less in the symptomatic group NWB. Significant differences were observed between the NWB and WB data sets for logarithmic decrement (D). NWB D demonstrated significantly (p<0.05) higher scores than the WB condition.

CONCLUSION

This study demonstrated that there was a significant reduction in stiffness of the gastrocnemius muscle in participants with Achilles tendinopathy compared with the two control groups. The WB MyotonPRO measures for the symptomatic groups of F and S were significantly lower, indicating a decrease in the tonal properties (F) and dynamic stiffness (S) of the muscle. The application of MyotonPRO technology to measure changes in stiffness in the gastrocnemius muscle may be useful to measure as part of a rehabilitation programme where specific attention could be placed to increase the tonal properties of the muscle. Further studies are required to develop a robust clinical application of this technology, particularly with regard to Achilles tendinopathy.

Strain state dependent anisotropic viscoelasticity of tendon-to-bone insertion

Tendon-to-bone insertion tissues may be considered as functionally-graded connective tissues, providing a gradual transition from soft tendon to hard bone tissue, and functioning to alleviate stress concentrations at the junction of these tissues. The tendon-to-bone insertion tissues demonstrate pronounced viscoelastic behavior, like many other biological tissues, and are designed by the nature to alleviate stress at physiological load rates and strains states. In this paper we present experimental data showing that under biaxial tension tendon-to-bone insertion demonstrates rate-dependent behavior and that stress-strain curves for the in-plane components of stress and strain become less steep when strain rate is increased, contrary to a typical viscoelastic behavior, where the opposite trend is observed. Such behavior may indicate the existence of a protective viscoelastic mechanism reducing stress and strain during a sudden increase in mechanical loading, known to exist in some biological tissues. The main purpose of the paper is to show that such viscoelastic stress reduction indeed possible and is thermodynamically consistent. We, therefore, propose an anisotropic viscoelasticity model for finite strain. We identify the range of parameters for this model which yield negative viscoelastic contribution into in-plane stress under biaxial state of strain and simultaneously satisfy requirements of thermodynamics. We also find optimal parameters maximizing the observed protective viscoelastic effect for this particular state of strain. This model will be useful for testing and describing viscoelastic materials and for developing interfaces for dissimilar materials, considering rate effect and multiaxial loadings.

Objective assessment of stiffness in Achilles tendinopathy: a novel approach using the MyotonPRO

Objectives

The aim of this study was to establish quantitative values for asymptomatic and symptomatic Achilles tendons.

Design

Cohort study with a single (cross-sectional) time point of patients diagnosed with unilateral Achilles tendinopathy and an asymptomatic group with comparative homogeneity.

Methods

A sample of 50 participants: 25 diagnosed with symptomatic unilateral Achilles tendinopathy (AT group) and 25 with asymptomatic Achilles tendons (control group 2). The asymptomatic side of the AT group was used as a control (control group 1). Measurements at 2 cm intervals on the tendon from its insertion at the calcaneum up to the musculotendinous junction were taken non-weight bearing (NWB) and weight bearing (WB) using the MyotonPRO.

Results

There was a significant (p<0.005) decrease in natural oscillation frequency (F) at points 2, 3 and 4 of the AT group (NWB condition) and points 2 and 3 for the WB condition. There was a significant (p<0.005) increase in logarithmic decrement (D) at points 2 and 3 signifying a decrease in elasticity. Dynamic stiffness (S) was significantly (p<0.005) reduced in the AT group at points 2 and 3 WB and point 3 WB. There was no significant difference in creep (C) observed between the symptomatic and asymptomatic tendons. There was a significant (p<0.005) increase in mechanical stress relaxation time (R) at point 2 NWB.There was a correlation between body weight and gender on tendon mechanics, with the symptomatic tendons. No significant differences were observed between the control group 1 and control group 2.

Conclusions

The MyotonPRO measured decreased stiffness over a section of the tendon corresponding clinically with Achilles tendinopathy. This may have potential in identifying risk of injury and informing rehabilitation, however further extensive research is required to generate baseline data for specific population groups monitoring variables over time. Age, gender and body mass index appear to have some bearing on the mechanical properties of the tendon but mainly in the tendinopathy group.

Dynamic Loading and Tendon Healing Affect Multiscale Tendon Properties and ECM Stress Transmission

The extracellular matrix (ECM) is the primary biomechanical environment that interacts with tendon cells (tenocytes). Stresses applied via muscle contraction during skeletal movement transfer across structural hierarchies to the tenocyte nucleus in native uninjured tendons. Alterations to ECM structural and mechanical properties due to mechanical loading and tissue healing may affect this multiscale strain transfer and stress transmission through the ECM. This study explores the interface between dynamic loading and tendon healing across multiple length scales using living tendon explants. Results show that macroscale mechanical and structural properties are inferior following high magnitude dynamic loading (fatigue) in uninjured living tendon and that these effects propagate to the microscale. Although similar macroscale mechanical effects of dynamic loading are present in healing tendon compared to uninjured tendon, the microscale properties differed greatly during early healing. Regression analysis identified several variables (collagen and nuclear disorganization, cellularity, and F-actin) that directly predict nuclear deformation under loading. Finite element modeling predicted deficits in ECM stress transmission following fatigue loading and during healing. Together, this work identifies the multiscale response of tendon to dynamic loading and healing, and provides new insight into microenvironmental features that tenocytes may experience following injury and after cell delivery therapies.

Regenerative Engineering of the Rotator Cuff of the Shoulder

Rotator cuff tears often heal poorly, leading to re-tears after repair. This is in part attributed to the low proliferative ability of the resident cells (tendon fibroblasts and tendon-stem cells) upon injury to the rotator cuff tissue and the low vascularity of the tendon insertion. In addition, surgical outcomes of current techniques used in clinical settings are often suboptimal, leading to the formation of neo-tissue with poor biomechanics and structural characteristics, which results in re-tears. This has prompted interest in a new approach, which we term as "Regenerative Engineering", for regenerating rotator cuff tendons. In the Regenerative Engineering paradigm, roles played by stem cells, scaffolds, growth factors/small molecules, the use of local physical forces, and morphogenesis interplayed with clinical surgery techniques may synchronously act, leading to synergistic effects and resulting in successful tissue regeneration. In this regard, various cell sources such as tendon fibroblasts and adult tissue-derived stem cells have been isolated, characterized, and investigated for regenerating rotator cuff tendons. Likewise, numerous scaffolds with varying architecture, geometry, and mechanical characteristics of biologic and synthetic origin have been developed. Furthermore, these scaffolds have been also fabricated with biochemical cues (growth factors and small molecules), facilitating tissue regeneration. In this Review, various strategies to regenerate rotator cuff tendons using stem cells, advanced materials, and factors in the setting of physical forces under the Regenerative Engineering paradigm are described.

Mechanisms of Plastic Deformation in Collagen Networks Induced by Cellular Forces

Contractile cells can reorganize fibrous extracellular matrices and form dense tracts of fibers between neighboring cells. These tracts guide the development of tubular tissue structures and provide paths for the invasion of cancer cells. Here, we studied the mechanisms of the mechanical plasticity of collagen tracts formed by contractile premalignant acinar cells and fibroblasts. Using fluorescence microscopy and second harmonic generation, we quantified the collagen densification, fiber alignment, and strains that remain within the tracts after cellular forces are abolished. We explained these observations using a theoretical fiber network model that accounts for the stretch-dependent formation of weak cross-links between nearby fibers. We tested the predictions of our model using shear rheology experiments. Both our model and rheological experiments demonstrated that increasing collagen concentration leads to substantial increases in plasticity. We also considered the effect of permanent elongation of fibers on network plasticity and derived a phase diagram that classifies the dominant mechanisms of plasticity based on the rate and magnitude of deformation and the mechanical properties of individual fibers. Plasticity is caused by the formation of new cross-links if moderate strains are applied at small rates or due to permanent fiber elongation if large strains are applied over short periods. Finally, we developed a coarse-grained model for plastic deformation of collagen networks that can be employed to simulate multicellular interactions in processes such as morphogenesis, cancer invasion, and fibrosis.

The development and validation of a numerical integration method for non-linear viscoelastic modeling

Compelling evidence that many biological soft tissues display both strain- and time-dependent behavior has led to the development of fully non-linear viscoelastic modeling techniques to represent the tissue’s mechanical response under dynamic conditions. Since the current stress state of a viscoelastic material is dependent on all previous loading events, numerical analyses are complicated by the requirement of computing and storing the stress at each step throughout the load history. This requirement quickly becomes computationally expensive, and in some cases intractable, for finite element models. Therefore, we have developed a strain-dependent numerical integration approach for capturing non-linear viscoelasticity that enables calculation of the current stress from a strain-dependent history state variable stored from the preceding time step only, which improves both fitting efficiency and computational tractability. This methodology was validated based on its ability to recover non-linear viscoelastic coefficients from simulated stress-relaxation (six strain levels) and dynamic cyclic (three frequencies) experimental stress-strain data. The model successfully fit each data set with average errors in recovered coefficients of 0.3% for stress-relaxation fits and 0.1% for cyclic. The results support the use of the presented methodology to develop linear or non-linear viscoelastic models from stress-relaxation or cyclic experimental data of biological soft tissues.

Viscoelasticity of Tendons Under Transverse Compression

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.

Impact of rest duration on Achilles tendon structure and function following isometric training

Intervention programs are often sought to strengthen the Achilles tendon (AT) due to its high injury rate. Long rest periods between loading cycles have been found to increase collagen synthesis by tenocytes, suggesting rest duration may be important for tendon adaptation in vivo; however, exercise programs comparing long and short rest duration have not been directly compared. Fourteen adults completed a 12-week progressive training intervention; training sessions consisted of 5×10 isometric plantarflexion contractions each of 3-s duration performed at 90% of MVC three times weekly. Each leg was randomly allocated to long (LRT, 10-s rest) or short rest training (SRT, 3-s rest). We hypothesized that the leg allocated to LRT would demonstrate superior AT collagen organization compared to the leg receiving SRT, which would be related to improved biomechanical function. AT collagen organization and morphology were measured using ultrasound tissue characterization. AT properties were assessed before and after the intervention using a combination of dynamometry, ultrasound imaging, EMG, and motion capture. Contrary to our hypothesis, collagen organization did not improve following either training protocol; conversely, an unexpected decrease in echotype I proportion was seen after SRT (P<.001) but not LRT (P=.58), indicating an apparent protective effect of rest on collagen organization during isometric training. In contrast, AT adaptation was not appreciably enhanced by increasing intercycle rest duration; both protocols were equally effective at inducing significant strength gains and AT mechanical and material adaptation (P≤.001). Further research is necessary to identify optimal loading characteristics for injury prevention and rehabilitation.

Investigating mechanisms of tendon damage by measuring multi-scale recovery following tensile loading

Tendon pathology is associated with damage. While tendon damage is likely initiated by mechanical loading, little is known about the specific etiology. Damage is defined as an irreversible change in the microstructure that alters the macroscopic mechanical parameters. In tendon, the link between mechanical loading and microstructural damage, resulting in macroscopic changes, is not fully elucidated. In addition, tendon damage at the macroscale has been proposed to initiate when tendon is loaded beyond a strain threshold, yet the metrics to define the damage threshold are not determined. We conducted multi-scale mechanical testing to investigate the mechanism of tendon damage by simultaneously quantifying macroscale mechanical and microstructural changes. At the microscale, we observe full recovery of the fibril strain and only partial recovery of the interfibrillar sliding, indicating that the damage initiates at the interfibrillar structures. We show that non-recoverable sliding is a mechanism for tendon damage and is responsible for the macroscale decreased linear modulus and elongated toe-region observed at the fascicle-level, and these macroscale properties are appropriate metrics that reflect tendon damage. We concluded that the inflection point of the stress-strain curve represents the damage threshold and, therefore, may be a useful parameter for future studies. Establishing the mechanism of damage at multiple length scales can improve prevention and rehabilitation strategies for tendon pathology.

STATEMENT OF SIGNIFICANCE

Tendon pathology is associated with mechanically induced damage. Damage, as defined in engineering, is an irreversible change in microstructure that alters the macroscopic mechanical properties. Although microstructural damage and changes to macroscale mechanics are likely, this link to microstructural change was not yet established. We conducted multiscale mechanical testing to investigate the mechanism of tendon damage by simultaneously quantifying macroscale mechanical and microstructural changes. We showed that non-recoverable sliding between collagen fibrils is a mechanism for tendon damage. Establishing the mechanism of damage at multiple length scales can improve prevention and rehabilitation strategies for tendon pathology.

Simple empirical model for identifying rheological properties of soft biological tissues

Understanding the rheological properties of soft biological tissue is a key issue for mechanical systems used in the health care field. We propose a simple empirical model using fractional dynamics and exponential nonlinearity (FDEN) to identify the rheological properties of soft biological tissue. The model is derived from detailed material measurements using samples isolated from porcine liver. We conducted dynamic viscoelastic and creep tests on liver samples using a plate-plate rheometer. The experimental results indicated that biological tissue has specific properties: (i) power law increase in the storage elastic modulus and the loss elastic modulus of the same slope; (ii) power law compliance (gain) decrease and constant phase delay in the frequency domain; (iii) power law dependence between time and strain relationships in the time domain; and (iv) linear dependence in the low strain range and exponential law dependence in the high strain range between stress-strain relationships. Our simple FDEN model uses only three dependent parameters and represents the specific properties of soft biological tissue.

Development of array piezoelectric fingers towards in vivo breast tumor detection

We have investigated the development of a handheld 4 × 1 piezoelectric finger (PEF) array breast tumor detector system towards in vivo patient testing, particularly, on how the duration of the DC applied voltage, the depression depth of the handheld unit, and breast density affect the PEF detection sensitivity on 40 patients. The tests were blinded and carried out in four phases: with DC voltage durations 5, 3, 2, to 0.8 s corresponding to scanning a quadrant, a half, a whole breast, and both breasts within 30 min, respectively. The results showed that PEF detection sensitivity was unaffected by shortening the applied voltage duration from 5 to 0.8 s nor was it affected by increasing the depression depth from 2 to 6 mm. Over the 40 patients, PEF detected 46 of the 48 lesions (46/48)-with the smallest lesion detected being 5 mm in size. Of 28 patients (some have more than one lesion) with mammography records, PEF detected 31/33 of all lesions (94%) and 14/15 of malignant lesions (93%), while mammography detected 30/33 of all lesions (91%) and 12/15 of malignant lesions (80%), indicating that PEF could detect malignant lesions not detectable by mammography without significantly increasing false positives. PEF's detection sensitivity is also shown to be independent of breast density, suggesting that PEF could be a potential tool for detecting breast cancer in young women and women with dense breasts.

Interference screw fixation of free tendon grafts: significant time-dependent decrease of the initial contact forces

PURPOSE

Interference screw fixation of tendon grafts is a common practice in ACL surgery. Tissues like tendons and bone show a complex viscoelastic behaviour, which could affect the contact forces in interference screw fixation. These effects are not well investigated, especially over prolonged periods of time. The time-dependent behaviour of tendons was thus the subject of the study. It was our hypothesis that a substantial decrease of the contact forces will be observed.

METHODS

Using an artificial bone surrogate and pig tendons, the time-dependent behaviour of the contact force in a simulated interference screw fixation was investigated over a 12-h period. As the screwing in can have deleterious effects on tendons, two scenarios, screwing in (A) and pressing the screw against the tendon (B), were investigated.

RESULTS

The initial contact forces showed a magnitude of 1,299 N (A) and 2,156 N (B), respectively. A significant decrease to 530 N (A) and 461 N (B) after 12 h was observed (p < 0.001). However, more than 80 % of the relaxation occurred during the first hour.

CONCLUSION

Significant relaxation of the contact force in interference screw fixation of ACL grafts occurs, which has implications for research and clinical practice. The strength of ACL fixation methods should not be assessed immediately after assembly of the specimens and comparisons should be done only when the same time intervals from assembly to testing were used. Also, in clinical practice, the initial fixation strength will probably not be maintained. Therefore, a backup fixation might be advisable.

Strain-enhanced stress relaxation impacts nonlinear elasticity in collagen gels

The extracellular matrix (ECM) is a complex assembly of structural proteins that provides physical support and biochemical signaling to cells in tissues. The mechanical properties of the ECM have been found to play a key role in regulating cell behaviors such as differentiation and malignancy. Gels formed from ECM protein biopolymers such as collagen or fibrin are commonly used for 3D cell culture models of tissue. One of the most striking features of these gels is that they exhibit nonlinear elasticity, undergoing strain stiffening. However, these gels are also viscoelastic and exhibit stress relaxation, with the resistance of the gel to a deformation relaxing over time. Recent studies have suggested that cells sense and respond to both nonlinear elasticity and viscoelasticity of ECM, yet little is known about the connection between nonlinear elasticity and viscoelasticity. Here, we report that, as strain is increased, not only do biopolymer gels stiffen but they also exhibit faster stress relaxation, reducing the timescale over which elastic energy is dissipated. This effect is not universal to all biological gels and is mediated through weak cross-links. Mechanistically, computational modeling and atomic force microscopy (AFM) indicate that strain-enhanced stress relaxation of collagen gels arises from force-dependent unbinding of weak bonds between collagen fibers. The broader effect of strain-enhanced stress relaxation is to rapidly diminish strain stiffening over time. These results reveal the interplay between nonlinear elasticity and viscoelasticity in collagen gels, and highlight the complexity of the ECM mechanics that are likely sensed through cellular mechanotransduction.

Modelling approaches for evaluating multiscale tendon mechanics

Tendon exhibits anisotropic, inhomogeneous and viscoelastic mechanical properties that are determined by its complicated hierarchical structure and varying amounts/organization of different tissue constituents. Although extensive research has been conducted to use modelling approaches to interpret tendon structure-function relationships in combination with experimental data, many issues remain unclear (i.e. the role of minor components such as decorin, aggrecan and elastin), and the integration of mechanical analysis across different length scales has not been well applied to explore stress or strain transfer from macro- to microscale. This review outlines mathematical and computational models that have been used to understand tendon mechanics at different scales of the hierarchical organization. Model representations at the molecular, fibril and tissue levels are discussed, including formulations that follow phenomenological and microstructural approaches (which include evaluations of crimp, helical structure and the interaction between collagen fibrils and proteoglycans). Multiscale modelling approaches incorporating tendon features are suggested to be an advantageous methodology to understand further the physiological mechanical response of tendon and corresponding adaptation of properties owing to unique in vivo loading environments.

Shear loads induce cellular damage in tendon fascicles

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

A fibre-reinforced poroviscoelastic model accurately describes the biomechanical behaviour of the rat Achilles tendon

Background

Computational models of Achilles tendons can help understanding how healthy tendons are affected by repetitive loading and how the different tissue constituents contribute to the tendon’s biomechanical response. However, available models of Achilles tendon are limited in their description of the hierarchical multi-structural composition of the tissue. This study hypothesised that a poroviscoelastic fibre-reinforced model, previously successful in capturing cartilage biomechanical behaviour, can depict the biomechanical behaviour of the rat Achilles tendon found experimentally.

Materials and Methods

We developed a new material model of the Achilles tendon, which considers the tendon’s main constituents namely: water, proteoglycan matrix and collagen fibres. A hyperelastic formulation of the proteoglycan matrix enabled computations of large deformations of the tendon, and collagen fibres were modelled as viscoelastic. Specimen-specific finite element models were created of 9 rat Achilles tendons from an animal experiment and simulations were carried out following a repetitive tensile loading protocol. The material model parameters were calibrated against data from the rats by minimising the root mean squared error (RMS) between experimental force data and model output.

Results and Conclusions

All specimen models were successfully fitted to experimental data with high accuracy (RMS 0.42-1.02). Additional simulations predicted more compliant and soft tendon behaviour at reduced strain-rates compared to higher strain-rates that produce a stiff and brittle tendon response. Stress-relaxation simulations exhibited strain-dependent stress-relaxation behaviour where larger strains produced slower relaxation rates compared to smaller strain levels. Our simulations showed that the collagen fibres in the Achilles tendon are the main load-bearing component during tensile loading, where the orientation of the collagen fibres plays an important role for the tendon’s viscoelastic response. In conclusion, this model can capture the repetitive loading and unloading behaviour of intact and healthy Achilles tendons, which is a critical first step towards understanding tendon homeostasis and function as this biomechanical response changes in diseased tendons.

Generation of electrospun nanofibers with controllable degrees of crimping through a simple, plasticizer-based treatment

Electrospun nanofibers with controllable degrees of crimping are fabricated by simply exposing the samples to a plasticizer at preset shrinkage ratios. Compared with their straight counterparts, the crimped nanofibers are able to mechanically mimic native tendon tissue and better protect tendon fibroblasts under uniaxial strains.

Mechanical properties of the compass depressors of the sea-urchin Paracentrotus lividus (Echinodermata, Echinoidea) and the effects of enzymes, neurotransmitters and synthetic tensilin-like protein

The compass depressors (CDs) of the sea-urchin lantern are ligaments consisting mainly of discontinuous collagen fibrils associated with a small population of myocytes. They are mutable collagenous structures, which can change their mechanical properties rapidly and reversibly under nervous control. The aims of this investigation were to characterise the baseline (i.e. unmanipulated) static mechanical properties of the CDs of Paracentrotus lividus by means of creep tests and incremental force-extension tests, and to determine the effects on their mechanical behaviour of a range of agents. Under constant load the CDs exhibited a three-phase creep curve, the mean coefficient of viscosity being 561±365 MPa.s. The stress-strain curve showed toe, linear and yield regions; the mean strain at the toe-linear inflection was 0.86±0.61; the mean Young's modulus was 18.62±10.30 MPa; and the mean tensile strength was 8.14±5.73 MPa. Hyaluronidase from Streptomyces hyalurolyticus had no effect on creep behaviour, whilst chondroitinase ABC prolonged primary creep but had no effect on secondary creep or on any force-extension parameters; it thus appears that neither hyaluronic acid nor sulphated glycosaminoglycans have an interfibrillar load transfer function in the CD. Acetylcholine, the muscarinic agonists arecoline and methacholine, and the nicotinic agonists nicotine and 1-[1-(3,4-dimethyl-phenyl)-ethyl]-piperazine produced an abrupt increase in CD viscosity; the CDs were not differentially sensitive to muscarinic or nicotinic agonists. CDs showed either no, or no consistent, response to adrenaline, L-glutamic acid, 5-hydroxytryptamine and γ-aminobutyric acid. Synthetic echinoid tensilin-like protein had a weak and inconsistent stiffening effect, indicating that, in contrast to holothurian tensilins, the echinoid molecule may not be involved in the regulation of collagenous tissue tensility. We compare in detail the mechanical behaviour of the CD with that of mammalian tendon and highlight its potential as a model system for investigating poorly understood aspects of the ontogeny and phylogeny of vertebrate collagenous tissues.

Viscoelasticity using reactive constrained solid mixtures

This study presents a framework for viscoelasticity where the free energy density depends on the stored energy of intact strong and weak bonds, where weak bonds break and reform in response to loading. The stress is evaluated by differentiating the free energy density with respect to the deformation gradient, similar to the conventional approach for hyperelasticity. The breaking and reformation of weak bonds is treated as a reaction governed by the axiom of mass balance, where the constitutive relation for the mass supply governs the bond kinetics. The evolving mass contents of these weak bonds serve as observable state variables. Weak bonds reform in an energy-free and stress-free state, therefore their reference configuration is given by the current configuration at the time of their reformation. A principal advantage of this formulation is the availability of a strain energy density function that depends only on observable state variables, also allowing for a separation of the contributions of strong and weak bonds. The Clausius-Duhem inequality is satisfied by requiring that the net free energy from all breaking bonds must be decreasing at all times. In the limit of infinitesimal strains, linear stress-strain responses and first-order kinetics for breaking and reforming of weak bonds, the reactive framework reduces exactly to classical linear viscoelasticity. For large strains, the reactive and classical quasilinear viscoelasticity theories produce different equations, though responses to standard loading configurations behave similarly. This formulation complements existing tools for modeling the nonlinear viscoelastic response of biological soft tissues under large deformations.

Shear load transfer in high and low stress tendons

BACKGROUND

Tendon is an integral part of joint movement and stability, as it functions to transmit load from muscle to bone. It has an anisotropic, fibrous hierarchical structure that is generally loaded in the direction of its fibers/fascicles. Internal load distributions are altered when joint motion rotates an insertion site or when local damage disrupts fibers/fascicles, potentially causing inter-fiber (or inter-fascicular) shear. Tendons with different microstructures (helical versus linear) may redistribute loads differently.

METHOD OF APPROACH

This study explored how shear redistributes axial loads in rat tail tendon (low stress tendons with linear microstructure) and porcine flexor tendon (high stress with helical microstructure) by creating lacerations on opposite sides of the tendon, ranging from about 20% to 60% of the tendon width, to create various magnitudes of shear. Differences in fascicular orientation were quantified using polarized light microscopy.

RESULTS AND CONCLUSIONS

Unexpectedly, both tendon types maintained about 20% of pre-laceration stress values after overlapping cuts of 60% of tendon width (no intact fibers end to end) suggesting that shear stress transfer can contribute more to overall tendon strength and stiffness than previously reported. All structural parameters for both tendon types decreased linearly with increasing laceration depth. The tail tendon had a more rapid decline in post-laceration elastic stress and modulus parameters as well as a more linear and less tightly packed fascicular structure, suggesting that positional tendons may be less well suited to redistribute loads via a shear mechanism.

Subfailure overstretch induces persistent changes in the passive mechanical response of cerebral arteries

Cerebral blood vessels are critical in maintaining the health of the brain, but their function can be disrupted by traumatic brain injury (TBI). Even in cases without hemorrhage, vessels are deformed with the surrounding brain tissue. This subfailure deformation could result in altered mechanical behavior. This study investigates the effect of overstretch on the passive behavior of isolated middle cerebral arteries (MCAs), with the hypothesis that axial stretch beyond the in vivo length alters this response. Twenty nine MCA sections from 11 ewes were tested. Vessels were subjected to a baseline test consisting of an axial stretch from a buckled state to 1.05* in vivo stretch (λIV) while pressurized at 13.3 kPa. Specimens were then subjected to a target level of axial overstretch between 1.05*λIV (λz = 1.15) and 1.52*λIV (λz = 1.63). Following overstretch, baseline tests were repeated immediately and then every 10 min, for 60 min, to investigate viscoelastic recovery. Injury was defined as an unrecoverable change in the passive mechanical response following overstretch. Finally, pressurized MCAs were pulled axially to failure. Post-overstretch response exhibited softening such that stress values at a given level of stretch were lower after injury. The observed softening also generally resulted in increased non-linearity of the stress-stretch curve, with toe region slope decreasing and large deformation slope increasing. There was no detectable change in reference configuration or failure values. As hypothesized, the magnitude of these alterations increased with overstretch severity, but only once overstretch exceeded 1.2*λIV (p < 0.001). These changes were persistent over 60 min. These changes may have significant implications in repeated TBI events and in increased susceptibility to stroke post-TBI.

Biaxial mechanical properties of swine uterosacral and cardinal ligaments

Mechanical alterations to pelvic floor ligaments may contribute to the development and progression of pelvic floor disorders. In this study, the first biaxial elastic and viscoelastic properties were determined for uterosacral ligament (USL) and cardinal ligament (CL) complexes harvested from adult female swine. Biaxial stress-stretch data revealed that the ligaments undergo large strains. They are orthotropic, being typically stiffer along their main physiological loading direction (i.e., normal to the upper vaginal wall). Biaxial stress relaxation data showed that the ligaments relax equally in both loading directions and more when they are less stretched. In order to describe the experimental findings, a three-dimensional constitutive law based on the Pipkin-Rogers integral series was formulated. The model accounts for incompressibility, large deformations, nonlinear elasticity, orthotropy, and stretch-dependent stress relaxation. This combined theoretical and experimental study provides new knowledge about the mechanical properties of USLs and CLs that could lead to the development of new preventive and treatment methods for pelvic floor disorders.