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

On the contribution of solid and fluid behavior to the modeling of the time-dependent mechanics of tendons under semi-confined compression

The present work aims to investigate whether it is possible to identify and quantify the contributions of the interstitial fluid and the solid skeleton to the overall time-dependent behavior of tendons based on a single mechanical test. For this purpose, the capabilities of three different time-dependent models (a viscoelastic, a poroelastic and a poroviscoelastic) were investigated in the modeling of the experimental behavior obtained from semi-confined compression with stress relaxation tests transverse to collagen fibers. The main achieved result points out that the poroviscoelastic model was the only one capable to characterize both the experimental responses of the force and volume changes of the tissue samples. Moreover, further analysis of this model shows that while the kinematics of the sample are mainly governed by the fluid flow (pore pressure contribution of the model), the behavior intrinsically associated with the viscoelastic solid skeleton makes a significant contribution to the experimental force response. This study reinforces the importance of taking both the experimental kinematics and kinetics of tendon tissues into account during the constitutive characterization procedure.

Multimodal and multiscale characterization reveals how tendon structure and mechanical response are altered by reduced loading

Tendons are collagen-based connective tissues where the composition, structure and mechanics respond and adapt to the local mechanical environment. Adaptation to prolonged inactivity can result in stiffer tendons that are more prone to injury. However, the complex relation between reduced loading, structure, and mechanical performance is still not fully understood. This study combines mechanical testing with high-resolution synchrotron X-ray imaging, scattering techniques and histology to elucidate how reduced loading affects the structural properties and mechanical response of rat Achilles tendons on multiple length scales. The results show that reduced in vivo loading leads to more crimped and less organized fibers and this structural inhomogeneity could be the reason for the altered mechanical response. Unloading also seems to change the fibril response, possibly by altering the strain partitioning between hierarchical levels, and to reduce cell density. This study elucidates the relation between in vivo loading, the Achilles tendon nano-, meso‑structure and mechanical response. The results provide fundamental insights into the mechanoregulatory mechanisms guiding the intricate biomechanics, tissue structural organization, and performance of complex collagen-based tissues. STATEMENT OF SIGNIFICANCE: Achilles tendon properties allow a dynamic interaction between muscles and tendon and influence force transmission during locomotion. Lack of physiological loading can have dramatic effects on tendon structure and mechanical properties. We have combined the use of cutting-edge high-resolution synchrotron techniques with mechanical testing to show how reduced loading affects the tendon on multiple hierarchical levels (from nanoscale up to whole organ) clarifying the relation between structural changes and mechanical performance. Our findings set the first step to address a significant healthcare challenge, such as the design of tailored rehabilitations that take into consideration structural changes after tendon immobilization.

Is the fluid volume fraction equal to the water content in tendons? Insights on biphasic modeling

The mass density of highly hydrated soft tissues is generally assumed to be very close to that of the water, resulting that the fluid mass fraction (water content) being equal to the fluid volume fraction. Within this context, the present study aims to investigate whether such an assumption actually holds for tendon tissues and to what extent it may affect the constitutive characterizations based on biphasic (poroelastic) models. Once the water content was assessed by a classical drying assay, the fluid volume fraction was obtained based on an image segmentation approach. The main achieved results point out that the fluid volume fraction is ∼20% higher than the water content in the studied tendons (flexor digitorum profundus bovine tendons). Based on this, it is shown that the use of the water content instead of the fluid volume fraction may considerably bias the results drawn by biphasic modeling of tendons. Accordingly, a proper measurement of the fluid volume fraction is then required.

Adaptation of Fibril-Reinforced Poroviscoelastic Properties in Rabbit Collateral Ligaments 8 Weeks After Anterior Cruciate Ligament Transection

Ligaments of the knee provide stability and prevent excessive motions of the joint. Rupture of the anterior cruciate ligament (ACL), a common sports injury, results in an altered loading environment for other tissues in the joint, likely leading to their mechanical adaptation. In the collateral ligaments, the patterns and mechanisms of biomechanical adaptation following ACL transection (ACLT) remain unknown. We aimed to characterize the adaptation of elastic and viscoelastic properties of the lateral and medial collateral ligaments eight weeks after ACLT. Unilateral ACLT was performed in six rabbits, and collateral ligaments were harvested from transected and contralateral knee joints after eight weeks, and from an intact control group (eight knees from four animals). The cross-sectional areas were measured with micro-computed tomography. Stepwise tensile stress-relaxation testing was conducted up to 6% final strain, and the elastic and viscoelastic properties were characterized with a fibril-reinforced poroviscoelastic material model. We found that the cross-sectional area of the collateral ligaments in the ACL transected knees increased, the nonlinear elastic collagen network modulus of the LCL decreased, and the amount of fast relaxation in the MCL decreased. Our results indicate that rupture of the ACL leads to an early adaptation of the elastic and viscoelastic properties of the collagen fibrillar network in the collateral ligaments. These adaptations may be important to consider when evaluating whole knee joint mechanics after ACL rupture, and the results aid in understanding the consequences of ACL rupture on other tissues.

Lose the stress: Viscoelastic materials for cell engineering

Biomaterials are widely used to study and control a variety of cell behaviors, including stem cell differentiation, organogenesis, and tumor invasion. While considerable attention has historically been paid to biomaterial elastic (storage) properties, it has recently become clear that viscous (loss) properties can also powerfully influence cell behavior. Here we review advances in viscoelastic materials for cell engineering. We begin by discussing collagen, an abundant naturally occurring biomaterial that derives its viscoelastic properties from its fibrillar architecture, which enables dissipation of applied stresses. We then turn to two other naturally occurring biomaterials that are more frequently modified for engineering applications, alginate and hyaluronic acid, whose viscoelastic properties may be tuned by modulating network composition and crosslinking. We also discuss the potential of exploiting engineered fibrous materials, particularly electrospun fiber-based materials, to control viscoelastic properties. Finally, we review mechanisms through which cells process viscous and viscoelastic cues as they move along and within these materials. The ability of viscoelastic materials to relax cell-imposed stresses can dramatically alter migration on two-dimensional surfaces and confinement-imposed barriers to engraftment and infiltration in three-dimensional scaffolds. STATEMENT OF SIGNIFICANCE: Most tissues and many biomaterials exhibit some viscous character, a property that is increasingly understood to influence cell behavior in profound ways. This review discusses the origin and significance of viscoelastic properties of common biomaterials, as well as how these cues are processed by cells to influence migration. A deeper understanding of the mechanisms of viscoelastic behavior in biomaterials and how cells interpret these inputs should aid the design and selection of biomaterials for specific applications.

Structure, composition and fibril-reinforced poroviscoelastic properties of bovine knee ligaments and patellar tendon

Tissue-level stress-relaxation of ligaments and tendons in the toe region is characterized by fast and long-term relaxations and an increase in relaxation magnitude with strain. Characterizing the compositional and structural origins of these phenomena helps in the understanding of mechanisms of ligament and tendon function and adaptation in health and disease. A three-step tensile stress-relaxation test was conducted on dumbbell-shaped pieces of bovine knee ligaments and patellar tendon (PT) (n = 10 knees). Their mechanical behaviour was characterized by a fibril-reinforced poroviscoelastic material model, able to describe characteristic times and magnitudes of fast and long-term relaxations. The crimp angle and length of tissues were measured with polarized light microscopy, while biochemical contents were determined by colorimetric biochemical methods. The long-term relaxation time was longer in the anterior cruciate ligament (ACL) and PT compared with collateral ligaments (p < 0.05). High hydroxyproline content predicted greater magnitude and shorter time of both fast and long-term relaxation. High uronic acid content predicted longer time of long-term relaxation, whereas high crimp angle predicted higher magnitude of long-term relaxation. ACL and PT are better long-term stabilizers than collateral ligaments. The long-term relaxation behaviour is affected or implied by proteoglycans and crimp angle, possibly relating to slow structural reorganization of the tissue.

Comparison of material models for anterior cruciate ligament in tension: from poroelastic to a novel fibril-reinforced nonlinear composite model

Computational models of the knee joint are useful for evaluating stresses and strains within the joint tissues. However, the outcome of those models is sensitive to the material model and material properties chosen for ligaments, the collagen reinforced tissues connecting bone to bone. The purpose of this study was to investigate different compositionally motivated material models and further to develop a model that can accurately reproduce experimentally measured stress-relaxation data of bovine anterior cruciate ligament (ACL). Tensile testing samples were extracted from ACLs of bovine knee joints (N = 10) and subjected to a three-step stress-relaxation test at the toe region. Data from the experiments was averaged and one average finite element model was generated to replicate the experiment. Poroelastic and different fibril-reinforced poro(visco)elastic material models were applied, and their material parameters were optimized to reproduce the experimental force-time response. Material models with only fluid flow mediated relaxation were not able to capture the stress-relaxation behavior (R² = 0.806, 0.803 and 0.938). The inclusion of the viscoelasticity of the fibrillar network improved the model prediction (R² = 0.978 and 0.976), but the complex stress-relaxation behavior was best captured by a poroelastic model with a nonlinear two-relaxation-time strain-recruited viscoelastic fibrillar network (R² = 0.997). The results suggest that in order to replicate the multi-step stress-relaxation behavior of ACL in tension, the fibrillar network formulation should include the complex nonlinear viscoelastic phenomena.

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.

Understanding how reduced loading affects Achilles tendon mechanical properties using a fibre-reinforced poro-visco-hyper-elastic model

Understanding tendon mechanobiology is important for gaining insight into the development of tendon pathology and subsequent repair processes. The aim of this study was to investigate how experimentally observed mechanobiological adaptation of rat Achilles tendons translate to changes in constitutive mechanical properties and biomechanical behavior. In addition, we assessed the ability of the model to simulate tendon creep and stress-relaxation. A three dimensional finite element framework of rat Achilles tendon was implemented with a fibre-reinforced poro-visco-hyper-elastic constitutive model. Stress-relaxation and creep data from Achilles tendons of Sprague Dawley rats that had been subjected to both daily loading and a period of reduced loading were used to determine the constitutive properties of the tendons. Our results showed that the constitutive model captures creep and stress-relaxation data from rat Achilles tendons for both loaded and unloaded tendons with good accuracy (normalized root mean square error between model and experimental data were 0.010-0.027). Only when the model parameters were fitted to data from both mechanical tests simultaneously, were we able to also capture similar increase in elastic energy (increased stiffness) and decreased viscoelasticity in response to unloading, as was reported experimentally. Our study is the first to show that experimentally observed mechanobiological changes in tendon biomechanics, such as stiffness and viscoelasticity, can be designated to mechanical quantities in a constitutive model. Further investigation in this direction has potential to discriminate tissue components responsible for specific biomechanical response, and enable targeted treatment strategies for tendon health.

An experimental and numerical study on the transverse deformations in tensile test of tendons

The transverse deformations of tendons assessed in tensile tests seems to constitute a controversial issue in literature. On the one hand, large positive variations of the Poisson's ratio have been reported, indicating volume reduction under tensile states. On the other hand, negative values were also observed, pointing out an auxetic material response. Based on these experimental observations, the following question is raised: Are these large and discrepant transverse deformations intrinsically related to the constitutive response of tendons or they result from artifacts of the mechanical test setup? In order to provide further insights to this question, an experimental and numerical study on the transverse kinematics of tendons was carried out. Tensile experiments were performed in branches of deep digital flexor tendons of domestic porcine, where the transverse displacements were measured by two high-speed, high-accuracy optical digital micrometers placed transversely to one another. Aiming at a better understanding of the effects of the mechanical test setup in the transverse measurements, a three-dimensional finite element model is proposed to resemble the tensile experiment. The main achieved results strongly support the following hypotheses regarding tensile tests of tendons: the clamping region considerably affects the kinematics of the specimen even at a large distance from the clamps; the transverse deformations are mainly ruled by stiff fibers embedded in a soft matrix; the generalization of the Poisson's ratio to draw conclusions about changes in volume of tendons may lead to misinterpretations.

Biological connective tissues exhibit viscoelastic and poroelastic behavior at different frequency regimes: Application to tendon and skin biophysics

In this study, a poroviscoelastic finite element model (FEM) was developed and used in conjunction with an AFM-based wide-bandwidth nanorheology system to predict the frequency-dependent mechanical behavior of tendon and dermis subjected to compression via nanoindentation. The aim was to distinguish between loading rates that are dominated by either poroelasticity, viscoelasticity, or the superposition of these processes. Using spherical probe tips having different radii, the force and tip displacement were measured and the magnitude, E^∗, and phase angle, ϕ, of the dynamic complex modulus were evaluated for mouse supraspinatus tendon and mouse dermis. The peak frequencies of the phase angle were associated with the characteristic time constants of poroelastic and viscoelastic material behavior. The developed FE model could predict the separate poroelastic and viscoelastic responses of these soft tissues over a 4 decade frequency range, showing good agreement with experimental results. We observed that poroelasticity was the dominant energy dissipation mechanism for mouse dermis and supraspinatus tendon at higher indentation frequencies (10² to 10⁴ Hz) whereas viscoelasticity was typically dominant at lower frequencies (<10² Hz). These findings show the underlying mechanical behavior of biological connective tissues and give insight into the role played by these different energy dissipation mechanisms in governing the function of these tissues at nanoscale.

STATEMENT OF SIGNIFICANCE

Soft biological tissues exhibit complex, load- and time-dependent mechanical behavior. Evaluating their mechanical behavior requires sophisticated experimental tools and numerical models that can capture the fundamental mechanisms governing tissue function. Using an Atomic-force-microscopy-based rheology system and finite element models, the roles of the two most dominant time-dependent mechanisms (poroelasticity and viscoelasticity) that govern the dynamic loading behavior of mouse skin and tendon have been investigated. FE models were able to predict and quantify the contribution of each mechanism to the overall dynamic response and confirming the presence of these two distinct mechanisms in the mechanical response. Overall, these results provide novel insight into the viscoelastic and poroelastic properties of mouse skin and tendon and promote better understanding of the underlying origins of each mechanism.

The effect of constitutive representations and structural constituents of ligaments on knee joint mechanics

Ligaments provide stability to the human knee joint and play an essential role in restraining motion during daily activities. Compression-tension nonlinearity is a well-known characteristic of ligaments. Moreover, simpler material representations without this feature might give reasonable results because ligaments are primarily in tension during loading. However, the biomechanical role of different constitutive representations and their fibril-reinforced poroelastic properties is unknown. A numerical knee model which considers geometric and material nonlinearities of meniscus and cartilages was applied. Five different constitutive models for the ligaments (spring, elastic, hyperelastic, porohyperelastic, and fibril-reinforced porohyperelastic (FRPHE)) were implemented. Knee joint forces for the models with elastic, hyperelastic and porohyperelastic properties showed similar behavior throughout the stance, while the model with FRPHE properties exhibited lower joint forces during the last 50% of the stance phase. The model with ligaments as springs produced the lowest joint forces at this same stance phase. The results also showed that the fibril network contributed substantially to the knee joint forces, while the nonfibrillar matrix and fluid had small effects. Our results indicate that simpler material models of ligaments with similar properties in compression and tension can be used when the loading is directed primarily along the ligament axis in tension.

Mechanobiological modelling of tendons: Review and future opportunities

Tendons are adapted to carry large, repeated loads and are clinically important for the maintenance of musculoskeletal health in an increasing, actively ageing population, as well as in elite athletes. Tendons are known to adapt to mechanical loading. Also, their healing and disease processes are highly sensitive to mechanical load. Computational modelling approaches developed to capture this mechanobiological adaptation in tendons and other tissues have successfully addressed many important scientific and clinical issues. The aim of this review is to identify techniques and approaches that could be further developed to address tendon-related problems. Biomechanical models are identified that capture the multi-level aspects of tendon mechanics. Continuum whole tendon models, both phenomenological and microstructurally motivated, are important to estimate forces during locomotion activities. Fibril-level microstructural models are documented that can use these estimated forces to detail local mechanical parameters relevant to cell mechanotransduction. Cell-level models able to predict the response to such parameters are also described. A selection of updatable mechanobiological models is presented. These use mechanical signals, often continuum tissue level, along with rules for tissue change and have been applied successfully in many tissues to predict in vivo and in vitro outcomes. Signals may include scalars derived from the stress or strain tensors, or in poroelasticity also fluid velocity, while adaptation may be represented by changes to elastic modulus, permeability, fibril density or orientation. So far, only simple analytical approaches have been applied to tendon mechanobiology. With the development of sophisticated computational mechanobiological models in parallel with reporting more quantitative data from in vivo or clinical mechanobiological studies, for example, appropriate imaging, biochemical and histological data, this field offers huge potential for future development towards clinical applications.

Comparison of structural anisotropic soft tissue models for simulating Achilles tendon tensile behaviour

The incidence of tendon injury (tendinopathy) has increased over the past decades due to greater participation in sports and recreational activities. But little is known about the aetiology of tendon injuries because of our limited knowledge in the complex structure-function relationship in tendons. Computer models can capture the biomechanical behaviour of tendons and its structural components, which is essential for understanding the underlying mechanisms of tendon injuries. This study compares three structural constitutive material models for the Achilles tendon and discusses their application on different biomechanical simulations. The models have been previously used to describe cardiovascular tissue and articular cartilage, and one model is novel to this study. All three constitutive models captured the tensile behaviour of rat Achilles tendon (root mean square errors between models and experimental data are 0.50-0.64). They further showed that collagen fibres are the main load-bearing component and that the non-collagenous matrix plays a minor role in tension. By introducing anisotropic behaviour also in the non-fibrillar matrix, the new biphasic structural model was also able to capture fluid exudation during tension and high values of Poisson׳s ratio that is reported in tendon experiments.