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

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.

Analytical relationships for 2D Re-entrant auxetic metamaterials: An application to 3D printing flexible implants

Both 2D and 3D re-entrant designs are among the well-known prevalent auxetic structures exhibiting negative Poisson's ratio. The present study introduces novel analytical relationships for 2D re-entrant hexagonal honeycombs for both negative and positive ranges of the cell interior angle θ (θ<0 showing a negative Poisson's ratio). The derived analytical solutions are validated against finite element method (FEM) and experimental results. The results show that, compared to the analytical solutions available in the literature, the analytical relationships presented in this study provide the most accurate results for elastic modulus, Poisson's ratio, and yield stress. The analytical/computational tools are then implemented for designing Kinesio taping (KT) structures applicable to treatment of Achilles tendon injuries. One of the main features of the Achilles tendon is a natural auxetic behavior. Poisson's ratio distribution of an Achilles tendon is obtained using longitudinal and transverse strains and are then used to design and 3D print thermoplastic polyurethane (TPU) KT structures with non-uniform distribution of auxetic unit cells. The presented novel KT shows that it is capable of replicating the deformation and global and local Poisson's ratio distributions, similar to those of the Achilles tendon. Due to the absence of similar formulations and procedures in the literature, the results are expected to be instrumental for designing and 3D printing of flexible implants with unusual auxeticity.

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.

Design and validation of a finite element model of the aponeurotic and free Achilles tendon

The Achilles tendon (AT) is a common injury site. Ruptures are usually located in the free tendon but may cross the myotendinous junction into the aponeurotic region. Considering the possibility of aponeurotic region involvement in AT ruptures, a novel three dimensional (3D) finite element (FE) model that includes both the aponeurotic and free AT regions and features subtendon twisting and sliding was developed. It was hypothesized that the model would be able to predict in vivo data collected from the literature, thus being considered valid, and that model outputs would be most sensitive to subtendon twist configurations. The 3D model was constructed using magnetic resonance images. The model was divided into soleus and gastrocnemius subtendons. In addition to a frictionless contact condition, the interaction between subtendons was modeled using two contact formulations: sliding with anisotropic friction and no sliding. Loads were applied on the tendon's most proximal cross-section and anterior surface, with magnitudes estimated from in vivo studies. Model outputs were compared with experimental data regarding 3D deformation, transverse plane rotation, and nodal displacements in the free tendon. The FE model adequately simulated the free tendon behavior regarding longitudinal strain, cross-section area variation, transverse plane rotation, and sagittal nodal displacements, provided that subtendon sliding was allowed. The frictionless model exhibited noticeable medial transverse sliding of the soleus subtendon, which was present to a much lesser degree in the anisotropic friction model. Model outputs were most sensitive to variations in subtendon twist and dispersion of the collagen fiber orientations. Clinical Significance: This Achilles tendon finite element model, validated using in vivo experimental data, may be used to study its mechanical behavior, injury mechanisms, and rupture risk factors.

Predicting the formation of different tissue types during Achilles tendon healing using mechanoregulated and oxygen-regulated frameworks

During Achilles tendon healing in rodents, besides the expected tendon tissue, also cartilage-, bone- and fat-like tissue features have been observed during the first twenty weeks of healing. Several studies have hypothesized that mechanical loading may play a key role in the formation of different tissue types during healing. We recently developed a computational mechanobiological framework to predict tendon tissue production, organization and mechanical properties during tendon healing. In the current study, we aimed to explore possible mechanobiological related mechanisms underlying formation of other tissue types than tendon tissue during tendon healing. To achieve this, we further developed our recent framework to predict formation of different tissue types, based on mechanobiological models established in other fields, which have earlier not been applied to study tendon healing. We explored a wide range of biophysical stimuli, i.e., principal strain, hydrostatic stress, pore pressure, octahedral shear strain, fluid flow, angiogenesis and oxygen concentration, that may promote the formation of different tissue types. The numerical framework predicted spatiotemporal formation of tendon-, cartilage-, bone- and to a lesser degree fat-like tissue throughout the first twenty weeks of healing, similar to recent experimental reports. Specific features of experimental data were captured by different biophysical stimuli. Our modeling approach showed that mechanobiology may play a role in governing the formation of different tissue types that have been experimentally observed during tendon healing. This study provides a numerical tool that can contribute to a better understanding of tendon mechanobiology during healing. Developing these tools can ultimately lead to development of better rehabilitation regimens that stimulate tendon healing and prevent unwanted formation of cartilage-, fat- and bone-like tissues.

Impact of Glucose on the Nanostructure and Mechanical Properties of Calcium-Alginate Hydrogels

Alginate is a polysaccharide obtained from brown seaweed that is widely used in food, pharmaceutical, and biotechnological applications due to its versatility as a viscosifier and gelling agent. Here, we investigated the influence of the addition of glucose on the structure and mechanical properties of alginate solutions and calcium-alginate hydrogels produced by internal gelation through crosslinking with Ca²⁺. Using ¹H low-field nuclear magnetic resonance (NMR) and small angle neutron scattering (SANS), we showed that alginate solutions at 1 wt % present structural heterogeneities at local scale whose size increases with glucose concentration (15–45 wt %). Remarkably, the molecular conformation of alginate in the gels obtained from internal gelation by Ca²⁺ crosslinking is similar to that found in solution. The mechanical properties of the gels evidence an increase in gel strength and elasticity upon the addition of glucose. The fitting of mechanical properties to a poroelastic model shows that structural changes within solutions prior to gelation and the increase in solvent viscosity contribute to the gel strength. The nanostructure of the gels (at local scale, i.e., up to few hundreds of Å) remains unaltered by the presence of glucose up to 30 wt %. At 45 wt %, the permeability obtained by the poroelastic model decreases, and the Young’s modulus increases. We suggest that macro (rather than micro) structural changes lead to this behavior due to the creation of a network of denser zones of chains at 45 wt % glucose. Our study paves the way for the design of calcium-alginate hydrogels with controlled structure for food and pharmaceutical applications in which interactions with glucose are of relevance.

Predicting the effect of reduced load level and cell infiltration on spatio-temporal Achilles tendon healing

Mechanobiology plays an important role in tendon healing. However, the relationship between mechanical loading and spatial and temporal evolution of tendon properties during healing is not well understood. This study builds on a recently presented mechanoregulatory computational framework that couples mechanobiological tendon healing to tissue production and collagen orientation. In this study, we investigated how different magnitudes of mechanical stimulation (principal strain) affect the spatio-temporal evolution of tissue production and the temporal evolution of elastic and viscoelastic mechanical parameters. Specifically, we examined the effect of cell infiltration (mimicking migration and proliferation) in the callus on the resulting tissue production by modeling production to depend on local cell density. The model predictions were carefully compared with experimental data from Achilles tendons in rats, at 1, 2 and 4 weeks of healing. In the experiments, the rat tendons had been subjected to free cage activity or reduced load levels through intramuscular botox injections. The simulations that included cell infiltration and strain-regulated collagen production predicted spatio-temporal tissue distributions and mechanical properties similarly to that observed experimentally. In addition, lack of matrix-producing cells in the tendon core during early healing may result in reduced collagen content, regardless of the daily load level. This framework is the first to computationally investigate mechanobiological mechanisms underlying spatial and temporal variations during tendon healing for various magnitudes of loading. This framework will allow further characterization of biomechanical, biological, or mechanobiological processes underlying tendon healing.

A numerical framework for mechano-regulated tendon healing-Simulation of early regeneration of the Achilles tendon

Mechano-regulation during tendon healing, i.e. the relationship between mechanical stimuli and cellular response, has received more attention recently. However, the basic mechanobiological mechanisms governing tendon healing after a rupture are still not well-understood. Literature has reported spatial and temporal variations in the healing of ruptured tendon tissue. In this study, we explored a computational modeling approach to describe tendon healing. In particular, a novel 3D mechano-regulatory framework was developed to investigate spatio-temporal evolution of collagen content and orientation, and temporal evolution of tendon stiffness during early tendon healing. Based on an extensive literature search, two possible relationships were proposed to connect levels of mechanical stimuli to collagen production. Since literature remains unclear on strain-dependent collagen production at high levels of strain, the two investigated production laws explored the presence or absence of collagen production upon non-physiologically high levels of strain (>15%). Implementation in a finite element framework, pointed to large spatial variations in strain magnitudes within the callus tissue, which resulted in predictions of distinct spatial distributions of collagen over time. The simulations showed that the magnitude of strain was highest in the tendon core along the central axis, and decreased towards the outer periphery. Consequently, decreased levels of collagen production for high levels of tensile strain were shown to accurately predict the experimentally observed delayed collagen production in the tendon core. In addition, our healing framework predicted evolution of collagen orientation towards alignment with the tendon axis and the overall predicted tendon stiffness agreed well with experimental data. In this study, we explored the capability of a numerical model to describe spatial and temporal variations in tendon healing and we identified that understanding mechano-regulated collagen production can play a key role in explaining heterogeneities observed during tendon healing.

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.