Micromechanical model of a surrogate for collagenous soft tissues: development, validation and analysis of mesoscale size effects

Volume Loss and Recovery in Bovine Knee Meniscus Loaded in Circumferential Tension

Load-induced volume change is an important aspect of knee meniscus function because volume loss creates fluid pressure, which minimizes friction and helps support compressive loads. The knee meniscus is unusual amongst cartilaginous tissues in that it is loaded not only in axial compression, but also in circumferential tension between its tibial attachments. Despite the physiologic importance of the knee meniscus' tensile properties, its volumetric strain in tension has never been directly measured, and predictions of volume strain in the scientific literature are inconsistent. In this study, we apply uniaxial tension to bovine knee meniscus and use biplanar imaging to directly observe the resulting three-dimensional volume change and unloaded recovery, revealing that tension causes volumetric contraction. Compression is already known to also cause contraction; therefore, all major physiologic loads compress and pressurize the meniscus, inducing fluid outflow. Although passive unloaded recovery is often described as slow relative to loaded loss, here we show that at physiologic strains the volume recovery rate in the meniscus upon unloading is faster than the rate of volume loss. These measurements of volumetric strain are an important step toward a complete theory of knee meniscus fluid flow and load support.

An equine tendon model for studying intra-tendinous shear in tendons that have more than one muscle contribution

Human Achilles tendon is composed of three smaller sub-tendons and exhibits non-uniform internal displacements, which decline with age and after injury, suggesting a potential role in the development of tendinopathies. Studying internal sliding behaviour is therefore important but difficult in human Achilles tendon. Here we propose the equine deep digital flexor tendon (DDFT) and its accessory ligament (AL) as a model to understand the sliding mechanism. The AL-DDFT has a comparable sub-bundle structure, is subjected to high and frequent asymmetric loads and is a natural site of injury similar to human Achilles tendons. Equine AL-DDFT were collected and underwent whole tendon level (n=7) and fascicle level (n=7) quasi-static mechanical testing. Whole tendon level testing was performed by sequentially loading through the proximal AL and subsequently through the proximal DDFT and recording regional strain in the free structures and joined DDFT and AL. Fascicle level testing was performed with focus on the inter-sub-bundle matrix between the two structures at the junction. Our results demonstrate a significant difference in the regional strain between the joined DDFT and AL and a greater transmission of force from the AL to the DDFT than vice versa. These results can be partially explained by the mechanical properties and geometry of the two structures and by differences in the properties of the interfascicular matrices. In conclusion, this tendon model successfully demonstrates that high displacement discrepancy occurs between the two structures and can be used as an easy-access model for studying intra-tendinous shear mechanics at the sub-tendon level. STATEMENT OF SIGNIFICANCE: Our study provides a naturally occurring and easily accessible equine model to study the complex behaviour of sub-tendons within the human Achilles tendon, which is likely to play a critical role in the pathogenesis of tendon disease. Our results demonstrate that the difference in material stiffness between the equine AL and DDFT stems largely from differences in the inter-fascicular matrix and furthermore that differences in strain are maintained in distal parts of the tightly joined structure. Furthermore, our results suggest that distribution of load between sub-structures is highly dependent on the morphological relationship between them; a finding that has important implications for understanding Achilles tendon mechanical behaviour, injury mechanisms and rehabilitation.

Modeling the initial-volume dependent approximate compressibility of porcine liver tissues using a novel volumetric strain energy model

Experimental observations in the open literature indicate that soft tissues are slightly compressible, and this characteristic affects not only their overall elastic response but also their damage evolution and failure mechanism. In this study, we find that the compressibility of liver tissues is also closely related to the initial specimen volume according to the confined compression tests: the samples with smaller initial volume exhibit more compressible behavior compared to the larger ones. To include this initial-volume dependent effect, we developed a novel volumetric strain energy model with two variables, i.e., the bulk modulus and the compressibility factor. A detailed scheme was proposed as well to identify these two parameters, and the relationship between the bulk modulus and the initial volume was clarified. Findings from this study will help to deepen the understanding of the biomechanical properties of soft tissues. STATEMENT OF SIGNIFICANCE: Liver is a highly vascular organ and traditionally assumed to be an incompressible medium. However, through the confined compression tests, we found that the samples with smaller initial volumes exhibit more compressible behavior. Hence, we developed a novel strain energy density model to characterize the initial-volume dependent hyperelastic response, and found that the bulk modulus of liver tissues is positively related to the initial volume. Our results suggest that the compressibility of liver tissues should be considered in the future study of liver biomechanics.

Modulating Mechanical Properties of Collagen-Lignin Composites

Three-dimensional matrices of collagen type I (Col I) are widely used in tissue engineering applications for its abundance in many tissues, bioactivity with many cell types, and excellent biocompatibility. Inspired by the structural role of lignin in a plant tissue, we found that sodium lignosulfonate (SLS) and an alkali-extracted lignin from switchgrass (SG) increased the stiffness of Col I gels. SLS and SG enhanced the stiffness of Col I gels from 52 to 670 Pa and 52 to 320 Pa, respectively, and attenuated shear-thinning properties, with the formulation of 1.8 mg/mL Col I and 5.0 mg/mL SLS or SG. In 2D cultures, the cytotoxicity of collagen-SLS to adipose-derived stromal cells was not observed and the cell viability was maintained over 7 days in 3D cultures. Collagen-SLS composites did not elicit immunogenicity when compared to SLS-only groups. Our collagen-SLS composites present a case that exploits lignins as an enhancer of mechanical properties of Col I without adverse cytotoxicity and immunogenicity for in vitro scaffolds or in vivo tissue repairs.

Exploiting Viscoelastic Experimental Observations and Numerical Simulations to Infer Biomimetic Artificial Tendon Fiber Designs

Designing biomimetic artificial tendons requires a thorough, data-based understanding of the tendon's inner material properties. The current work exploits viscoelastic experimental observations at the tendon fascicle scale, making use of mechanical and data analysis methods. More specifically, based on reported elastic, volumetric and relaxation fascicle scale properties, we infer most probable, mechanically compatible material attributes at the fiber scale. In particular, the work provides pairs of elastic and viscous fiber-scale moduli, which can reproduce the upper scale tendon mechanics. The computed range of values for the fiber-scale tendon viscosity attest to the substantial stress relaxation capabilities of tendons. More importantly, the reported mechanical parameters constitute a basis for the design of tendon-specific restoration materials, such as fiber-based, engineering scaffolds.

Fabrication of dense anisotropic collagen scaffolds using biaxial compression

We developed a new method to manufacture dense, aligned, and porous collagen scaffolds using biaxial plastic compression of type I collagen gels. Using a novel compression apparatus that constricts like an iris diaphragm, low density collagen gels were compressed to yield a permanently densified, highly aligned collagen material. Micro-porosity scaffolds were created using hydrophilic elastomer porogens that can be selectively removed following biaxial compression, with porosity modulated by using different porogen concentrations. The resulting scaffolds exhibit collagen densities that are similar to native connective tissues (∼10% collagen by weight), pronounced collagen alignment across multiple length scales, and an interconnected network of pores, making them highly relevant for use in tissue culture, the study of physiologically relevant cell-matrix interactions, and tissue engineering applications. The scaffolds exhibited highly anisotropic material behavior, with the modulus of the scaffolds in the fiber direction over 100 times greater than the modulus in the transverse direction. Adipose-derived mesenchymal stem cells were seeded onto the biaxially compressed scaffolds with minimal cell death over seven days of culture, along with cell proliferation and migration into the pore spaces. This fabrication method provides new capabilities to manufacture structurally and mechanically relevant cytocompatible scaffolds that will enable more physiologically relevant cell culture studies. Further improvement of manufacturing techniques has the potential to produce engineered scaffolds for direct replacement of dense connective tissues such as meniscus and annulus fibrosus.

STATEMENT OF SIGNIFICANCE

In vitro studies of cell-matrix interactions and the engineering of replacement materials for collagenous connective tissues require biocompatible scaffolds that replicate the high collagen density (15-25%/wt), aligned fibrillar organization, and anisotropic mechanical properties of native tissues. However, methods for creating scaffolds with these characteristics are currently lacking. We developed a new apparatus and method to create high density, aligned, and porous collagen scaffolds using a biaxial compression with porogens technique. These scaffolds have a highly directional structure and mechanical properties, with the tensile strength and modulus up to 100 times greater in the direction of alignment. We also demonstrated that the scaffolds are a suitable material for cell culture, promoting cell adhesion, viability, and an aligned cell morphology comparable to the cell morphology observed in native aligned tissues.

Experimental evaluation of multiscale tendon mechanics

Tendon's primary function is a mechanical link between muscle and bone. The hierarchical structure of tendon and specific compositional constituents are believed to be critical for proper mechanical function. With increased appreciation for tendon importance and the development of various technological advances, this review paper summarizes recent experimental approaches that have been used to study multiscale tendon mechanics, includes an overview of studies that have evaluated the role of specific tissue constituents, and also proposes challenges/opportunities facing tendon study. Tendon has been demonstrated to have specific structural characteristics (e.g., multi-level hierarchy, crimp pattern, helix) and complex mechanical properties (e.g., non-linearity, anisotropy, viscoelasticity). Physical mechanisms including uncrimping, fiber sliding, and collagen reorganization have been shown to govern tendon mechanical responses under both static and dynamic loading. Several tendon constituents with relatively small quantities have been suggested to play a role in its mechanics, although some results are conflicting. Further research should be performed to understand the interplay and communication of tendon mechanical properties across levels of the hierarchical structure, and further show how each of these components contribute to tendon mechanics. The studies summarized and discussed in this review have helped elucidate important aspects of multiscale tendon mechanics, which is a prerequisite for analyzing stress/strain transfer between multiple scales and identifying key principles of mechanotransduction. This information could further facilitate interpreting the functional diversity of tendons from different species, different locations, and even different developmental stages, and then better understand and identify fundamental concepts related to tendon degeneration, disease, and healing. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 35:1353-1365, 2017.

Advances in Quantification of Meniscus Tensile Mechanics Including Nonlinearity, Yield, and Failure

The meniscus provides crucial knee function and damage to it leads to osteoarthritis of the articular cartilage. Accurate measurement of its mechanical properties is therefore important, but there is uncertainty about how the test procedure affects the results, and some key mechanical properties are reported using ad hoc criteria (modulus) or not reported at all (yield). This study quantifies the meniscus' stress-strain curve in circumferential and radial uniaxial tension. A fiber recruitment model was used to represent the toe region of the stress-strain curve, and new reproducible and objective procedures were implemented for identifying the yield point and measuring the elastic modulus. Patterns of strain heterogeneity were identified using strain field measurements. To resolve uncertainty regarding whether rupture location (i.e., midsubstance rupture versus at-grip rupture) influences the measured mechanical properties, types of rupture were classified in detail and compared. Dogbone (DB)-shaped specimens are often used to promote midsubstance rupture; to determine if this is effective, we compared DB and rectangle (R) specimens in both the radial and circumferential directions. In circumferential testing, we also compared expanded tab (ET) specimens under the hypothesis that this shape would more effectively secure the meniscus' curved fibers and thus produce a stiffer response. The fiber recruitment model produced excellent fits to the data. Full fiber recruitment occurred approximately at the yield point, strongly supporting the model's physical interpretation. The strain fields, especially shear and transverse strain, were extremely heterogeneous. The shear strain field was arranged in pronounced bands of alternating positive and negative strain in a pattern similar to the fascicle structure. The site and extent of failure showed great variation, but did not affect the measured mechanical properties. In circumferential tension, ET specimens underwent earlier and more rapid fiber recruitment, had less stretch at yield, and had greater elastic modulus and peak stress. No significant differences were observed between R and DB specimens in either circumferential or radial tension. Based on these results, ET specimens are recommended for circumferential tests and R specimens for radial tests. In addition to the data obtained, the procedural and modeling advances made in this study are a significant step forward for meniscus research and are applicable to other fibrous soft tissues.

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.

Development and initial evaluation of a finite element model of the pediatric craniocervical junction

OBJECT There is a significant deficiency in understanding the biomechanics of the pediatric craniocervical junction (CCJ) (occiput-C2), primarily because of a lack of human pediatric cadaveric tissue and the relatively small number of treated patients. To overcome this deficiency, a finite element model (FEM) of the pediatric CCJ was created using pediatric geometry and parameterized adult material properties. The model was evaluated under the physiological range of motion (ROM) for flexion-extension, axial rotation, and lateral bending and under tensile loading. METHODS This research utilizes the FEM method, which is a numerical solution technique for discretizing and analyzing systems. The FEM method has been widely used in the field of biomechanics. A CT scan of a 13-month-old female patient was used to create the 3D geometry and surfaces of the FEM model, and an open-source FEM software suite was used to apply the material properties and boundary and loading conditions and analyze the model. The published adult ligament properties were reduced to 50%, 25%, and 10% of the original stiffness in various iterations of the model, and the resulting ROMs for flexion-extension, axial rotation, and lateral bending were compared. The flexion-extension ROMs and tensile stiffness that were predicted by the model were evaluated using previously published experimental measurements from pediatric cadaveric tissues. RESULTS The model predicted a ROM within 1 standard deviation of the published pediatric ROM data for flexion-extension at 10% of adult ligament stiffness. The model's response in terms of axial tension also coincided well with published experimental tension characterization data. The model behaved relatively stiffer in extension than in flexion. The axial rotation and lateral bending results showed symmetric ROM, but there are currently no published pediatric experimental data available for comparison. The model predicts a relatively stiffer ROM in both axial rotation and lateral bending in comparison with flexion-extension. As expected, the flexion-extension, axial rotation, and lateral bending ROMs increased with the decrease in ligament stiffness. CONCLUSIONS An FEM of the pediatric CCJ was created that accurately predicts flexion-extension ROM and axial force displacement of occiput-C2 when the ligament material properties are reduced to 10% of the published adult ligament properties. This model gives a reasonable prediction of pediatric cervical spine ligament stiffness, the relationship between flexion-extension ROM, and ligament stiffness at the CCJ. The creation of this model using open-source software means that other researchers will be able to use the model as a starting point for research.

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

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

Cell-generated traction forces and the resulting matrix deformation modulate microvascular alignment and growth during angiogenesis

The details of the mechanical factors that modulate angiogenesis remain poorly understood. Previous in vitro studies of angiogenesis using microvessel fragments cultured within collagen constructs demonstrated that neovessel alignment can be induced via mechanical constraint of the boundaries (i.e., boundary conditions). The objective of this study was to investigate the role of mechanical boundary conditions in the regulation of angiogenic alignment and growth in an in vitro model of angiogenesis. Angiogenic microvessels within three-dimensional constructs were subjected to different boundary conditions, thus producing different stress and strain fields during growth. Neovessel outgrowth and orientation were quantified from confocal image data after 6 days. Vascularity and branching decreased as the amount of constraint imposed on the culture increased. In long-axis constrained hexahedral constructs, microvessels aligned parallel to the constrained axis. In contrast, constructs that were constrained along the short axis had random microvessel orientation. Finite element models were used to simulate the contraction of gels under the various boundary conditions and to predict the local strain field experienced by microvessels. Results from the experiments and simulations demonstrated that microvessels aligned perpendicular to directions of compressive strain. Alignment was due to anisotropic deformation of the matrix from cell-generated traction forces interacting with the mechanical boundary conditions. These findings demonstrate that boundary conditions and thus the effective stiffness of the matrix regulate angiogenesis. This study offers a potential explanation for the oriented vascular beds that occur in native tissues and provides the basis for improved control of tissue vascularization in both native tissues and tissue-engineered constructs.