Swelling of fiber-reinforced soft tissues is affected by fiber orientation, fiber stiffness, and lamella structure

Structure, composition and anisotropic swelling of the bovine acetabular labrum

The fibro-cartilaginous labrum surrounds the acetabular rim and is important for hip joint stability and sealing. Sealing may be enhanced by swelling pressure within the normal labrum. Swelling of the degenerated or torn labrum might occur and potentially contribute to the development of osteoarthritis, through altered load transmission. This study aimed to characterize the three-dimensional swelling behaviour, the collagen fiber orientation and spatial proteoglycan distribution of the bovine acetabular labrum. Specimens were harvested from bovine donors (192-652 days, male, n = 6 donors). Structure was analyzed by scanning electron microscopy, histology, and dimethylmethylene blue assay. Specimen dimensions were measured before and after incubation in phosphate buffered saline to assess the swelling. Results showed that the articulating surface is composed of a collagen mesh network. Collagen fiber bundles showed a low degree of alignment close to the surface and were circumferentially aligned in the deep tissue. Proteoglycans were identified clustered between the collagen bundles. Glycosaminoglycan content was 10 x lower than that of cartilage (23.1 ± 6.4 compared to 299.5 ± 19.1 μg/mg dry weight) with minor regional differences. Specimens swelled significantly more in the orthogonal direction (swelling ratio 124.7 ± 10.2%) compared to the swelling parallel to the articulating surface (108.8 ± 6.1% and 102.8 ± 4.1%). In the deep tissue, swelling was also restricted in the main collagen fiber bundle direction (circumferentially), with a swelling ratio of 109.5 ± 4.0% in the main fiber bundle direction compared to 126.8 ± 7.3 % and 122.3 ± 5.8% radially. The findings demonstrate that the labrum shows anisotropic swelling properties, which reflect the anisotropy in the tissue structure and inter-fiber localisation of proteoglycans.

A swelling-based biphasic analysis on the quasi-static biomechanical behaviors of healthy and degenerative intervertebral discs

BACKGROUND AND OBJECTIVE

The degeneration of intervertebral discs is significantly dependent of the changes in tissue composition ratio and tissue structure. Up to the present, the effects of degeneration on the quasi-static biomechanical responses of discs have not been well understood. The goal of this study is to quantitatively analyze the quasi-static responses of healthy and degenerative discs.

METHODS

Four biphasic swelling-based finite element models are developed and quantitatively validated. Four quasi-static test protocols, including the free-swelling, slow-ramp, creep and stress-relaxation, are implemented. The double Voigt and double Maxwell models are further used to extract the immediate (or residual), short-term and long-term responses of these tests.

RESULTS

Simulation results show that both the swelling-induced pressure in the nucleus pulposus and the initial modulus decrease with degeneration. In the free-swelling test of discs possessing healthy cartilage endplates, simulation results show that over 80% of the total strain is contributed by the short-term response. The long-term response is dominant for discs with degenerated permeability in cartilage endplates. For the creep test, over 50% of the deformation is contributed by the long-term response. In the stress-relaxation test, the long-term stress contribution occupies approximately 31% of total response and is independent of degeneration. Both the residual and short-term responses vary monotonically with degeneration. In addition, both the glycosaminoglycan content and permeability affect the engineering equilibrium time constants of the rheologic models, in which the determining factor is the permeability.

CONCLUSIONS

The content of glycosaminoglycan in intervertebral soft tissues and the permeability of cartilage endplates are two critical factors that affect the fluid-dependent viscoelastic responses of intervertebral discs. The component proportions of the fluid-dependent viscoelastic responses depend also strongly on test protocols. In the slow-ramp test, the glycosaminoglycan content is responsible for the changes of the initial modulus. Since existing computational models simulate disc degenerations only by altering disc height, boundary conditions and material stiffness, the current work highlights the significance of biochemical composition and cartilage endplates permeability in the biomechanical behaviors of degenerated discs.

Impact of extracellular matrix and collagen network properties on the cervical intervertebral disc response to physiological loads: A parametric study

Current intervertebral disc finite element models are hard to validate since they describe multi-physical phenomena and contain a huge number of material properties. This work aims to simplify numerical validation/identification studies by prioritizing the sensitivity of intervertebral disc behavior to mechanical properties. A 3D fiber-reinforced hyperelastic model of a C6-C7 intervertebral disc is used to carry out the parametric study. 10 parameters describing the extracellular matrix and the collagen network behaviors are included in the parametric study. The influence of varying these parameters on the disc response is estimated during physiological movements of the head, including compression, lateral bending, flexion, and axial rotation. The obtained results highlight the high sensitivity of the disc behavior to the stiffness of the annulus fibrosus extracellular matrix for all the studied loads with a relative increase in the disc apparent stiffness by 67% for compression and by 57% for axial rotation when the annulus stiffness increases from 0.4 to 2 MPa. It is also shown that varying collagen network orientation, stiffness, and stiffening in the studied configuration range have a noticeable effect on rotational motions with a relative apparent stiffness difference reaching 6.8%, 10%, and 22%, respectively, in lateral bending. However, the collagen orientation does not affect disc response to axial load.

Saline-polyethylene glycol blends preserve in vitro annulus fibrosus hydration and mechanics: An experimental and finite-element analysis

Precise control of tissue water content is essential for ensuring accurate, repeatable, and physiologically relevant measurements of tissue mechanics and biochemical composition. While previous studies have found that saline and polyethylene glycol (PEG) blends were effective at controlling tendon and ligament hydration levels, this work has yet to be extended to the annulus fibrosus (AF). Thus, the first objective of this study was to determine and validate an optimal buffer solution for targeting and maintaining hydration levels of tissue-level AF specimens in vitro. This was accomplished by measuring the transient swelling behavior of bovine AF specimens in phosphate-buffered saline (PBS) and PEG buffers across a wide range of concentrations. Sub-failure, failure, and post-failure mechanics were measured to determine the relationship between changes in tissue hydration and tensile mechanical response. The effect of each buffer solution on tissue composition was also assessed. The second objective of this study was to assess the feasibility and effectiveness of using multi-phasic finite element models to investigate tissue swelling and mechanical responses in different external buffer solutions. A solution containing 6.25%w/v PBS and 6.25%w/v PEG effectively maintained tissue-level AF specimen hydration at fresh-frozen levels after 18 h in solution. Modulus, failure stress, failure strain, and post-failure toughness of specimens soaked in this solution for 18 h closely matched those of fresh-frozen specimens. In contrast, specimens soaked in 0.9%w/v PBS swelled over 100% after 18 h and exhibited significantly diminished sub-failure and failure properties compared to fresh-frozen controls. The increased cross-sectional area with swelling contributed to but was not sufficient to explain the diminished mechanics of PBS-soaked specimens, suggesting additional sub-tissue scale mechanisms. Computational simulations of these specimens generally agreed with experimental results, highlighting the feasibility and importance of including a fluid-phase description when models aim to provide accurate predictions of biological tissue responses. As numerous previous studies suggest that tissue hydration plays a central role in maintaining proper mechanical and biological function, robust methods for controlling hydration levels are essential as the field advances in probing the relationship between tissue hydration, aging, injury, and disease.

Sensitivity of Intervertebral Disc Finite Element Models to Internal Geometric and Non-geometric Parameters

Finite element models are useful for investigating internal intervertebral disc (IVD) behaviours without using disruptive experimental techniques. Simplified geometries are commonly used to reduce computational time or because internal geometries cannot be acquired from CT scans. This study aimed to (1) investigate the effect of altered geometries both at endplates and the nucleus-anulus boundary on model response, and (2) to investigate model sensitivity to material and geometric inputs, and different modelling approaches (graduated or consistent fibre bundle angles and glued or cohesive inter-lamellar contact). Six models were developed from 9.4 T MRIs of bovine IVDs. Models had two variations of endplate geometry (a simple curved profile from the centre of the disc to the periphery, and precise geometry segmented from MRIs), and three variations of NP-AF boundary (linear, curved, and segmented). Models were subjected to axial compressive loading (to 0.86 mm at a strain rate of 0.1/s) and the effect on stiffness and strain distributions, and the sensitivity to modelling approaches was investigated. The model with the most complex geometry (segmented endplates, curved NP-AF boundary) was 3.1 times stiffer than the model with the simplest geometry (curved endplates, linear NP-AF boundary), although this difference may be exaggerated since segmenting the endplates in the complex geometry models resulted in a shorter average disc height. Peak strains were close to the endplates at locations of high curvature in the segmented endplate models which were not captured in the curved endplate models. Differences were also seen in sensitivity to material properties, graduated fibre angles, cohesive rather than glued inter-lamellar contact, and NP:AF ratios. These results show that FE modellers must take care to ensure geometries are realistic so that load is distributed and passes through IVDs accurately.

Identifiability of tissue material parameters from uniaxial tests using multi-start optimization

Determining tissue biomechanical material properties from mechanical test data is frequently required in a variety of applications. However, the validity of the resulting constitutive model parameters is the subject of debate in the field. Parameter optimization in tissue mechanics often comes down to the "identifiability" or "uniqueness" of constitutive model parameters; however, despite advances in formulating complex constitutive relations and many classic and creative curve-fitting approaches, there is currently no accessible framework to study the identifiability of tissue material parameters. Our objective was to assess the identifiability of material parameters for established constitutive models of fiber-reinforced soft tissues, biomaterials, and tissue-engineered constructs and establish a generalizable procedure for other applications. To do so, we generated synthetic experimental data by simulating uniaxial tension and compression tests, commonly used in biomechanics. We then fit this data using a multi-start optimization technique based on the nonlinear least-squares method with multiple initial parameter guesses. We considered tendon and sclera as example tissues, using constitutive models that describe these fiber-reinforced tissues. We demonstrated that not all the model parameters of these constitutive models were identifiable from uniaxial mechanical tests, despite achieving virtually identical fits to the stress-stretch response. We further show that when the lateral strain was considered as an additional fitting criterion, more parameters are identifiable, but some remain unidentified. This work provides a practical approach for addressing parameter identifiability in tissue mechanics.

Alterations in the Geometry, Fiber Orientation, and Mechanical Behavior of the Lumbar Intervertebral Disc by Nucleus Swelling

Soft tissues observed in clinical medical images are often prestrained in tension by internal pressure or tissue hydration. For a native disc, nucleus swelling occurs in equilibrium with osmotic pressure induced by the high concentration of proteoglycan in the nucleus. The objective of this computational study was to investigate the effects of nucleus swelling on disc geometry, fiber orientation, and mechanical behavior by comparing those of prestrained and zero-pressure (unswelled) discs. Thermoelastic analysis techniques were repurposed in order to determine the zero-pressure disc geometry which, when pressurized, matches the prestrained disc geometry observed in clinical images. The zero-pressure geometry was then used in simulations to approximately represent a degenerated disc, which loses the ability of nucleus swelling but has not undergone distinct soft tissue remodeling/disruption. Our simulation results demonstrated that the loss of nucleus swelling caused a slight change in the disc geometry and fiber orientation, but a distinct deterioration in the resistance to intervertebral rotations including sagittal bending, lateral bending, and axial torsion. Different from rotational loading, in compression (with a displacement of 0.45 mm applied), a much larger stiffness (3.02 KN/mm) and a greater intradiscal pressure (IDP) (0.61 MPa) were measured in the zero-pressure disc, compared to the prestrained disc (1.41 KN/mm and 0.52 MPa). This computational study could be useful to understand mechanisms of disc degeneration, and guide the future design of disc tissue engineering material and biomimic disc implants.

Stress-Swelling Finite Element Modeling of Cervical Response With Homeostatic Collagen Fiber Distributions

During pregnancy, the cervix experiences significant mechanical property change due to tissue swelling, and to ongoing changes in the collagen content. In this paper, we model how these two effects contribute to cervical deformation as the pressure load on top of the cervix increases. The cervix and its surrounding supporting ligaments are taken into consideration in the resulting mechanical analysis. The cervix itself is treated as a multilayered tube-like structure, with layer-specific collagen orientation. The cervical tissue in each layer is treated in terms of a collagen constituent that remodels with time within a ground substance matrix that experiences swelling. The load and swelling are taken to change sufficiently slowly so that the collagen properties at any instant can be regarded as being in a state of homeostasis. Among other things, the simulations show how the luminal cross-sectional area varies along its length as a function of pressure and swelling. In general, an increase in pressure causes an overall shortening of the lumen while an increase in swelling has the opposite effect.

Intervertebral disc swelling maintains strain homeostasis throughout the annulus fibrosus: A finite element analysis of healthy and degenerated discs

Tissues in the intervertebral disc have a large capacity to absorb water, partially due to the high glycosaminoglycan (GAG) content, which decreases linearly from the nucleus pulposus (NP) in the center to the outer annulus. Our recent work showed that fiber network and GAG distribution contributes to development of residual stresses and strains that were compressive in the inner annulus to tensile in the outer annulus. GAG loss in the inner annulus, as observed with early to moderate degeneration, reduced swelling capacity and circumferential-direction stress by over 50%. However, our previous model was not capable of evaluating interactions between the NP and annulus fibrosus (AF) during swelling. In this study, we evaluated the effect of degeneration (GAG content or swelling capacity) on residual stress development throughout the disc. Simulations of moderate to severe degeneration showed a 40% decrease in NP swelling capacity, with a 25% decrease in AF and cartilaginous endplate swelling. Together, these changes in tissue swelling resulted in a decrease in NP pressure (healthy = 0.21 MPa; severe degeneration = 0.03 MPa) that was comparable to observations in human discs. There was a 60% decrease in circumferential-direction residual deformations with early degeneration. Radial-direction stretch switched from compressive to tensile with degeneration, which may increase the risk for tears or delamination. Degeneration had a significant impact on residual stress/stretch and fiber stretch in the posterior AF, which is important for understanding herniation risk. In conclusion, degenerative changes in disc geometry and intradiscal deformations was recreated by only altering NP and AF GAG composition. Since most computational models simulate degeneration by altering material stiffness, this work highlights the importance of directly simulating biochemical composition and distribution to study disc biomechanics with degeneration. STATEMENT OF SIGNIFICANCE: Tissues in the intervertebral disc have a large swelling capacity, due to its high glycosaminoglycan content. Our recent work demonstrated the importance of fiber network and glycosaminoglycan distribution residual stresses and strains development. In this study, we evaluated the effect of swelling on intradiscal deformations between the nucleus pulposus and annulus fibrosus. We also investigated the effect of degenerative glycosaminoglycan loss on swelling-based intradiscal deformations of the intact disc and its subcomponents. Decreases in nucleus glycosaminoglycan content resulted in morphological changes observed with degenerated discs and may help to explain mechanisms behind the increases in annular tears and mechanical dysfunction with degeneration.

Influences of sodium and glycosaminoglycans on skin oedema and the potential for ulceration: a finite-element approach

Venous ulcers are chronic transcutaneous wounds common in the lower legs. They are resistant to healing and have a 78% chance of recurrence within 2 years. It is commonly accepted that venous ulcers are caused by the insufficiency of the calf muscle pump, leading to blood pooling in the lower legs, resulting in inflammation, skin oedema, tissue necrosis and eventually skin ulceration. However, the detailed physiological events by which inflammation contributes to wound formation are poorly understood. We therefore sought to develop a model that simulated the inflammation, using it to determine the internal stresses and pressure on the skin that contribute to venous ulcer formation. A three-layer finite-element skin model (epidermis, dermis and hypodermis) was developed to explore the roles in wound formation of two inflammation identifiers: glycosaminoglycans (GAG) and sodium. A series of parametric studies showed that increased GAG and sodium content led to oedema and increased tissue stresses of 1.5 MPa, which was within the reported range of skin tissue ultimate tensile stress (0.1-40 MPa). These results suggested that both the oedema and increased fluid pressure could reach a threshold for tissue damage and eventual ulcer formation. The models presented here provide insights to the pathological events associated with venous insufficiency, including inflammation, oedema and skin ulceration.