Biaxial tension of fibrous tissue: using finite element methods to address experimental challenges arising from boundary conditions and anisotropy

Evaluation of an Inverse Method for Quantifying Spatially Variable Mechanics

Soft biological tissues often function as highly deformable membranes in vivo and exhibit impressive mechanical behavior effectively characterized by planar biaxial testing. The Generalized Anisotropic Inverse Mechanics (GAIM) method links full-field deformations and boundary forces from mechanical testing to quantify material properties of soft, anisotropic, heterogeneous tissues. In this study, we introduced an orthotropic constraint to GAIM to improve the quality and physical significance of its mechanical characterizations. We evaluated the updated GAIM method using simulated and experimental biaxial testing datasets obtained from soft tissue analogs (PDMS and TissueMend) with well-defined mechanical properties. GAIM produced stiffnesses (first Kelvin moduli, K1) that agreed well with previously published Young's moduli of PDMS samples. It also matched the stiffness moduli determined via uniaxial testing for TissueMend, a collagen-rich patch intended for tendon repair. We then conducted the first biaxial testing of TissueMend and confirmed that the sample was mechanically anisotropic via a relative anisotropy metric produced by GAIM. Next, we demonstrated the benefits of full-field laser micrometry in distinguishing between spatial variations in thickness and stiffness. Finally, we conducted an analysis to verify that results were independent of partitioning scheme. The success of the newly implemented constraints on GAIM suggests notable potential for applying this tool to soft tissues, particularly following the onset of pathologies that induce mechanical and structural heterogeneities.

Evaluation of the parallel coupling constitutive model for biomaterials using a fully coupled network-matrix model

In this article we discuss the effective properties of composites containing a crosslinked athermal fiber network embedded in a continuum elastic matrix, which are representative for a broad range of biological materials. The goal is to evaluate the accuracy of the widely used biomechanics parallel coupling model in which the tissue response is defined as the additive superposition of the network and matrix contributions, and the interaction of the two components is neglected. To this end, explicit, fully coupled models are used to evaluate the linear and non-linear response of the composite. It is observed that in the small strain, linear regime the parallel model leads to errors when the ratio of the individual stiffnesses of the two components is in the range 0.1-10, and the error increases as the matrix approaches the incompressible limit. The data presented can be used to correct the parallel model to improve the accuracy of the overall stiffness prediction. In the non-linear large deformation regime linear superposition does not apply. The data shows that the matrix reduces the stiffening rate of the network, and the response is softer than that predicted by the parallel model. The correction proposed for the linear regime mitigates to a large extent the error in the non-linear regime as well, provided the matrix Poisson ratio is not close to 0.5. The special case in which the matrix is rendered auxetic is also evaluated and it is seen that the auxeticity of the matrix may compensate the stiffening introduced by the network, leading to a composite with linear elastic response over a broad range of strains.

Can axial loading restore in vivo disc geometry, opening pressure, and T2 relaxation time?

Background

Cadaveric intervertebral discs are often studied for a variety of research questions, and outcomes are interpreted in the in vivo context. Unfortunately, the cadaveric disc does not inherently represent the LIVE condition, such that the disc structure (geometry), composition (T2 relaxation time), and mechanical function (opening pressure, OP) measured in the cadaver do not necessarily represent the in vivo disc.

Methods

We conducted serial evaluations in the Yucatan minipig of disc geometry, T2 relaxation time, and OP to quantify the changes that occur with progressive dissection and used axial loading to restore the in vivo condition.

Results

We found no difference in any parameter from LIVE to TORSO; thus, within 2 h of sacrifice, the TORSO disc can represent the LIVE condition. With serial dissection and sample preparation the disc height increased (SEGMENT height 18% higher than TORSO), OP decreased (POTTED was 67% lower than TORSO), and T2 time was unchanged. With axial loading, an imposed stress of 0.20-0.33 MPa returned the disc to in vivo, LIVE disc geometry and OP, although T2 time was decreased. There was a linear correlation between applied stress and OP, and this was conserved across multiple studies and species.

Conclusion

To restore the LIVE disc state in human studies or other animal models, we recommend measuring the OP/stress relationship and using this relationship to select the applied stress necessary to recover the in vivo condition.

Geometric determinants of the mechanical behavior of image-based finite element models of the intervertebral disc

The intervertebral disc is an important structure for load transfer through the spine. Its injury and degeneration have been linked to pain and spinal fractures. Disc injury and spine fractures are associated with high stresses; however, these stresses cannot be measured, necessitating the use of finite element (FE) models. These models should include the disc's complex structure, as changes in disc geometry have been linked to altered mechanical behavior. However, image-based models using disc-specific structures have yet to be established. This study describes a multiphasic FE modeling approach for noninvasive estimates of subject-specific intervertebral disc mechanical behavior based on medical imaging. The models (n = 22) were used to study the influence of disc geometry on the predicted global mechanical response (moments and forces), internal local disc stresses, and tractions at the interface between the disc and the bone. Disc geometry was found to have a strong influence on the predicted moments and forces on the disc (R2 = 0.69-0.93), while assumptions regarding the side curvature (bulge) of the disc had only a minor effect. Strong variability in the predicted internal disc stresses and tractions was observed between the models (mean absolute differences of 5.1%-27.7%). Disc height had a systematic influence on the internal disc stresses and tractions at the disc-to-bone interface. The influence of disc geometry on mechanics highlights the importance of disc-specific modeling to estimate disc injury risk, loading on the adjacent vertebral bodies, and the mechanical environment present in disc tissues.

An investigation of how specimen dimensions affect biaxial mechanical characterizations with CellScale BioTester and constitutive modeling of porcine tricuspid valve leaflets

Biaxial mechanical characterizations are the accepted approach to determine the mechanical response of many biological soft tissues. Although several computational and experimental studies have examined how experimental factors (e.g., clamped vs. suture mounting) affect the acquired tissue mechanical behavior, little is known about the role of specimen dimensions in data acquisition and the subsequent modeling. In this study, we combined our established mechanical characterization framework with an iterative size-reduction protocol to test the hypothesis that specimen dimensions affect the observed mechanical behavior of biaxial characterizations. Our findings indicated that there were non-significant differences in the peak equibiaxial stretches of tricuspid valve leaflets across four specimen dimensions ranging from 4.5×4.5mm to 9 × 9mm. Further analyses revealed that there were significant differences in the low-tensile modulus of the circumferential tissue direction. These differences resulted in significantly different constitutive model parameters for the Tong-Fung model between different specimen dimensions of the posterior and septal leaflets. Overall, our findings demonstrate that specimen dimensions play an important role in experimental characterizations, but not necessarily in constitutive modeling of soft tissue mechanical behavior during biaxial testing with the commercial CellScale BioTester.

Simulation Analysis of Equibiaxial Tension Tests for Rubber-like Materials

For rubber-like materials, there are three popular methods of equibiaxial tension available: inflation tension, equibiaxial planar tension, and radial tension. However, no studies have addressed the accuracy and comparability of these tests. In this work, we model the tension tests for a hyperelastic electroactive polymer (EAP) membrane material using finite element method (FEM) and investigate their experimental accuracy. This study also analyzes the impact of apparatus structure parameters and specimen dimensions on experimental performances. Additionally, a tensile efficiency is proposed to assess non-uniform deformation in equibiaxial planar tension and radial tension tests. The sample points for calculating deformation in inflation tensions should be taken near the top of the inflated balloon to obtain a more accurate characteristic curve; the deformation simulation range will be constrained by the material model and its parameters within a specific limit (λ ≈ 1.9); if the inflation hole size is halved, the required air pressure must be doubled to maintain equivalent stress and strain values, resulting in a reduction in half in inflation height and decreased accuracy. The equibiaxial planar tension test can enhance uniform deformation and reduce stress errors to as low as 2.1% (at λ = 4) with single-corner-point tension. For circular diaphragm specimens in radial tension tests, increasing the number of cuts and using larger punched holes results in more uniform deformation and less stress error, with a minimum value of 3.83% achieved for a specimen with 24 cuts and a 5 mm punched hole. In terms of tensile efficiency, increasing the number of tensile points in the equibiaxial planar tension test can improve it; under radial tension, increasing the number of cuts and decreasing the diameter of the punched hole on the specimen has a hedging effect. The findings of this study are valuable for accurately evaluating various equibiaxial tension methods and analyzing their precision, as well as providing sound guidance for the effective design of testing apparatus and test plans.

Techniques for characterizing mechanical properties of soft tissues

The characterization of soft tissues remains a vital need for various bioengineering and medical fields. Developing areas such as regenerative medicine, robot-aided surgery, and surgical simulations all require accurate knowledge about the mechanical properties of soft tissues to replicate their mechanics. Mechanical properties can be characterized through several different characterization techniques such as atomic force microscopy, compression testing, and tensile testing. However, many of these methods contain considerable differences in ability to accurately characterize the mechanical properties of soft tissues. As a result of these variations, there are often discrepancies in the reported values for numerous studies. This paper reviews common characterization methods that have been applied to obtain the mechanical properties of soft tissues and highlights their advantages as well as disadvantages. The limitations, accuracies, repeatability, in-vivo testing capability, and types of properties measurable for each method are also discussed.

Region- and layer-specific investigations of the human menisci using SHG imaging and biaxial testing

In this paper, we examine the region- and layer-specific collagen fiber morphology via second harmonic generation (SHG) in combination with planar biaxial tension testing to suggest a structure-based constitutive model for the human meniscal tissue. Five lateral and four medial menisci were utilized, with samples excised across the thickness from the anterior, mid-body, and posterior regions of each meniscus. An optical clearing protocol enhanced the scan depth. SHG imaging revealed that the top samples consisted of randomly oriented fibers with a mean fiber orientation of 43.3 ^o . The bottom samples were dominated by circumferentially organized fibers, with a mean orientation of 9.5 ^o . Biaxial testing revealed a clear anisotropic response, with the circumferential direction being stiffer than the radial direction. The bottom samples from the anterior region of the medial menisci exhibited higher circumferential elastic modulus with a mean value of 21 MPa. The data from the two testing protocols were combined to characterize the tissue with an anisotropic hyperelastic material model based on the generalized structure tensor approach. The model showed good agreement in representing the material anisotropy with a mean r ² = 0.92.

Combining Unique Planar Biaxial Testing with Full-Field Thickness and Displacement Measurement for Spatial Characterization of Soft Tissues

Soft tissues rely on the incredible complexity of their microstructure for proper function. Local variations in material properties arise as tissues develop and adapt, often in response to changes in loading. A barrier to investigating the heterogeneous nature of soft tissues is the difficulty of developing experimental protocols and analysis tools that can accurately capture spatial variations in mechanical behavior. In this article, we detail protocols enabling mechanical characterizations of anisotropic, heterogeneous soft tissues or tissue analogs. We present a series of mechanical tests designed to maximize inhomogeneous strain fields and in-plane shear forces. A customized, 3D-printable gripping system reduces tissue handling and enhances shear. High-resolution imaging and laser micrometry capture full-field displacement and thickness, respectively. As the equipment necessary to conduct these protocols is commercially available, the experimental methods presented offer an accessible route toward addressing heterogeneity. © 2022 The Authors. Current Protocols published by Wiley Periodicals LLC. Basic Protocol 1: Unique biaxial testing of soft tissues and tissue analogs Basic Protocol 2: Full-field thickness measurement of soft tissues and tissue analogs Support Protocol 1: Creating and speckling cruciform-shaped samples for mechanical testing Support Protocol 2: Creating custom gripping system to minimize sample handling.

The role of elastin on the mechanical properties of the anterior leaflet in porcine tricuspid valves

Elastin is present in the extracellular matrix (ECM) of connective tissues, and its mechanical properties are well documented. In Marfan syndrome, however, the inability to properly code for the protein fibrillin-1 prematurely leads to the degradation and loss of elastin fiber integrity in the ECM. In this study, the role of elastin in the ECM of the anterior leaflet of the tricuspid valve was investigated by examining the biomechanical behavior of porcine leaflets before and after the application of the enzyme elastase. Five loading protocols were applied to the leaflet specimens in two groups (elastase-treated and control samples). The mechanical response following elastase application yielded a significantly stiffer material in both the radial and circumferential directions. At a physiological level of stress (85 kPa), the elastase group had an average strain of 26.21% and 6.32% in the radial and circumferential directions, respectively, at baseline prior to elastase application. Following elastase treatment, the average strain was 5.28% and 0.97% in the radial and circumferential directions, respectively. No statistically significant change was found in the control group following sham treatment with phosphate-buffered saline (PBS). Two-photon microscopy images confirmed that after the removal of elastin, the collagen fibers displayed a loss of undulation. With a significant reduction in radial compliance, the ability to withstand physiological loads may be compromised. As such, an extracellular matrix that is structurally deficient in elastin may hinder normal tricuspid valve function.

Experimental Bi-axial tensile tests of spinal meningeal tissues and constitutive models comparison

Introduction This study aims at identifying mechanical characteristics under bi-axial loading conditions of extracted swine pia mater (PM) and dura and arachnoid complex (DAC). Methods 59 porcine spinal samples have been tested on a bi-axial experimental device with a pre-load of 0.01 N and a displacement rate of 0.05 mm·s^-1. Post-processing analysis included an elastic modulus, as well as constitutive model identification for Ogden model, reduced Gasser Ogden Holzapfel (GOH) model, anisotropic GOH model, transverse isotropic and anisotropic Gasser models as well as a Mooney-Rivlin model including fiber strengthening for PM. Additionally, micro-structure of the tissue was investigated using a bi-photon microscopy. Results Linear elastic moduli of 108 ± 40 MPa were found for DAC longitudinal direction, 53 ± 32 MPa for DAC circumferential direction, with a significant difference between directions (p < 0.001). PM presented significantly higher longitudinal than circumferential elastic moduli (26 ± 13 MPa vs 13 ± 9 MPa, p < 0.001). Transversely isotropic and anisotropic Gasser models were the most suited models for DAC (r²  =  0.99 and RMSE:0.4 and 0.3 MPa) and PM (r² = 1 and RMSE:0.06 and 0.07 MPa) modelling. Conclusion This work provides reference values for further quasi-static bi-axial studies, and is the first for PM. Collagen structures observed by two photon microscopy confirmed the use of anisotropic Gasser model for PM and the existence of fenestration. The results from anisotropic Gasser model analysis depicted the best fit to experimental data as per this protocol. Further investigations are required to allow the use of meningeal tissue mechanical behaviour in finite element modelling with respect to physiological applications. STATEMENT OF SIGNIFICANCE: This study is the first to present biaxial tensile test of pia mater as well as constitutive model comparisons for dura and arachnoid complex tissue based on such tests. Collagen structures observed by semi-quantitative analysis of two photon microscopy confirmed the use of anisotropic Gasser model for pia mater and existence of fenestration. While clear identification of fibre population was not possible in DAC, results from anisotropic Gasser model depicted better fitting on experimental data as per this protocol. Bi-axial mechanical testing allows quasi-static characterization under conditions closer to the physiological context and the results presented could be used for further simulations of physiology. Indeed, the inclusion of meningeal tissue in finite element models will allow more accurate and reliable numerical simulations.

Multiaxial validation of a finite element model of the intervertebral disc with multigenerational fibers to establish residual strain

Finite element models of the intervertebral disc are used to address research questions that cannot be tested through typical experimentation. A disc model requires complex geometry and tissue properties to be accurately defined to mimic the physiological disc. The physiological disc possesses residual strain in the annulus fibrosus (AF) due to osmotic swelling and due to inherently pre-strained fibers. We developed a disc model with residual contributions due to swelling-only, and a multigeneration model with residual contributions due to both swelling and AF fiber pre-strain and validated it against organ-scale uniaxial, quasi-static and multiaxial, dynamic mechanical tests. In addition, we demonstrated the models' ability to mimic the opening angle observed following radial incision of bovine discs. Both models were validated against organ-scale experimental data. While the swelling only model responses were within the experimental 95% confidence interval, the multigeneration model offered outcomes closer to the experimental mean and had a bovine model opening angle within one SD of the experimental mean. The better outcomes for the multigeneration model, which allowed for the inclusion of inherently pre-strained fibers in AF, is likely due to its uniform fiber contribution throughout the AF. We conclude that the residual contribution of pre-strained fibers in the AF should be included to best simulate the physiological disc and its behaviors.

Evaluation of affine fiber kinematics in porcine tricuspid valve leaflets using polarized spatial frequency domain imaging and planar biaxial testing

Collagen fibers are the primary load-bearing microstructural constituent of bodily soft tissues, and, when subjected to external loading, the collagen fibers reorient, uncrimp, and elongate. Specific to the atrioventricular heart valve leaflets, the collagen fiber kinematics form the basis of many constitutive models; however, some researchers claim that modeling the affine fiber kinematics (AFK) are sufficient for accurately predicting the macroscopic tissue deformations, while others state that modeling the non-affine kinematics (i.e., fiber uncrimping together with elastic elongation) is required. Experimental verification of the AFK theory has been previously performed for the mitral valve leaflets in the left-side heart; however, this same evaluation has yet to be performed for the morphologically distinct tricuspid valve (TV) leaflets in the right-side heart. In this work, we, for the first time, evaluated the AFK theory for the TV leaflets using an integrated biaxial testing-polarized spatial frequency domain imaging device to experimentally quantify the load-dependent collagen fiber reorientations for comparison to the AFK theory predictions. We found that the AFK theory generally underpredicted the fiber reorientations by 3.1°, on average, under the applied equibiaxial loading with greater disparity when the tissue was subjected to the applied non-equibiaxial loading. Furthermore, increased AFK errors were observed with increasing collagen fiber reorientations (Pearson coefficient r = -0.36, equibiaxial loading), suggesting the AFK theory is better suited for relatively smaller reorientations. Our findings suggest the AFK theory may require modification for more accurate predictions of the collagen fiber kinematics in the TV leaflets, which will be useful in refining modeling efforts for more accurate TV simulations.

Febio finite element models of the human cervical spine

Finite element (FE) analysis has proven to be useful when studying the biomechanics of the cervical spine. Although many FE studies of the cervical spine have been published, they typically develop their models using commercial software, making the sharing of models between researchers difficult. They also often model only one part of the cervical spine. The goal of this study was to develop and evaluate three FE models of the adult cervical spine using open-source software and to freely provide these models to the scientific community. The models were created from computed tomography scans of 26-, 59-, and 64-year old female subjects. These models were evaluated against previously published experimental and FE data. Despite the fact that all three models were assigned identical material properties and boundary conditions, there was notable variation in their biomechanical behavior. It was therefore apparent that these differences were the result of morphological differences between the models.

Balancing biological and biomechanical performance in intervertebral disc repair: a systematic review of injectable cell delivery biomaterials

Discogenic back pain is a common condition without approved intervertebral disc (IVD) repair therapies. Cell delivery using injectable biomaterial carriers offers promise to restore disc height and biomechanical function, while providing a functional niche for delivered cells to repair degenerated tissues. This systematic review advances the injectable IVD cell delivery biomaterials field by characterising its current state and identifying themes of promising strategies. Preferred Reporting Items for Systematic Reviews and Meta- Analyses (PRISMA) guidelines were used to screen the literature and 183 manuscripts met the inclusion criteria. Cellular and biomaterial inputs, and biological and biomechanical outcomes were extracted from each study. Most identified studies targeted nucleus pulposus (NP) repair. No consensus exists on cell type or biomaterial carrier, yet most common strategies used mesenchymal stem cell (MSC) delivery with interpenetrating network/co-polymeric (IPN/CoP) biomaterials composed of natural biomaterials. All studies reported biological outcomes with about half the studies reporting biomechanical outcomes. Since the IVD is a load-bearing tissue, studies reporting compressive and shear moduli were analysed and two major themes were found. First, a competitive balance, or 'seesaw' effect, between biomechanical and biological performance was observed. Formulations with higher moduli had inferior cellular performance, and vice versa. Second, several low-modulus biomaterials had favourable biological performance and matured throughout culture duration with enhanced extracellular matrix synthesis and biomechanical moduli. Findings identify an opportunity to develop next-generation biomaterials that provide high initial biomechanical competence to stabilise and repair damaged IVDs with a capacity to promote cell function for long-term healing.

Anisotropic and viscoelastic tensile mechanical properties of aponeurosis: Experimentation, modeling, and tissue microstructure

Aponeuroses are stiff sheath-like components of the muscle-tendon unit that play a vital role in force transmission and thus locomotion. There is clear importance of the aponeurosis in musculoskeletal function, but there have been relatively few studies of aponeurosis material properties to date. The goals of this work were to: 1) perform tensile stress-relaxation tests, 2) perform planar biaxial tests, 3) employ computational modeling to the data from 1 to 2, and 4) perform scanning electron microscopy to determine collagen fibril organization for aponeurosis tissue. Viscoelastic modeling and statistical analysis of stress-relaxation data showed that while relaxation rate differed statistically between strain levels (p = 0.044), functionally the relaxation behavior was nearly the same. Biaxial testing and associated modeling highlighted the nonlinear (toe region of ~2-3% strain) and anisotropic (longitudinal direction linear modulus ~50 MPa, transverse ~2.5 MPa) tensile mechanical behavior of aponeurosis tissue. Comparisons of various constitutive formulations showed that a transversely isotropic Ogden approach balanced strong fitting (goodness of fit 0.984) with a limited number of parameters (five), while damage modeling parameters were also provided. Scanning electron microscopy showed a composite structure of highly aligned, partially wavy collagen fibrils with more random collagen cables for aponeurosis microstructure. Future work to expand microstructural analysis and use these data to inform computational modeling would benefit this work and the field.

A structural-based computational model of tendon-bone insertion tissues

Tendon-to-bone insertion provides a gradual transition from soft tendon to hard bone tissue, functioning to alleviate stress concentrations at the junction of these tissues. Such macroscopic mechanical properties are achieved due to the internal structure in which collagen fibers and mineralization levels are key ingredients. We develop a structural-based model of tendon-to-bone insertion incorporating such details as fiber preferred orientation, fiber directional dispersion, mineralization level, and their inhomogeneous spatial distribution. A python script is developed to alter the tapered tendon-bone transition zone and to provide spatial grading of material properties, which may be rather complex as experiments suggest. A simple linear interpolation between tendon and bone material properties is first used to describe the graded property within the insertion region. Stress distributions are obtained and compared for spatially graded and various piece-wise materials properties. It is observed that spatial grading results in more smooth stress distributions and significantly reduces maximum stresses. The geometry of the tissue model is optimized by minimizing the peak stress to mimic in-vivo tissue remodeling. The in-silico elastic models constructed in this work are verified and modified by comparing to our in-situ biaxial mechanical testing results, thereby serving as translational tools for accurately predicting the material behavior of the tendon-to-bone insertions. This model will be useful for understanding how tendon-to-bone insertion develops during tissue remodeling, as well as for developing orthopedic implants.

Historical Review of Combined Experimental and Computational Approaches for Investigating Annulus Fibrosus Mechanics

Intervertebral disc research has sought to develop a deeper understanding of spine biomechanics, the complex relationship between disc health and back pain, and the mechanisms of spinal injury and repair. To do so, many researchers have focused on characterizing tissue-level properties of the disc, where the roles of tissue subcomponents can be more systematically investigated. Unfortunately, experimental challenges often limit the ability to measure important disc tissue- and subtissue-level behaviors, including fiber-matrix interactions, transient nutrient and electrolyte transport, and damage propagation. Numerous theoretical and numerical modeling frameworks have been introduced to explain, complement, guide, and optimize experimental research efforts. The synergy of experimental and computational work has significantly advanced the field, and these two aspects have continued to develop independently and jointly. Meanwhile, the relationship between experimental and computational work has become increasingly complex and interdependent. This has made it difficult to interpret and compare results between experimental and computational studies, as well as between solely computational studies. This paper seeks to explore issues of model translatability, robustness, and efficient study design, and to propose and motivate potential future directions for experimental, computational, and combined tissue-level investigations of the intervertebral disc.

Multiscale composite model of fiber-reinforced tissues with direct representation of sub-tissue properties

In many fiber-reinforced tissues, collagen fibers are embedded within a glycosaminoglycan-rich extrafibrillar matrix. Knowledge of the structure-function relationship between the sub-tissue properties and bulk tissue mechanics is important for understanding tissue failure mechanics and developing biological repair strategies. Difficulties in directly measuring sub-tissue properties led to a growing interest in employing finite element modeling approaches. However, most models are homogeneous and are therefore not sufficient for investigating multiscale tissue mechanics, such as stress distributions between sub-tissue structures. To address this limitation, we developed a structure-based model informed by the native annulus fibrosus structure, where fibers and the matrix were described as distinct materials occupying separate volumes. A multiscale framework was applied such that the model was calibrated at the sub-tissue scale using single-lamellar uniaxial mechanical test data, while validated at the bulk scale by predicting tissue multiaxial mechanics for uniaxial tension, biaxial tension, and simple shear (13 cases). Structure-based model validation results were compared to experimental observations and homogeneous models. While homogeneous models only accurately predicted bulk tissue mechanics for one case, structure-based models accurately predicted bulk tissue mechanics for 12 of 13 cases, demonstrating accuracy and robustness. Additionally, six of eight structure-based model parameters were directly linked to tissue physical properties, further broadening its future applicability. In conclusion, the structure-based model provides a powerful multiscale modeling approach for simultaneously investigating the structure-function relationship at the sub-tissue and bulk tissue scale, which is important for studying multiscale tissue mechanics with degeneration, disease, or injury.

Development of an improved parameter fitting method for planar biaxial testing using rakes

A correct estimation of the material parameters from a planar biaxial test is crucial since they will affect the outcome of the finite element model in which they are used. In a virtual planar biaxial experiment, a difference can be noticed in the stress calculated from the force measured experimentally at the rakes and the actual stress at the center of the sample. As a consequence, a classic parameter fitting does not result in a correct estimation of the material parameters. This difference is caused by the boundary conditions of the set-up and is among others dependent on the sample material. To overcome this problem, a new parameter fitting procedure is proposed that takes this difference into account by calculating a finite element-based correction vector. This paper describes the methodology to apply this new parameter fitting procedure on real experimental data from a planar biaxial test using rakes. To this end, image processing is used to extract the experiment characteristics. This information is used to construct a finite element model. Two variations of the new parameter fitting procedure are investigated using two human aortic samples: a basic approach and an image-based approach. The performance of the method is assessed by the difference between the force measured at the rakes during the experiment and the force at the rakes obtained from the finite element simulation. Both approaches of the new parameter fitting procedure lead to an improved estimation of the sample behavior compared with the classic approach.

Swine Vagina Under Planar Biaxial Loads: An Investigation of Large Deformations and Tears

Vaginal tears are very common and can lead to severe complications such as hemorrhaging, fecal incontinence, urinary incontinence, and dyspareunia. Despite the implications of vaginal tears on women's health, there are currently no experimental studies on the tear behavior of vaginal tissue. In this study, planar equi-biaxial tests on square specimens of vaginal tissue, with sides oriented along the longitudinal direction (LD) and circumferential direction (CD), were conducted using swine as animal model. Three groups of specimens were mechanically tested: the NT group (n = 9), which had no pre-imposed tear, the longitudinal tear (LT) group (n = 9), and the circumferential tear (CT) group (n = 9), which had central pre-imposed elliptically shaped tears with major axes oriented in the LD and the CD, respectively. Through video recording during testing, axial strains were measured for the NT group using the digital image correlation (DIC) technique and axial displacements of hook clamps were measured for the NT, LT, and CT groups in the LD and CD. The swine vaginal tissue was found to be highly nonlinear and somewhat anisotropic. Up to normalized axial hook displacements of 1.15, no tears were observed to propagate, suggesting that the vagina has a high resistance to further tearing once a tear has occurred. However, in response to biaxial loading, the size of the tears for the CT group increased significantly more than the size of the tears for the LT group (p = 0.003). The microstructural organization of the vagina is likely the culprit for its tear resistance and orientation-dependent tear behavior. Further knowledge on the structure–function relationship of the vagina is needed to guide the development of new methods for preventing the severe complications of tearing.

How important is sample alignment in planar biaxial testing of anisotropic soft biological tissues? A finite element study

Finite element models of biomedical applications increasingly use anisotropic hyperelastic material formulations. Appropriate material parameters are essential for a reliable outcome of these simulations, which is why planar biaxial testing of soft biological tissues is gaining importance. However, much is still to be learned regarding the ideal methodology for performing this type of test and the subsequent parameter fitting procedure. This paper focuses on the effect of an unknown sample orientation or a mistake in the sample orientation in a planar biaxial test using rakes. To this end, finite element simulations were conducted with various degrees of misalignment. Variations to the test method and subsequent fitting procedures are compared and evaluated. For a perfectly aligned sample and for a slightly misaligned sample, the parameters of the Gasser-Ogden-Holzapfel model can be found to a reasonable accuracy using a planar biaxial test with rakes and a parameter fitting procedure that takes into account the boundary conditions. However, after a certain threshold of misalignment, reliable parameters can no longer be found. The level of this threshold seems to be material dependent. For a sample with unknown sample orientation, material parameters could theoretically be obtained by increasing the degrees of freedom along which test data is obtained, e.g. by adding the data of a rail shear test. However, in the situation and the material model studied here, the inhomogeneous boundary conditions of the test set-ups render it impossible to obtain the correct parameters, even when using the parameter fitting method that takes into account boundary conditions. To conclude, it is always important to carefully track the sample orientation during harvesting and preparation and to minimize the misalignment during mounting. For transversely isotropic samples with an unknown orientation, we advise against parameter fitting based on a planar biaxial test, even when combined with a rail shear test.

Mechanical Analysis of the Uterosacral Ligament: Swine vs. Human

The uterosacral ligament (USL) is a major suspensory structure of the female pelvic floor, providing support to the cervix and/or upper vagina. It plays a pivotal role in surgical procedures for pelvic organ prolapse (POP) aimed at restoring apical support. Despite its important mechanical function, little is known about the mechanical properties of the USL due to the constraints associated with in vivo testing of human USL and the lack of validated large animal models that enable such investigations. In this study, we provide the first comparison of the mechanical properties of swine and human USLs. Preconditioning and pre-creep data up to a 2 N load and creep data under a 2 N load over 1200 s were obtained on swine (n = 9) and human (n = 9) USL specimens by performing planar equi-biaxial tensile tests and using the digital image correlation method. No differences in the peak strain during preconditioning tests, secant modulus of the pre-creep response, and strain at the end of creep tests were detected in the USLs from the two species along both axial loading directions (the main in vivo loading direction and the direction that is perpendicular to it). These findings suggest that the swine holds promise as large animal model for studying the mechanical role of the USL in apical vaginal support and treatment of POP.

FEBio finite element models of the human lumbar spine

Finite element analysis has proven to be a viable method for assessing many structure-function relationships in the human lumbar spine. Several validated models of the spine have been published, but they typically rely on commercial packages and are difficult to share between labs. The goal of this study is to present the development of the first open-access models of the human lumbar spine in FEBio. This modeling framework currently targets three deficient areas in the field of lumbar spine modeling: 1) open-access models, 2) accessibility for multiple meshing schemes, and 3) options to include advanced hyperelastic and biphasic constitutive models.

A Uniaxial Testing Approach for Consistent Failure in Vascular Tissues

Although uniaxial tensile testing is commonly used to evaluate failure properties of vascular tissue, there is no established protocol for specimen shape or gripping method. Large percentages of specimens are reported to fail near the clamp and can potentially confound the studies, or, if discarded will result in sample waste. The objective of this study is to identify sample geometry and clamping conditions that can achieve consistent failure in the midregion of small arterial specimens, even for vessels from older individuals. Failure location was assessed in 17 dogbone specimens from human cerebral and sheep carotid arteries using soft inserts. For comparison with commonly used protocols, an additional 22 rectangular samples were tested using either sandpaper or foam tape inserts. Midsample failure was achieved in 94% of the dogbone specimens, while only 14% of the rectangular samples failed in the midregion, the other 86% failing close to the clamps. Additionally, we found midregion failure was more likely to be abrupt, caused by cracking or necking. In contrast, clamp failure was more likely to be gradual and included a delamination mode not seen in midregion failure. Hence, this work provides an approach that can be used to obtain consistent midspecimen failure, avoiding confounding clamp-related artifacts. Furthermore, with consistent midregion failure, studies can be designed to image the failure process in small vascular samples providing valuable quantitative information about changes to collagen and elastin structure during the failure process.

Perilimbal sclera mechanical properties: Impact on intraocular pressure in porcine eyes

There is extensive knowledge on the relationship of posterior scleral biomechanics and intraocular pressure (IOP) load on glaucomatous optic neuropathy; however, the role for biomechanical influence of the perilimbal scleral tissue on the aqueous humor drainage pathway, including the distal venous outflow system, and IOP regulation is not fully understood. The purpose of this work is to study the outflow characteristics of perfused porcine eyes relative to the biomechanical properties of the perilimbal sclera, the posterior sclera and the cornea. Enucleated porcine eyes from eleven different animals were perfused with surrogate aqueous at two fixed flow rates while monitoring their IOP. After perfusion, mechanical stress-strain and relaxation tests were conducted on specimens of perilimbal sclera, posterior sclera, and cornea from the same perfused eyes. Statistical analysis of the data demonstrated a strong correlation between increased tangent modulus of the perilimbal sclera tissues and increased perfusion IOP (R² = 0.74, p = 0.0006 at lower flow rate and R² = 0.71, p = 0.0011 at higher flow rate). In contrast, there were no significant correlations between IOP and the tangent modulus of the other tissues (Posterior sclera: R² = 0.17 at lower flow rate and R² = 0.30 at higher flow rate; cornea: R² = 0.02 at lower flow rate and R²<0.01 at higher flow rate) nor the viscoelastic properties of any tissue (R² ≤ 0.08 in all cases). Additionally, the correlation occurred for IOP and not net outflow facility (R² ≤ 0.12 in all cases). These results provide new evidence that IOP in perfused porcine eyes is strongly influenced by the tangent modulus, sometimes called the tissue stiffness, of the most anterior portion of the sclera, i.e. the limbus.

A Novel Small-Specimen Planar Biaxial Testing System With Full In-Plane Deformation Control

Simulations of soft tissues require accurate and robust constitutive models, whose form is derived from carefully designed experimental studies. For such investigations of membranes or thin specimens, planar biaxial systems have been used extensively. Yet, all such systems remain limited in their ability to: (1) fully prescribe in-plane deformation gradient tensor F2D, (2) ensure homogeneity of the applied deformation, and (3) be able to accommodate sufficiently small specimens to ensure a reasonable degree of material homogeneity. To address these issues, we have developed a novel planar biaxial testing device that overcomes these difficulties and is capable of full control of the in-plane deformation gradient tensor F2D and of testing specimens as small as ∼4 mm × ∼4 mm. Individual actuation of the specimen attachment points, combined with a robust real-time feedback control, enabled the device to enforce any arbitrary F2D with a high degree of accuracy and homogeneity. Results from extensive device validation trials and example tissues illustrated the ability of the device to perform as designed and gather data needed for developing and validating constitutive models. Examples included the murine aortic tissues, allowing for investigators to take advantage of the genetic manipulation of murine disease models. These capabilities highlight the potential of the device to serve as a platform for informing and verifying the results of inverse models and for conducting robust, controlled investigation into the biomechanics of very local behaviors of soft tissues and membrane biomaterials.

A Novel Method for Repeatable Failure Testing of Annulus Fibrosus

Tears in the annulus fibrosus (AF) of the intervertebral disk can result in disk herniation and progressive degeneration. Understanding AF failure mechanics is important as research moves toward developing biological repair strategies for herniated disks. Unfortunately, failure mechanics of fiber-reinforced tissues, particularly tissues with fibers oriented off-axis from the applied load, is not well understood, partly due to the high variability in reported mechanical properties and a lack of standard techniques ensuring repeatable failure behavior. Therefore, the objective of this study was to investigate the effectiveness of midlength (ML) notch geometries in producing repeatable and consistent tissue failure within the gauge region of AF mechanical test specimens. Finite element models (FEMs) representing several notch geometries were created to predict the location of bulk tissue failure using a local strain-based criterion. FEM results were validated by experimentally testing a subset of the modeled specimen geometries. Mechanical testing data agreed with model predictions (∼90% agreement), validating the model's predictive power. Two of the modified dog-bone geometries (“half” and “quarter”) effectively ensured tissue failure at the ML for specimens oriented along the circumferential-radial and circumferential-axial directions. The variance of measured mechanical properties was significantly lower for notched samples that failed at the ML, suggesting that ML notch geometries result in more consistent and reliable data. In addition, the approach developed in this study provides a framework for evaluating failure properties of other fiber-reinforced tissues, such as tendons and meniscus.

Effects of repeated biaxial loads on the creep properties of cardinal ligaments

The cardinal ligament (CL) is one of the major pelvic ligaments providing structural support to the vagina/cervix/uterus complex. This ligament has been studied mainly with regards to its important function in the treatment of different diseases such as surgical repair for pelvic organ prolapse and radical hysterectomy for cervical cancer. However, the mechanical properties of the CL have not been fully determined, despite the important in vivo supportive role of this ligament within the pelvic floor. To advance our limited knowledge about the elastic and viscoelastic properties of the CL, we conducted three consecutive planar equi-biaxial tests on CL specimens isolated from swine. Specifically, the CL specimens were divided into three groups: specimens in group 1 (n = 7) were loaded equi-biaxially to 1 N, specimens in group 2 (n = 8) were loaded equi-biaxially to 2N, and specimens in group 3 (n = 7) were loaded equi-biaxially to 3N. In each group, the equi-biaxial loads of 1N, 2N, or 3N were applied and kept constant for 1200s three times. The two axial loading directions were selected to be the main in-vivo loading direction of the CL and the direction that is perpendicular to it. Using the digital image correlation (DIC) method, the in-plane Lagrangian strains in these two loading directions were measured throughout the tests. The results showed that CL was elastically anisotropic, as statistical differences were found between the mean strains along the two axial loading directions for specimens in group 1, 2, or 3 when the equi-biaxial load reached 1N, 2N, or 3N, respectively. For specimens in group 1 and 2, no statistical differences were detected in the mean normalized strains (or, equivalently, the increase in strain over time) between the two axial loading directions for each creep test. For specimens in group 3, some differences were noted but, by the end of the 3rd creep test, there were no statistical differences in the mean normalized strains between the two axial loading directions. These findings indicated that the increase in strain over time by the end of the 3rd creep test were comparable along these directions. The greatest mean normalized strain (or, equivalently, the largest increase in strain over time) was measured at the end of the 1st creep test (t=1200s), regardless of the equi-biaxial load magnitude or loading direction. Mean normalized strains during the 2nd and 3rd creep tests (t = 100, 600, and 1200s), along each loading direction, were not statistically different. Isochronal data collected at 1N, 2N, or 3N equi-biaxial loads indicated that the CL may be a nonlinear viscoelastic material. Overall, this experimental study offers new knowledge of the mechanical properties of the CL that can guide the development of better treatment methods such as surgical reconstruction for pelvic organ prolapse and radical hysterectomy for cervical cancer.

Efficient isogeometric thin shell formulations for soft biological materials

This paper presents three different constitutive approaches to model thin rotation-free shells based on the Kirchhoff-Love hypothesis. One approach is based on numerical integration through the shell thickness while the other two approaches do not need any numerical integration and so they are computationally more efficient. The formulation is designed for large deformations and allows for geometrical and material nonlinearities, which makes it very suitable for the modeling of soft tissues. Furthermore, six different isotropic and anisotropic material models, which are commonly used to model soft biological materials, are examined for the three proposed constitutive approaches. Following an isogeometric approach, NURBS-based finite elements are used for the discretization of the shell surface. Several numerical examples are investigated to demonstrate the capabilities of the formulation. Those include the contact simulation during balloon angioplasty.

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.

An anisotropic hyperelastic constitutive model of brain white matter in biaxial tension and structural-mechanical relationships

Computational models of the brain require accurate and robust constitutive models to characterize the mechanical behavior of brain tissue. The anisotropy of white matter has been previously demonstrated; however, there is a lack of data describing the effects of multi-axial loading, even though brain tissue experiences multi-axial stress states. Therefore, a biaxial tensile experiment was designed to more fully characterize the anisotropic behavior of white matter in a quasi-static loading state, and the mechanical data were modeled with an anisotropic hyperelastic continuum model. A probabilistic analysis was used to quantify the uncertainty in model predictions because the mechanical data of brain tissue can show a high degree of variability, and computational studies can benefit from reporting the probability distribution of model responses. The axonal structure in white matter can be heterogeneous and regionally dependent, which can affect computational model predictions. Therefore, corona radiata and corpus callosum regions were tested, and histology and transmission electron microscopy were performed on tested specimens to relate the distribution of axon orientations and the axon volume fraction to the mechanical behavior. These measured properties were implemented into a structural constitutive model. Results demonstrated a significant, but relatively low anisotropic behavior, yet there were no conclusive mechanical differences between the two regions tested. The inclusion of both biaxial and uniaxial tests in model fits improved the accuracy of model predictions. The mechanical anisotropy of individual specimens positively correlated with the measured axon volume fraction, and, accordingly, the structural model exhibited slightly decreased uncertainty in model predictions compared to the model without structural properties.

Microstructural heterogeneity directs micromechanics and mechanobiology in native and engineered fibrocartilage

Treatment strategies to address pathologies of fibrocartilaginous tissue are in part limited by an incomplete understanding of structure-function relationships in these load-bearing tissues. There is therefore a pressing need to develop micro-engineered tissue platforms that can recreate the highly inhomogeneous tissue microstructures that are known to influence mechanotransductive processes in normal and diseased tissue. Here, we report the quantification of proteoglycan-rich microdomains in developing, ageing and diseased fibrocartilaginous tissues, and the impact of these microdomains on endogenous cell responses to physiologic deformation within a native-tissue context. We also developed a method to generate heterogeneous tissue-engineered constructs (hetTECs) with non-fibrous proteoglycan-rich microdomains engineered into the fibrous structure, and show that these hetTECs match the microstructural, micromechanical and mechanobiological benchmarks of native tissue. Our tissue-engineered platform should facilitate the study of the mechanobiology of developing, homeostatic, degenerating and regenerating fibrous tissues.

Planar biaxial testing of soft biological tissue using rakes: A critical analysis of protocol and fitting process

Mechanical characterization of soft biological tissue is becoming more and more prevalent. Despite the growing use of planar biaxial testing for soft tissue characterization, testing conditions and subsequent data analysis have not been standardized and vary widely. This also influences the quality of the result of the parameter fitting. Moreover, the testing conditions and data analysis are often not or incompletely reported, which impedes the proper comparison of parameters obtained from different studies. With a focus on planar biaxial tests using rakes, this paper investigates varying testing conditions and varying data analysis methods and their effect on the quality of the parameter fitting results. By means of a series of finite element simulations, aspects such as number of rakes, rakes׳ width, loading protocol, constitutive model, material stiffness and anisotropy are evaluated based on the degree of homogeneity of the stress field, and on the correlation between the experimentally obtained stress and the stress derived from the constitutive model. When calculating the aforementioned stresses, different definitions of the section width and deformation gradient are used in literature, each of which are looked into. Apart from this degree of homogeneity and correlation, also the effect on the quality of the parameter fitting result is evaluated. The results show that inhomogeneities can be reduced to a minimum for wise choices of testing conditions and analysis methods, but never completely eliminated. Therefore, a new parameter optimization procedure is proposed that corrects for the inhomogeneities in the stress field and induces significant improvements to the fitting results. Recommendations are made for best practice in rake-based planar biaxial testing of soft biological tissues and subsequent parameter fitting, and guidelines are formulated for reporting thereof in publications.

A comparison of stress in cracked fibrous tissue specimens with varied crack location, loading, and orientation using finite element analysis

Cracks in fibrous soft tissue, such as intervertebral disc annulus fibrosus and knee meniscus, cause pain and compromise joint mechanics. A crack concentrates stress at its tip, making further failure and crack extension (fracture) more likely. Ex vivo mechanical testing is an important tool for studying the loading conditions required for crack extension, but prior work has shown that it is difficult to reproduce crack extension. Most prior work used edge crack specimens in uniaxial tension, with the crack 90° to the edge of the specimen. This configuration does not necessarily represent the loading conditions that cause in vivo crack extension. To find a potentially better choice for experiments aiming to reproduce crack extension, we used finite element analysis to compare, in factorial combination, (1) center crack vs. edge crack location, (2) biaxial vs. uniaxial loading, and (3) crack-fiber angles ranging from 0° to 90°. The simulated material was annulus fibrosus fibrocartilage with a single fiber family. We hypothesized that one of the simulated test cases would produce a stronger stress concentration than the commonly used uniaxially loaded 90° crack-fiber angle edge crack case. Stress concentrations were compared between cases in terms of fiber-parallel stress (representing risk of fiber rupture), fiber-perpendicular stress (representing risk of matrix rupture), and fiber shear stress (representing risk of fiber sliding). Fiber-perpendicular stress and fiber shear stress concentrations were greatest in edge crack specimens (of any crack-fiber angle) and center crack specimens with a 90° crack-fiber angle. However, unless the crack is parallel to the fiber direction, these stress components alone are insufficient to cause crack opening and extension. Fiber-parallel stress concentrations were greatest in center crack specimens with a 45° crack-fiber angle, either biaxially or uniaxially loaded. We therefore recommend that the 45° center crack case be tried in future experiments intended to study crack extension by fiber rupture.

Crack Propagation Versus Fiber Alignment in Collagen Gels: Experiments and Multiscale Simulation

It is well known that the organization of the fibers constituting a collagenous tissue can affect its failure behavior. Less clear is how that effect can be described computationally so as to predict the failure of a native or engineered tissue under the complex loading conditions that can occur in vivo. Toward the goal of a general predictive strategy, we applied our multiscale model of collagen gel mechanics to the failure of a double-notched gel under tension, comparing the results for aligned and isotropic samples. In both computational and laboratory experiments, we found that the aligned gels were more likely to fail by connecting the two notches than the isotropic gels. For example, when the initial notches were 30% of the sample width (normalized tip-to-edge distance = 0.7), the normalized tip-to-tip distance at which the transition occurred from between-notch failure to across-sample failure shifted from 0.6 to 1.0. When the model predictions for the type of failure event (between the two notches versus across the sample width) were compared to the experimental results, the two were found to be strongly covariant by Fisher's exact test (p < 0.05) for both the aligned and isotropic gels with no fitting parameters. Although the double-notch system is idealized, and the collagen gel system is simpler than a true tissue, it presents a simple model system for studying failure of anisotropic tissues in a controlled setting. The success of the computational model suggests that the multiscale approach, in which the structural complexity is incorporated via changes in the model networks rather than via changes to a constitutive equation, has the potential to predict tissue failure under a wide range of conditions.

Validation and application of an intervertebral disc finite element model utilizing independently constructed tissue-level constitutive formulations that are nonlinear, anisotropic, and time-dependent

Finite element (FE) models are advantageous in the study of intervertebral disc mechanics as the stress-strain distributions can be determined throughout the tissue and the applied loading and material properties can be controlled and modified. However, the complicated nature of the disc presents a challenge in developing an accurate and predictive disc model, which has led to limitations in FE geometry, material constitutive models and properties, and model validation. The objective of this study was to develop a new FE model of the intervertebral disc, to validate the model's nonlinear and time-dependent responses without tuning or calibration, and to evaluate the effect of changes in nucleus pulposus (NP), cartilaginous endplate (CEP), and annulus fibrosus (AF) material properties on the disc mechanical response. The new FE disc model utilized an analytically-based geometry. The model was created from the mean shape of human L4/L5 discs, measured from high-resolution 3D MR images and averaged using signed distance functions. Structural hyperelastic constitutive models were used in conjunction with biphasic-swelling theory to obtain material properties from recent tissue tests in confined compression and uniaxial tension. The FE disc model predictions fit within the experimental range (mean ± 95% confidence interval) of the disc's nonlinear response for compressive slow loading ramp, creep, and stress-relaxation simulations. Changes in NP and CEP properties affected the neutral-zone displacement but had little effect on the final stiffness during slow-ramp compression loading. These results highlight the need to validate FE models using the disc's full nonlinear response in multiple loading scenarios.