A comparison of uniaxial and biaxial mechanical properties of the annulus fibrosus: a porcine model

Biaxial mechanical properties of the bronchial tree: Characterization of elasticity, extensibility, and energetics, including the effect of strain rate and preconditioning

Distal airways commonly obstruct in lung disease and despite their importance, their mechanical properties are vastly underexplored. The lack of bronchial experiments restricts current airway models to either assume rigid structures, or extrapolate the material properties of the trachea to represent the small airways. Furthermore, past works are exclusively limited to uniaxial testing; investigating the multidirectional tensile loads of both the proximal and distal pulmonary airways is long overdue. Here we present comprehensive mechanical and viscoelastic properties of the porcine airway tree, including the trachea, trachealis muscle, large bronchi, and small bronchi, via measures of elasticity, extensibility, and energetics to explore regional and directional dependencies, cross-examining strain rate and preconditioning effects using planar equibiaxial tensile tests for the first time. We find bronchial regions are notably heterogeneous, where the trachea exhibits greater stiffness, energy loss, and preconditioning sensitivity than the smaller airways. Interestingly, the trachealis muscle is similar to the distal bronchi, despite being anatomically located adjacent to the proximal ring. Tissues are anisotropic and axially stiffer under initial loading, losing more energy with greater stress relaxation circumferentially. Strain rate dependency is also noted, where tissues are more energetically efficient at the faster strain rate, likely attributable to the microstructure. Findings highlight assumptions of homogeneity and isotropy are inadequate, and enable the improvement of aerosol flow and dynamic airway deformation computational predictive models. These results provide much needed fundamental material properties for future explorations contrasting healthy versus diseased pulmonary airway mechanics to better understand the relationship between structure and lung function. STATEMENT OF SIGNIFICANCE: We present comprehensive multiaxial mechanical tensile experiments of the proximal and distal airways via measures of maximum stress, initial and ultimate moduli, strain and stress transitions, hysteresis, energy loss, and stress relaxation, and further assess preconditioning and strain rate dependencies to examine the relationship between lung function and structure. The mechanical response of the bronchial tree demonstrates significant anisotropy and heterogeneity, even within the tracheal ring, and emphasizes that contrary to past studies, the behavior of the proximal airways cannot be extended to distal bronchial tree analyses. Establishing these material properties is critical to advancing our understanding of airway function and in developing accurate computational simulations to help diagnose and monitor pulmonary diseases.

Mechanical characterisation of the human dura mater, falx cerebri and superior sagittal sinus

The cranial meninges have been shown to play a pivotal role in traumatic brain injury mechanopathology. However, while the mechanical response of the brain and its many subregions have been studied extensively, the meninges have conventionally been overlooked. This paper presents the first comparative mechanical analysis of human dura mater, falx cerebri and superior sagittal sinus tissues. Biaxial tensile analysis identified that these tissues are mechanically heterogeneous, in contrast to the assumption that the tissues are mechanically homogeneous which is typically employed in FE model design. A thickness of 0.91 ± 0.05 (standard error) mm for the falx cerebri was also identified. This data can aid in improving the biofidelity of the influential falx structure in FE models. Additionally, the use of a collagen hybridizing peptide on the superior sagittal sinus suggests this structure is particularly susceptible to the effects of circumferential stretch, which may have important implications for clinical treatment of dural venous sinus pathologies. Collectively, this research progresses understanding of meningeal mechanical and structural characteristics and may aid in elucidating the behaviour of these tissues in healthy and diseased conditions. STATEMENT OF SIGNIFICANCE: This study presents the first evaluation of human falx cerebri and superior sagittal sinus mechanical, geometrical and structural properties, along with a comparison to cranial dura mater. To mechanically characterise the tissues, biaxial tensile testing is conducted on the tissues. This analysis identifies, for the first time, mechanical stiffness differences between these tissues. Additionally, geometrical analysis identifies that there are thickness differences between the tissues. The evaluation of human meningeal tissues allows for direct implementation of the novel data to finite element head injury models to enable improved biofidelity of these influential structures in traumatic brain injury simulations. This work also identifies that the superior sagittal sinus may be easily damaged during clinical angioplasty procedures, which may inform the treatment of dural sinus pathologies.

The mechano-response of murine annulus fibrosus cells to cyclic tensile strain is frequency dependent

The intervertebral disk (IVD) is a composite structure essential for spine stabilization, load bearing, and movement. Biomechanical factors are important contributors to the IVD microenvironment regulating joint homeostasis; however, the cell type-specific effectors of mechanotransduction in the IVD are not fully understood. The current study aimed to determine the effects of cyclic tensile strain (CTS) on annulus fibrosus (AF) cells and identify mechano-sensitive pathways. Using a cell-type specific reporter mouse to differentiation NP and AF cells from the murine IVD, we characterized AF cells in dynamic culture exposed to CTS (6% strain) at specific frequencies (0.1 Hz, 1.0 Hz, or 2.0 Hz). We demonstrate that our culture model maintains the phenotype of primary AF cells and that the bioreactor system delivers uniform biaxial strain across the cell culture surface. We show that exposure of AF cells to CTS induces cytoskeleton reorganization resulting in stress fiber formation, with acute exposure to CTS at 2.0 Hz inducing a significant yet transient increase ERK1/2 pathway activation. Using SYBPR-based qPCR to assess the expression of extracellular matrix (ECM) genes, ECM-remodeling genes, candidate mechano-sensitive genes, inflammatory cytokines and cell surface receptors, we demonstrated that exposure of AF cells to CTS at 0.1 Hz increased Acan, Prg4, Col1a1 and Mmp3 expression. AF cells exposed to CTS at 1.0 Hz showed a significant increase in the expression of Acan, Myc, and Tnfα. Exposure of AF cells to CTS at 2.0 Hz induced a significant increase in Acan, Prg4, Cox2, Myc, Fos, and Tnfα expression. Among the cell surface receptors assessed, AF cells exposed to CTS at 2.0 Hz showed a significant increase in Itgβ1, Itgα5, and Trpv4 expression. Our findings demonstrate that the response of AF cells to CTS is frequency dependent and suggest that mechanical loading may directly contribute to matrix remodeling and the onset of local tissue inflammation in the murine IVD.

Interlamellar matrix governs human annulus fibrosus multiaxial behavior

Establishing accurate structure–property relationships for intervertebral disc annulus fibrosus tissue is a fundamental task for a reliable computer simulation of the human spine but needs excessive theoretical-numerical-experimental works. The difficulty emanates from multiaxiality and anisotropy of the tissue response along with regional dependency of a complex hierarchic structure interacting with the surrounding environment. We present a new and simple hybrid microstructure-based experimental/modeling strategy allowing adaptation of animal disc model to human one. The trans-species strategy requires solely the basic knowledge of the uniaxial circumferential response of two different animal disc regions to predict the multiaxial response of any human disc region. This work demonstrates for the first time the determining role of the interlamellar matrix connecting the fibers-reinforced lamellae in the disc multiaxial response. Our approach shows encouraging multiaxial predictive capabilities making it a promising tool for human spine long-term prediction.

Rapid increase in intradiscal pressure in porcine cervical spine units negatively impacts annulus fibrosus strength

Vertebral endplate fracture is generally accepted to occur as a result of excessive, typically rapid, pressure developed within the intervertebral disc. Clinical evidence of disc disorders later in life following endplate fracture suggests that the disc is also impacted by the fracture event. There is an abundance of evidence to indicate that loss of disc pressure at the time of fracture alters annulus fibrosus loading which could impact disc health long-term. However, little is known regarding the isolated impact of the rapid disc pressurization during the fracture event. This study sought to determine if rapid disc pressurization impacts mechanical properties of the annulus. Intervertebral discs of porcine cervical functional spine units (FSU) were pressurized via rapid injection of hydraulic fluid (standard motor oil). FSUs were subsequently grouped according to whether the pressurization resulted in endplate fracture ('fracture'; n = 9) or not ('non-fracture'; n = 13). Annular tensile properties and lamellar adhesion strength were quantified for both fractured and non-fractured samples. A third group was also examined in which FSUs did not undergo the pressurization protocol ('control'; n = 10). Annular tensile properties were not found to be statistically different between the three conditions (p > 0.05). Lamellar adhesion strength, in contrast, was found to be, on average, 53% lower in specimens which were pressurized compared to control, non-pressurized samples (p = 0.03). Further, no statistical differences in adhesion strength was found between fractured and non-fractured pressurized samples (p = 0.990) indicating that rapid pressurization , and not the presence of an endplate fracture, impacted the mechanical properties of the annulus. Decreased lamellar adhesion strength increases the potential of delamination, which can lead to disc disorders.

Creep experimental study on the lumbar intervertebral disk under vibration compression load

The intervertebral disk cushions the load generated by human activity and absorbs energy to keep the spine moving steadily. Vibration condition is one of the important causes of disk degeneration. Creep experiments using the sheep lumbar intervertebral disk were carried out under vibration compression. Regularities of the strain of the disk with time were obtained and compared with those of static load. The influence of vibration frequency and time on the creep properties of the intervertebral disk was analyzed. An intervertebral disk three-parameter solid creep constitutive model considering vibration factors was established and the parameters in the model were identified. The results show that the strain of the lumbar intervertebral disk exhibits an exponential relationship with time and is unrelated to static compression or vibration load. Under the same vibration amplitude, the creep increases with vibration frequency and the relationship between them is nonlinear. The vibration frequency has a significant effect on the strain. The creep rate decreases gradually with time and is obviously influenced by vibration frequency at low vibration amplitudes. The creep prediction results obtained using the constitutive model with the time-varying material parameters are in good agreement with the experimental results. The two elastic moduli in the model decrease with time and the viscosity coefficient increases with time.

The Effect of Local Hydration Environment on the Mechanical Properties and Unloaded Temporal Changes of Isolated Porcine Annular Samples

Preventing dehydration during in vitro testing of isolated layers of annulus fibrosus tissue may require different test conditions than functional spine units. The purpose of the study was twofold: (A) to quantify changes in mass and thickness of multilayer annulus samples in four hydration environments over 120 min; and (B) to quantify cycle-varying biaxial tensile properties of annulus samples in the four environments. The environments included a saline bath, air, relative humidity control, and misting combined with controlled humidity. The loading protocol implemented 24 cycles of biaxial tensile loading to 20% strain at a rate of 2%/s with 3-, 8-, and 13-min of intermittent rest. Specimen mass increased an average (standard deviation) 72% (11) when immersed for 120 min (p < 0.0001). The air condition and the combined mist and relative humidity conditions reduced mass by 45% (15) and 25% (23), respectively, after 120 min (p < 0.0014). Stress at 16% stretch in the air condition was higher at cycle 18 (18 min of exposure) and cycle 24 (33 min of exposure) compared to all other environments in both the axial and circumferential directions (p < 0.0460). There was no significant change in mass or thickness over time in the relative humidity condition and the change in circumferential stress at 16% stretch between cycles 6 and 24 was a maximum of 0.099 MPa and not statistically significant. Implementation of a controlled relative humidity environment is recommended to maintain hydration of isolated annulus layers during cyclic tensile testing.

Peak Stress in the Annulus Fibrosus Under Cyclic Biaxial Tensile Loading

Numerous in vitro studies have examined the initiation and propagation of fatigue injury pathways in the annulus fibrosus (AF) using isolated motion segments; however, the cycle-varying changes to the AF under cyclic biaxial tensile loading conditions have yet to be examined. Therefore, the primary objective of this study was to characterize the cycle-varying changes in peak tensile stress in multilayer AF tissue samples within a range of physiologically relevant loading conditions at subacute magnitudes of tissue stretch up to 100 loading cycles. A secondary aim was to examine whether the stress-relaxation response would be different across loading axes (axial and circumferential) and whether this response would vary across regions of the intervertebral disk (IVD) (anterior and posterior-lateral). The results from the study demonstrate that several significant interactions emerged between independent factors that were examined in the study. Specifically, a three-way interaction between the radial location, magnitude of peak tissue stretch, and cycle rate (p = 0.0053) emerged. Significant two-way interactions between the magnitude of tissue stretch and cycle number (p < 0.0001) and the magnitude of tissue stretch and loading axis (p < 0.0001) were also observed. These findings are discussed in the context of known mechanisms for structural damage, which have been linked to fatigue loading in the IVD (e.g., cleft formation, radial tearing, increased neutral zone, disk bulging, and loss of intradiscal pressure).

On the Use of Biaxial Properties in Modeling Annulus as a Holzapfel-Gasser-Ogden Material

Besides the biology, stresses and strains within the tissue greatly influence the location of damage initiation and mode of failure in an intervertebral disk. Finite element models of a functional spinal unit (FSU) that incorporate reasonably accurate geometry and appropriate material properties are suitable to investigate such issues. Different material models and techniques have been used to model the anisotropic annulus fibrosus, but the abilities of these models to predict damage initiation in the annulus and to explain clinically observed phenomena are unclear. In this study, a hyperelastic anisotropic material model for the annulus with two different sets of material constants, experimentally determined using uniaxial and biaxial loading conditions, were incorporated in a 3D finite element model of a ligamentous FSU. The purpose of the study was to highlight the biomechanical differences (e.g., intradiscal pressure, motion, forces, stresses, strains, etc.) due to the dissimilarity between the two sets of material properties (uniaxial and biaxial). Based on the analyses, the biaxial constants simulations resulted in better agreements with the in vitro and in vivo data, and thus are more suitable for future damage analysis and failure prediction of the annulus under complex multiaxial loading conditions.

A generalized method for the analysis of planar biaxial mechanical data using tethered testing configurations

Simulation of the mechanical behavior of soft tissues is critical for many physiological and medical device applications. Accurate mechanical test data is crucial for both obtaining the form and robust parameter determination of the constitutive model. For incompressible soft tissues that are either membranes or thin sections, planar biaxial mechanical testing configurations can provide much information about the anisotropic stress-strain behavior. However, the analysis of soft biological tissue planar biaxial mechanical test data can be complicated by in-plane shear, tissue heterogeneities, and inelastic changes in specimen geometry that commonly occur during testing. These inelastic effects, without appropriate corrections, alter the stress-traction mapping and violates equilibrium so that the stress tensor is incorrectly determined. To overcome these problems, we presented an analytical method to determine the Cauchy stress tensor from the experimentally derived tractions for tethered testing configurations. We accounted for the measured testing geometry and compensate for run-time inelastic effects by enforcing equilibrium using small rigid body rotations. To evaluate the effectiveness of our method, we simulated complete planar biaxial test configurations that incorporated actual device mechanisms, specimen geometry, and heterogeneous tissue fibrous structure using a finite element (FE) model. We determined that our method corrected the errors in the equilibrium of momentum and correctly estimated the Cauchy stress tensor. We also noted that since stress is applied primarily over a subregion bounded by the tethers, an adjustment to the effective specimen dimensions is required to correct the magnitude of the stresses. Simulations of various tether placements demonstrated that typical tether placements used in the current experimental setups will produce accurate stress tensor estimates. Overall, our method provides an improved and relatively straightforward method of calculating the resulting stresses for planar biaxial experiments for tethered configurations, which is especially useful for specimens that undergo large shear and exhibit substantial inelastic effects.

Strain distribution in the intervertebral disc under unconfined compression and tension load by the optimized digital image correlation technique

The unconfined compression and tension experiments of the intervertebral disc were conducted by applying an optimized digital image correlation technique, and the internal strain distribution was analysed for the disc. It was found that the axial strain values of different positions increased obviously with the increase in loads, while inner annulus fibrosus and posterior annulus fibrosus experienced higher axial strains than the outer annulus fibrosus and anterior annulus fibrosus. Deep annulus fibrosus exhibited higher compressive and tensile axial strains than superficial annulus fibrosus for the anterior region, while there was an opposite result for the posterior region. It was noted that all samples demonstrated a nonlinear stress–strain profile in the process of deforming, and an elastic region was shown once the sample was deformed beyond its toe region.

Region specific response of intervertebral disc cells to complex dynamic loading: an organ culture study using a dynamic torsion-compression bioreactor

The spine is routinely subjected to repetitive complex loading consisting of axial compression, torsion, flexion and extension. Mechanical loading is one of the important causes of spinal diseases, including disc herniation and disc degeneration. It is known that static and dynamic compression can lead to progressive disc degeneration, but little is known about the mechanobiology of the disc subjected to combined dynamic compression and torsion. Therefore, the purpose of this study was to compare the mechanobiology of the intervertebral disc when subjected to combined dynamic compression and axial torsion or pure dynamic compression or axial torsion using organ culture. We applied four different loading modalities [1. control: no loading (NL), 2. cyclic compression (CC), 3. cyclic torsion (CT), and 4. combined cyclic compression and torsion (CCT)] on bovine caudal disc explants using our custom made dynamic loading bioreactor for disc organ culture. Loads were applied for 8 h/day and continued for 14 days, all at a physiological magnitude and frequency. Our results provided strong evidence that complex loading induced a stronger degree of disc degeneration compared to one degree of freedom loading. In the CCT group, less than 10% nucleus pulposus (NP) cells survived the 14 days of loading, while cell viabilities were maintained above 70% in the NP of all the other three groups and in the annulus fibrosus (AF) of all the groups. Gene expression analysis revealed a strong up-regulation in matrix genes and matrix remodeling genes in the AF of the CCT group. Cell apoptotic activity and glycosaminoglycan content were also quantified but there were no statistically significant differences found. Cell morphology in the NP of the CCT was changed, as shown by histological evaluation. Our results stress the importance of complex loading on the initiation and progression of disc degeneration.

Modeling Degenerative Disk Disease in the Lumbar Spine: A Combined Experimental, Constitutive, and Computational Approach

Using a continuum approach for modeling the constitutive mechanical behavior of the intervertebral disk’s annulus fibrosus holds the potential for facilitating the correlation of morphology and biomechanics of this clinically important tissue. Implementation of a continuum representation of the disk’s tissues into computational models would yield a particularly valuable tool for investigating the effects of degenerative disease. However, to date, relevant efforts in the literature towards this goal have been limited due to the lack of a computationally tractable and implementable constitutive function. In order to address this, annular specimens harvested from a total of 15 healthy and degenerated intervertebral disks were tested under planar biaxial tension. Predictions of a strain energy function, which was previously shown to be unconditionally convex, were fit to the experimental data, and the optimized coefficients were used to modify a previously validated finite element model of the L4/L5 functional spinal unit. Optimization of material coefficients based on experimental results indicated increases in the micro-level orientation dispersion of the collagen fibers and the mechanical nonlinearity of these fibers due to degeneration. On the other hand, the finite element model predicted a progressive increase in the stress generation in annulus fibrosus due to stepwise degeneration of initially the nucleus and then the entire disk. Range of motion was predicted to initially increase with the degeneration of the nucleus and then decrease with the degeneration of the annulus in all rotational loading directions, except for axial rotation. Overall, degeneration was observed to specifically impact the functional effectiveness of the collagen fiber network of the annulus, leading to changes in the biomechanical behavior at both the tissue level and the motion-segment level.

Characterization of the annulus fibrosus-vertebral body interface: identification of new structural features

Current surgical treatments for degenerative intervertebral disc disease do not restore full normal spinal movement. Tissue engineering a functional disc replacement may be one way to circumvent this limitation, but will require an integration of the different tissues making up the disc for this approach to be successful. Hence, an in-depth characterization of the native tissue interfaces, including annulus insertion into bone is necessary, as knowledge of this interface is limited. The objective of this study was to characterize the annulus fibrosus-vertebral bone (AF-VB) interface in immature (6-9 months old) and mature (18-24 months old) bovine discs, as well as to define these structures for normal adult human (22 and 45 years old) discs. Histological assessment showed that collagen fibers in the inner annulus, which are predominantly type II collagen, all appear to insert into the mineralized endplate zone. In contrast, some of the collagen fibers of the outer annulus, predominantly type I collagen, insert into this endplate, while other fibers curve laterally, at an ∼ 90° angle, to the outer aspect of the bone, and merge with the periosteum. This is seen in both human and bovine discs. Where the AF inserts into the calcified zone of the AF-VB interface, it passes through a chondroid region, rich in type II collagen and proteoglycans. Annulus cells (elongated cells that are not surrounded by proteoglycans) are present at this interface. This cartilage zone is evident in both human and bovine discs. Type X collagen and alkaline phosphatase are localized to the interface region. Age-associated differences in bovine spines are observed when examining the interface thickness and the matrix composition of the cartilaginous endplate, as well as the thickness of the mineralized endplate. These findings will assist with the design of the AF-VB interface in the tissue engineered disc.

Biomechanical properties of the transverse carpal ligament under biaxial strain

The transverse carpal ligament (TCL) influences carpal stability and carpal tunnel mechanics, yet little is known about its mechanical properties. We investigated the tissue properties of TCLs extracted from eight cadaver arms and divided into six tissue samples from the distal radial, distal middle, distal ulnar, proximal radial, proximal middle, and proximal ulnar regions. The 5% and 15% strains were applied biaxially to each sample at rates of 0.1, 0.25, 0.5, and 1%/s. Ligament thickness ranged from 1.22 to 2.90 mm. Samples from the middle of the TCL were thicker proximally than distally (p < 0.013). Tissue location significantly affected elastic modulus (p < 0.001). Modulus was greatest in the proximal radial samples (mean 2.8 MPa), which were 64% and 44% greater than the distal radial and proximal ulnar samples, respectively. Samples from the middle had a modulus that was 20-39% greater in the proximal versus more distal samples. The TCL exhibited different properties within different locations and in particular greater moduli were found near the carpal bone attachments. These properties contribute to the understanding of carpal tunnel mechanics that is critical to understanding disorders of the wrist.

Human annulus fibrosus material properties from biaxial testing and constitutive modeling are altered with degeneration

The annulus fibrosus (AF) of the intervertebral disk undergoes large and multidirectional stresses and strains. Uniaxial tensile tests are limited for measuring AF material properties, because freely contracting edges can prevent fiber stretch and are not representative of in situ boundary conditions. The objectives of this study were to measure human AF biaxial tensile mechanics and to apply and validate a constitutive model to determine material properties. Biaxial tensile tests were performed on samples oriented along the circumferential-axial and the radial-axial directions. Data were fit to a structurally motivated anisotropic hyperelastic model composed of isotropic extra-fibrillar matrix, nonlinear fibers, and fiber-matrix interactions (FMI) normal to the fibers. The validated model was used to simulate shear and uniaxial tensile behavior, to investigate AF structure-function, and to quantify the effect of degeneration. The biaxial stress-strain response was described well by the model (R (2) > 0.9). The model showed that the parameters for fiber nonlinearity and the normal FMI correlated with degeneration, resulting in an elongated toe-region and lower stiffness with degeneration. The model simulations in shear and uniaxial tension successfully matched previously published circumferential direction Young's modulus, provided an explanation for the low values in previously published axial direction Young's modulus, and was able to simulate shear mechanics. The normal FMI were important contributors to stress and changed with degeneration, therefore, their microstructural and compositional source should be investigated. Finally, the biaxial mechanical data and constitutive model can be incorporated into a disk finite element model to provide improved quantification of disk mechanics.