Elastic, permeability and swelling properties of human intervertebral disc tissues: A benchmark for tissue engineering

Characterizing baseline fixed charge density in human cervical intervertebral discs

This study provides quantification of fixed charge density in human cervical intervertebral discs. Fixed charge density, which occurs due to negatively charged proteoglycans in the extracellular matrix, is a key determinant of the intervertebral disc osmotic environment and swelling properties. While regional fixed charge density patterns have been characterized in lumbar discs, they remain unexplored in cervical discs. Using fresh-frozen cadaveric cervical discs from five donors, fixed charge density was measured using a two-point electrical conductivity method. Glycosaminoglycan content and porosity were also assessed. Fixed charge density (0.18 ± 0.1 mEq/g wet tissue) was highest in the cartilage endplate region and significantly greater than in that in the annulus fibrosus (p = 0.006). No significant difference in fixed charge density was observed between the nucleus pulposus and annulus fibrosus. Glycosaminoglycan content (40.3 ± 14.4 µg/mg wet tissue) showed a strong positive correlation with fixed charge density across regions (r = 0.65, p = 0.0047). Unlike lumbar discs, fixed charge density was found to be more homogeneous between the nucleus pulposus and annulus fibrosus regions. This result likely reflects adaptations for reduced tissue swelling in cervical discs to accommodate lower weight-bearing demands and increased flexibility. The elevated fixed charge density in the cervical endplates may protect the intervertebral disc-vertebral bone interface, potentially to avoid mechanical damage in a kinematically more mobile environment. These findings establish key benchmarks for understanding cervical disc electro-biomechanics and may inform other cervical disc tissue-characterization efforts.

Stress relaxation behavior of the transition zone in the intervertebral disc

The stress relaxation of the TZ region, located at the interface of the Annulus Fibrosus (AF) and Nucleus Pulposus (NP) of the disc, and how its stress is relaxed compared to the adjacent regions is unknown. The current study aimed to identify the TZ stress relaxation properties under different strain magnitudes (0.2, 0.4, and 0.6 mm/mm) and compared the TZ stress relaxation characteristics to the NP and inner AF (IAF) regions at a specific strain magnitude (0.6 mm/mm). The results of the current study revealed that the TZ region exhibited different stress relaxation properties under various strain magnitudes with significantly higher initial (p < 0.008) and reduced stresses (marginally; p = 0.06) at higher strains. Our experimental stress relaxation data revealed a significantly higher equilibrium stress for the IAF compared to the TZ and NP regions (p < 0.001) but not between the TZ and NP regions (p = 0.7). We found that NP radial stress relaxed significantly faster (p < 0.04) than the TZ and NP. Additionally, the current study proposed a simple mathematical model and identified that, consistent with experimental data, the overall effect of region on both the level of decayed stress and the rate at which stress is relaxed was significant (p < 0.006). The current study found a similar stress relaxation characteristic between the NP and TZ regions, while IAF exhibited different stress relaxation properties. It is possible that this mismatch in stress relaxation acts as a shape transformation mechanism triggered by viscoelastic behavior. STATEMENT OF SIGNIFICANCE: Our understanding of the biomechanical properties of the transition zone (TZ) in the IVD, a region at the interface of the Nucleus Pulposus (NP) and Annulus Fibrosus (AF), is sparse. Unfortunately, there are no current studies that investigate the TZ stress relaxation properties and how stress is relaxed in the TZ compared to the adjacent regions. For the first time, the current study characterized the stress relaxation properties of the TZ and described how the TZ stress is relaxed compared to its adjacent regions.

Global and local identifiability analysis of a nonlinear biphasic constitutive model in confined compression

Application of biomechanical models relies on model parameters estimated from experimental data. Parameter non-identifiability, when the same model output can be produced by many sets of parameter values, introduces severe errors yet has received relatively little attention in biomechanics and is subtle enough to remain unnoticed in the absence of deliberate verification. The present work develops a global identifiability analysis method in which cluster analysis and singular value decomposition are applied to vectors of parameter-output variable correlation coefficients. This method provides a visual representation of which specific experimental design elements are beneficial or harmful in terms of parameter identifiability, supporting the correction of deficiencies in the test protocol prior to testing physical specimens. The method was applied to a representative nonlinear biphasic model for cartilaginous tissue, demonstrating that confined compression data does not provide identifiability for the biphasic model parameters. This result was confirmed by two independent analyses: local analysis of the Hessian of a sum-of-squares error cost function and observation of the behaviour of two optimization algorithms. Therefore, confined compression data are insufficient for the calibration of general-purpose biphasic models. Identifiability analysis by these or other methods is strongly recommended when planning future experiments.

A data-driven microstructure-based model for predicting circumferential behavior and failure in degenerated human annulus fibrosus

The degeneration of the intervertebral disc annulus fibrosus poses significant challenges in understanding and predicting its mechanical behavior. In this article, we present a novel approach, enriched with detailed insights into microstructure and degeneration progression, to accurately predict the mechanics of the degenerated human annulus. Central to this framework is a fully three-dimensional continuum-based model that integrates hydration state and multiscale structural features, including proteoglycan macromolecules and interpenetrating collagen fibrillar networks across various hierarchical levels within the multi-layered lamellar/inter-lamellar soft tissue, capable of sustaining deformation-induced damage. To ensure accurate and comprehensive predictions of the degenerated annulus mechanical behavior, we establish a data-driven correlation between disc degeneration grade and individual age, which influences the composition and mechanical integrity of annulus constituents while accounting for regional variations. The methodology includes a thorough identification of age- and grade-related evolutions of model inputs, followed by a detailed quantitative evaluation of the model predictive capabilities, with a focus on circumferential behavior and failure. The model successfully replicates experimental data, accurately capturing stiffness, transverse response (Poisson's ratio), and ultimate properties across different annulus regions, while also accommodating the modulation of the age/grade relationship. The reduction rates between normal and severe degeneration align reasonably well with experimental data, with the inner region exhibiting the largest decrease in stiffness (34.63 %) and no significant change observed in the outer region. Failure stress drops considerably in both regions (49.86 % in the inner and 45.33 % in the outer), while failure strain decreases by 36.39 % in the outer and 24.74 % in the inner. Our findings demonstrate that the proposed framework significantly enhances the predictive accuracy of annulus mechanics across a spectrum of degeneration levels, from normal to severely degenerated states. This approach promises improved predictive accuracy, deeper insights into disc health and injury risk, and a robust foundation for further research on the impact of degeneration on disc integrity. STATEMENT OF SIGNIFICANCE: Understanding and predicting the mechanical behavior of degenerated human annulus fibrosus remains a significant challenge due to the complex interplay of structural, biochemical, and age-related factors. This study presents a microstructure-based approach to address this challenge by integrating hydration state, detailed structural features across hierarchical scales, and deformation-induced damage and failure, alongside age-related changes and degeneration grade factors. This approach enables accurate simulations of annulus mechanics across regions, with model results thoroughly compared to available data, reinforcing its applicability in capturing degeneration effects. By capturing the intricate interactions between microstructure and mechanical behavior in degenerated discs, the model lays a strong foundation for improving clinical assessments and guiding future treatment strategies for disc-related conditions.

Finite element model reveals the involvement of cartilage endplate in quasi-static biomechanics of intervertebral disc degeneration

Background and objective

The intrinsic link between the compositional and structural attributes and the biomechanical functionality is evident in intervertebral discs. However, it remains unclear from a biomechanical perspective whether cartilage endplate (CEP) degeneration exacerbates intervertebral disc degeneration.

Methods

This study developed and quantitatively validated four biphasic swelling-based finite element models. We then applied four quasi-static tests and simulated daily loading scenarios to examine the effects of CEP degradation.

Results

Under free-swelling conditions, short-term responses were prevalent, with CEP performance changes not significantly impacting response proportionality. The creep test results showed the more than 50 % of the strain was attributed to long-term responses. Stress-relaxation testing indicated that all responses increased with disc degeneration, yet CEP degeneration's impact was minimal. Daily load analyses revealed that disc degeneration significantly reduces nucleus pulposus pressure and disc height, whereas CEP degeneration marginally increases nucleus pressure and slightly decreases disc height.

Conclusions

Glycosaminoglycan content and CEP permeability are critical to the fluid-dependent viscoelastic response of intervertebral discs. Our findings suggest that CEP contributes to disc degeneration under daily loading conditions.

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.

Regional structure-function relationships of lumbar cartilage endplates

Cartilage endplates (CEPs) act as protective mechanical barriers for intervertebral discs (IVDs), yet their heterogeneous structure-function relationships are poorly understood. This study addressed this gap by characterizing and correlating the regional biphasic mechanical properties and biochemical composition of human lumbar CEPs. Samples from central, lateral, anterior, and posterior portions of the disc (n = 8/region) were mechanically tested under confined compression to quantify swelling pressure, equilibrium aggregate modulus, and hydraulic permeability. These properties were correlated with CEP porosity and glycosaminoglycan (s-GAG) content, which were obtained by biochemical assays of the same specimens. Both swelling pressure (142.79 ± 85.89 kPa) and aggregate modulus (1864.10 ± 1240.99 kPa) were found to be regionally dependent (p = 0.0001 and p = 0.0067, respectively) in the CEP and trended lowest in the central location. No significant regional dependence was observed for CEP permeability (1.35 ± 0.97 * 10-16 m4/Ns). Porosity measurements correlated significantly with swelling pressure (r = -0.40, p = 0.0227), aggregate modulus (r = -0.49, p = 0.0046), and permeability (r = 0.36, p = 0.0421), and appeared to be the primary indicator of CEP biphasic mechanical properties. Second harmonic generation microscopy also revealed regional patterns of collagen fiber anchoring, with fibers inserting the CEP perpendicularly in the central region and at off-axial directions in peripheral regions. These results suggest that CEP tissue has regionally dependent mechanical properties which are likely due to the regional variation in porosity and matrix structure. This work advances our understanding of healthy baseline endplate biomechanics and lays a groundwork for further understanding the role of CEPs in IVD degeneration.

Structure, composition and anisotropic swelling of the bovine acetabular labrum

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

Mechanical characterization and design of biomaterials for nucleus pulposus replacement and regeneration

Biomaterials for nucleus pulposus (NP) replacement and regeneration have great potential to restore normal biomechanics in degenerated intervertebral discs following nucleotomy. Mechanical characterizations are essential for assessing the efficacy of biomaterial implants for clinical applications. While traditional compression tests are crucial to quantify various modulus values, relaxation behaviors and fatigue resistance, rheological measurements should also be conducted to investigate the viscoelastic properties, injectability, and overall stability upon deformation. To recapitulate the physiological in vivo environment, the use of spinal models is necessary to evaluate the risk of implant extrusion and the restoration of biomechanics under different loading conditions. When designing devices for NP replacement, injectable materials are ideal to fully fill the nucleus cavity and prevent implant migration. In addition to achieving biocompatibility and desirable mechanical characteristics, biomaterial implants should be optimized to avoid implant extrusion or re-herniation post-operatively. This review discusses the most commonly used testing protocols for assessing mechanical properties of biomaterial implants and serves as reference material for enabling researchers to characterize NP implants through a unified approach whereby newly developed biomaterials may be compared and contrasted to existing devices.

An anatomically-realistic computational framework for evaluating the efficacy of protective plates in mitigating non-penetrating ballistic impacts

BACKGROUND

A major threat in combat scenarios is the 'behind armor blunt trauma' (BABT) of a non-penetrating ballistic impact with a ballistic protective plate (BPP). This impact results in pressure waves that propagate through tissues, potentially causing life-threatening damage. To date, there is no standardized procedure for rapid virtual testing of the effectiveness of BPP designs. The objective of this study was to develop a novel, anatomically-accurate, finite element modeling framework, as a decision-making tool to evaluate and rate the biomechanical efficacy of BPPs in protecting the torso from battlefield-acquired non-penetrating impacts.

METHODS

To simulate a blunt impact with a BPP, two types of BPPs representing generic designs of threat-level III and IV plates, and a generic 5.56 mm bullet were modeled, based on their real dimensions, physical and mechanical characteristics (plate level-III is smaller, thinner, and lighter than plate level-IV). The model was validated by phantom testing.

RESULTS

Plate level-IV induced greater strains and stresses in the superficial tissues post the ballistic impact, due to the fact that it is larger, thicker and heavier than plate level-III; the shock wave which is transferred to the superficial tissues behind the BPP is greater in the case of a non-penetrating impact. For example - the area under volumetric tissue exposure histograms of strains and stresses for the skin and adipose tissues were 16.6-19.2% and 17.3-20.3% greater in the case of plate level-IV, for strains and stresses, respectively. The validation demonstrates a strong agreement between the physical phantom experiment and the simulation, with only a 6.37% difference between them.

CONCLUSIONS

Our modelling provides a versatile, powerful testing framework for both industry and clients of BPPs at the prototype design phase, or for quantitative standardized evaluations of candidate products in purchasing decisions and bids.

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

BACKGROUND AND OBJECTIVE

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

METHODS

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

RESULTS

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

CONCLUSIONS

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

Mechanical characterization of a novel biomimetic artificial disc for the cervical spine

A novel biomimetic artificial intervertebral disc (bioAID) replacement implant has been developed containing a swelling hydrogel representing the nucleus pulposus, a tensile strong fiber jacket as annulus fibrosus and titanium endplates with pins to primarily secure the device between the vertebral bodies. In this study, the design safety of this novel implant was evaluated based on several biomechanical parameters, namely compressive strength, shear-compressive strength, risk of subsidence and device expulsion as well as identifying the diurnal creep-recovery characteristics of the device. The bioAID remained intact up to 1 kN under static axial compression and only 0.4 mm of translation was observed under a compressive shear load of 20 N. No subsidence was observed after 0.5 million cycles of sinusoidal compressive loading between 50 and 225 N. After applying 400 N in antero-posterior direction under 100 N axial compressive preload, approximately 2 mm displacement was found, being within the range of displacements reported for other commercially available cervical disc replacement devices. The diurnal creep recovery behavior of the bioAID closely resembled what has been reported for natural intervertebral discs in literature. Overall, these results indicate that the current design can withstand (shear-compression loads and is able to remain fixed in a mechanical design resembling the vertebral bodies. Moreover, it is one of the first implants that can closely mimic the poroelastic and viscoelastic behavior of natural disc under a diurnal loading pattern.

MRI-based measurement of in vivo disc mechanics in a young population due to flexion, extension, and diurnal loading

Background

Intervertebral disc degeneration is often implicated in low back pain; however, discs with structural degeneration often do not cause pain. It may be that disc mechanics can provide better diagnosis and identification of the pain source. In cadaveric testing, the degenerated disc has altered mechanics, but in vivo, disc mechanics remain unknown. To measure in vivo disc mechanics, noninvasive methods must be developed to apply and measure physiological deformations.

Aim

Thus, this study aimed to develop methods to measure disc mechanical function via noninvasive MRI during flexion and extension and after diurnal loading in a young population. This data will serve as baseline disc mechanics to later compare across ages and in patients.

Materials & Methods

To accomplish this, subjects were imaged in the morning in a reference supine position, in flexion, in extension, and at the end of the day in a supine position. Disc deformations and vertebral motions were used to quantify disc axial strain, changes in wedge angle, and anterior-posterior (A-P) shear displacement. T2 weighted MRI was also used to evaluate disc degeneration via Pfirrmann grading and T2 time. All measures were then tested for effect of sex and disc level.

Results

We found that flexion and extension caused level-dependent strains in the anterior and posterior of the disc, changes in wedge angle, and A-P shear displacements. Flexion had higher magnitude changes overall. Diurnal loading did not cause level-dependent strains but did cause small level-dependent changes in wedge angle and A-P shear displacements.

Discussion

Correlations between disc degeneration and mechanics were largest in flexion, likely due to the smaller contribution of the facet joints in this condition.

Conclusion

In summary, this study established methods to measure in vivo disc mechanical function via noninvasive MRI and established a baseline in a young population that may be compared to older subjects and clinical disorders in the future.

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

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

Anatomically and Biomechanically Relevant Monolithic Total Disc Replacement Made of 3D-Printed Thermoplastic Polyurethane

Various implant treatments, including total disc replacements, have been tried to treat lumbar intervertebral disc (IVD) degeneration, which is claimed to be the main contributor of lower back pain. The treatments, however, come with peripheral issues. This study proposes a novel approach that complies with the anatomical features of IVD, the so-called monolithic total disc replacement (MTDR). As the name suggests, the MTDR is a one-part device that consists of lattice and rigid structures to mimic the nucleus pulposus and annulus fibrosus, respectively. The MTDR can be made of two types of thermoplastic polyurethane (TPU 87A and TPU 95A) and fabricated using a 3D printing approach: fused filament fabrication. The MTDR design involves two configurations-the full lattice (FLC) and anatomy-based (ABC) configurations. The MTDR is evaluated in terms of its physical, mechanical, and cytotoxicity properties. The physical characterization includes the geometrical evaluations, wettability measurements, degradability tests, and swelling tests. The mechanical characterization comprises compressive tests of the materials, an analytical approach using the Voigt model of composite, and a finite element analysis. The cytotoxicity assays include the direct assay using hemocytometry and the indirect assay using a tetrazolium-based colorimetric (MTS) assay. The geometrical evaluation shows that the fabrication results are tolerable, and the two materials have good wettability and low degradation rates. The mechanical characterization shows that the ABC-MTDR has more similar mechanical properties to an IVD than the FLC-MTDR. The cytotoxicity assays prove that the materials are non-cytotoxic, allowing cells to grow on the surfaces of the materials.

Detergent-Free Decellularization of Notochordal Cell-Derived Matrix Yields a Regenerative, Injectable, and Swellable Biomaterial

Porcine notochordal cell-derived matrix (NCM) has anti-inflammatory and regenerative effects on degenerated intervertebral discs. For its clinical use, safety must be assured. The porcine DNA is concerning because of (1) the transmission of endogenous retroviruses and (2) the inflammatory potential of cell-free DNA. Here, we present a simple, detergent-free protocol: tissue lyophilization lyses cells, and matrix integrity is preserved by limiting swelling during decellularization. DNA is digested quickly by a high nuclease concentration, followed by a short washout. Ninety-four percent of DNA was removed, and there was no loss of glycosaminoglycans or collagen. Forty-three percent of the total proteins remained in the decellularized NCM (dNCM). dNCM stimulated as much GAG production as NCM in nucleus pulposus cells but lost some anti-inflammatory effects. Reconstituted pulverized dNCM yielded a soft, shear-thinning biomaterial with a swelling ratio of 350% that also acted as an injectable cell carrier (cell viability >70%). dNCM can therefore be used as the basis for future biomaterials aimed at disc regeneration on a biological level and may restore joint mechanics by creating swelling pressure within the intervertebral disc.

Importance of Matrix Cues on Intervertebral Disc Development, Degeneration, and Regeneration

Back pain is one of the leading causes of disability worldwide and is frequently caused by degeneration of the intervertebral discs. The discs’ development, homeostasis, and degeneration are driven by a complex series of biochemical and physical extracellular matrix cues produced by and transmitted to native cells. Thus, understanding the roles of different cues is essential for designing effective cellular and regenerative therapies. Omics technologies have helped identify many new matrix cues; however, comparatively few matrix molecules have thus far been incorporated into tissue engineered models. These include collagen type I and type II, laminins, glycosaminoglycans, and their biomimetic analogues. Modern biofabrication techniques, such as 3D bioprinting, are also enabling the spatial patterning of matrix molecules and growth factors to direct regional effects. These techniques should now be applied to biochemically, physically, and structurally relevant disc models incorporating disc and stem cells to investigate the drivers of healthy cell phenotype and differentiation. Such research will inform the development of efficacious regenerative therapies and improved clinical outcomes.

Development of a Finite Element Model of the Pediatric Thoracic and Lumbar Spine, Ribcage, and Pelvis with Orthotropic Region-Specific Vertebral Growth

Finite element (FE) modeling of the spine has increasingly been applied in orthopedic precision-medicine approaches. Previously published FE models of the pediatric spine growth have made simplifications in geometry of anatomical structures, material properties, and representation of vertebral growth. To address those limitations, a comprehensive FE model of a pediatric (10-year-old) osteo-ligamentous thoracic and lumbar spine (T1-L5 with intervertebral discs (IVDs) and ligaments), ribcage, and pelvis with age- and level-specific ligament properties and orthotropic region-specific vertebral growth was developed and validated. Range of motion (ROM) measures, namely lateral bending, flexion-extension, and axial rotation, of the current 10 YO FE model were generally within reported ranges of scaled in vitro adult ROM data. Changes in T1-L5 spine height, as well as kyphosis (T2-T12) and lordosis (L1-L5) angles in the current FE model for two years of growth (from ages 10 to 12 years) were within ranges reported from corresponding pediatric clinical data. The use of such comprehensive pediatric FE models can provide clinically relevant insights into normative and pathological biomechanical responses of the spine, and also contribute to the development and optimization of clinical interventions for spine deformities.

Impact of Variations in Water Concentration on the Nanomechanical Behavior of Type I Collagen Microfibrils in Annulus Fibrosus

Radial variation in water concentration from outer to inner lamellae is one of the characteristic features of annulus fibrosus (AF). In addition, water concentration changes are also associated with intervertebral disc (IVD) degeneration. Such changes alter the chemo-mechanical interactions among the biomolecular constituents at molecular level, affecting the load-bearing nature of IVD. This study investigates mechanistic impacts of water concentration on the collagen type I microfibrils in AF using molecular dynamics simulations. Results show, in axial tension, that increase in water concentration (WC) from 0% to 50% increases the elastic modulus from 2.7 GPa to 3.9 GPa. This is attributed to combination of shift in deformation from backbone straightening to combined backbone stretching- intermolecular sliding and subsequent strengthening of tropocollagen-water (TC-water-TC) interfaces through water bridges and intermolecular electrostatic attractions. Further increase in WC to 75% reduces the modulus to 1.8 GPa due to shift in deformation to polypeptide straightening and weakening of TC-water-TC interface due to reduced electrostatic attraction and increase in the number of water molecules in a water bridge. During axial compression, increase in WC to 50% results in increase in modulus from 0.8 GPa to 4.5 GPa. This is attributed to the combination of the development of hydrostatic pressure and strengthening of the TC-water-TC interface. Further increase in WC to 75% shifts load-bearing characteristic from collagen to water, resulting in a decrease in elastic modulus to 2.8 GPa. Such water-mediated alteration in load-bearing properties acts as foundations toward AF mechanics and provides insights toward understanding degeneration-mediated altered spinal stiffness.

Self-Assembling Peptide Hydrogels as Functional Tools to Tackle Intervertebral Disc Degeneration

Low back pain (LBP), caused by intervertebral disc (IVD) degeneration, is a major contributor to global disability. In its healthy state, the IVD is a tough and well-hydrated tissue, able to act as a shock absorber along the spine. During degeneration, the IVD is hit by a cell-driven cascade of events, which progressively lead to extracellular matrix (ECM) degradation, chronic inflammation, and pain. Current treatments are divided into palliative care (early stage degeneration) and surgical interventions (late-stage degeneration), which are invasive and poorly efficient in the long term. To overcome these limitations, alternative tissue engineering and regenerative medicine strategies, in which soft biomaterials are used as injectable carriers of cells and/or biomolecules to be delivered to the injury site and restore tissue function, are currently being explored. Self-assembling peptide hydrogels (SAPHs) represent a promising class of de novo synthetic biomaterials able to merge the strengths of both natural and synthetic hydrogels for biomedical applications. Inherent features, such as shear-thinning behaviour, high biocompatibility, ECM biomimicry, and tuneable physiochemical properties make these hydrogels appropriate and functional tools to tackle IVD degeneration. This review will describe the pathogenesis of IVD degeneration, list biomaterials requirements to attempt IVD repair, and focus on current peptide hydrogel materials exploited for this purpose.

Biphasic Properties of PVAH (Polyvinyl Alcohol Hydrogel) Reflecting Biomechanical Behavior of the Nucleus Pulposus of the Human Intervertebral Disc

PVAH is a mixture of solid and fluid, but its mechanical behavior has usually been described using solid material models. The purpose of this study was to obtain material properties that can reflect the mechanical behavior of polyvinyl alcohol hydrogel (PVAH) using finite element analysis, a biphasic continuum model, and to optimize the composition ratio of PVAH to replace the nucleus pulposus (NP) of the human intervertebral disc. Six types of PVAH specimens (3, 5, 7, 10, 15, 20 wt%) were prepared, then unconfined compression experiments were performed to acquire their material properties using the Holmes–Mow biphasic model. With an increasing weight percentage of PVA in PVAH, the Young’s modulus increased while the permeability parameter decreased. The Young’s modulus and permeability parameter were similar to those of the NP at 15 wt% and 20 wt%. The range of motion, facet joint force, and NP pressures measured from dynamic motional analysis of the lumbar segments with the NP model also exhibited similar values to those with 15~20 wt% PVAH models. Considering the structural stability and pain of the lumbar segments, it appears that 20 wt% PVAH is most suitable for replacing the NP.

Torque- and Muscle-Driven Flexion Induce Disparate Risks of In Vitro Herniation: A Multiscale and Multiphasic Structure-Based Finite Element Study

The intervertebral disc is a complex structure that experiences multiaxial stresses regularly. Disc failure through herniation is a common cause of lower back pain, which causes reduced mobility and debilitating pain, resulting in heavy socioeconomic burdens. Unfortunately, herniation etiology is not well understood, partially due to challenges in replicating herniation in vitro. Previous studies suggest that flexion elevated risks of herniation. Thus, the objective of this study was to use a multiscale and multiphasic finite element model to evaluate the risk of failure under torque- or muscle-driven flexion. Models were developed to represent torque-driven flexion with the instantaneous center of rotation (ICR) located on the disc, and the more physiologically representative muscle-driven flexion with the ICR located anterior of the disc. Model predictions highlighted disparate disc mechanics regarding bulk deformation, stress-bearing mechanisms, and intradiscal stress-strain distributions. Specifically, failure was predicted to initiate at the bone-disc boundary under torque-driven flexion, which may explain why endplate junction failure, instead of herniation, has been the more common failure mode observed in vitro. By contrast, failure was predicted to initiate in the posterolateral annulus fibrosus under muscle-driven flexion, resulting in consistent herniation. Our findings also suggested that muscle-driven flexion combined with axial compression could be sufficient for provoking herniation in vitro and in silico. In conclusion, this study provided a computational framework for designing in vitro testing protocols that can advance the assessment of disc failure behavior and the performance of engineered disc implants.

A Mathematical Model for Transport in Poroelastic Materials with Variable Volume: Derivation, Lie Symmetry Analysis and Examples—Part 2

The model for perfused tissue undergoing deformation taking into account the local exchange between tissue and blood and lymphatic systems is presented. The Lie symmetry analysis in order to identify its symmetry properties is applied. Several families of steady-state solutions in closed formulae are derived. An analysis of the impact of the parameter values and boundary conditions on the distribution of hydrostatic pressure, osmotic agent concentration and deformation of perfused tissue is provided applying the solutions obtained in examples describing real-world processes.

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

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

A Robust Multiscale and Multiphasic Structure-Based Modeling Framework for the Intervertebral Disc

A comprehensive understanding of multiscale and multiphasic intervertebral disc mechanics is crucial for designing advanced tissue engineered structures aiming to recapitulate native tissue behavior. The bovine caudal disc is a commonly used human disc analog due to its availability, large disc height and area, and similarities in biochemical and mechanical properties to the human disc. Because of challenges in directly measuring subtissue-level mechanics, such as in situ fiber mechanics, finite element models have been widely employed in spinal biomechanics research. However, many previous models use homogenization theory and describe each model element as a homogenized combination of fibers and the extrafibrillar matrix while ignoring the role of water content or osmotic behavior. Thus, these models are limited in their ability in investigating subtissue-level mechanics and stress-bearing mechanisms through fluid pressure. The objective of this study was to develop and validate a structure-based bovine caudal disc model, and to evaluate multiscale and multiphasic intervertebral disc mechanics under different loading conditions and with degeneration. The structure-based model was developed based on native disc structure, where fibers and matrix in the annulus fibrosus were described as distinct materials occupying separate volumes. Model parameters were directly obtained from experimental studies without calibration. Under the multiscale validation framework, the model was validated across the joint-, tissue-, and subtissue-levels. Our model accurately predicted multiscale disc responses for 15 of 16 cases, emphasizing the accuracy of the model, as well as the effectiveness and robustness of the multiscale structure-based modeling-validation framework. The model also demonstrated the rim as a weak link for disc failure, highlighting the importance of keeping the cartilage endplate intact when evaluating disc failure mechanisms in vitro. Importantly, results from this study elucidated important fluid-based load-bearing mechanisms and fiber-matrix interactions that are important for understanding disease progression and regeneration in intervertebral discs. In conclusion, the methods presented in this study can be used in conjunction with experimental work to simultaneously investigate disc joint-, tissue-, and subtissue-level mechanics with degeneration, disease, and injury.

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.

Fiber engagement accounts for geometry-dependent annulus fibrosus mechanics: A multiscale, Structure-Based Finite Element Study

A comprehensive understanding of biological tissue mechanics is crucial for designing engineered tissues that aim to recapitulate native tissue behavior. Tensile mechanics of many fiber-reinforced tissues have been shown to depend on specimen geometry, which makes it challenging to compare data between studies. In this study, a validated multiscale, structure-based finite element model was used to evaluate the effect of specimen geometry on multiscale annulus fibrosus tensile mechanics through a fiber engagement analysis. The relationships between specimen geometry and modulus, Poisson's ratio, tissue stress-strain distributions, and fiber reorientation behaviors were investigated at both tissue and sub-tissue levels. It was observed that annulus fibrosus tissue level tensile properties and stress transmission mechanisms were dependent on specimen geometry. The model also demonstrated that the contribution of fiber-matrix interactions to tissue mechanical response was specimen size- and orientation-dependent. The results of this study reinforce the benefits of structure-based finite element modeling in studies investigating multiscale tissue mechanics. This approach also provides guidelines for developing optimal combined computational-experimental study designs for investigating fiber-reinforced biological tissue mechanics. Additionally, findings from this study help explain the geometry dependence of annulus fibrosus tensile mechanics previously reported in the literature, providing a more fundamental and comprehensive understanding of tissue mechanical behavior. In conclusion, the methods presented here can be used in conjunction with experimental tissue level data to simultaneously investigate tissue and sub-tissue scale mechanics, which is important as the field of soft tissue biomechanics advances toward studies that focus on diminishing length scales.

Injectable Disc-Derived ECM Hydrogel Functionalised with Chondroitin Sulfate for Intervertebral Disc Regeneration

Low back pain resulting from intervertebral disc (IVD) degeneration is a significant socioeconomic burden. The main effect of the degeneration process involves the alteration of the nucleus pulposus (NP) via cell-mediated enzymatic breakdown of key extracellular matrix (ECM) components. Thus, the development of injectable and biomimetic biomaterials that can instruct the regenerative cell component to produce tissue-specific ECM is pivotal for IVD repair. Chondroitin sulfate (CS) and type II collagen are the primary components of NP tissue and together create the ideal environment for cells to deposit de-novo matrix. Given their high matrix synthesis capacity potential post-expansion, nasal chondrocytes (NC) have been proposed as a potential cell source to promote NP repair. The overall goal of this study was to assess the effects of CS incorporation into disc derived self-assembled ECM hydrogels on the matrix deposition of NCs. Results showed an increased sGAG production with higher amounts of CS in the gel composition and that its presence was found to be critical for the synthesis of collagen type II. Taken together, our results demonstrate how the inclusion of CS into the composition of the material aids the preservation of a rounded cell morphology for NCs in 3D culture and enhances their ability to synthesise NP-like matrix.

Transient swelling behavior of the bovine caudal disc

The intervertebral disc is an avascular composite structure, comprised of the nucleus pulposus (NP) and the annulus fibrosus (AF). Previous tissue-level experiments either examined relative differences in swelling capacity of the two disc regions at a single time point or tested explant structures that did not replicate in situ boundary conditions. Previous joint-level studies that investigated time-dependent fluid flow into the disc provided limited information about swelling-induced intradiscal strains with respect to time and boundary constraints. Therefore, the objective of this study was to investigate time-dependent swelling behavior of the intervertebral disc ex situ. The first study investigated time-dependent free-swelling response of the whole disc and the disc's subcomponents separately (i.e., NP and AF). Findings from this study showed that the swelling rate and swelling capacity of NP explants under free-swelling conditions were greater than AF explants. The second study evaluated the effect of boundary conditions on in-plane strain distributions of intact discs and AF rings. Swelling-induced strain was highly heterogeneous in AF rings, where negative circumferential strains were observed in the inner AF and tensile circumferential strains were observed in the outer AF. Radial strains in AF rings were an order of magnitude greater than circumferential strains. Restricting fluid flow only to the outer AF periphery reduced the swelling of the inner AF. Swelling of intact discs affected both NP and AF swelling behaviors, where NP hydration decreased by 60%. Furthermore, the presence of the NP reduced peak radial strains in the AF and resulted in uniform strain distribution throughout the AF. In conclusion, these studies highlight that tissue hydration and swelling-induced strains largely depend on regional biochemical composition and geometric boundary constraints.

Evaluation of transverse poroelastic mechanics of tendon using osmotic loading and biphasic mixture finite element modeling

Tendon's viscoelastic behaviors are important to the tissue mechanical function and cellular mechanobiology. When loaded in longitudinal tension, tendons often have a large Poisson's ratio (ν>2) that exceeds the limit of incompressibility for isotropic material (ν=0.5), indicating that tendon experiences volume loss, inducing poroelastic fluid exudation in the transverse direction. Therefore, transverse poroelasticity is an important contributor to tendon material behavior. Tendon hydraulic permeability which is required to evaluate the fluid flow contribution to viscoelasticity, is mostly unavailable, and where available, varies by several orders of magnitude. In this manuscript, we quantified the transverse poroelastic material parameters of rat tail tendon fascicles by conducting transverse osmotic loading experiments, in both tension and compression. We used a multi-start optimization method to evaluate the parameters using biphasic finite element modeling. Our tendon samples had a transverse hydraulic permeability of 10^-4 to 10^-5 mm⁴. (Ns)^-1 and showed a significant tension-compression nonlinearity in the transverse direction. Further, using these results, we predict hydraulic permeability during longitudinal (fiber-aligned) tensile loading, and the spatial distribution of fluid flow during osmotic loading. These results reveal novel aspects of tendon mechanics and can be used to study the physiomechanical response of tendon in response to mechanical loading.

Effect of aggrecan degradation on the nanomechanics of hyaluronan in extra-fibrillar matrix of annulus fibrosus: A molecular dynamics investigation

Intervertebral Disc (IVD) Degeneration is one of the primary causes of low back pain among the adult population - the most significant cause being the degradation of aggrecan present in the extra-fibrillar matrix (EFM). Aggrecan degradation is closely associated with loss of water content leading to an alteration in the mechanical behaviour of the IVD. The loss in water content has a significant impact on the chemo-mechanical interplay of IVD biochemical constituents at the fundamental level. This work presents a mechanistic understanding of the effect of hydration, closely associated with aggrecan degradation, on the nanoscale mechanical behaviour of the hyaluronan present in the EFM of the Annulus Fibrosus. For this purpose, explicit three-dimensional molecular dynamics analyses of tensile and compressive tests are performed on a representative atomistic model of the hyaluronan present in the EFM. To account for the degradation of aggrecan, hydration levels are varied from 0 to 75% by weight of water. Analyses show that an increase in the hydration levels decreases the elastic modulus of hyaluronan in tension from ~4.6 GPa to ~2.1 GPa. On the other hand, the increase in hydration level increases the elastic moduli in axial compression from ~1.6 GPa in un-hydrated condition to ~6 GPa in 50% hydrated condition. But as the hydration levels increase to 75%, the elastic modulus reduces to ~3.5 GPa signifying a shift in load-bearing characteristic, from the solid hyaluronan component to the fluid component. Furthermore, analyses show a reduction in the intermolecular energy between hyaluronan and water, under axial tensile loading, indicating a nanoscale intermolecular debonding between hyaluronan and water molecules. This is attributed to the ability of hyaluronan to form stabilizing intra-molecular hydrogen bonds between adjacent residues. Compressive loading, on the other hand, causes intensive coiling of hyaluronan molecule, which traps more water through hydrogen bonding and aids in bearing compressive loads. Overall, study shows that hydration level has a strong influence on the atomistic level interactions between hyaluronan molecules and hyaluronan and water molecules in the EFM which influences the nanoscale mechanics of the Annulus Fibrosus.

The Importance of the Mixing Energy in Ionized Superabsorbent Polymer Swelling Models

The Flory–Rehner theoretical description of the free energy in a hydrogel swelling model can be broken into two swelling components: the mixing energy and the ionic energy. Conventionally for ionized gels, the ionic energy is characterized as the main contributor to swelling and, therefore, the mixing energy is assumed negligible. However, this assumption is made at the equilibrium state and ignores the dynamics of gel swelling. Here, the influence of the mixing energy on swelling ionized gels is quantified through numerical simulations on sodium polyacrylate using a Mixed Hybrid Finite Element Method. For univalent and divalent solutions, at initial porosities greater than 0.90, the contribution of the mixing energy is negligible. However, at initial porosities less than 0.90, the total swelling pressure is significantly influenced by the mixing energy. Therefore, both ionic and mixing energies are required for the modeling of sodium polyacrylate ionized gel swelling. The numerical model results are in good agreement with the analytical solution as well as experimental swelling tests.

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.

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

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

Characterization of breast tissue permeability for detection of vascular breast tumors: An in vitro study

The biological tissue could be considered as a porous matrix filled with the interstitial fluid. The tumoral tissue has a different permeability from the healthy tissue. With regard to this knowledge, the main objective of the present study is to study the tissue permeability as a diagnostic parameter for the detection of breast cancer. To this end, the healthy and the cancerous specimens of the breast tissue are taken from 17 female cases. All cancerous tumors are in the vascular phase of the growth. The samples undergo a uniaxial compression test by a robotic system while the strain rate is set to remain unchanged. Using the stress and the strain rate data, the strain-dependent permeability is determined, which is an exponential function of the strain level. The permeability function is identified by the initial permeability at the zero compressive strain and a material constant. Results show that the initial permeability of the healthy breast tissue is significantly different from the corresponding value for the cancerous tissue. For all cancerous samples, the permeability is less than the healthy tissue samples; as 40-70% reduction in the initial permeability is observed compared to the healthy breast tissue. The evaluation of the permeability between the healthy and the cancerous specimens is accompanied by the biopsy reports and observing structural images of the specimens using environmental scanning electron microscope. Based on the results, the permeability is suggested to have a diagnostic application for the detection of vascular breast tumors.

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.

Ethanol-mediated compaction and cross-linking enhance mechanical properties and degradation resistance while maintaining cytocompatibility of a nucleus pulposus scaffold

Intervertebral disc degeneration is a complex, cell-mediated process originating in the nucleus pulposus (NP) and is associated with extracellular matrix catabolism leading to disc height loss and impaired spine kinematics. Previously, we developed an acellular bovine NP (ABNP) for NP replacement that emulated human NP matrix composition and supported cell seeding; however, its mechanical properties were lower than those reported for human NP. To address this, we investigated ethanol-mediated compaction and cross-linking to enhance the ABNP's dynamic mechanical properties and degradation resistance while maintaining its cytocompatibility. First, volumetric and mechanical effects of compaction only were confirmed by evaluating scaffolds after various immersion times in buffered 28% ethanol. It was found that compaction reached equilibrium at ~30% compaction after 45 min, and dynamic mechanical properties significantly increased 2-6× after 120 min of submersion. This was incorporated into a cross-linking treatment, through which scaffolds were subjected to 120 min precompaction in buffered 28% ethanol prior to carbodiimide cross-linking. Their dynamic mechanical properties were evaluated before and after accelerated degradation by ADAMTS-5 or MMP-13. Cytocompatibility was determined by seeding stem cells onto scaffolds and evaluating viability through metabolic activity and fluorescent staining. Compacted and cross-linked scaffolds showed significant increases in DMA properties without detrimentally altering their cytocompatibility, and these mechanical gains were maintained following enzymatic exposure. © 2019 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater 107B:2488-2499, 2019.

A Dynamic Radiographic Imaging Study of Lumbar Intervertebral Disc Morphometry and Deformation In Vivo

Intervertebral discs are important structural components of the spine but also are significant sources of morbidity, especially for the “low back” lumbar region. Mechanical damage to, or degeneration of, the lumbar discs can diminish their structural integrity and elicit debilitating low back pain. Advancement of reparative or regenerative means to treat damaged or degenerated discs is hindered by a lack of basic understanding of the disc load-deformation characteristics in vivo. The current study presents an in vivo analysis of the morphometry and deformation of lumbar (L2-S1) intervertebral discs in 10 healthy participants while performing a common lifting act, using novel dynamic radiographic imaging of the lumbar vertebral body motion. Data analyses show uniquely different (p < 0.05) characteristics in morphometry, normal and shear strain patterns of the L5S1 discs, while the rest of lumbar discs exhibit great similarity. In particular shear strains in L2-L5 discs exhibited stronger linear correlations (R² ≥ 0.80) between strain changes and amount of lumbar flexion-extension motion compared to L5S1 (R² ≤ 0.5). The study therefore advances the state of knowledge on in vivo mechanical responses of the lumbar intervertebral discs during functional tasks.

Radial variation in biochemical composition of the bovine caudal intervertebral disc

Bovine caudal discs have been widely used in spine research due to their increased availability, large size, and mechanical and biochemical properties that are comparable to healthy human discs. However, despite their extensive use, the radial variations in bovine disc composition have not yet been rigorously quantified with high spatial resolution. Previous studies were limited to qualitative analyses or provided limited spatial resolution in biochemical properties. Thus, the main objective of this study was to provide quantitative measurements of biochemical composition with higher spatial resolution than previous studies that employed traditional biochemical techniques. Specifically, traditional biochemical analyses were used to measure water, sulfated glycosaminoglycan, collagen, and DNA contents. Gravimetric water content was compared to data obtained through Raman spectroscopy and differential scanning calorimetry. Additionally, spatial distribution of lipids in the disc's collagen network was visualized and quantified, for the first time, using multi-modal second harmonic generation (SHG) and Coherent anti-Stokes Raman (CARS) microscopy. Some heterogeneity was observed in the nucleus pulposus, where the water content and water-to-protein ratio of the inner nucleus were greater than the outer nucleus. In contrast, the bovine annulus fibrosus exhibited a more heterogeneous distribution of biochemical properties. Comparable results between orthohydroxyproline assay and SHG imaging highlight the potential benefit of using SHG microscopy as a less destructive method for measuring collagen content, particularly when relative changes are of interest. CARS images showed that lipid deposits were distributed equally throughout the disc and appeared either as individual droplets or as clusters of small droplets. In conclusion, this study provided a more comprehensive assessment of spatial variations in biochemical composition of the bovine caudal disc.

Frequency-dependent shear properties of annulus fibrosus and nucleus pulposus by magnetic resonance elastography

Aging and degeneration are associated with changes in mechanical properties in the intervertebral disc, generating interest in the establishment of mechanical properties as early biomarkers for the degenerative cascade. Magnetic resonance elastography (MRE) of the intervertebral disc is usually limited to the nucleus pulposus, as the annulus fibrosus is stiffer and less hydrated. The objective of this work was to adapt high-frequency needle MRE to the characterization of the shear modulus of both the nucleus pulposus and annulus fibrosus. Bovine intervertebral discs were removed from fresh oxtails and characterized by needle MRE. The needle was inserted in the center of the disc and vibrations were generated by an amplified piezoelectric actuator. MRE acquisitions were performed on a 4.7-T small-animal MR scanner using a spin echo sequence with sinusoidal motion encoding gradients. Acquisitions were repeated over a frequency range of 1000-1800 Hz. The local frequency estimation inversion algorithm was used to compute the shear modulus. Stiffness maps allowed the visualization of the soft nucleus pulposus surrounded by the stiffer annulus fibrosus surrounded by the homogeneous gel. A significant difference in shear modulus between the nucleus pulposus and annulus fibrosus, and an increase in the shear modulus with excitation frequency, were observed, in agreement with the literature. This study demonstrates that global characterization of both the nucleus pulposus and annulus fibrosus of the intervertebral disc is possible with needle MRE using a preclinical magnetic resonance imaging (MRI) scanner. MRE can be a powerful method for the mapping of the complex properties of the intervertebral disc. The developed method could be adapted for in situ use by preserving adjacent vertebrae and puncturing the side of the intervertebral disc, thereby allowing an assessment of the contribution of osmotic pressure to the mechanical behavior of the intervertebral disc.

Dynamic properties of hydrogels and fiber-reinforced hydrogels

Hydrophilic polymers, or hydrogels, are used for a wide variety of biomedical applications, due to their inherent ability to withhold a high-water content. In recent years, a large effort has been focused on tailoring the mechanical properties of these hydrogels to become more appropriate materials for use as anatomical and physiological structural supports. A few of these such methods include using diverse types of polymers, both natural and synthetic, varying the type of molecular cross-linking, as well as combining these efforts to form interpenetrating polymer network hydrogels. While multiple research groups have characterized these various hydrogels under quasi-static conditions, their dynamic properties, representative of native physiological loading scenarios, have been scarcely reported. In this study, an E-glass fiber reinforced family of alginate/PAAm hydrogels cross-linked by both divalent and trivalent cations are fabricated and investigated. The effect of the reinforcement phase on the dynamic and hydration behaviors is then explicated. Additionally, a micromechanics framework for short cylindrical chopped fibers is utilized to discern the contribution of the matrix and fiber constituents on the hydrogel composite. The addition of E-glass fibers resulted in the storage modulus exhibiting a ~50%, 5%, and ~120%, increase with a mere addition of 2 wt% of the reinforcing fibers to Na-, Sr-, and Al-alginate/PAAm, respectively. In studying the cross-linking effect of various divalent (Ba, Ca, Sr) and trivalent (Al, Fe) cations, it was noteworthy that the hydrogels were found to be effective in dissipating energy while resisting mechanical deformation when they are cross-linked with higher molecular weight elements, regardless of valency. This report on the dynamic properties of these hydrogels will help to improve their optimization for future use in biomedical load-bearing applications.

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

Native and engineered fiber-reinforced tissues are composites comprised of stiff collagen fibers embedded within an extrafibrillar matrix that is capable of swelling by absorbing water molecules. Tissue swelling is important for understanding stress distributions between collagen fibers and extrafibrillar matrix, as well as for understanding mechanisms of tissue failure. The swelling behavior of fiber-reinforced tissues in the musculoskeletal system has been largely attributed to the glycosaminoglycan content. Recent work demonstrated anisotropy in the swelling response of the annulus fibrosus in the intervertebral disc. It is well known that collagen fiber orientation affects elastic behavior, but the effect of collagen fiber network on tissue swelling behavior is not well understood. In this study, we developed three series of models to evaluate the effect of collagen fiber orientation, fiber network architecture (i.e., single or multi-fiber families within a layer), and fiber stiffness on bulk tissue swelling, which was simulated by describing the extrafibrillar matrix as a triphasic material, as proposed by Lai et al. Model results were within one standard deviation of reported mean values for changes in tissue volume, width, and thickness under free swelling conditions. The predicted swelling response of single-fiber family structures was highly dependent on fiber orientation and the number of lamellae in the bulk tissue. Moreover, matrix swelling resulted in tissue to twist, which reduced fiber deformations, demonstrating a balance between fiber deformation and matrix swelling. Large changes in fiber stiffness (20 × increase) had a relatively small effect on tissue swelling (~ 2% decrease in swelling). In conclusion, fiber angle, fiber architecture (defined as single- versus multiple fiber families in a layer), and the number of layers in a single fiber family structure directly affected tissue swelling behavior, including fiber stretch, fiber reorientation, and tissue deformation. These findings support the need to develop computational models that closely mimic the native architecture in order to understand mechanisms of stress distributions and tissue failure.

FEBio: History and Advances

The principal goal of the FEBio project is to provide an advanced finite element tool for the biomechanics and biophysics communities that allows researchers to model mechanics, transport, and electrokinetic phenomena for biological systems accurately and efficiently. In addition, because FEBio is geared toward the research community, the code is designed such that new features can be added easily, thus making it an ideal tool for testing novel computational methods. Finally, because the success of a code is determined by its user base, integral goals of the FEBio project have been to offer support and outreach to our community; to provide mechanisms for dissemination of results, models, and data; and to encourage interaction between users. This review presents the history of the FEBio project, from its initial developments through its current funding period. We also present a glimpse into the future of FEBio.