Heterogeneous mechanical hyperelastic behavior in the porcine annulus fibrosus explained by fiber orientation: An experimental and numerical approach

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.

Comprehensive analysis of damage evolution in human annulus fibrosus: Numerical exploration of mechanical sensitivity to biological age-dependent alteration

BACKGROUND AND OBJECTIVE

The annulus fibrosus is an essential part of the intervertebral disc, critical for its structural integrity. Mechanical deterioration in this component can lead to complete disc failure, particularly through tears development, with radial tears being the most common. These tears are often the result of both mechanical and biological factors. This study aims to numerically investigate the mechanisms of radial failure in the annulus tissue, taking into account the mechanical and age-dependent biological damage origins. A newly developed microstructure-based model was upgraded to predict damage evolution in the different annulus regions.

METHODS

The study employs a computational model to predict mechanical failures in various annulus regions, using experimental data for comparison. The model incorporates age-dependent microstructural changes to evaluate the effects of biological aging on the mechanical behavior. It specifically includes a detailed analysis of the temporal changes in circumferential rigidity and failure strain of the annulus.

RESULTS

The model demonstrated a strong ability to replicate the experimental responses of the different annulus regions to failure. It revealed that age-related microstructural changes significantly impact the rigidity and failure response of the annulus, particularly in the posterior regions and as well the anterior inner side. These changes increase susceptibility to rupture with aging. A correlation was also observed between the composition of collagen fibers, water content, and the annulus transversal response in both radial and axial directions.

CONCLUSION

The findings challenge previous assumptions, showing that age-dependent microstructural changes have a notable effect on the annulus mechanical properties. The computational model closely aligns with experimental observations, underscoring the determinant role of oriented collagen fibers in radial failure. This study enhances the understanding of annulus failure and provides a foundation for further research on the impact of aging on disc mechanical integrity and failure.

Blueprints of Architected Materials: A Guide to Metamaterial Design for Tissue Engineering

Mechanical metamaterials are rationally designed structures engineered to exhibit extraordinary properties, often surpassing those of their constituent materials. The geometry of metamaterials' building blocks, referred to as unit cells, plays an essential role in determining their macroscopic mechanical behavior. Due to their hierarchical design and remarkable properties, metamaterials hold significant potential for tissue engineering; however their implementation in the field remains limited. The major challenge hindering the broader use of metamaterials lies in the complexity of unit cell design and fabrication. To address this gap, a comprehensive guide is presented detailing the design principles of well-established metamaterials. The essential unit cell geometric parameters and design constraints, as well as their influence on mechanical behavior, are summarized highlighting essential points for effective fabrication. Moreover, the potential integration of artificial intelligence techniques is explored in meta-biomaterial design for patient- and application-specific design. Furthermore, a comprehensive overview of current applications of mechanical metamaterials is provided in tissue engineering, categorized by tissue type, thereby showcasing the versatility of different designs in matching the mechanical properties of the target tissue. This review aims to provide a valuable resource for tissue engineering researchers and aid in the broader use of metamaterials in the field.

Poisson function and volume ratio of soft anisotropic materials under large deformations

Accurate transverse deformation measurements are required for the estimation of the Poisson function and volume ratio. In this study, pure silicone and soft composite specimens were subjected to uniaxial tension, and the digital image correlation method was used to measure longitudinal and in- and out-of-plane transverse stretches. To minimize the effects of measurement errors on parameter estimation, the measured transverse stretches were defined in terms of the longitudinal stretch using a new formulation based on Poisson's ratios and two stretch-dependent parameters. From this formulation, Poisson functions and volume ratio for soft materials under large deformations were obtained. The results showed that pure silicone can be considered isotropic and nearly incompressible under large deformations, as expected. In contrast, Poisson's ratio of silicone reinforced with extensible fabric can exceed classical bounds, including negative value (auxetic behavior). The incompressibility assumption can be employed for describing the stress-stretch curve of pure silicone, while volume ratios are required for soft composites. Data of human skin, aortic wall, and annulus fibrosus from the literature were selected and analyzed. Except for the aortic wall, which can be considered nearly incompressible, the studied soft tissues must be regarded as compressible. All tissues presented anisotropic behavior.

Fiber orientation and crimp level might control the auxetic effect of biological tissues

We propose an analytical micromechanical model for studying the lamellar-composite-like structure of fibrous soft tissue. The tissue under consideration is made up of several lamellae, and is designed to resemble the annulus fibrosus (AF) tissue or media layer of arterial tissue, for example. The collagen fibers are arranged in parallel in each lamella and the fiber orientation differs from one lamella to its neighbors. The parallel fibers in each lamella of AF tissue, for example, have been observed to have a crimped microstructure. The proposed model incorporates this quality, considering fiber waviness as a sinusoidal shape and taking into account the fiber dispersion in different layers, where both fiber and matrix are considered as solid phases. We find that collagen-fiber waviness and layer orientation have a significant influence on Poisson's ratio. The effective Poisson's ratio predicted by the proposed model demonstrates that the crimped collagen fiber microstructure might weaken the auxetic effect of fibrous soft tissue, which might explain why, as the literature suggests, the auxetic behavior is more difficult to observe than large Poisson's ratios. As opposed to the many studies that use the well-known hyperelastic fiber-based constitutive model, in which out-of-plane expansion is often observed, the present work explains the auxetic response found in modeling and in experimental data from the perspective of collagen fiber microstructure.

Auxeticity as a Mechanobiological Tool to Create Meta-Biomaterials

Mechanical and morphological design parameters, such as stiffness or porosity, play important roles in creating orthopedic implants and bone substitutes. However, we have only a limited understanding of how the microarchitecture of porous scaffolds contributes to bone regeneration. Meta-biomaterials are increasingly used to precisely engineer the internal geometry of porous scaffolds and independently tailor their mechanical properties (e.g., stiffness and Poisson's ratio). This is motivated by the rare or unprecedented properties of meta-biomaterials, such as negative Poisson's ratios (i.e., auxeticity). It is, however, not clear how these unusual properties can modulate the interactions of meta-biomaterials with living cells and whether they can facilitate bone tissue engineering under static and dynamic cell culture and mechanical loading conditions. Here, we review the recent studies investigating the effects of the Poisson's ratio on the performance of meta-biomaterials with an emphasis on the relevant mechanobiological aspects. We also highlight the state-of-the-art additive manufacturing techniques employed to create meta-biomaterials, particularly at the micrometer scale. Finally, we provide future perspectives, particularly for the design of the next generation of meta-biomaterials featuring dynamic properties (e.g., those made through 4D printing).

Bioinspired Construction of Annulus Fibrosus Implants with a Negative Poisson's Ratio for Intervertebral Disc Repair and Restraining Disc Herniation

Inspired by the negative Poisson's ratio (NPR) effects of the annulus fibrosus (AF) in intervertebral discs (IVDs), we designed a re-entrant honeycomb model and then 3D printed it into a poly(ε-caprolactone) (PCL) scaffold with NPR effects, which was followed by in situ polymerization of polypyrrole (PPy), thus constructing a PPy-coated NPR-structured PCL scaffold (-vPCL-PPy) to be used as the AF implant for the treatment of lumbar herniated discs. Mechanical testing and finite element (FE) simulation indicated that the NPR composite implant could sustain axial spine loading and resist nucleus pulposus (NP) swelling while displaying uniform stress diffusion under NP swelling and contraction. More interestingly, the NPR-structured composite scaffold could also apply a reacting force to restrain NP herniation owing to the NPR effect. In addition, the in vitro biological assessment and in vivo implantation demonstrated that the NPR composite scaffold exhibited good biocompatibility and exerted the ability to restore the physiological function of the disc segments.

Modeling of human intervertebral disc annulus fibrosus with complex multi-fiber networks

Collagen fibers within the annulus fibrosus (AF) lamellae are unidirectionally aligned with alternating orientations between adjacent layers. AF constitutive models often combine two adjacent lamellae into a single equivalent layer containing two fiber networks with a crisscross pattern. Additionally, AF models overlook the inter-lamellar matrix (ILM) as well as elastic fiber networks in between lamellae. We developed a nonhomogenous micromechanical model as well as two coarser homogenous hyperelastic and microplane models of the human AF, and compared their performances against measurements (tissue level uniaxial and biaxial tests as well as whole disc experiments) and seven published hyperelastic models. The micromechanical model had a realistic non-homogenous distribution of collagen fiber networks within each lamella and elastic fiber network in the ILM. For small matrix linear moduli (<0.2 MPa), the ILM showed substantial anisotropy (>10%) due to the elastic fiber network. However, at moduli >0.2 MPa, the effects of the elastic fiber network on differences in stress-strain responses at different directions disappeared (<10%). Variations in sample geometry and boundary conditions (due to uncertainty) markedly affected stress-strain responses of the tissue in uniaxial and biaxial tests (up to 16 times). In tissue level tests, therefore, simulations should represent testing conditions (e.g., boundary conditions, specimen geometry, preloads) as closely as possible. Stress/strain fields estimated from the single equivalent layer approach (conventional method) yielded different results from those predicted by the anatomically more accurate apparoach (i.e., layerwise). In addition, in a disc under a compressive force (symmetric loading), asymmetric stress-strain distributions were computed when using a layerwise simulation. Although all developed and selected published AF models predicted gross compression-displacement responses of the whole disc within the range of measured data, some showed excessively stiff or compliant responses under tissue-level uniaxial/biaxial tests. This study emphasizes, when constructing and validating constitutive models of AF, the importance of the proper simulation of individual lamellae as distinct layers, and testing parameters (sample geometric dimensions/loading/boundary conditions).

The use of auxetic materials in tissue engineering

A number of biological tissues have been reported as behaving in an auxetic manner, defined by a negative Poisson's ratio. This describes the deformation of tissue which expands in the axial and the transverse directions simultaneously while under uniaxial tension; and contracts axially and transversely upon uniaxial compression. The discovery of auxetic behaviour within biological tissues has implications for the recreation of the auxetic loading environment within tissue engineering. Tissue engineers strive to recreate the natural properties of biological tissue and in order to recreate the unique loading environment of cells from auxetic tissue, an auxetic scaffold is required. A number of studies have used a variety of auxetic scaffolds within tissue engineering. Investigation into the effect of auxetic micro-environments created by auxetic scaffolds on cellular behaviour has demonstrated an increased cellular proliferation and enhanced differentiation. Here, we discuss studies which have identified auxetic behaviour within biological tissues, and where cells have been cultured within auxetic scaffolds, bringing together current knowledge of the potential use of auxetic materials in tissue engineering applications and biomedical devices.