Fiber engagement accounts for geometry-dependent annulus fibrosus mechanics: A multiscale, Structure-Based Finite Element Study
Introduction
Fiber-reinforced biological tissues are complex composite structures consisting of collagen fibers embedded in a hydrated extrafibrillar matrix, resulting in excellent load-bearing and energy absorption capabilities. A comprehensive understanding of fiber-reinforced tissue mechanics is important for developing tissue repair strategies that recapitulate healthy native tissue mechanical behavior (Long et al., 2016; O'Connell et al., 2015). Previous studies, as well as work within our lab, have suggested that differences in test-specimen geometry may lead to significant differences in reported tissue-level tensile mechanics, particularly in tissues with fibers oriented off-axis from the applied load (e.g. annulus fibrosus (AF) and meniscus; Adams and Green 1993; Lechner et al., 2000; Werbner et al., 2017). Unfortunately, the large variability of reported values within studies in the literature makes it impossible to directly attribute differences in mechanics between studies to differences in the test-specimen geometry used (coefficient of variation for healthy human anterior AF: 0.56–0.82; Acaroglu et al., 1995; Elliott and Setton 2001; Guerin and Elliott 2006; O'Connell et al., 2009; Żak and Pezowicz 2013; Żak and Pezowicz 2016). This may in part be due to limited tissue availability hindering the development of standardized mechanical testing protocols for fiber-reinforced biological tissues (Werbner et al., 2017). Thus, in many cases, it remains unclear whether variations in reported mechanical properties arise from inconsistent experimental protocols (e.g. specimen geometry, boundary conditions, etc.) or tissue structural and compositional changes.
Previous investigators hypothesized that variations in specimen geometry alter fiber engagement during loading, resulting in variations in AF tensile modulus (Adams and Green 1993). Adams and Green (1993) used a mathematical model developed based on specimen geometry to show that wider specimens have more engaged fibers during testing, resulting in larger measured modulus values. However, this model was only validated for AF specimens with a fixed length that were loaded along the axial direction. It was also not capable of examining fiber stress or strain distributions, which were strongly associated with fiber engagement and fiber–matrix interactions (Adams and Green 1993). Subsequent studies using constitutive models demonstrated the contribution of fiber–matrix interactions to AF tensile mechanics (Klisch and Lotz 1999; Elliott and Setton 2001; Guerin and Elliott 2007; O’Connell et al. 2009, 2012; Wagner and Lotz 2004; Wagner et al., 2006). However, many of these models were validated using a two-dimensional framework, where hypothesized invariant terms were often physiologically irrelevant and difficult to compare across studies (Guo et al., 2012; Eskandari et al., 2019; Zhou et al., 2020a, Zhou et al., 2020b). Predicting tissue mechanics using composite-based frameworks is also limited by tissue heterogeneity, nonlinearity, as well as challenges in experimentally characterizing the structure and mechanics of individual tissue subcomponents (Eberlein et al., 2001; Spilker et al., 1986).
Thus, many researchers have turned to finite element models (FEMs), which can provide three-dimensional predictions of stress–strain distributions throughout fiber-reinforced tissues. In our previous work, a series of FEMs were created based on homogenization theory to guide the development of a robust protocol for AF tensile failure testing (Werbner et al., 2017). This work reported the geometry dependence of AF tensile mechanics, which was accurately replicated by the model. However, it was difficult to evaluate fiber engagement using this model due to the homogenization of tissue subcomponents. To address this limitation, we developed and validated a multiscale, structure-based FEM to further investigate AF tensile mechanics (“separate model” or SEP) (Zhou et al., 2020a, Zhou et al., 2020b). This model was developed based on native human AF, where fibers and extrafibrillar matrix were described as distinct materials occupying separate volumes. This model accurately predicted AF tensile modulus under various loading configurations (e.g. uniaxial tension, biaxial tension, and simple shear) and was able to describe a nonlinear relationship between specimen geometry and linear-region modulus (Zhou et al., 2020a, Zhou et al., 2020b). Moreover, the multiscale model calibration and validation framework allowed us to directly link physical tissue properties with model parameters, broadening its applicability by making parameters modifiable based on structural or compositional changes occurring with degeneration or disease.
Understanding the effect of specimen geometry on fiber-reinforced tissue mechanics is essential for a fundamental understanding of the tissue response under a variety of physiological loads, which benefits the development of tissue repair strategies that aim to recapitulate native tissue behavior. Characterization of the tissue geometry dependence also facilitate the development of experimental designs that capture tissue properties most relevant to the intended applications. Since the separate model is structure-based, AF tensile mechanics can be more comprehensively investigated at both tissue and sub-tissue levels (Zhou et al., 2020a, Zhou et al., 2020b). Therefore, the objective of this study was to use the separate model to systematically evaluate the effect of specimen geometry on AF tensile mechanics using a structure-based fiber engagement analysis. While this study was conducted using AF properties, the approach presented here can be easily adapted and applied to other fiber-reinforced biological tissues and engineered composites.
Section snippets
Methods
Finite element models were developed to represent rectangular specimens commonly used in uniaxial AF tensile testing (Solidworks 2019; Abaqus 6.14; ANSA 15.2.0; PreView 2.1; FEBio 2.8.5; Maas et al., 2012). Model geometry was created in Solidworks and finite element meshes were generated by ABAQUS and ANSA pre-processor. PreView was used to define the model boundary and loading conditions and the developed model was solved by FEBio. Specimens were oriented along the circumferential-axial
Results
In circumferential specimens, less than 1% of fiber elements were considered damaged, while 30–51% of fiber elements were not engaged at 1.09 stretch. Fiber engagement ranged from 49 to 70% across all circumferential specimens and exhibited a decreasing trend with increasing specimen aspect ratio (Fig. 3A). Due to the varying engagement of different fiber groups (i.e. two-, one-, and no-grip fibers), large differences in model-predicted linear-region modulus were observed in specimens with
Discussion
This study utilized finite element modeling to investigate the effect of specimen geometry on AF tissue and sub-tissue level tensile mechanics. In particular, our previously validated, multiscale, structure-based FEM was applied to examine the geometry dependence of AF tensile modulus, Poisson's ratio, fiber reorientation behavior, and sub-tissue level stress and strain distributions. The results of this study help explain previously observed variations in AF mechanical properties with respect
CRediT authorship contribution statement
Minhao Zhou: Conceptualization, Methodology, Software, Validation, Investigation, Data collection and analysis, Writing - review & editing, Visualization, Project administration. Benjamin Werbner: Validation, Investigation, Data analysis, Writing - review & editing, Visualization. Grace D. O'Connell: Supervision, Writing - review & editing, Project administration, Funding acquisition.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The work was supported by the National Science Foundation (CMMI: 1760467).
References (74)
- et al.
The correspondence between equilibrium biphasic and triphasic material properties in mixture models of articular cartilage
J. Biomech.
(2004) - et al.
Elastic, permeability and swelling properties of human intervertebral disc tissues: a benchmark for tissue engineering
J. Biomech.
(2014) - et al.
The measurement of the variation in the surface strains of Achilles tendon grafts using imaging techniques
J. Biomech.
(2006) - et al.
Mechanical characterization of collagen fibers and scaffolds for tissue engineering
Biomaterials
(2003) - et al.
Degeneration affects the fiber reorientation of human annulus fibrosus under tensile load
J. Biomech.
(2006) - et al.
A composites-based hyperelastic constitutive model for soft tissue with application to the human annulus fibrosus
J. Mech. Phys. Solid.
(2006) - et al.
Fibre–matrix interaction in the human annulus fibrosus
Journal of the mechanical behavior of biomedical materials
(2012) The influence of specimen length on the tensile failure properties of tendon collagen
J. Biomech
(1986)- et al.
The nonlinear characteristics of soft gels and hydrated connective tissues in ultrafiltration
J. Biomech.
(1990) - et al.
Mechanisms for mechanical damage in the intervertebral disc annulus fibrosus
J. Biomech.
(2004)
Degeneration affects the anisotropic and nonlinear behaviors of human anulus fibrosus in compression
J. Biomech.
Mechanical properties of collagen fibres: a comparison of reconstituted and rat tail tendon fibres
Biomaterials
Advanced glycation end-products diminish tendon collagen fiber sliding
Matrix Biol.
Fluid transport and mechanical properties of articular cartilage: a review
J. Biomech.
Tensile behaviour of individual fibre bundles in the human lumbar anulus fibrosus
J. Biomech.
The influence of swelling and matrix degradation on the microstructural integrity of tendon
Acta Biomater.
Effects of maturation and advanced glycation on tensile mechanics of collagen fibrils from rat tail and Achilles tendons
Acta Biomater.
Interfibrillar shear stress is the loading mechanism of collagen fibrils in tendon
Acta Biomater.
The measurement of fixed charged density in the intervertebral disc
Biochim. Biophys. Acta Gen. Subj.
Lamellar and fibre bundle mechanics of the annulus fibrosus in bovine intervertebral disc
Acta Biomater.
Theoretical model and experimental results for the nonlinear elastic behavior of human annulus fibrosus
J. Orthop. Res.
Glycation increases human annulus fibrosus stiffness in both experimental measurements and theoretical predictions
J. Biomech.
Bovine annulus fibrosus hydration affects rate-dependent failure mechanics in tension
J. Biomech.
Mechanical properties of the human achilles tendon
Clin. Biomech.
Tensile properties of fresh human calcaneal (Achilles) tendons
Clin. Anat.: The Official Journal of the American Association of Clinical Anatomists and the British Association of Clinical Anatomists
Degeneration and aging affect the tensile behavior of human lumbar anulus fibrosus
Spine
Tensile properties of the annulus fibrosus
Eur. Spine J.
What is intervertebral disc degeneration, and what causes it?
Spine
The human lumbar intervertebral disc: evidence for changes in the biosynthesis and denaturation of the extracellular matrix with growth, maturation, ageing, and degeneration
J. Clin. Invest.
An integrated inverse model-experimental approach to determine soft tissue three-dimensional constitutive parameters: application to post-infarcted myocardium
Biomech. Model. Mechanobiol.
The micromechanical role of the annulus fibrosus components under physiological loading of the lumbar spine
J. Biomech. Eng.
Modeling degenerative disk disease in the lumbar spine: a combined experimental, constitutive, and computational approach
J. Biomech. Eng.
Comparison of animal discs used in disc research to human lumbar disc: axial compression mechanics and glycosaminoglycan content
Spine
Hierarchical structure of the intervertebral disc
Connect. Tissue Res.
Tensile properties of nondegenerate human lumbar anulus fibrosus
Spine
An anisotropic model for annulus tissue and enhanced finite element analyses of intact lumbar disc bodies
Comput. Methods Biomech. Biomed. Eng.
Anisotropic and inhomogeneous tensile behavior of the human anulus fibrosus: experimental measurement and material model predictions
J. Biomech. Eng.
Cited by (12)
Emerging tissue engineering strategies for annulus fibrosus therapy
2023, Acta BiomaterialiaA finite element-peridynamic combined multiscale analysis strategy based on implicit integration scheme
2022, StructuresCitation Excerpt :The PD model needs a small grid size (e.g., 10−3 – 100 mm) and numerous bonds defining interactions between particles. In reality, the failure of civil structures often concentrates in a very small area, whereas other parts still keep linear elastic state [14,15]. To take advantage of the ability of the PD method in solving the discontinuous problems, some researchers proposed various coupling approaches of the PD and FE methods.
Saline-polyethylene glycol blends preserve in vitro annulus fibrosus hydration and mechanics: An experimental and finite-element analysis
2022, Journal of the Mechanical Behavior of Biomedical MaterialsCitation Excerpt :For example, poroelastic material descriptions have been used to investigate the stress-bearing role of interstitial water content and time-dependent rheological behavior [Natarajan et al., 2006; Wilson et al., 2007; Galbusera et al., 2011a, b; Barthelemy et al., 2016; Rijsbergen et al., 2018; Castro and Alves, 2021]. Despite these advances, few computational studies investigating tissue mechanics have employed material descriptions that adequately represent Donnan equilibrium effects, which play a pivotal role in active tissue swelling, mechanics, and metabolic behavior [Jacobs et al., 2014; Yang and O'Connell, 2018; Zhou et al., 2019; Zhou et al., 2021a, b]. Thus, it is noteworthy that the transient swelling simulations conducted in the current study agreed so well with the experiment results (Fig. 2).
Modeling multiaxial damage regional variation in human annulus fibrosus
2021, Acta BiomaterialiaCitation Excerpt :Modeling multiaxial damage regional variation in annulus can provide a better understanding of the failure onset and location in the disc, beyond experimental observations. Modeling mechanics of the healthy annulus was developed in several papers considering different approaches as physically realistic as possible, to name a few recently published [21–29]. The quantitative prediction of the annulus damage is less reported.