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

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Abstract

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.

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).

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