Contents lists available at ScienceDirect Journal of the Mechanical Behavior of Biomedical Materials journal homepage: www.elsevier.com/locate/jmbbm Contributions of elastic fibers, collagen, and extracellular matrix to the multiaxial mechanics of ligament Heath B. Henninger a,b,c , Benjamin J. Ellis a,b , Sara A. Scott a , Jeffrey A. Weiss a,b,c,* a Department of Biomedical Engineering, University of Utah, Salt Lake City, UT, USA b Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT, USA c Department of Orthopaedics, University of Utah, Salt Lake City, UT, USA ARTICLEINFO Keywords: Elastin Ligament Constitutive model Mixture FEBio ABSTRACT Elastin is a biopolymer known to provide resilience to extensible biologic tissues through elastic recoil of its highly crosslinked molecular network. Recent studies have demonstrated that elastic fibers in ligament provide significant resistance to tensile and especially shear stress. We hypothesized that the biomechanics of elastic fibers in ligament could be described as transversely isotropic with both fiber and matrix components in a multi- material mixture. Similarly, we hypothesized that material coefficients derived using the experimental tensile responsecouldbeusedtopredicttheexperimentalshearresponse.Experimentaldataforuniaxialandtransverse tensile testing of control tissues, and those enzymatically digested to disrupt elastin, were used as inputs to a material coefficient optimization algorithm. An additive decomposition of the strain energy was used to model the total stress as the sum of contributions from collagen fibers, elastic fibers, elastic matrix, and ground sub- stance matrix. Matrices were modeled as isotropic Veronda-Westmann hyperelastic materials, whereas fiber families were modeled as piecewise exponential-linear hyperelastic materials. Optimizations provided excellent fits to the tensile experimental data for each treatment case and material model. Given the disparity in mag- nitude of stresses between longitudinal and transverse/shear tests and agreement between models and experi- ments, the hypothesized transversely isotropic material of elastin symmetry was supported. In addition, the coefficients derived from uniaxial and transverse tensile experiments provided reasonable predictions of the experimental behavior during shear deformation. The magnitudes of coefficients representing stress, non- linearity, and stiffness supported the experimental evidence that elastic fibers dominate the low strain tensile and shear response of ligament. These findings demonstrate that the additive decomposition modeling strategy can represent each discrete fiber and matrix constituent and their relative contribution to the material response of the tissue. These experimental data and the validated constitutive model provide essential inputs and a fra- mework to refine existing computational models of ligament and tendon mechanics by explicitly representing the mechanical contributions of elastic fibers. 1. Introduction Numerous studies have established that the mechanics of ligament and tendon are dominated by fibrillar collagen, but more recently elastin has also emerged as a contributor (Henninger et al., 2013, 2015). Collagen provides tensile stiffness and strength, whereas the biopolymer elastin, in the form of elastic fibers, provides compliance and supports stress during multiaxial deformation. During tissue de- formation, the recoil of elastin occurs via entropy of the disordered network conformation and high numbers of hydrophobic residues in and along the elastin backbone (Muiznieks et al., 2010). In normally developed tissues, alanine and lysine residues within tropoelastin monomers oxidize to form highly stable (iso)desmosine crosslinks (Muramoto et al., 1984; Uitto, 1979). This stability provides elastin with an exceptionally long in vivo half-life of up to 74 years (Shapiro et al., 1991). In connective tissues such as ligament, tendon, and skin, elastin makes up 4–7% of the tissue dry weight (Baldwin et al., 2013; Gacko, 2000; Henninger et al., 2013; Reddy et al., 2012). Highly extensible tissues such as artery, lung and nuchal ligament have proportionally higher elastin content, often over 50% of their dry weight (Greenwald et al., 1997; Lee et al., 2001; Miskolczi et al., 1997). Genetic mutations in elastin expression in conditions such as cutis laxa (Halper and Kjaer, 2014) and Marfan syndrome (Carta et al., 2009) affect the structural https://doi.org/10.1016/j.jmbbm.2019.07.018 Received 5 December 2018; Received in revised form 29 May 2019; Accepted 19 July 2019 * Corresponding author. Department of Biomedical Engineering, University of Utah, 50 South Central Campus Dr., Room 2480, Salt Lake City, UT, 84112, USA. E-mail address: jeff.weiss@utah.edu (J.A. Weiss). Journal of the Mechanical Behavior of Biomedical Materials 99 (2019) 118–126 Available online 20 July 2019 1751-6161/ © 2019 Elsevier Ltd. All rights reserved. T