A novel fibre-ensemble level constitutive model for exogenous cross-linked collagenous tissues

Abstract

Exogenous cross-linking of soft collagenous tissues is a common method for biomaterial development and medical therapies. To enable improved applications through computational methods, physically realistic constitutive models are required. Yet, despite decades of research, development and clinical use, no such model exists. In this study, we develop the first rigorous full structural model (i.e. explicitly incorporating various features of the collagen fibre architecture) for exogenously cross-linked soft tissues. This was made possible, in-part, with the use of native to cross-linked matched experimental datasets and an extension to the collagenous structural constitutive model so that the uncross-linked collagen fibre responses could be mapped to the cross-linked configuration. This allowed us to separate the effects of cross-linking from kinematic changes induced in the cross-linking process, which in turn allowed the non-fibrous tissue matrix component and the interaction effects to be identified. It was determined that the matrix could be modelled as an isotropic material using a modified Yeoh model. The most novel findings of this study were that: (i) the effective collagen fibre modulus was unaffected by cross-linking and (ii) fibre-ensemble interactions played a large role in stress development, often dominating the total tissue response (depending on the stress component and loading path considered). An important utility of the present model is its ability to separate the effects of exogenous cross-linking on the fibres from changes due to the matrix. Applications of this approach include the utilization in the design of novel chemical treatments to produce specific mechanical responses and the study of fatigue damage in bioprosthetic heart valve biomaterials.

Modeling the response of exogenously crosslinked tissue to cyclic loading: The effects of permanent set

“…We have previously developed the first constitutive model for exogenously crosslinked collagenous tissues [26] and determined the following three contributors to the mechanical response: collagen fibers, EXL matrix and fiber-fiber interactions, where the total strain energy density function is given by…”

“…Thus, having a full structural model, including a full structural derivation of the fiber-fiber interactions, is crucial. As in the previous model form [26], we will only keep the extensional component $I_8^{\text{ext}}$. In addition, since collagen fibers do not bear stress until fully straightened [4], we also assume that collagen fibers do not play a role in the interactions of the fiber ensembles until they are straightened .…”

“…We previously found that exogenous crosslinking increases the bending stiffness of the matrix by four time the original stiffness [25]. We also tested the mechanical response of exogenously crosslinked BP before and after crosslinking, and developed the first constitutive model for exogenously crosslinked soft tissue [26]. Interestingly, we also found that exogenously crosslinking does not increase the collagen fiber modulus, but significantly increases the interactions between collagen fibers [26], which is responsible for up to 30% of the stress in the fully loaded state.…”

Tissue constructs: platforms for basic research and drug discovery

“…These are the focus of the following discussion. Although detailed anisotropic models for the mechanics of nonlinear collagenous tissues are becoming more advanced [75,[97][98][99][100][101], we focus on isotropic approximations of cell, ECM and tissue construct moduli. In response to a rapid, step-like stretch of a tissue construct followed by an isometric hold (inset), an initial rise in force is observed, followed by a relaxation.…”

Integrated multiscale biomaterials experiment and modelling: a perspective

“…Additionally, the interactions between loaded collagen fibrils and fibres are difficult to model. A major modelling advance accounting for cross-linking between collagen fibres is presented by Sacks et al [11], and a major step forward in our understanding of interactions between the many types of collagen within connective tissues is presented by Connizzo et al [12]. However, balancing these substantial advances in understanding is a substantial advance in confusion put forth by Susilo et al [13], who present a new and unprecedented finding that collagen is sensitive to the way in which it is loaded: although strain-dependent enzymatic digestion of collagen has been well documented, Susilo et al [13] report for the first time, to the best of our knowledge, that cyclical loading fundamentally stiffens networks of collagen.…”