Stress-controlled viscoelastic tensile response of bovine cornea

Abstract

The viscoelastic response of bovine corneas was characterized using in vitro load-controlled uniaxial tension experiments. Specifically, two types of tests were employed: cycled ramp tests over a range of loading rates and creep tests over a range of hold stresses. Multiple replicates of each were used to quantify natural variability as well as mean trends. A preconditioning protocol was used to obtain a unique reference state before testing and to overcome the effects of non-physiological loading. A quasi-linear viscoelastic model incorporating a representation of the microstructure of the cornea was compared to the experimental results. For low stresses and moderate durations this model compares favorably, but overall the material displays non-linearities that cannot be represented within the quasi-linear framework.

Introduction

The cornea's structural performance is dominated by the stroma which constitutes 90% of the cornea thickness. The stroma consists of stacked lamellar sheets of collagen fibrils embedded in a hydrated matrix of proteoglycans, glycoproteins, and keratocytes (Cogan, 1951, Maurice, 1957). Each layer of (nearly) parallel fibrils lies obliquely to the neighboring layers, see, e.g., Pinsky et al. (2005, Fig. 1). Within the central cornea, the fibrils tend to run from limbus to limbus, and are preferentially aligned along inferior–superior (IS) and nasal-temporal (NT) axes (Meek et al., 1987, Boote et al., 2005). Near the edge of the cornea, the fibrils tend to be aligned circumferentially. Since the collagen fibers are the stiffest component of the cornea's structure, the alignment and density of these fibrils within lamellae largely determine the mechanical response of the cornea (Hukins, 1984, Boote et al., 2005).

Previous studies on cornea mechanics have typically employed a tensile strip method (Nyquist, 1968, Andreassen et al., 1980, Hoeltzel et al., 1992, Kampmeier et al., 2000, Zeng et al., 2001, Wollensak et al., 2003), or a more physiologically relevant inflation method (Woo et al., 1972, Jue and Maurice, 1991, Hjortdal, 1996, Shin et al., 1997). These types of measurements have been used, for example, to study the efficacy of cross-linking agents as means to counteract keratoconous (Wollensak et al., 2003, Spoerl et al., 1998). However, very few of the previous investigations have explicitly characterized viscoelastic response, with the notable exception being the study Nyquist (1968). Moreover, while there have been fiber–matrix models of the cornea developed to describe its anisotropic mechanical response (Pinsky and Datye, 1991, Pinsky et al., 2005), there do not to appear to be any viscoelasticity models.

Viscoelastic response has been studied more thoroughly in other soft tissues, including ligament, tendon, articular cartilage, muscle, and cardiovascular tissues, where the physiological manifestations of viscoelasticity are more apparent. For example, in ligament research, experimental results have guided development of a series of models (Kennedy et al., 1976, Pioletti et al., 1998, Provenzano et al., 2001, Weiss et al., 2002, Hingorani et al., 2004). The most commonly employed formulation is quasi-linear viscoelastic (QLV) theory (Fung, 1993). However, recent work has called into question the ability of QLV theory to represent observed behavior (Pioletti et al., 1998, Hingorani et al., 2004).

The present study seeks to characterize the viscoelastic response of the cornea and evaluate the fidelity of QLV theory. We hypothesize, based on aforementioned observations in ligament tissue, that the QLV theory will not adequately describe cornea behavior. To explore this hypothesis, in vitro bovine cornea tensile stress rate and creep tests were used to evaluate a newly developed microstructurally based QLV formulation.