Stress-controlled viscoelastic tensile response of bovine cornea
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.
Section snippets
Materials and methods
Experimental: Bovine cornea was selected for this study because its large size facilitates strip extraction, and it is not subjected to scalding which can damage porcine corneas during slaughter. Moreover, its response appears to be closer to human than porcine cornea (see Section 4 and Fig. 7). Untreated bovine ocular globes from beef cattle 18–24 months in age were obtained from a medical supplier within 24 h after slaughter. During this time, the intact ocular globes were stored in a sealed
Results
Experimental: Multi-stress-rate tests were performed on six left/right pairs of corneas under nominally identical conditions. The axial component of engineering strain, , is plotted versus time in Fig. 3 for three different stress rates and two different tensile orientations. The trend lines represent the average loading/unloading response from 12 tests and the error bars represent one standard deviation. The average strains observed at peak loading for the two orientations and three
Discussion
The stress–strain response of bovine cornea exhibited significant non-linearity, resulting in the well-known J-shape shown in Fig. 4. As shown in Fig. 7, the present study measured a much stiffer response than other studies which did not employ preconditioning. A more direct comparison was made by extracting the stress–strain response in this study from the first preconditioning cycle. These un-preconditioned data exhibited similar behavior to the bovine experiments of Hoeltzel et al. (1992).
Acknowledgments
The authors wish to thank Prof. R. Regueiro (CU-Boulder), Dr. R. Chambers (SNL), and Prof. S.D. McLeod (UCSF). This work was funded by the LDRD program at Sandia. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under Contract DE-ACO4-94AL85000.
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