Material properties of the posterior human sclera

Abstract

To characterize the material properties of posterior and peripapillary sclera from human donors, and to investigate the macro- and micro-scale strains as potential control mechanisms governing mechanical homeostasis. Posterior scleral shells from 9 human donors aged 57–90 years were subjected to IOP elevations from 5 to 45 mmHg and the resulting full-field displacements were recorded using laser speckle interferometry. Eye-specific finite element models were generated based on experimentally measured scleral shell surface geometry and thickness. Inverse numerical analyses were performed to identify material parameters for each eye by matching experimental deformation measurements to model predictions using a microstructure-based constitutive formulation that incorporates the crimp response and anisotropic architecture of scleral collagen fibrils. The material property fitting produced models that fit both the overall and local deformation responses of posterior scleral shells very well. The nonlinear stiffening of the sclera with increasing IOP was well reproduced by the uncrimping of scleral collagen fibrils, and a circumferentially aligned ring of collagen fibrils around the scleral canal was predicted in all eyes. Macroscopic in-plane strains were significantly higher in peripapillary region then in the mid-periphery. In contrast, the meso- and micro-scale strains at the collagen network and collagen fibril level were not significantly different between regions. The elastic response of the posterior human sclera can be characterized by the anisotropic architecture and crimp response of scleral collagen fibrils. The similar collagen fibril strains in the peripapillary and mid-peripheral regions support the notion that the scleral collagen architecture including the circumpapillary ring of collagen fibrils evolved to establish optimal load bearing conditions at the collagen fibril level.

Introduction

Biomechanics is likely to be important in the development and progression of glaucoma, as it provides a direct link between intraocular pressure (IOP) and the microenvironment of the optic nerve head (ONH) where glaucomatous damage to the retinal ganglion cell axons is thought to occur (Burgoyne et al., 2005, Downs et al., 2008). The sclera is an important driver of ONH biomechanics, as it imposes the principal mechanical boundary condition on the contained lamina cribrosa and neural canal tissues and the intrascleral branches of the short posterior ciliary arteries provide the primary blood supply for the lamina cribrosa. Several computational studies have shown the sclera to be among the most important determinants of ONH stress and strain (Sigal et al., 2005, Sigal et al., 2011a, Sigal et al., 2011b).

Computational modeling studies are necessary to study ONH biomechanics, as no experimental methods are available to measure or estimate stress and strain in the ONH in vivo. However, without accurate material properties, these models yield inaccurate stress and strain predictions in the sclera, and hence ONH. No previous studies have reported material property estimates for the posterior and peripapillary human sclera that incorporate the inhomogeneous, hyperelastic, anisotropic nature of its material response. Histologic studies have shown that there is a circumferential ring of highly aligned collagen fibrils surrounding the ONH, and computational simulations have suggested that this ring serves to shield the relatively compliant ONH from excessive strains (Girard et al., 2009b, Grytz et al., 2011a, Coudrillier et al., in press). Experimental studies have shown that the sclera's mechanical response changes in response to age (Girard et al., 2009c, Coudrillier et al., 2012) and exposure to chronically elevated IOP (Girard et al., 2011b), although no work has been done to elucidate the mechanical factors driving these changes.

In this study, we estimated eye-specific scleral material properties by matching the inflation response of an eye-specific computational model to the experimentally measured displacements of the same posterior scleral shell subjected to an inflation test. The material properties were iteratively fit to a mechanistic constitutive model formulated such that its parameters capture physiologically relevant mechanical behavior at the macro- and micro-scale. This constitutive model represents the collagen fibril, network, and non-fibrillar extracellular matrix (ECM) as separate components that combine to determine the overall mechanical response of the tissue. As such, the material properties fit with this mechanistic model can help elucidate the mechanisms underlying changes in scleral biomechanics with age, race, and IOP-driven remodeling associated with aging or disease. This is not the case with many existing phenomenological constitutive models (Coudrillier et al., 2012, Downs et al., 2005, Elsheikh et al., 2010, Woo et al., 1972), which are accurate mathematical descriptions of the mechanical behavior but lack parameters that describe the underlying behavior of the connective tissue constituents, e.g., collagen fibrils and non-fibrillar extracellular matrix (ECM).

The sclera is a living soft tissue and its material properties evolve and change over time, e.g., through growth remodeling of its collagen structure. The underlying stimuli remain unclear, although different mechanical stimuli have been proposed to drive growth and remodeling in collagenous soft tissues. Most existing computational formulations use macroscopic stress or strain variables at the tissue level to motivate growth and remodeling (Taber and Humphrey, 2001, Gleason and Humphrey, 2004, Hariton et al., 2007, Ricken et al., 2007, Driessen et al., 2004, Kuhl et al., 2005, Himpel et al., 2008, Kuhl and Holzapfel, 2007, Driessen et al., 2008, Hariton et al., 2007, Grytz and Meschke, 2010, Grytz et al., 2011a). An increasing number of studies of anisotropic growth and remodeling theories assume the existence of a homeostatic tissue strain or stress value in the direction of the collagen fibril (Watton et al., 2009, Nagel and Kelly, in press, Zeinali-Davarani et al., 2011a, Zeinali-Davarani et al., 2011b, Martufi and Gasser, 2012). Recently, we proposed a homeostatic strain control mechanism at the collagen fibril level to motivate the thickening of the lamina cribrosa in early stages of experimental glaucoma (Grytz et al., 2011b). Recent experimental evidence also points toward the existence of a homeostatic control mechanism at the collagen fibril level in collagenous soft tissues (Camp et al., 2011, Flynn et al., 2010, Bhole et al., 2009, Foolen and van Donkelaar, 2010). To investigate the potential homeostatic strain control mechanism in the posterior sclera, we calculated the relative differences in different strain variables across the scleral shell. We computed strain variables at the different length scales of our constitutive model to determine if these variables were uniform across the scleral shell and therefore could be considered as candidate variables driving homeostatic strain control.

The outline of this manuscript is as follows. In Section 2 the experimental and computational methods are presented that were used to estimate the material properties of the posterior human sclera. The results of the inverse analysis and the investigation of the different strain measures are presented in Section 3. We discuss the obtained results and the limitations of this study in Section 4. The theoretical background of our microstructure based constitutive formulation and the calculation of the cost function, which was used for the inverse analysis, are summarized in the Appendix A Microstructure based constitutive model, Appendix B Cost function, respectively.