Predicted extension, compression and shearing of optic nerve head tissues
Introduction
The causes of retinal ganglion cell (RGC) degeneration in glaucoma are still poorly understood, but elevated intraocular pressure (IOP) has been identified as a primary risk factor for the development and progression of glaucomatous optic neuropathy. A biomechanical theory of glaucoma proposes that mechanical effects on the tissues of the optic nerve head (ONH) are, at least in part, responsible for the damaging effects of IOP. Consistent with this theory, it is generally accepted that increases in IOP deform the ONH (Burgoyne et al., 2005, Jonas et al., 2004, Yan et al., 1994), which results in high levels of mechanical strain (Burgoyne et al., 2005, Quigley, 2005, Sigal et al., 2004). Several mechanisms by which strain could lead to tissue degeneration and the ultrastructural changes of the ONH observed in glaucoma have been proposed, and are supported by evidence about the effects of strain and stress on the load-bearing connective fibres (Hernandez, 1992, Morrison et al., 1990, Quigley et al., 1991a, Quigley et al., 1991b), capillaries and on the axons of the RGCs, astrocytes and endothelial cells (Hernandez et al., 1989, Morrison et al., 1990), as recently reviewed by Burgoyne et al. (2005).
Mechanical strain is a measure of deformation, and can be interpreted as the change in length of a material region (e.g. a cell) divided by the resting length of that region. Studies have shown that strain is an important mechanobiological factor that causes effects in many cell types (Bandak, 1995, Edwards et al., 2001, LaPlaca et al., 2005, Pedersen and Swartz, 2005, Tan et al., 2006, Triyoso and Good, 1999, Vossoughi and Bandak, 1995, Wang and Thampatty, 2006). Strain is usually reported as a single value, e.g. “the cells were strained by 5%”. The situation is more complex than this simple description would imply, however. Cells and tissues can deform in different ways, or “modes”, such as extension, compression or shearing, although these modes of strain are not independent of one another, as described in more detail in the Appendix. This is not merely a matter of semantics, as it has been established that the mechanobiologic response of tissues (Bain and Meaney, 2000, Edwards et al., 2001) and cells (LaPlaca et al., 2005, Morrison et al., 2005, Pedersen and Swartz, 2005, Tan et al., 2006, Wang and Thampatty, 2006) depends on the mode of deformation (extension, compression or shearing), as well as the magnitude and temporal profile of the stimulus, and the type of tissue or cell and its biological state. It is therefore of interest to determine which modes of strain the tissues of the ONH are exposed to as IOP is elevated.
As IOP changes, different regions of the ONH deform by different amounts and therefore experience different amounts of strain. Even within a single tissue region (e.g. the lamina cribrosa), the strain can vary substantially from location to location. Previously, our group (Sigal et al., 2004, Sigal et al., 2005a, Sigal et al., 2005b) and others (Bellezza et al., 2000) have simply used mean and peak values of strain to describe the distribution of strain. These quantities, while useful, do not fully describe the strain distribution, and there is a need to better characterize how strains are distributed in various tissue regions.
Strain does not occur within tissues without accompanying stress, which is a measure of the force being carried by the tissue. More specifically, stress is the force in a tissue region divided by the cross-sectional area over which that force acts, and high levels of stress can lead to mechanical failure (tearing) of connective tissue components. For example, Burgoyne has suggested that elevated stresses might cause collagen fibrils in the lamina cribrosa to fail, thereby contributing to optic nerve head remodelling in glaucoma (Burgoyne et al., 2005). It is therefore of interest to quantify the stress distribution in ONH tissues. As is the case for strain, there are different modes of stress, and we will examine the relative magnitudes of these modes throughout the ONH.
The objective of this work was to analyze this previously overlooked aspect of the biomechanical response of an ONH to increases in IOP: the spatial and volumetric distribution of different modes of strain. We found that compressive strains were the dominant mode of strain found in the lamina cribrosa.
Section snippets
Materials and methods
Experimental measurements of the biomechanical environment of the ONH are extremely challenging. We therefore employ a standard engineering technique known as finite element modeling (FEM) that allows the biomechanics of the ONH to be simulated while accounting for the geometric complexity of the relevant tissue regions (Meakin et al., 2003, Stay et al., 2005, Viceconti et al., 2006).
Results
Different measures of strain and stress were plotted on cross sections through an individual-specific model (Fig. 3) and a generic model of the ONH (Fig. 4). For all models, there were substantial differences in the magnitudes and distribution of the various modes of strain. Considering the modes of strain that have a simple physical interpretation, the largest strain magnitudes occurred in compression (third principal strain), followed by shear and finally by extension (first principal
Discussion and conclusions
Three main results have been obtained from this work: First, elevation of IOP causes the tissues of the ONH to be subjected to a complex strain environment, characterized by multiple modes of strain (extension, compression and shearing) whose magnitude and distribution vary through the ONH. Second, the highest magnitudes of all modes of strain occurred within the neural tissue regions, not within the lamina cribrosa. Third, the largest strain magnitudes were in compression, followed by shearing
Acknowledgments
This work was supported by the Consejo Nacional de Ciencia y Tecnologia de Mexico (IAS), the Canadian Institutes for Health Research (CRE, JGF), the Canada Research Chairs Program (CRE) and Glaucoma Research Society of Canada. We thank the Eye Bank of Canada for providing donor tissue.
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Present address: Ocular Biomechanics Laboratory, Devers Eye Institute, Portland, OR, USA.