There is some arbitrariness in how the ocular geometry was specified. We defined 14 geometric factors that together spanned a wide range of possible globe sizes and ONH shapes (see
Fig. 1for definitions). These geometric input factors included the thickness of the prelaminar neural tissue, LC, pia mater, and sclera at different points; the shapes of the scleral canal and optic cup; the eye globe radius and thickness; the curvature of the LC; and the shape of the peripapillary sclera. Herein, we give notes explaining how some of these factors were defined. The scleral point closest to the axis of symmetry was defined as the scleral tip, and its distance to the axis of symmetry as the radius of the scleral canal. Directly anterior (i.e., on a line parallel to the axis of symmetry) to the tip of the sclera, at a distance defined as rim height, was the retinal rim top. From the retinal rim top, away from the axis of symmetry, the prelaminar neural tissue thinned smoothly, attaining the retina shell thickness at a point that represented the rim perimeter. Orthogonal to the axis of symmetry, we defined a reference level 50 μm posterior to the rim perimeter (
Fig. 1 ; dashed line), representing the scanning laser tomograph’s reference plane (Heidelberg Retina Tomograph; Heidelberg Engineering, Heidelberg, Germany).
25 The shape of the cup was characterized by a cup-to-disc ratio, as measured at this reference level. The shape of the cup varied from a relatively small cup with steep walls (cup-to-disc ratio of 0.1) to a relatively large, flat cup (cup-to-disc ratio of 0.5). Cup depth was defined as the distance from the bottom of the cup to the reference level. We varied the curvature of the LC by changing the depth of the anterior LC surface at the axis of symmetry with respect to the same surface at the edge of the LC. As this depth increases, the LC shape varies from flat (depth 0) to more curved. The shape of the posterior peripapillary sclera was parameterized and varied from 0 to 1, representing variations with little to significant scleral thinning. The optic nerve and canal wall angles are related to parameters identified by Burgoyne et al.
7 that help determine the thickness of the peripapillary sclera—namely, the angle of the neural canal wall and the oblique orientation of the canal’s passage through the sclera. In our models, which are asymmetric, these input factors measured the rate of enlargement of the canal diameter and retrobulbar optic nerve.
For each input factor, the baseline value and range of admissible values were defined from the literature, when available, or from our own estimates, based on measurements on serial sections of the ONH from ostensibly healthy donor human eyes.
8 For a number of input factors the range of physiologically reasonable values is unknown. An unnaturally large range could make a factor artificially influential and conversely make other factors artificially modest. We therefore tried to reduce the arbitrariness of the input factor ranges by varying input factors over comparable ranges. Specifically, all tissue stiffnesses (Young’s moduli) were varied from one-third to three times the values in the baseline model, which is within the range of reported experimental values. The prelaminar tissue Poisson ratio varied from practically incompressible (ν = 0.49) to relatively low (ν = 0.4). Many geometric factors were varied in the range ±20% around the values of the baseline model.
In addition, we evaluated the possible effects of input factor ranges by repeating the study under three conditions: full factor ranges, as described earlier, halved factor ranges (for all factors, except IOP), and minimal factor ranges defined as one twenty-fourth of the full range. The advantage of using smaller input factor ranges is that it allows us to minimize nonlinear effects that are seen in some outcome measures, as will be described in the following sections.