IOP-induced lamina cribrosa deformation and scleral canal expansion: independent or related?

Abstract

Purpose: To study the association between the intraocular pressure (IOP)-induced anterior-posterior lamina cribrosa deformation (LCD) and scleral canal expansion (SCE).

Methods: 3D eye-specific models of the lamina and sclera of the eyes of three normal monkeys were constructed. Morphing techniques were used to produce 768 models with controlled variations in geometry and materials. Finite element analysis was used to predict the LCD and SCE resulting from an increase in IOP. We analyzed the association between LCD and SCE for the population as a whole, and for subsets.

Results: For some conditions, such as deep and stiff lamina, the association between LCD and SCE was strong and consistent with the concept of "the sclera pulls the lamina taut" as IOP increases. For other conditions, such as shallow and compliant lamina, there was no association. Further, for other conditions, such as for thin and stiff sclera, the association was opposite to the tautening. Although most of the models had similar response to IOP, some cases had peculiarly large LCD and SCE. The properties of the lamina cribrosa (LC) greatly influenced its response to variations in IOP; for example, deep laminas tended to displace anteriorly, whereas shallow LCs displaced little or posteriorly.

Conclusions: The association between LCD and SCE varied greatly depending on the properties of the lamina and sclera, which shows that it is critical to consider the characteristics of the population when interpreting measurements of LCD and SCE. This work is the first systematic analysis of the relationship between LCD and SCE.

Figure 1.

Schematic representation of how the deformations of the sclera and lamina may be related. When describing the effects of IOP on the LC, a useful conceptual framework has emerged in the last few years: that of the balance between the direct effects of IOP “pushing” the lamina posteriorly, and the indirect effects of IOP deforming the sclera, expanding the canal, which in turn “pulls” the lamina taut from the sides.^,,,,,,,,,, A stiff sclera deforms little under IOP (right), with a small SCE, allowing the lamina to be displaced posteriorly by the action of IOP on its anterior surface. Conversely, in the case of a compliant sclera (left), an increase in IOP induces large scleral deformations, which are transmitted to the scleral canal, resulting in a large SCE that pulls the lamina taut. Tautening of the lamina reduces posterior LCD or even results in anterior LCD, despite the effects of IOP on the LC (adapted from Sigal and Ethier).

Figure 2.

Model geometry and examples of geometry variations. Top left: Cut-out view of a baseline eye-specific model, with the lamina cribrosa in blue and the sclera in yellow. Bottom left: Detail of the ONH region illustrating the orientation of the LC relative to the system of coordinates, and the reference plane. The reference plane was fit by least-squares to the anterior lamina insertion into the sclera (ALI, dashed line), and used to define lamina position. Five features of the model geometry were defined and varied with morphing techniques (right side): lamina cribrosa position and thickness, scleral thickness, and scleral canal size and eccentricity. The morphed models are shown at the extremes of the corresponding factor (high on the left side column, and low on the right side column). LCD was defined as IOP-induced changes of lamina position. SCE was defined as IOP-induced changes in canal size.

Figure 3.

Scatterplot of LCD versus SCE for all cases. Each point represents the LCD and SCE predicted for a given combination of ONH characteristics (one model), and therefore the plot has 768 points. On the left side of the vertical dotted line are cases where the increase in IOP caused the lamina to displace anteriorly (negative LCD), whereas on the right are cases with posterior LCD; 94% of the cases resulted in a small LCD (−15 to 15 μm). Only 6% of the factor combinations resulted in substantial (>20 μm) posterior LCD, and 25% of those also had large (>9 μm) SCE. Notably, there are no points on the bottom left, which means that some SCE was necessary for the lamina to displace anteriorly. The framework of a relationship between SCE and LCD described in Figure 1 would appear in this plot as a trend where points on the right are lower than points on the left, such that increased SCE is associated with decreased posteriorly LCD or increased anteriorly LCD. Both parametric and nonparametric analyses concluded that there was indeed a negative association between LCD and SCE, thus supporting the conceptual framework. The linear regression (dashed line) was added to show how the linear fit, although significant, is not a good description of the data, and that there is more to understand of LCD versus SCE than a linear correlation.

Figure 4.

Selected cases with a variety of LCD and SCE combinations. Shown are cross-sections of six models with factors selected to illustrate how these may combine to produce a variety of LCD and SCE. The models (A–F) are morphed versions of the eye-specific baseline geometry reconstructed for the OD of monkey 1 (G). The shaded regions are the undeformed model with the lamina cribrosa in lighter gray than the sclera. The black outlines show the deformed models, relative to the anterior lamina insertion, with deformations exaggerated fivefold for clarity. In regions with many points we selected a representative example from the many combinations that can produce similar response.

Figure 5.

SCE versus LCD for all cases colored by each of the parameters. All panels are identical, except for the parameter used to color the symbols. The label above each plot indicates the parameter used to color the points: red for high level and blue for low level, except for Eye where each eye has a different color. The 12 cases with large LCD and SCE (top right of the scatterplots) combined compliant lamina and sclera, thin lamina and sclera, shallow lamina, and large canal size. Anteriorly LCDs were possible, as long as there was some SCE, which occurred most often, but not only, with compliant and thin sclera. The largest anteriorly LCDs occurred for cases with stiff laminas and did not have the largest SCEs. The largest SCEs had compliant and thin sclera, large canal size, and deep and compliant lamina. A thin and more elliptical lamina also increased slightly the maximum SCE, but this effect is probably too small to be important. The differences between the distribution of the points in blue and the points in red indicate the strength of the parameter or, conversely, the sensitivity of the measure on the parameter. For example, LCD was most sensitive to LC modulus (E), position (B) thickness (H), and canal size (C). SCE was most sensitive to sclera modulus (D) and thickness (G). Both responses were essentially insensitive to canal eccentricity (F) and the eye used as baseline (A). Since within a panel points with the same color share a particular level of a factor, the spread of points with a given color represents the influence of all other factors. We see, for example, that when the lamina was stiff (red points, E) the points spread over a smaller range of LCD, than when the lamina was compliant (blue points, E), and therefore that a stiff lamina reduced the sensitivity of LCD to the other factors. Similarly, the cases with stiff (D) or thick sclera (G) cover a smaller range on SCE than cases with compliant or thin sclera, again illustrating how these two parameters control, to some extent, the influence of other factors on SCE. A change in the effect of one factor, depending on the level of another factor is an interaction between the two factors.

Figure 6.

Scatterplot of LCD versus SCE for all cases, and for groups and subgroups split by lamina position and modulus. (A) Top left panel: Includes all cases and is equivalent to Figure 3. Grouping by one factor, either lamina modulus (B and C) or position (D and G), produces groups with statistically significant associations between LCD and SCE. Grouping by modulus produces one strong (B) and one weak (C) association, both in the direction expected from the conceptual framework above (Fig. 1). Grouping by lamina position results in something surprising: one relatively strong and significant relationship in the expected direction (D) and one mixed (G). The group with the mixed result was interesting because the association between LCD and SCE was significant in the direction opposite to the theory in the parametric analysis and not significant in the nonparametric one. More refined splitting of the cases into subgroups by lamina modulus and position revealed the effects of the strong interaction between the two factors. Three subgroups (E, F, and H) show clear, strong, and significant (in both analyses) LCD versus SCE relationships in the expected direction. However, the relationship was not significant in either analysis in the subgroup of deep and soft LCs. In addition, this figure also clearly shows some effects of the interaction between lamina modulus and position. For example, the effect of a change in lamina modulus is smaller in deep laminas (E versus F) than in shallow laminas (H versus I). Conversely, the effect of lamina depth is smaller in stiff laminas (E versus H) than that in soft laminas (F versus I). Each panel is labeled with the Pearson's product moment correlation coefficient (ρ) and Kendall's rank correlation (τ), colored blue if statistically significant (P < 0.01) or gray if not.

Figure 7.

Scatterplot of LCD versus SCE for all cases, and for groups and subgroups split by sclera thickness and modulus. With the parametric analysis none of the subgroups shows a significant negative association between LCD and SCE, that is, consistent with the concept that “the sclera pulls the lamina taut” as IOP increases. Moreover, three of the quarter-set subgroups (E, H, and I) show a relationship in the direction opposite to that expected and seen on the whole (A). In the fourth subgroup (F) the relationship was not significant. This is an example of an effect called “reversal” and is an example of Simpson's paradox. The largest SCEs occurred with thin and soft sclera, whereas the smallest ones occurred with thick and stiff sclera. Interestingly, the SCEs were similar for thin and stiff sclera and thick and soft sclera, consistent with our previous application of the concept of structural stiffness. Each panel is labeled with the Pearson's product moment correlation coefficient (ρ) and Kendall's rank correlation (τ), colored blue if statistically significant (P < 0.01) or gray if not.

Figure 8.

Simpson's paradox. Positive associations occur for two data groups (blue and red). When the groups are combined the association is negative. (Based on a diagram in Wikipedia: http://en.wikipedia.org/wiki/Simpson%27s_paradox; accessed on February 15, 2011).

Figure A1.

Relative influences of all factors and interactions. Percentage contributions of the factors and interactions to the sum of squares corrected by the mean, as a measure of relative influence. The bar lengths are proportional to the numbers and are intended to simplify seeing the influences at a glance. Factors with a statistically significant effect (P < 0.01) are shown in black, the rest in gray. The influential factors were different for each response: LCD was most influenced by lamina position and modulus, whereas SCE was most influenced by scleral thickness and modulus. Both LCD and SCE were influenced by interactions, LCD more strongly than SCE. Recall that interactions may be interpreted as curvature in response space. Thus, even relatively small contributions to the sum of squares may represent a large effect on the actual response. Simplified from Sigal et al.