IOP-induced lamina cribrosa displacement and scleral canal expansion: an analysis of factor interactions using parameterized eye-specific models

Abstract

Purpose: To study the anterior-posterior lamina cribrosa deformation (LCD) and the scleral canal expansion (SCE) produced by an increase in IOP and identify the main factors and interactions that determine these responses in the monkey.

Methods: Eye-specific baseline models of the LC and sclera of both eyes of three normal monkeys were constructed. Morphing techniques were used to generate 888 models with controlled variations in LC thickness, position and modulus (stiffness), scleral thickness and modulus, and scleral canal size and eccentricity. Finite element modeling was used to simulate an increase in IOP from 10 to 15 mm Hg. A two-level, full-factorial experimental design was used to select factor combinations and to determine the sensitivity of LCD and SCE to the eight factors, independently and in interaction.

Results: LCD was between 53.6 μm (posteriorly) and -12.9 μm (anteriorly), whereas SCE was between 0.5 and 15.2 μm (all expansions). LCD was most sensitive to laminar modulus and position (24% and 21% of the variance in LCD, respectively), whereas SCE was most sensitive to scleral modulus and thickness (46% and 36% of the variance in SCE, respectively). There were also strong interactions between factors (35% and 7% of the variance in LCD and SCE, respectively).

Conclusions: IOP-related LCD and SCE result from a complex combination of factors, including geometry and material properties of the LC and sclera. This work lays the foundation for interpreting the range of individual sensitivities to IOP and illustrates that predicting individual ONH response to IOP will require the measurement of multiple factors.

Figure 1.

Geometry factor definitions. Top left: cutaway view of a baseline eye-specific model of a normal monkey eye, with the lamina in blue and the sclera in yellow. Top right: detail of the optic nerve head (ONH) region illustrating the location and orientation of the LC relative to the coordinate's origin. The model was translated and rotated so that the centroid of the anterior lamina insertion was located at the coordinate's origin. Also shown are the anterior lamina insertions into the sclera (ALI, dashed red line), a least-squares, best-fit reference plane to the ALI (dotted black line). Five features of the model geometry were defined. Bottom left: canal eccentricity as the ratio of the major to minor axes of the anterior lamina insertion; bottom right: canal size as the average canal radius, itself computed as the distance from the anterior lamina insertion to its centroid (yellow arrows); LC thickness, as the average distance between the anterior and posterior surfaces of the LC (green arrows); scleral thickness, as the distance between the interior and exterior surfaces of the sclera averaged over the sclera region located between 1.5 and 1.6 times the canal radius from the anterior lamina insertion centroid (red arrows); and LC position, as the average distance between the anterior surface of the lamina and a least-squares, best-fit plane to the anterior lamina insertion (pink arrows).

Figure 2.

Geometry factor ranges. Geometry factor ranges were derived from histomorphometry of the ONH of 21 normal monkey eyes, 6 of which were used as models in this study (see the Methods section for details of the manuscripts in which these data have been presented). The range for each factor was defined as the minimum and maximum value of the measure over the 21 eyes. See Figure 1 for the factor definitions and Figure 3 for an illustration of models with various levels of the factors.

Figure 3.

The experimental design and examples of model geometries and variations. Distribution of the factor combinations studied (top row). Shown are two-dimensional projections of the eight-dimensional parameter space. Note that in the two-level, full-factorial design all the models studied were at the corners of the factor space. Starting from a center model, five geometry factors were varied. Cutaway views of models produced by varying the factors one by one (middle row). Two extreme cases produced by setting all the factors at the low (left side, bottom row) or high (right side, bottom row) levels.

Figure 4.

Graphical representation of the relative magnitude of the factor and interaction influences shown in Table 2. The bar lengths are proportional to the magnitude of the numbers in the table and are intended to simplify seeing the influences at-a-glance. Factors with a statistically significant effect (P < 0.01) are shown with a bar, the rest with a gray dash. Canal eccentricity is included here for completeness. 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 responses were influenced by interactions, LCD more strongly than SCE. Recall that interactions may be interpreted as curvature in response space. Hence, relatively small contributions to the sum of squares in Table 2 (short bars in the figure) may still have large effects on the response within some regions of the factor space.

Figure 5.

Sensitivity of LCD and SCE to laminar and scleral thickness and modulus. Effects of scleral and laminar thickness and modulus on LCD (A, C) and SCE (B, D). Similar levels of LCD and SCE could be produced for various combinations of scleral modulus and thickness. A similar effect could be obtained from the laminar modulus and thickness, although they do not balance as symmetrically. Star: combinations with the maximum effective stiffness (thick and stiff tissue); pentagon:combinations with the minimum effective stiffness (thin and compliant tissue). Note the different ranges in the y-axes (LCD) between (A) and (C). The axes' ranges were chosen to illustrate clearly the factor interaction. The smaller range in (A) than in (B) illustrates the limited influence on LCD of the scleral properties compared with the laminar properties.

Figure 6.

Examples of models with various combinations of scleral and laminar material properties. Cross sections through a model with the geometry of monkey 1 at the center of the parameter space in the undeformed (black line, 10 mm Hg IOP) and in the deformed state (colored lines, 15 mm Hg IOP). The deformations are relative to the equator to illustrate global deformations (top), or relative to the anterior laminar insertion to highlight local deformations (bottom), and have been exaggerated 10-fold. In the top panel it is easy to distinguish the cases with the compliant sclera (blue and red) by the large posterior displacement of the whole ONH. Similarly, in the bottom panel it is easy to distinguish the cases with the compliant lamina (green and red) by the large posterior displacement of the lamina. Note the anterior laminar displacement (negative LCD), larger for compliant sclera and stiff lamina (blue) than for both tissues stiff (brown). A stiff lamina also reduced the bending, or bowing, of the peripapillary sclera.

Figure 7.

Sensitivity of LCD to laminar modulus, position and thickness and to canal size. (A) The three-factor interaction involving the laminar modulus, lamina position, and canal size. The effect of laminar position is represented by the distance between the surfaces. Deeper laminas tended to displace anteriorly, whereas the shallow laminas could displace anteriorly or posteriorly depending on the size of the canal and the laminar modulus. When the lamina was deep (bottom surface) the effects of the two other factors were smaller than when the lamina was shallow (upper surface)—that is, the top surface is steeper than the bottom surface. The effects of stiffening of the LC were larger when the canal was large than when it was small, and when the lamina was shallow than when it was deep. (B, C) Two traditional interaction plots. In the interaction between lamina thickness and canal size the effects of canal size were larger when the lamina was thin than when it was thick. Conversely, lamina thickness had a larger influence when the canal was large than when it was small. For the interaction between lamina thickness and position, lamina thickness reduced LCD when the lamina was shallow, but not when the lamina was deep. Conversely, when the lamina was thick its position had little influence on LCD, but when the lamina was thin the position had large influence. Thicker, stiffer or deeper laminas within a small canal had smaller posterior displacements and were more likely to displace anteriorly. Factors not explicitly varied were at the center levels.

Figure 8.

Sensitivity of SCE to scleral modulus and thickness and laminar modulus and position. (A) The distance between the surfaces is the effect of the sclera modulus. When the sclera was stiff (bottom surface) the effects of the other two factors were smaller than when the sclera was compliant (top surface). Similarly, when the sclera was thick (right side), stiffening the lamina or the sclera had smaller effects than when the sclera was thin (left side). (B, C) The effects of laminar position and modulus, and how their effects depend also on the sclera modulus. When the sclera was stiff (B), neither lamina modulus nor lamina position affected an already low SCE. However, when the sclera was compliant (C), SCE was reduced by increased lamina modulus, more so if the lamina was shallow than if it was deep. Conversely, the laminar position reduced SCE slightly if the lamina was compliant and substantially if it was stiff. (B, C). These plots illustrate how the lamina could influence SCE, if the circumstances were right (e.g., when the sclera was compliant and thin and the lamina shallow).

Figure 9.

Sensitivity of LCD to the laminar modulus, independently and in interaction with six other factors. Each plot illustrates the effects of an interaction between the lamina and a second factor. The line slope indicates the sensitivity to laminar modulus, whereas the distance between the lines indicates the influence of the second factor. For example, eccentricity had almost no effect, and so both lines overlap. Increased lamina modulus always resulted in more anterior displacement (or reduced posterior displacement). Nonparallel lines indicate an interaction since the effect of one factor depends on the level of the other factor. LCD was more sensitive to laminar modulus when the canal was large, when the lamina was thin or when it was shallow. The stiffness and modulus of the sclera affected LCD but did not interact with the laminar modulus (i.e., the lines in the two rightmost plots are parallel).