Cerebrospinal Fluid Pressure: Revisiting Factors Influencing Optic Nerve Head Biomechanics

Abstract

Purpose: To model the sensitivity of the optic nerve head (ONH) biomechanical environment to acute variations in IOP, cerebrospinal fluid pressure (CSFP), and central retinal artery blood pressure (BP).

Methods: We extended a previously published numerical model of the ONH to include 24 factors representing tissue anatomy and mechanical properties, all three pressures, and constraints on the optic nerve (CON). A total of 8340 models were studied to predict factor influences on 98 responses in a two-step process: a fractional factorial screening analysis to identify the 16 most influential factors, followed by a response surface methodology to predict factor effects in detail.

Results: The six most influential factors were, in order: IOP, CON, moduli of the sclera, lamina cribrosa (LC) and dura, and CSFP. IOP and CSFP affected different aspects of ONH biomechanics. The strongest influence of CSFP, more than twice that of IOP, was on the rotation of the peripapillary sclera. CSFP had similar influence on LC stretch and compression to moduli of sclera and LC. On some ONHs, CSFP caused large retrolamina deformations and subarachnoid expansion. CON had a strong influence on LC displacement. BP overall influence was 633 times smaller than that of IOP.

Conclusions: Models predict that IOP and CSFP are the top and sixth most influential factors on ONH biomechanics. Different IOP and CSFP effects suggest that translaminar pressure difference may not be a good parameter to predict biomechanics-related glaucomatous neuropathy. CON may drastically affect the responses relating to gross ONH geometry and should be determined experimentally.

Figure 1

Input factor definitions. Only the optic nerve head region is shown. See Table 1 for input factor ranges. In addition to the input factors shown, the compressibility (Poisson's ratio) of the prelaminar and retrolaminar neural tissues and the stiffness of each tissue region were varied, for a total of 24 input factors. The illustration represents the model geometry at IOP of 5 mm Hg, BP of 50 mm Hg, and CSFP of 0 mm Hg.

Figure 2

Strength of factor influences as determined by response surface methodology. Columns 1 through 4 present the top four principal components (PCs). Columns 5 through 14 present the 10 representative responses. Columns 15 and 16 present the maximum and average influence of factors on the 10 representative responses (columns 5–14). Rows 1 through 16 present the 16 most influential factors, sorted from highest (top) to lowest (bottom) average influence. Cells are colored according to the strength of a factor influence (row) on a response (column). These were computed as the percentage of a response variance due to each of the factors, with strong influences shown in red and weak influences in blue. Strengths of factor interactions were calculated, but are not shown.

Figure 3

Biplots of the top four principal components (PCs). Left: PC1 and PC2; right: PC3 and PC4. The top four PCs accounted for over 96% of the total variance. A biplot shows two-dimensional projections of the responses (black lines) and factors (red lines). The angle between lines represents the strength of the correlation between variables. Strongly correlated variables are parallel (0°) or antiparallel (180°), and independent variables are orthogonal (90°). All lines have a length of 1 in a 98-dimensional space. Line length in a biplot is the variance accounted for by the two PCs. The factors were not included when computing the PCs and are shown only as covariates to illustrate their relationship with the responses and the PCs. (Readers unfamiliar with principal component analysis or biplots may refer to our previous publication.)

Figure 4

Scatter plot of model responses on the top four principal components (PCs). The axes are the same as in Figure 3. Each dot represents the response of one of the 7316 models in the second-phase response surface methodology analysis. The large red numbers are the five archetypes. As expected, the archetypes are spread on the periphery of the response cloud.

Figure 5

Contour plots of maximum principal strain in the five archetypes. Rows represent the five archetypes. Columns represent the strain response of each archetype to elevations in IOP only, CSFP only, and both IOP and CSFP. The interpretation of each archetype is listed in the rightmost column. Deformations are shown exaggerated five times for clarity. Recall that, by definition of archetype, the responses of all other ONHs are linear combinations of these five archetypes. Note how in all of these cases, the effects of IOP and CSFP did not balance out; they added up. Although the largest retrolaminar strains were also accompanied by a large enlargement of the subarachnoidal space, it was still possible to have substantial retrolaminar deformations without much enlargement.

Figure 6

Schematic description of three mechanisms by which increases in CSFP cause ONH deformations. Undeformed ONH is shown with continuous lines, and deformed ONH with dashed lines. (a) CSFP acts inwardly compressing the pia mater and the retrolaminar neural tissue within. Due to the Poisson effect, lateral compression may cause expansion in the axial direction, increasing retrolaminar pressure “pushing” anteriorly on the lamina and causing clockwise rotation of the PPS. The extent of this effect depends on the compressibility of the retrolaminar tissue, which is still not well characterized. (b) CSFP acts outwardly on the dura mater away from the pia mater, causing the known distension of the dural sheath, rotating the PPS counterclockwise, and displaces the periphery of the lamina posteriorly. (c) CSFP “pushes” the PPS anteriorly, causing flattening of the globe and clockwise rotation of the PPS, and displacing the periphery of the lamina anteriorly. The magnitude of each of these effects will depend on different factors. For example, (a) will depend on the stiffness and thickness of the pia mater, as well as the stiffness and compressibility of the retrolaminar neural tissues; (b) is influenced by the stiffness of the dura and flexibility of the sclera (a combination of its stiffness and thickness). Hence, the various mechanisms will add up or cancel out in various proportions in a given eye.