April 2016
Volume 57, Issue 4
Open Access
Anatomy and Pathology/Oncology  |   April 2016
Finite Element Modeling of Factors Influencing Optic Nerve Head Deformation Due to Intracranial Pressure
Author Affiliations & Notes
  • Andrew J. Feola
    Department of Biomedical Engineering Georgia Institute of Technology/Emory University, Atlanta, Georgia, United States
  • Jerry G. Myers
    NASA Glenn Research Center, Cleveland, Ohio, United States
  • Julia Raykin
    Department of Biomedical Engineering Georgia Institute of Technology/Emory University, Atlanta, Georgia, United States
  • Lealem Mulugeta
    Universities Space Research Association, Houston, Texas, United States
  • Emily S. Nelson
    NASA Glenn Research Center, Cleveland, Ohio, United States
  • Brian C. Samuels
    Department of Ophthalmology, University of Alabama at Birmingham, Birmingham, Alabama, United States
  • C. Ross Ethier
    Department of Biomedical Engineering Georgia Institute of Technology/Emory University, Atlanta, Georgia, United States
Investigative Ophthalmology & Visual Science April 2016, Vol.57, 1901-1911. doi:10.1167/iovs.15-17573
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      Andrew J. Feola, Jerry G. Myers, Julia Raykin, Lealem Mulugeta, Emily S. Nelson, Brian C. Samuels, C. Ross Ethier; Finite Element Modeling of Factors Influencing Optic Nerve Head Deformation Due to Intracranial Pressure. Invest. Ophthalmol. Vis. Sci. 2016;57(4):1901-1911. doi: 10.1167/iovs.15-17573.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

Purpose: Visual impairment and intracranial pressure (VIIP) syndrome is a health concern for long-duration spaceflight, and a proposed risk factor is elevation of intracranial pressure (ICP). Our goal was to use finite element modeling to simulate how elevated ICP and interindividual differences affect tissue deformation within the optic nerve head (ONH).

Methods: We considered three ICP conditions: the upright and supine position on earth and an elevated ICP assumed to occur in chronic microgravity. Within each condition we used Latin hypercube sampling to consider a range of pressures and ONH tissue mechanical properties, determining the influence of each input on the following outcome measures: peak strains in the prelaminar tissue, lamina cribrosa, and retrolaminar optic nerve. Elevated strains can alter cell phenotype and induce tissue remodeling.

Results: Elevating ICP increased the strains in the retrolaminar optic nerve. Variations in IOP, ICP, and in optic nerve and lamina cribrosa stiffness had the strongest influence on strains within the ONH. We predicted that 5% to 47% of individuals in microgravity would experience peak strains in the retrolaminar optic nerve larger than expected on earth. Having a soft optic nerve or pia mater and elevated ICP were identified as risk factors for these “extreme” strains.

Conclusions: Intracranial pressure and mechanical properties of the ONH influence the risk for experiencing extreme strains in the retrolaminar optic nerve. These extreme strains may activate mechanosensitive cells that induce tissue remodeling and are a risk factor for the development of VIIP. Future studies must also consider variations in ONH anatomy.

Exposure to microgravity induces numerous physiological and pathological adaptations.1 One such (mal)adaptation involves vision: 41.7% of astronauts returning from long-duration missions (>30 days) suffer from changes in visual acuity and characteristic ophthalmic anatomic changes1,2 in a condition known as visual impairment and intracranial pressure (VIIP) syndrome. Anatomic changes in VIIP include choroidal folds, optic disc edema, optic sheath dilation, and optic nerve kinking,2,3 some of which appear to persist permanently after return to earth. Visual impairment and intracranial pressure syndrome has thus become a major health concern for astronauts. 
The mechanism(s) causing VIIP are not fully elucidated. Although accurate measures of intracranial pressure (ICP) during long-duration space flight are not yet possible,4,5 several lines of evidence suggest that elevated ICP plays an important role in VIIP. First, some astronauts with VIIP syndrome exhibit a moderately elevated opening pressure by lumbar puncture; average opening pressure was 18.3 mm Hg compared with lower than 15 mm Hg for healthy nonobese adults, even 2 or more months after returning to earth.2,4 Second, anatomic changes, including disc edema, optic nerve sheath kinking, and choroidal folds in affected astronauts, are similar to those reported in patients with idiopathic intracranial hypertension (IIH),13,5,6 and similar to VIIP may also cause visual impairment. 
It has therefore been hypothesized that a risk factor for developing VIIP is an increase in ICP resulting from the cephalad fluid shift that occurs in microgravity.1,3,6 However, the mechanism(s) by which elevated ICP contributes to the anatomic and functional changes characteristic of VIIP are essentially unknown. We know that altered biomechanics leads to soft tissue remodeling (anatomic changes) in other situations,7,8 and it has long been thought that biomechanics plays a role in glaucomatous optic neuropathy.9,10 Although the effects of IOP on optic nerve head (ONH) biomechanics are well described both experimentally1114 and through computer modeling,1518 much less is known about the effects of ICP on ONH biomechanics. 
We hypothesized that elevated ICP above typical levels will alter the peak strains in the tissues of the ONH, which in turn contribute to tissue remodeling/anatomic changes and visual function changes in VIIP. Our present goal was to characterize the biomechanical environment within the lamina cribrosa (LC), anterior optic nerve, and prelaminar neural tissue under various levels of ICP. To do so, we used a combination of finite element (FE) computer modeling and Latin hypercube sampling (LHS), the latter allowing us to assess the role of interindividual differences in influencing ONH biomechanics. 
Methods
Overview
It is challenging to experimentally measure the biomechanical environment within the ONH due to its small size and relative inaccessibility. In addition, there is inherent interindividual variability in the mechanical properties and pressures experienced by ONH tissues,1922 which leads to interindividual differences in ONH biomechanics.23 We overcome these difficulties by the use of FE computer modeling. This approach, pioneered in the ONH by Bellezza et al.,17 has subsequently been widely used by a number of groups to examine the effects of elevated IOP on the biomechanical environment in the ONH, particularly on the LC in glaucoma.15,17,18,2325 Notably, Sigal et al.18,23 used this approach to study interindividual variability by altering the geometry or mechanical properties of ONH tissues. 
We use mechanical strain, or normalized deformation, of ONH tissues as our key outcome measure, as it has been shown that many cell types, including fibroblasts and ONH astrocytes,26,27 are mechanosensitive (i.e., cells alter their phenotype in response to mechanical strain). 
Intracranial pressure is believed to play an important role in VIIP, and it can vary with posture and gravitational environment. Therefore, investigating the impact of ICP on the tissues of the eye posterior played a central role in this study. We also considered the effects of varying IOP and central retinal vessel mean arterial pressure (MAP), because it was expected that these pressures would affect biomechanical strain in ONH tissues. For each input into the model (pressures and tissue mechanical properties) we selected a “baseline” value based on previous studies,18 and examined the effect of elevating ICP on the mechanical strains in the ONH. We then conducted simulations for a range of parameter values around this baseline using LHS, as described below. In brief, we considered three ICP conditions, each with its own baseline value and range based on published data.5,2831 The first two conditions, denoted as “upright” and “supine,” corresponded to situations typically experienced on earth, whereas the last condition (“elevated”) corresponded to moderately elevated ICP thought to occur in microgravity. For each ICP condition, the IOP, ICP, MAP, and tissue mechanical properties were varied. 
Geometry and FE Meshing
Our model geometry was built on established models of the posterior eye.15,23 The sclera and prelaminar neural tissue extended to the equator of the eye, where the outer scleral radius was fixed to represent attachment to the extraocular muscles (Fig. 1). The LC had a thickness of 0.3 mm, and radii of 0.9 mm and 1.0 mm for the anterior and posterior LC faces, respectively.15,23,32 We included the dura mater and pia mater of the optic nerve sheath because these components can exhibit significant anatomic changes in VIIP. Based on measurements,32 the outer radius of the dura mater at the peripapillary sclera was taken to be 1.875 mm, increasing to 2.7 mm at 3.0 mm posterior to the LC, and then tapering to a constant radius of 2.1 mm. The dura mater and pia mater were thicker at their respective scleral insertions before attaining a constant thickness; specifically, the thickness of the dura mater tapered from 0.75 mm at the peripapillary sclera to 0.40 mm at 3.0 mm posterior to its insertion.33 Similarly, the pia mater thickness decreased from 0.14 mm to 0.06 mm over the same distance.34 We also included an annular ring immediately surrounding the scleral canal, accounting for the circumferential alignment of scleral collagen fibers around the ONH.35,36 The annular ring extended outward from the scleral canal to a surface defined by points on the inner (outer) sclera at a radial location approximately four-thirds the anterior (posterior) radius of the LC.3739 
Figure 1
 
The three-dimensional geometry created for FE analysis. Left: Overview of the model formed by rotating a cross-section through 3° to create a wedge representing our posterior eye axisymmetric geometry, necessary because FEBio cannot solve a “pure” two-dimensional axisymmetric problem. Right: A zoomed image of the boxed region on the left, in cross-section, identifying key tissue components of the ONH.
Figure 1
 
The three-dimensional geometry created for FE analysis. Left: Overview of the model formed by rotating a cross-section through 3° to create a wedge representing our posterior eye axisymmetric geometry, necessary because FEBio cannot solve a “pure” two-dimensional axisymmetric problem. Right: A zoomed image of the boxed region on the left, in cross-section, identifying key tissue components of the ONH.
We also included a single central retinal vessel to model the effects of blood pressure. Representing the retinal vasculature as only a single vessel is a simplification of the real situation, in which both a central retinal artery and vein are present; we assumed that most of the mechanical load on ONH tissues due to blood pressure would arise from the central retinal artery and therefore considered only this vessel. The central retinal vessel was idealized as a tube with an outer radius of 0.09 mm and a wall thickness of 0.05 mm.15 The dura mater, optic nerve, pia mater, and central retinal vessel extended posteriorly 10 mm from the sclera, which is the typical location at which vessels enter/exit the optic nerve in humans.32 This length allowed us to incorporate variations in the thickness of the pia mater and dura mater, and to account for the posterior bulging of the optic nerve sheath that occurs roughly 3 mm behind the ONH. Simulations with a longer (25 mm) optic nerve did not result in changes in the strain contours at the ONH, suggesting that a length of 10 mm was a good trade-off between accuracy and computational cost. Similar to previous models, the posterior edge of the optic nerve, pia mater, dura mater, and central retinal vessel were unconstrained.15,23 
The geometric model was created and meshed in the open-source program Gmsh (V2.8.3a).40 FEBio (V2.0)41 was used as the FE solver for all simulations. Due to axisymmetry, the geometry could have been represented as a two-dimensional model; however, axisymmetric models in FEBio require using a three-dimensional wedge of the entire geometric. We thus created a three-dimensional FE model consisting of a 3° wedge centered about an axis of rotation passing through the central retinal vessel. The geometry was discretized with eight-node hexahedral FEs except for six-node prism elements used in the central retinal vessel about the axis of rotation. A mesh convergence study comparing the average effective strain for each tissue region computed by progressively refined meshes (element counts ranging from 13,199–319,320) ensured mesh-independence of our results was performed at ICPs of both 0 and 20 mm Hg. The production mesh, containing 26,438 elements in the 3° wedge, had less than a 5% relative error compared with results obtained on the most refined mesh. 
Pressure Loads
We specified three pressures acting on the tissues of the ONH: IOP, ICP, and MAP (Table 1). In-flight IOP values, measured by applanation tonometry, were applied on the anterior surface of the prelaminar neural tissue in the FE model. Similarly, MAP was calculated from in-flight diastolic and systolic blood pressure measurements and applied to the inner luminal surface of the central retinal vessel. In-flight data were kindly provided by Lifetime Surveillance of Astronaut Health Program (NASA Johnson Space Center, Houston, TX, USA). The arterial pressure in an upright posture at the level of the eye is commonly taken to be 2/3*MAP; this formula accounts for the hydrostatic offset between the heart and the eye (brachial and ophthalmic arteries).42 We used this formula for simulations in the upright posture, whereas the central retinal arterial pressure for the supine and microgravity conditions, where the hydrostatic offset is absent, was assumed to be equal to MAP. 
Table 1
 
Pressures and ONH Tissue Mechanical Properties for Linear-Elastic Tissue Components Used as Inputs for Our FE Model
Table 1
 
Pressures and ONH Tissue Mechanical Properties for Linear-Elastic Tissue Components Used as Inputs for Our FE Model
As noted above, we considered three ICP conditions: upright position, supine position, and elevated, estimated to occur in microgravity. Intracranial pressure was applied within the subarachnoid space (i.e., to the inner surface of the dura mater and external surface of the pia mater). The upright and supine conditions represented a characteristic range of ICP values experienced by individuals on earth in either upright or supine postures.2831,4345 The elevated ICP condition was estimated from lumbar puncture opening pressures performed on postflight astronauts suffering from VIIP syndrome, and head-down tilt studies performed on earth that bear some similarity to microgravity environments by substantially reducing the gravitational forces acting along the body axis (i.e., ICP is more uniform along the body axis).1,5 Currently, we assume that no compartmentalization occurs within the optic nerve, as this event can drastically affect ICP. 
Tissue Mechanical Models
In this study, the LC, optic nerve, retinal vessel, and prelaminar neural tissue were modeled as isotropic, linear-elastic, and homogeneous. With these assumptions, each tissue's mechanical behavior was described by a Young's modulus (a measure of stiffness) and a Poisson ratio (ν, a measure of deformation coupling in orthogonal directions). Young's modulus values were based on previous experimental studies and FE models of the posterior eye (Table 1).18,23,46 In addition, similar to earlier FE models, the neural tissue was considered to be partially compressible (Table 1), whereas all other tissues were modeled as nearly incompressible (ν = 0.49).18,23,43 These material models are simplifications of the complex behavior of these tissues; however, due to the limited information on the biomechanical properties of ocular neural tissue and the complex structure of the LC, we elected to use these simplified material models. This approach represented a balance among complexity, availability of information, computational cost, and fidelity. Although improved treatments are warranted, these simulations provide us with an initial foundation to investigate the effect of ICP on ONH strains. 
In addition, the posterior sclera, peripapillary sclera, annular ring, pia mater, and dura mater were modeled bu using an anisotropic hyperelastic constitutive model,35 which treated the tissue as a Mooney-Rivlin solid with embedded collagen fibers. The fiber orientations for each tissue were assumed to follow a von Mises distribution,36,39 specified by parameters representing the local preferred fiber direction, θP, and collagen fiber concentration factor, kf. The orientation of collagen fibers in the posterior sclera, peripapillary sclera, and annular ring were taken from recently published reports using human specimens.38,39 In the peripapillary sclera, the annular ring, and the posterior sclera, fibers were assumed to lie in the local tangent plane to the sclera. In the peripapillary sclera and the annular ring, fibers were preferentially aligned circumferentially about the scleral canal, with values of kf = 0.85 and 1.85, respectively, adapted from previous measurements on human scleral tissues.3739 In the posterior sclera, the fiber distribution was assumed to be planar isotropic, obtained by setting kf = 0.38,39,47 There are differing reports on collagen fiber orientation in the pia mater and dura mater, with one report stating fibers are primarily oriented parallel to the optic nerve with some circumferential wrapping, and another reporting a planar isotropic orientation.48,49 For simplicity, we treated the fiber distributions in the pia mater and dura mater as planar isotropic (kf = 0).48,49 
This material model has six coefficients in each tissue region, representing tissue mechanical properties35,39: two to describe the ground substance (c1 and c2), three to describe the collagen fibers (c3, c4, and c5), and a bulk modulus (K). Similar to previous studies and to simplify our model,37,39 we assumed that the ground substance could be represented as a neo-Hookean material (c2 = 0) and that loading of the collagen fibers was only loaded within their nonlinear region, so that defining c5 was not required. Thus, we were left with the following parameters: c1, representing the stiffness of the ground substance; c3 and c4, representing the stiffness of the collagen fibers; and K, representing the bulk modulus. To enforce tissue incompressibility, we took K = 100 MPa.35 
For modeling, it was necessary to specify values for all parameters (Table 2). Because collagen is the major load-bearing structure within tissues, we assumed that differences in tissue mechanical behavior arose mainly from differences in the orientation and stiffness of the collagen fibers. Therefore, we assumed that the ground substance (Mooney-Rivlin material) had the same mechanical properties (coefficient c1) for all tissue components. Values for the coefficients c1, c3, and c4 were taken from previous reports (Table 2).39 We note that these parameters were derived from data fit to nonhuman primate scleral tissue, and that we have assumed that the mechanical properties of the collagen fibers are preserved across species. To determine the stiffness of the collagen fibers (c3 and c4) for the pia mater and dura mater, we used experimental published data.5052 In brief, data describing the stress-strain response of the pia mater and dura mater were digitized and fit to a Mooney-Rivlin solid with collagen fibers following a transverse isotopic distribution (kf = 0). 
Table 2
 
Mechanical Properties (Baseline Values and Ranges) Specified for Sclera, Peripapillary Sclera, Annular Ring, Pia Mater, and Dura Mater
Table 2
 
Mechanical Properties (Baseline Values and Ranges) Specified for Sclera, Peripapillary Sclera, Annular Ring, Pia Mater, and Dura Mater
Outcome Measures
Our primary outcome measure was computed strain in selected ocular tissues. Mathematically, strain is a second-order tensor that can be decomposed into three principal components in orthogonal directions.53 Under our model assumptions, the first principal strain quantified the largest positive stretch experienced by the tissue, whereas the third principal strain represented the largest negative (i.e., compressive) strain experienced by the tissue. 
Because our goal was to examine biomechanical effects in the ONH, we focused our analysis on computed strains in the prelaminar neural tissue, LC, and retrolaminar optic nerve. Specifically, we analyzed the anterior optic nerve defined as 1 mm immediately behind the posterior margin of the LC. The prelaminar neural tissue was analyzed directly anterior to the LC and overlaying the adjacent annular ring and peripapillary sclera. The strains in each of these tissue volumes were spatially nonuniform (i.e., each tissue volume produced a distribution of strains). These strain distributions were weighted by element volume to account for differences in element size and used to create strain histograms as a quantification of the local strain environment. We were interested in extreme values of strain, thought to produce maximum mechanobiologic effects. Therefore, we extracted the 95th percentile of the first principal strain and the 5th percentile of the third principal strain in each tissue region, denoting these values as the “peak” tensile and compressive strains, respectively. The absolute maximum and minimal values of these principal strains (100th and 1st percentiles) were not used because they can be sensitive to numerical artifacts (e.g., due to irregularly shaped elements in the FE mesh),54 and thus can be unreliable. 
Latin Hypercube Sampling
We adopted an LHS approach to examine the effects of natural variations in relevant pressures and tissue mechanical properties. Latin hypercube sampling, introduced by Mckay et al.,55 is similar to Monte Carlo sampling methods, but uses “stratified sampling” without replacement to explore an entire parameter space. Latin hypercube sampling is an unbiased sampling approach that varies each input parameter independently along a prescribed statistical distribution, which allowed us to efficiently assess the computed strains in the ONH for a population with different pressures and tissue material properties. Further, LHS allows us to reduce the number of simulations required to explore our parameter space compared with traditional random-sampling Monte Carlo approaches. Latin hypercube sampling ensures that samples are taken from the entire distribution by dividing the statistical distribution into bins and sampling within each of these bins. As mentioned, LHS requires specification of the distribution of each input parameter. Tissue mechanical properties were assumed to follow uniform distributions (Table 1) as previously described.18 Intraocular pressure, MAP, and ICP were assumed to follow truncated normal distributions (i.e., they followed standard normal distributions modified to have zero probability density for values outside defined lower and upper bounds). These distributions ensured the simulated IOP and MAP values fell within the measured in-flight ranges. Further, it allowed us to define three nonoverlapping ICP ranges for the upright, supine, and elevated conditions (Fig. 2). The upright ICP range was obtained from measurements at the lumbar spine28,29,56 or the upper cervical spine43,57 in the seated position, the supine ICP range was derived from lumbar opening pressure measurements in the supine or lateral decubitus positions,2831,43 and the elevated ICP range encompassed the range of pressures measured in astronauts suffering from VIIP after return to earth2 and head-down tilt studies.45,58,59 
Figure 2
 
Input parameter distributions used for the LHS approach. Intraocular pressure, ICP, and MAP inputs followed truncated normal distributions, whereas material properties were assumed to follow uniform distributions (Tables 1, 2).
Figure 2
 
Input parameter distributions used for the LHS approach. Intraocular pressure, ICP, and MAP inputs followed truncated normal distributions, whereas material properties were assumed to follow uniform distributions (Tables 1, 2).
For each ICP condition (upright, supine, and elevated), the three ONH pressures and 20 material properties were independently varied (Fig. 2). As mentioned above, the LHS approach ensured that input parameters were sampled over the entire distribution, thus reducing the number of simulations required to represent the entire parameter space; however, performing too few simulations can underrepresent the parameter space. Within each ICP condition, the LHS method was applied four times with 75 divisions per iteration, resulting in 300 simulations at each ICP condition for a total of 900 simulations. To ensure no sampling bias in our input parameters, we performed a nonparametric sign test for all our input parameters for all pressure conditions. This test examined whether the sampled input parameters had a median value different from the specified population median value. We wanted to ensure that we adequately represented the parameter space, which was verified by examining the SDs in the peak tensile and compressive strains with increasing numbers of LHS iterations; a small and nonchanging value of this parameter implied that our outcome measure was stable. Specifically, we examined the SD of each output parameter after each LHS iteration, corresponding to 75, 150, 225, and 300 simulations. When a sufficient number of simulations had been performed, the variation in the outcome measures approached an asymptotic value6062 (Supplementary Fig. S1). 
To quantitatively compare each ICP condition, the peak tensile and compressive strains were recorded for the prelaminar neural tissue, LC, and retrolaminar optic nerve, as described above. An LHS/partial rank correlation coefficient (PRCC) sensitivity analysis was conducted to identify the key factors influencing the peak strains in the ONH. Further, this allowed us to create histograms and cumulative distribution functions (CDFs) for the peak tensile and compressive strains in each tissue region of interest. These CDFs can be thought of as representing the distributions of peak strains over a population of individuals whose characteristics are described by the range of our input parameters. 
Statistics
First, we performed a sensitivity analysis using an LHS/PRCC approach,55,63,64 which allowed us to evaluate how each input parameter influenced the peak tensile and compressive strains in the prelaminar neural tissue, LC, and retrolaminar optic nerve. Specifically, this approach assessed the sensitivity of the outcome measures to the uncertainty in the input parameters. As previously described,64 a correlation coefficient lying in the range −1 to 1 was computed for each pair of input parameters and outcome measures. Values close to −1 or 1 indicate a strong influence of the input parameter on the outcome measure, with a negative value indicating that the input parameter is inversely correlated with the outcome measure. Within each ICP condition, our LHS/PRCC analysis resulted in a correlation coefficient for the pairs formed from the 23 input and six outcome measures. We then ranked the magnitude of the correlation value for each output variable (rank 23 implied greatest influence; rank 1 implied smallest influence). We summed ranks across each outcome measure and normalized the sum to the highest possible ranking (i.e., to 138). This yielded a single normalized value that quantified the influence of a given input parameter on all outcome measures. For brevity, we call this normalized value a “cumulative influence factor.” This process was repeated for each ICP condition: upright, supine, and elevated. 
To compare the CDFs, representing a sample population, we used Kruskal-Wallis 1-way ANOVA to test for an effect of ICP condition, followed by a two-sample Kolmogorov-Smirnov test for pairwise comparisons between each ICP condition. All statistical comparisons were performed in Matlab (Mathworks, Inc., Natick, MA, USA) with a significance threshold (Type I error) of α = 0.05. 
The CDFs were directly used to estimate the probability of a given individual having a peak tensile or peak compressive strain value greater than a specific threshold. Specifically, we asked the question: would individuals in microgravity experience strains more extreme than those encountered on earth in the supine and upright positions? To answer this question, we identified thresholds as the largest peak tensile and smallest peak compressive strains that were computed in the supine ICP condition; these threshold values represented the most extreme strains encountered under terrestrial conditions. Because the input parameters were appropriate for a healthy population, we took these threshold values as being the most extreme strains that do not typically lead to ocular pathology. We then used the elevated ICP CDF to determine the probability that an individual exposed to microgravity conditions would experience peak strains more extreme than these terrestrial threshold values. 
Last, if the CDFs resulted in biomechanical strains more extreme than the terrestrial threshold values, we identify characteristics, IOP, ICP, MAP, or tissue biomechanical properties, associated with the existence of these extreme strains in the elevated ICP condition. Specifically, we took the simulations within the elevated ICP condition and divided them into two groups: one in which the peak strains did not exceed the terrestrial thresholds, and the second in which they did. Input parameters were then compared between these two groups by using a Mann-Whitney U test. Because there were multiple input parameters, and hence multiple comparisons, we used Bonferroni correction to account for multiple comparisons (for 23 input parameters the Bonferroni-corrected significance level was taken as α = 0.05/23 = 0.002). 
Results
To get a general understanding of how strains in the ONH are affected by ICP, we set all input parameters except ICP to their baseline values, and allowed ICP to vary from 0 to 20 mm Hg. As ICP increased, we observed higher strains occurring at the lateral anterior optic nerve and a decrease in strains within the prelaminar neural tissue anterior to the LC (Fig. 3). Proportionately, the 5th and 95th percentile strains increased substantially in the retrolaminar optic nerve; however, the absolute magnitude of changes in the prelaminar neural tissue and LC strains were modest (Fig. 3). 
Figure 3
 
Computed first and third principal strains in ONH tissues as ICP is varied from 0 to 20 mm Hg. All other parameter values are assigned to the “baseline” values shown in Tables 1 and 2; specifically, IOP is set to 15 mm Hg. Tissue extension (tension) is shown in red and compression is shown in blue. An increase in the tension and compression of the anterior region of the retrolaminar optic nerve is observed as ICP is elevated. The peak strains experienced in each region of interest (top left inset) are also shown.
Figure 3
 
Computed first and third principal strains in ONH tissues as ICP is varied from 0 to 20 mm Hg. All other parameter values are assigned to the “baseline” values shown in Tables 1 and 2; specifically, IOP is set to 15 mm Hg. Tissue extension (tension) is shown in red and compression is shown in blue. An increase in the tension and compression of the anterior region of the retrolaminar optic nerve is observed as ICP is elevated. The peak strains experienced in each region of interest (top left inset) are also shown.
Latin hypercube sampling was used to investigate the effects of interindividual variations within the upright, supine, and elevated ICP conditions. Using a sign test, we found no sampling bias in the input parameters at each ICP condition (P > 0. 48 for all parameters). Further, visual inspection of the input parameter values generated by LHS showed no evidence of sampling bias, for all input parameters and all ICP conditions (Supplementary Fig. S2). Further, there was little variation in the SD of the peak strains between LHS iterations (<0.04 for all ICP categories), indicating that we had adequately sampled our parameter space with four LHS iterations. 
From our sensitivity analysis, we found that several input parameters had a large influence on our outcome measures. Our results showed that IOP and ICP were particularly influential (Fig. 4). In addition, the optic nerve and LC stiffness parameters also had a large effect on ONH strains. Interestingly, the sclera farther away from the optic canal did not have a large influence on peak strains; however, closer to the ONH, the fiber stiffness parameters of the peripapillary sclera and annular ring both influenced the peak strains within the ONH. 
Figure 4
 
A “tornado plot,” ranking the effect that variations in each input parameter (listing on left side of plot) had on outcome measures for each ICP condition. The plotted quantity is the cumulative influence factor (see text for definition). Larger values indicate a greater overall influence for the indicated input parameter. For materials represented by the Mooney-Rivlin solid embedded with collagen fibers, c1 represents the stiffness of the ground substance, whereas c2 and c3 are the stiffness of the collagen fibers. See Tables 1 and 2 for tissue abbreviations.
Figure 4
 
A “tornado plot,” ranking the effect that variations in each input parameter (listing on left side of plot) had on outcome measures for each ICP condition. The plotted quantity is the cumulative influence factor (see text for definition). Larger values indicate a greater overall influence for the indicated input parameter. For materials represented by the Mooney-Rivlin solid embedded with collagen fibers, c1 represents the stiffness of the ground substance, whereas c2 and c3 are the stiffness of the collagen fibers. See Tables 1 and 2 for tissue abbreviations.
There were clear changes in the CDF profiles, representing peak strains across a population of individuals (Fig. 5), with an intensification of peak strains as ICP increased. The effect of ICP condition was significant (P < 0.001), and pairwise comparisons using Kolmogorov-Smirnov testing found differences between each ICP category for both tensile and compressive strains (P < 0.001) for all peak strain CDFs, except for peak compressive strains in the retrolaminar optic nerve between the upright and supine ICP conditions and for peak compressive strains in the prelaminar neural tissue between the supine and elevated ICP conditions. 
Figure 5
 
Peak strains in ONH tissues from LHS simulations. The solid lines represent the CDF of the peak tensile and peak compressive strains for three ICP conditions: upright, supine, and elevated. The dashed lines represent the 95% confidence bounds of the CDF calculated using the Greenwood's formula.77,78 Although many of the peak strains overlapped between the upright, supine, and elevated conditions, elevating ICP still resulted in a significant shift in the peak tension and peak compression (P < 0.001 for all comparisons excluding the peak compression of the retrolaminar optic nerve between upright and supine and the prelaminar neural tissue between supine and elevated). The shaded regions illustrate the ranges of peak strains predicted under terrestrial conditions. The horizontal lines in the retrolaminar optic nerve show the percentage of the simulated population exposed to elevated ICP that was predicted to experience “extreme strains” (i.e., strains lying outside the shaded ranges).
Figure 5
 
Peak strains in ONH tissues from LHS simulations. The solid lines represent the CDF of the peak tensile and peak compressive strains for three ICP conditions: upright, supine, and elevated. The dashed lines represent the 95% confidence bounds of the CDF calculated using the Greenwood's formula.77,78 Although many of the peak strains overlapped between the upright, supine, and elevated conditions, elevating ICP still resulted in a significant shift in the peak tension and peak compression (P < 0.001 for all comparisons excluding the peak compression of the retrolaminar optic nerve between upright and supine and the prelaminar neural tissue between supine and elevated). The shaded regions illustrate the ranges of peak strains predicted under terrestrial conditions. The horizontal lines in the retrolaminar optic nerve show the percentage of the simulated population exposed to elevated ICP that was predicted to experience “extreme strains” (i.e., strains lying outside the shaded ranges).
Further analysis of the CDF plots allowed us to estimate the percentage of individuals who would experience “extreme strain” values under elevated ICP conditions (i.e., individuals whose strains would exceed the most extreme peak strain values experienced in the upright and supine ICP situations on earth) (Fig. 5). Considering only the prelaminar neural tissue and LC, there were no individuals predicted to experience such “extreme strains”; however, considering the retrolaminar optic nerve, we predicted that approximately 47% of individuals would experience “extreme strains” under elevated ICP. 
We next sought characteristics that predisposed individuals to experience these “extreme strains” in the retrolaminar optic nerve. When comparing simulations in which peak strains in the retrolaminar optic nerve exceeded the terrestrial threshold values with those in which peak strains did not, we found several significant differences between the ONH input parameters. A lower optic nerve tissue stiffness and higher ICPs were associated with extreme tensile and compressive strains. Further, lower pia mater ground substance stiffness (c1) and fiber stiffness (c3 and c4) were associated with extreme tensile strains, whereas low MAP and optic nerve Poisson's ratio were associated with extreme compressive strains (all P < 0.002). 
Discussion
Our goal was to understand how elevations in ICP, assumed to occur in microgravity, altered the biomechanical environment within the ONH. First, we found that for baseline IOP, MAP and tissue mechanical properties increasing ICP from 0 mm Hg to 20 mm Hg, decreased the peak tensile and compressive strains in the prelaminar neural tissue and LC, while increasing these strains in the retrolaminar optic nerve. Although values of computed strains were modest and consistent with earlier FE models of the posterior eye,15 relative changes in these strains in the retrolaminar optic nerve could be potentially significant. 
To examine the effects of interindividual differences in input parameters on the strains in the ONH, LHS was applied in a procedure intended to replicate “numerical sampling” across a hypothetical population of individuals under different ICP conditions. Although each ICP condition showed a range of computed strains, there was a clear effect of increased ICP leading to larger peak tensile and compressive strains in the retrolaminar optic nerve. In fact, our simulations predicted that, under elevated ICP conditions, approximately 47% of individuals would experience strains in their retrolaminar optic nerve tissues more extreme than would occur on earth. Experiencing these extreme strains may influence cellular phenotype and induce connective tissue remodeling; although the exact level of strain that leads to pathophysiology in the optic nerve head and retrolaminar optic nerve is not known, there is some evidence that strains between 4% and 6% may lie outside the physiological loading range for ocular tissues and alter cellular phenotype.26,6568 In our model, elevating ICP increased the compressive strains experienced in the anterior region of the retrolaminar optic nerve, which could thus possibly initiate a cellular response in the ONH. Examining the principal strain eigenvector orientations (Supplementary Fig. S3) showed that elevated ICP caused radial compression of the optic nerve, resulting in a perpendicular (anterior-posterior) stretch. We believe that the Poisson effect, compression along one direction leading to extension in the orthogonal directions, explains why an elevated ICP increases both the peak tensile and compressive strains observed in the retrolaminar optic nerve (Fig. 3). Interestingly, we observed a decrease in the largest peak tensile and compressive strains within the LC and prelaminar neural tissue as ICP increased. The decrease of these peak strains with increasing ICP can be associated with the so-called Poisson effect, the tendency of a material that is compressed (in our case, the retrolaminar optic nerve) to expand in the orthogonal direction(s). As ICP increases, the retrolaminar optic nerve is radially compressed, and thus expands anteriorly-posteriorly to push against the posterior LC. This effect acts to counteract the effect of IOP, leading to a decrease in strains within the lamina (Supplementary Fig. S3). Although these strains all fell within the range experienced in the upright and supine (terrestrial) conditions, it should be noted that decreases in stress and strain experienced by a tissue can also result in a remodeling response.6971 Although it is not known what strain levels are required to maintain homeostasis, if elevated ICP in fact reduces strains within the LC and prelaminar neural tissue, characterizing how reduced strains alter the behavior of local cell populations (e.g., astrocytes) in the posterior eye and optic nerve sheath warrants future investigation. 
It is noteworthy that not all astronauts develop VIIP even after 1 month in space. This suggests that there must be individual-specific risk factors for VIIP development, and it would be of great interest to identify such risk factors. It is also of interest that our modeling predicted that not all individuals with elevated ICP would experience peak strains beyond the terrestrial thresholds. The details of which input parameters led to extreme strains depended on which tissue region and strain type was considered. Our sensitivity analysis illustrated that aside from IOP and ICP, the material properties of the peripapillary sclera, annular ring, LC, optic nerve, and pia mater strongly influenced the peak strains in the ONH. In addition, our data suggested that having a weak (soft) pia mater and optic nerve was statistically associated with having extreme strains in ONH tissues, as were large values of ICP, MAP, and the neural Poisson's ratio. This result motivates further studies of these parameters as risk factors for development of large tissue strains and possibly even as risk factors for VIIP. Unfortunately, these tissue stiffness values are not currently measurable in a clinical setting, and thus laboratory (animal) experiments will need to be used to investigate the role of these parameters. 
Overall, these results illustrate how elevations in ICP influence the strains in the ONH, with strains in the retrolaminar optic nerve being significantly increased with elevated ICP. Our finding that approximately 47% of our simulated population exposed to elevated ICP experiences “extreme strains” is noteworthy, as 41% of astronauts experience VIIP syndrome. This similarity could be coincidental, but suggests that further investigation of the strains experienced within the retrolaminar optic nerve and their possible role in VIIP syndrome is warranted. It is also important to note that elevations in ICP can occur from causes other than microgravity; specifically, our findings may be relevant for patients suffering from idiopathic intracranial hypertension, normal-tension glaucoma, or papilledema.1,19,72 Therefore, expanding this model to simulate ICP and IOP conditions and patient populations relevant for these conditions is a logical next step. 
Limitations
This study had several limitations. First was the use of a generic geometric model and simplified material properties for some tissue components of the model. Our model uses a single, idealized anatomy based on average tissue dimensions taken from various studies. Previous studies have shown that eye geometry (e.g., scleral thickness,17,23 eye radius,23 and LC curvature23) affects computed strains. Additional studies have shown benefits of using subject-specific geometry to gain additional insights about the strain distributions in the ONH.52 Although limiting our analysis to studying the effects of the ONH mechanical properties and pressures helped to simplify our interpretation and to still address our research question, future FE models that couple interindividual variations in pressures, anatomy, and tissue mechanical properties would provide additional insight into how astronauts with different anatomical characteristics may be predisposed to extreme ONH strains. 
In addition, several tissues were modeled as linear-elastic, isotropic tissue properties, whereas most soft biological tissues, such as the LC, display nonlinear and viscoelastic behavior and have a complex collagen matrix. Several groups are examining the nonlinear behavior and collagen fiber orientation of ocular structures.36,39,73 Further, although we did incorporate nonlinear tissue behavior and anisotropy into several tissue components, there is a significant lack of data on mechanical properties of the tissues located in the posterior eye and optic nerve sheath. This initial study relied on determining the pia mater and dura mater collagen properties from mechanical tests under nonphysiological loading conditions. To help examine a range of input parameters and understand the effect of interindividual variation on peak strains in the ONH, we used an LHS approach. It is possible that astronauts experience pressures or have tissue properties outside the ranges we examined, which would likely have an impact on the peak strains in each tissue region. Further, we assumed that input parameters varied independently; however, it is possible that several factors vary together. For example, a weak sclera may imply that all material coefficients (c1, c3, and c4) representing the sclera are lower. Understanding if these parameters covary would help improve our interpretations of these FE simulations. Unfortunately, we were limited by the amount of information available for each input parameter. To account for interindividual variations, we assumed that input parameters could vary by ±60% from baseline values. We emphasize the need for additional research on the mechanical properties of these tissues to improve our understanding of how interindividual variations may affect susceptibility to changes in ICP. 
A third limitation is that our model predicted only small anterior displacement of the ONH, specifically the LC and peripapillary sclera, as ICP was increased. Optical coherence tomography (OCT)-based measurements have documented significant anterior displacement of the ONH with increased ICP in patients; further, decreasing ICP in such patients can cause up to 300 μm posterior displacement of the ONH.72 We speculate that this discrepancy between our models and clinical observations is due in part to our use of simplified material models for ONH tissues. Specifically, nonlinear material models may predict a softer peripapillary sclera as ICP acts to oppose deformations (strains) due to IOP, which could in turn lead to more anterior displacement as ICP is elevated. Further, our models do not account for axoplasmic stasis that may contribute to swelling of prelaminar neural tissue and that is visible by OCT. Our FE models cannot account for the latter effect at the present time, and as indicated above, we plan to implement nonlinear material models to account for the former effect. 
A third, and very important, limitation is the inadequate knowledge of ICP in astronauts under chronic microgravity conditions. This led to epistemic uncertainty in specifying the pressure range associated with the elevated ICP condition. Although an important recent study measured ICP during parabolic flights that simulated microgravity for 20 to 30 seconds,74 it is not known how data from such relatively brief exposures to microgravity can be extrapolated to chronic exposure to microgravity in long-duration spaceflight and/or secondary mechanisms that may affect ICP, such as radiation, resistive exercise, or sodium intake.1,75 Therefore, measurements of ICP under chronic microgravity conditions will be an invaluable input for future computational and experimental models. 
Summary
We found that interindividual variations in pressures and tissue mechanical properties changed the biomechanical environment of the ONH. In addition, elevated ICP led to strains beyond those expected on earth in some individuals, specifically those with a weak (soft) pia mater stiffness. Further work is indicated to determine whether such extreme strains contribute to VIIP and, if so, by what mechanism. One possible mechanism is by activation of mechanosensitive cells, leading to tissue remodeling in the posterior eye/optic nerve. 
Acknowledgments
The authors thank Wafa Taiym for providing in-flight measurements of the astronauts' IOP and blood pressure. We also thank DeVon Griffin and Beth Lewandowski for administrative support. 
Supported by NASA grant NNX13AP91G and the Georgia Research Alliance. 
Disclosure: A.J. Feola, None; J.G. Myers, None; J. Raykin, None; L. Mulugeta, None; E.S. Nelson, None; B.C. Samuels, None; C.R. Ethier, None 
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Figure 1
 
The three-dimensional geometry created for FE analysis. Left: Overview of the model formed by rotating a cross-section through 3° to create a wedge representing our posterior eye axisymmetric geometry, necessary because FEBio cannot solve a “pure” two-dimensional axisymmetric problem. Right: A zoomed image of the boxed region on the left, in cross-section, identifying key tissue components of the ONH.
Figure 1
 
The three-dimensional geometry created for FE analysis. Left: Overview of the model formed by rotating a cross-section through 3° to create a wedge representing our posterior eye axisymmetric geometry, necessary because FEBio cannot solve a “pure” two-dimensional axisymmetric problem. Right: A zoomed image of the boxed region on the left, in cross-section, identifying key tissue components of the ONH.
Figure 2
 
Input parameter distributions used for the LHS approach. Intraocular pressure, ICP, and MAP inputs followed truncated normal distributions, whereas material properties were assumed to follow uniform distributions (Tables 1, 2).
Figure 2
 
Input parameter distributions used for the LHS approach. Intraocular pressure, ICP, and MAP inputs followed truncated normal distributions, whereas material properties were assumed to follow uniform distributions (Tables 1, 2).
Figure 3
 
Computed first and third principal strains in ONH tissues as ICP is varied from 0 to 20 mm Hg. All other parameter values are assigned to the “baseline” values shown in Tables 1 and 2; specifically, IOP is set to 15 mm Hg. Tissue extension (tension) is shown in red and compression is shown in blue. An increase in the tension and compression of the anterior region of the retrolaminar optic nerve is observed as ICP is elevated. The peak strains experienced in each region of interest (top left inset) are also shown.
Figure 3
 
Computed first and third principal strains in ONH tissues as ICP is varied from 0 to 20 mm Hg. All other parameter values are assigned to the “baseline” values shown in Tables 1 and 2; specifically, IOP is set to 15 mm Hg. Tissue extension (tension) is shown in red and compression is shown in blue. An increase in the tension and compression of the anterior region of the retrolaminar optic nerve is observed as ICP is elevated. The peak strains experienced in each region of interest (top left inset) are also shown.
Figure 4
 
A “tornado plot,” ranking the effect that variations in each input parameter (listing on left side of plot) had on outcome measures for each ICP condition. The plotted quantity is the cumulative influence factor (see text for definition). Larger values indicate a greater overall influence for the indicated input parameter. For materials represented by the Mooney-Rivlin solid embedded with collagen fibers, c1 represents the stiffness of the ground substance, whereas c2 and c3 are the stiffness of the collagen fibers. See Tables 1 and 2 for tissue abbreviations.
Figure 4
 
A “tornado plot,” ranking the effect that variations in each input parameter (listing on left side of plot) had on outcome measures for each ICP condition. The plotted quantity is the cumulative influence factor (see text for definition). Larger values indicate a greater overall influence for the indicated input parameter. For materials represented by the Mooney-Rivlin solid embedded with collagen fibers, c1 represents the stiffness of the ground substance, whereas c2 and c3 are the stiffness of the collagen fibers. See Tables 1 and 2 for tissue abbreviations.
Figure 5
 
Peak strains in ONH tissues from LHS simulations. The solid lines represent the CDF of the peak tensile and peak compressive strains for three ICP conditions: upright, supine, and elevated. The dashed lines represent the 95% confidence bounds of the CDF calculated using the Greenwood's formula.77,78 Although many of the peak strains overlapped between the upright, supine, and elevated conditions, elevating ICP still resulted in a significant shift in the peak tension and peak compression (P < 0.001 for all comparisons excluding the peak compression of the retrolaminar optic nerve between upright and supine and the prelaminar neural tissue between supine and elevated). The shaded regions illustrate the ranges of peak strains predicted under terrestrial conditions. The horizontal lines in the retrolaminar optic nerve show the percentage of the simulated population exposed to elevated ICP that was predicted to experience “extreme strains” (i.e., strains lying outside the shaded ranges).
Figure 5
 
Peak strains in ONH tissues from LHS simulations. The solid lines represent the CDF of the peak tensile and peak compressive strains for three ICP conditions: upright, supine, and elevated. The dashed lines represent the 95% confidence bounds of the CDF calculated using the Greenwood's formula.77,78 Although many of the peak strains overlapped between the upright, supine, and elevated conditions, elevating ICP still resulted in a significant shift in the peak tension and peak compression (P < 0.001 for all comparisons excluding the peak compression of the retrolaminar optic nerve between upright and supine and the prelaminar neural tissue between supine and elevated). The shaded regions illustrate the ranges of peak strains predicted under terrestrial conditions. The horizontal lines in the retrolaminar optic nerve show the percentage of the simulated population exposed to elevated ICP that was predicted to experience “extreme strains” (i.e., strains lying outside the shaded ranges).
Table 1
 
Pressures and ONH Tissue Mechanical Properties for Linear-Elastic Tissue Components Used as Inputs for Our FE Model
Table 1
 
Pressures and ONH Tissue Mechanical Properties for Linear-Elastic Tissue Components Used as Inputs for Our FE Model
Table 2
 
Mechanical Properties (Baseline Values and Ranges) Specified for Sclera, Peripapillary Sclera, Annular Ring, Pia Mater, and Dura Mater
Table 2
 
Mechanical Properties (Baseline Values and Ranges) Specified for Sclera, Peripapillary Sclera, Annular Ring, Pia Mater, and Dura Mater
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