purpose. The biomechanical environment within the optic nerve head (ONH) may play a role in retinal ganglion cell loss in glaucomatous optic neuropathy. This was a systematic analysis in which finite element methods were used to determine which anatomic and biomechanical factors most influenced the biomechanical response of the ONH to acute changes in IOP.

methods. Based on a previously described computational model of the eye, each of 21 input factors, representing the biomechanical properties of relevant ocular tissues, the IOP, and 14 geometric factors were independently varied. The biomechanical response of the ONH tissues was quantified through a set of 29 outcome measures, including peak and mean stress and strain within each tissue, and measures of geometric changes in ONH tissues. Input factors were ranked according to their aggregated influence on groups of outcome measures.

results. The five input factors that had the largest influence across all outcome measures were, in ranked order: stiffness of the sclera, radius of the eye, stiffness of the lamina cribrosa, IOP, and thickness of the scleral shell. The five least influential factors were, in reverse ranked order: retinal thickness, peripapillary rim height, cup depth, cup-to-disc ratio, and pial thickness. Factor ranks were similar for various outcome measure groups and factor ranges.

conclusions. The model predicts that ONH biomechanics are strongly dependent on scleral biomechanical properties. Acute deformations of ONH tissues, and the consequent high levels of neural tissue strain, were less strongly dependent on the action of IOP directly on the internal surface of the ONH than on the indirect effects of IOP on the sclera. This suggests that interindividual variations in scleral properties could be a risk factor for the development of glaucoma. Eye size and lamina cribrosa biomechanical properties also have a strong influence on ONH biomechanics.

^{ 1 }

^{ 2 }

^{ 3 }However, the “safe” level of IOP is patient specific,

^{ 4 }a difference that is likely due, at least in part, to differences in optic nerve head (ONH) geometry and biomechanical properties. An improved understanding of the ONH biomechanical environment, and of the dependence of this environment on the geometry and biomechanical properties of the ONH tissues, is necessary to understand better how biomechanical effects may play a role in glaucomatous optic neuropathy.

^{ 5 }). More recently, computational models based on the finite element approach have been able to overcome some of these limitations. For example, studies using a simplified (generic) ONH shape can match the general magnitude and shape of observed vitreoretinal interface deformations due to changes in IOP

^{ 5 }and have highlighted how scleral canal shape can affect ONH biomechanics.

^{ 6 }More sophisticated individual-specific models are now being developed, reproducing in detail the anatomy of an individual optic nerve head in monkeys

^{ 7 }and humans.

^{ 8 }

^{ 5 }likely reflecting interindividual differences and aging effects. Moreover, models based on a “generic” ONH geometry make assumptions about which tissue components to consider and their shape. Individual-specific models reduce the arbitrary geometric nature of generic models, but still make important assumptions about which tissue components to consider, the level of detail in modeling, the size of the region to model, and material properties.

^{ 5 }Briefly, the model was axisymmetric and consisted of five tissue regions: corneoscleral shell, LC, prelaminar neural tissue (including the retina), and postlaminar neural tissue (including the optic nerve), and pia mater. The ONH was modeled in some detail, whereas the rest of the eye was modeled as a spherical shell of constant thickness. For the study presented herein, we used a slightly modified form of Model 3 from our prior study,

^{ 5 }in which the geometry of the region where the pia mater meets the sclera was simplified, with the intention of reducing artifactual concentrations of stress and strain, and preventing the occurrence of computationally inefficient (and possibly inaccurate) high-aspect ratio elements. As before, all tissues were assumed to be linearly elastic and isotropic, with their mechanical behavior determined by their Young’s modulus and Poisson ratio.

^{ 1 }

^{ 51 }We assumed that all tissues were linearly elastic and isotropic and that all tissues except for the prelaminar neural tissues were incompressible.

^{ 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.

^{ 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.

^{ 5 }a mesh refinement analysis was performed based on the structural percentage error in energy norm (SEPC), a measure of the discontinuity of the stresses, sequentially refining the baseline model until the SEPC measure dropped below 1%. The resultant element size was halved and used as the target element size when meshing each of the models in the study. If during the parametric analysis a model predicted particularly large stress or strain levels, its SEPC value was checked to confirm that it was below 1%. There was never a need to remesh a model to guarantee a converged solution.

^{ 1 }It is important to differentiate between stress and strain when evaluating mechanical effects on cells and tissues, which is why we have considered both of these quantities. Unfortunately, strain and stress are tensor quantities that cannot be completely specified by a single value at a given location. For this work, we chose the maximum principal strain as a measure of maximum tissue strain and von Mises stress as a measure of stress.

^{ 52 }Assuming isotropic linearly elastic tissue, all stresses and strains scale linearly with the applied loads. Therefore, we report stresses as multiples of the baseline IOP (25 mm Hg).

**absolute response**of an outcome measure to a single input factor as the range (maximum − minimum) of the outcome measure values while varying only that input factor. Therefore, there is one absolute response number for every pairing of input factor and outcome measure. For each outcome measure, we then summed the absolute responses of all input factors to obtain the outcome measure

**total response**, and then quantified the influence of a single input factor, a

**relative response**, as the percentage of this total response. The relative response therefore quantifies the relative importance of a single input factor for only one outcome measure. A more global view is obtained by adding the relative responses of a single input factor over a set of outcome measures. This was defined as the input factor’s

**total influence**.

^{ 14 }

^{ 15 }

^{ 34 }

^{ 37 }

^{ 38 }

^{ 53 }

^{ 26 }

^{ 27 }although a recent article calls into question some of these conclusions.

^{ 9 }Perhaps central corneal thickness is a surrogate measure for some essential biomechanical property or properties of the sclera. If true, this could explain why central corneal thickness, independent of corrected IOP, was associated with the risk of development of glaucomatous optic neuropathy.

^{ 6 }who proposed increases in IOP-related tissue stresses with increased neural canal size (corresponding here to the LC radius) and peripapillary sclera thinning. Increased scleral compliance occurs, for example, in myopia, either because of scleral thinning

^{ 54 }or due to alterations to the scleral extracellular matrix,

^{ 55 }

^{ 56 }which could help explain the higher incidence of glaucomatous optic nerve damage in highly myopic eyes at a given IOP.

^{ 28 }

^{ 57 }Increased scleral deformations may also affect blood flow through the posterior ciliary arteries,

^{ 1 }also with possible harmful effects on neural tissue. This study suggests that the LC is a high-strain region, even if there is no stiffness mismatch between the LC and peripapillary sclera, contrary to previous suggestions.

^{ 3 }This is because compliance depends both on biomechanical and geometric properties (e.g., thickness).

^{ 58 }

^{ 59 }

^{ 60 }

^{ 5 }which could affect the mechanical interactions between the constituent tissues. In addition, the ONH geometry may differ between individuals in more complex ways that can be captured by the input factors considered. For example, the canal wall shape may vary in ways that cannot be expressed by an angle and thickness. Efforts are already under way to address these limitations by developing individual-specific models that reproduce the details of the anatomy of an individual human ONH.

^{ 8 }An important aspect of this interindividual variation will be to incorporate more accurate constitutive models of the connective tissue in the ONH region. For example, the effects of collagen fiber orientation in the peripapillary sclera could be important in influencing peripapillary scleral biomechanics.

Name | Coded Name | Units | Baseline | Low | High | Sources | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Input factors defining the geometry of the eye and ONH | ||||||||||||

Internal radius of eye shell | EyeRadius | mm | 12.0 | 9.6 | 14.4 | 9–13 | ||||||

Scleral thickness at canal | ScThickAtCanal | mm | 0.4 | 0.32 | 0.48 | 13–16 | ||||||

Laminar thickness at axis | LCThickAxis | mm | 0.3 | 0.24 | 0.36 | 13,16–18 | ||||||

Retinal thickness | RetThickShell | mm | 0.2 | 0.16 | 0.24 | 19,20 | ||||||

Scleral shell thickness | ScThickShell | mm | 0.8 | 0.64 | 0.96 | 11,14,15 | ||||||

LC anterior surface radius | LCRadius | mm | 0.95 | 0.76 | 1.14 | 10,12,13,16,18,21–24 | ||||||

Pia mater thickness | PiaThick | mm | 0.06 | 0.048 | 0.072 | 13 | ||||||

Laminar curvature | LCDepth | mm | 0.2 | 0 | 0.2 | ^{*} | ||||||

Cup-to-disc ratio/shape of the cup | Cup2DiscRatio | — | 0.25 | 0.1 | 0.5 | 19,21 | ||||||

Canal wall angle to the horizontal | AngleScCanal | deg | 60 | 48 | 72 | ^{*} | ||||||

Optic nerve angle | AngleON | deg | 80 | 64 | 96 | ^{*} | ||||||

Scleral thinning/peripapillary scleral tapering | ScThinFactor | — | 0.5 | 0 | 1.0 | 11,15 | ||||||

Peripapillary rim height | RimHeight | mm | 0.3 | 0.24 | 0.36 | 19,21,25 | ||||||

Cup depth | CupDepth | mm | 0.33 | 0.26 | 0.4 | 19,21 | ||||||

Input factors defining the load on ONH tissues | ||||||||||||

Intraocular pressure | IOP | mm Hg | 25 | 20 | 30 | 26,27 | ||||||

Input factors defining the biomechanical properties of relevant optic tissues | ||||||||||||

Poisson ratio of retina | RetPoisson | — | 0.49 | 0.4 | 0.49 | 28–30 | ||||||

Pia mater Young’s modulus | PiaModulus | MPa | 3 | 1 | 9 | 31–33 | ||||||

Lamina cribrosa Young’s modulus | LCModulus | MPa | 0.3 | 0.1 | 0.9 | 6,34–36 | ||||||

Sclera Young’s modulus | ScModulus | MPa | 3 | 1 | 9 | 29,37–44,54 | ||||||

Retina Young’s modulus | RetModulus | MPa | 0.03 | 0.01 | 0.09 | 45–50 | ||||||

Optic nerve Young’s modulus | ONModulus | MPa | 0.03 | 0.01 | 0.09 | Same as for retina |

**Figure 1.**

**Figure 1.**

Outcome Measure | Code | Units | Min | Max | ||||
---|---|---|---|---|---|---|---|---|

Outcome measures related to mechanical stress and strain in ONH tissues | ||||||||

Peak maximum principal strain | ||||||||

Retina | RetE5 | % | 1.94 | 6.19 | ||||

Lamina cribrosa | LcE5 | % | 1.89 | 7.94 | ||||

Optic nerve | OnE5 | % | 2.12 | 9.68 | ||||

Sclera | ScE5 | % | 0.74 | 4.48 | ||||

Pia mater | PiaE5 | % | 1.07 | 5.01 | ||||

Peak von Mises stress | ||||||||

Retina | RetS5 | kPa | 0.62 | 4.04 | ||||

Lamina cribrosa | LcS5 | kPa | 7.35 | 45.24 | ||||

Optic nerve | OnS5 | kPa | 0.70 | 5.30 | ||||

Sclera | ScS5 | kPa | 49.04 | 74.17 | ||||

Pia mater | PiaS5 | kPa | 43.28 | 232.57 | ||||

Mean maximum principal strain | ||||||||

Retina | RetE100 | % | 0.54 | 2.77 | ||||

Lamina cribrosa | LcE100 | % | 1.53 | 5.30 | ||||

Optic nerve | OnE100 | % | 1.04 | 2.50 | ||||

Sclera | ScE100 | % | 0.33 | 2.42 | ||||

Pia mater | PiaE100 | % | 0.29 | 1.04 | ||||

Mean von Mises stress | ||||||||

Retina | RetS100 | kPa | 0.28 | 1.48 | ||||

Lamina cribrosa | LcS100 | kPa | 6.50 | 30.67 | ||||

Optic nerve | OnS100 | kPa | 0.25 | 1.59 | ||||

Sclera | ScS100 | kPa | 28.61 | 42.92 | ||||

Pia mater | PiaS100 | kPa | 7.91 | 48.73 | ||||

Outcome measures related to ONH geometry | ||||||||

Retinal thickness at axis of symmetry | RetThickAxis | μm | −26.1 | −3.05 | ||||

Retinal thickness midway from axis to canal rim | RetThickMidway | μm | 7.1 | 41.0 | ||||

Radius of scleral canal at opening | CanalRadius | μm | 5.24 | 38.8 | ||||

Cup-to-disc ratio | CupToDiscRatio | 0.00 | 0.02 | |||||

Lamina cribrosa thickness at axis of symmetry | LcThickAxis | μm | −24.4 | −8.38 | ||||

Lamina cribrosa thickness midway from axis to rim | LcThickMidway | μm | −25.5 | −7.7 | ||||

Lamina cribrosa thickness at rim | LcThickRim | μm | −10.5 | −1.36 | ||||

Angle to the horizontal of scleral canal wall | AngleScCanal | deg | −5.27 | −1.3 | ||||

Bottom of cup depth from HRT level | CupDepth | μm | −14.3 | 0.11 |

**Figure 2.**

**Figure 2.**

**Figure 3.**

**Figure 3.**

**Figure 4.**

**Figure 4.**

**Figure 5.**

**Figure 5.**