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.
Glaucoma, the second leading cause of blindness worldwide,
1 is characterized by a particular pattern of irreversible damage to the retinal ganglion cell axons.
2 The damage is believed to initiate within the optic nerve head (ONH), where the axons pass through the lamina cribrosa (LC) and exit the eye.
3,4 IOP is considered to be the most important modifiable risk factor for the optic neuropathy of glaucoma, regardless of the level of IOP at which the neuropathy occurs.
5,6 Although the mechanism by which elevated IOP contributes to axon damage remains unclear, it is often considered that IOP affects the susceptibility to glaucoma by causing an altered biomechanical environment within the ONH. Within this framework, the forces from IOP distort the tissues of the ONH, and LC within, triggering events such as compromised axoplasmic flow, vascular perfusion, and astrocyte activation that eventually lead to glaucomatous optic neuropathy.
7–9 However, the ONH is exposed not only to IOP from within the globe, but also to cerebrospinal fluid pressure (CSFP) within the subarachnoid space and blood pressure (BP) within the central retinal vessels. CSFP and BP can also potentially influence the biomechanical environment within the ONH,
10–13 and thus contribute to determine the susceptibility to glaucoma. In fact, in recent years, evidence has been mounting that the susceptibility to glaucoma may be influenced by CSFP.
14–17 Evidence has also been presented that BP may influence the susceptibility to glaucoma.
18,19
Whilst many studies have addressed the effects of IOP on the ONH using experimental,
20–22 theoretical,
23–25 and numerical
26–29 methods, the potential effects of CSFP or BP on the ONH biomechanical environment have not been studied in nearly as much detail. A better understanding of the effects of these pressures and the potential interactions between their effects is necessary to understand the etiology of glaucoma and the puzzling range of sensitivities to IOP.
Our goal was to model the sensitivity of the ONH biomechanical environment to acute variations in IOP, CSFP, and BP. To do so, we extended a previously published numerical model of the ONH
30 to include a central retinal vessel and more detailed retrolaminar anatomy. We endeavored for this to be the most comprehensive analysis to date of the factors influencing ONH biomechanics. Hence, we studied the effects of 24 factors, including the three pressures and 21 other factors representing ONH and globe geometry and tissue mechanical properties, and the constraints on the optic nerve (CON). We simulated ONH biomechanics using a broad set of 98 responses, including pressure-induced local deformations (strains) and forces (stresses) as well as gross deformations (e.g., peripapillary sclera [PPS] rotation or bowing).
The general strategy was to produce a large set of models representing a diversity of ONHs with varying tissue anatomy and mechanical properties and optic nerve constraints, and then use finite element (FE) modeling to simulate the effects on each of the models of acute changes in IOP, CSFP, and/or BP. Due to the large number of factors and responses of interest, we split the analysis into two phases. In a first screening phase, we predicted the main effects and interactions of 24 factors on 98 responses. We identified the 16 most influential factors and 10 responses representative of the whole response set. The representative responses were selected in a process informed by dimensionality reduction techniques and principles of mechanobiology. In a second phase, we focused on the most influential factors from phase 1 to predict factor effects in detail. We then inspected the results using archetypal analysis to identify ONHs representative of the diversity of potential ONH biomechanical responses to the pressures. The steps are described in detail below.
Commercial FE software (ANSYS, ver. 8; ANSYS, Inc., Canonsburg, PA, USA) was used to develop and analyze the models. The process was scripted in Ansys parametric design language. A configuration could be produced, solved, and analyzed without user intervention, typically requiring less than a minute per configuration on a desktop workstation with 32 GB of RAM.
All tissue regions were meshed with eight-node quadrilateral elements (PLANE 82 in Ansys). Optimal element size was determined in a preliminary mesh refinement study.
43 Once sufficient element resolution was determined for a particular geometry, the resolution was quadrupled (element side length divided by two in each direction) to allow for the higher resolution requirements of other configurations. After the study, cases with particularly high strain or stress levels were refined and solved again to verify that the default resolution was sufficient.
The screening analysis showed that, among all 24 factors considered, 16 factors and their interactions accounted for between 94.4% and 99.7% of the variance in the responses. These factors were the pressures (IOP, CSFP, and BP), CON, the eye radius, the properties of the sclera (modulus and shell thickness), LC (modulus, depth, thickness, and radius), dura mater (modulus), pia mater (modulus), retina (modulus), optic nerve (modulus), and vessel (modulus).
Our goal was to model the sensitivity of the ONH biomechanical environment to acute variations in IOP, CSFP, and BP. Four main predictions arose from this work: First, IOP and moduli of the sclera and lamina are among the most influential factors on the biomechanical environment within the ONH. Second, retrolaminar factors, including CSFP, the dura modulus, and CON, have important influence on ONH biomechanics. Third, IOP and CSFP affect different aspects of ONH biomechanics, and these effects do not balance one another. Fourth, BP has only modest effects on the biomechanics of the ONH. Below we discuss each of these predictions in detail.
Our sensitivity study revealed that IOP and moduli of the sclera and lamina were among the most influential factors on the biomechanical environment within the ONH. This prediction is consistent with previous results obtained from ONH models without detailed retrolaminar factors.
30 The effects of IOP and moduli of the sclera and lamina on ONH biomechanics have been extensively discussed elsewhere,
26–28,30,32–34,46 and we will not discuss them here. Note that although in this study IOP was predicted to be the most influential factor, this was not the case in some of our previous studies.
30,32 There are three reasons for this. First, some of our previous studies did not consider the interactions of IOP with other factors, as we do here. Not considering such interactions will underestimate the influence of IOP. Second, in this study we monitored a broad set of 98 responses, many more than the 29 of the previous one. For example, we predicted that IOP would have substantial effects on the displacement of the retina (
Fig. 2), a response that was not included in the previous study. Third, while some factors influence a few responses, IOP is a consistently influential factor on the majority of the responses. Hence, as more factors and responses are considered, the rank influence of IOP increases.
Our models also predicted that retrolaminar factors, including CSFP, the dura modulus, and CON, may have important influence on ONH biomechanics (
Fig. 2). In fact, these factors were more influential than some previously identified influential factors, such as the scleral thickness and lamina radius. The importance of CSFP has also been identified by two recent computational studies that conducted parametric analysis to investigate the effects of CSFP on ONH biomechanics.
10,11 Both studies predicted that increasing CSFP would induce large deformation within the ONH, especially in the retrolaminar neural tissue. The importance of CSFP conforms to its association with susceptibility for optic neuropathy. Berdahl et al.
14,15 retrospectively reviewed medical records of over 50,000 patients and compared CSFP in subjects with and without glaucoma. They found that CSFP was significantly (
P < 0.0001) lower in subjects with normal-tension glaucoma (8.7 ± 1.16 mm Hg) and primary open-angle glaucoma (9.1 ± 0.77 mm Hg) than in the control group (11.8 ± 0.71 mm Hg). Similar observations were found in prospective studies by Ren et al.
16 and Wang et al.
17 Yang et al.
54 found that chronic reduction of CSFP in monkeys led to decreased retinal nerve fiber layer thickness and neuroretinal rim area of the ONH, features of progressive optic neuropathy. Despite the associations, the mechanistic relationship between CSFP and glaucoma, or other optic neuropathies, is still not fully understood, and further studies are needed.
Dura modulus was predicted as the fifth most influential factor in ONH biomechanics, even more influential than CSFP, although this varied between responses (
Fig. 2). Despite its importance, there is little information about the mechanical properties of the dura mater, especially the portion surrounding the optic nerve. Raykin et al.
55 recently characterized the mechanical properties of porcine dura mater in vitro. We analyzed their results and calculated a dura modulus of approximately 4 MPa, within the range considered in this study, that is, 1 to 5 MPa. Considering the predicted importance of dura modulus in ONH biomechanics, characterization of the mechanical properties of human dura mater is worthful.
The movement of the optic nerve would be constrained at the point of orbit exit, but the degree and exact nature of the constraints, and how these are transmitted to the ONH region, remain unclear. Elsewhere simulations have assumed completely free
10,11,30,32 or fully constrained
42 optic nerves. Acknowledging this uncertainty, and to avoid a potentially biased decision, we considered CON as a categorical parameter with two levels: a completely free boundary and a boundary with fully constrained displacements. These two constraints represent two extremes and the true physiological situation is likely somewhere in between. The fully free condition is also important to study because it mimics the boundary conditions of most ex vivo inflation tests. Surprisingly, our models predicted that CON would rank as the second most influential factor in ONH biomechanics, with effects mainly on those responses relating to gross ONH geometry. Whether CON vary between individuals or may even change with aging or disease is unknown, but seems unlikely. In this sense CON would not be considered as much a risk factor, but as a key parameter that must be determined experimentally and incorporated into biomechanical models. The importance of CON also indicates that it is essential to carry out further studies to better understand the boundary conditions of the optic nerve at the orbit exit, as well as other nerve characteristics that affect how these boundary conditions may interact with the ONH and globe. These include optic nerve tortuosity and tissue incompressibility. Interestingly, recent work shows that changes in gaze may result in optic nerve exerting forces on the ONH and PPS.
42,56,57 Further experiments and nonaxisymmetric models are needed to understand this.
Our model predictions also showed that IOP and CSFP affected different aspects of ONH biomechanics and that these effects did not balance one another (
Fig. 5). This can be explained by the distinct manner in which IOP and CSFP deform the ONH, directly and indirectly. IOP affects the ONH directly by “pushing” the cup and LC posteriorly, and indirectly by deforming the sclera, causing expansion of the scleral canal, which in turn “pulls” the lamina taut from the sides.
58,59 The CSFP also has direct and indirect effects on the LC. We note three mechanisms (
Fig. 6). The magnitude of each effect and the overall response when also under elevated IOP will depend on the specific anatomy and mechanical properties of the eye. Considering how different mechanisms of action of IOP and CSFP are, it came as no surprise that their effects generally did not balance out.
Our model predictions showed that BP would have only modest effects on the biomechanics of the ONH. This is counter to our original expectation that BP would be influential, considering that the increase in BP (30 mm Hg) was twice that of IOP and CSFP (15 mm Hg). Note that herein we studied the effects of normal variations in BP on overall ONH biomechanics. Variations in BP may also have local biomechanical effects on neighboring neural tissues and on the LC that should be studied and better understood. These studies are important in light of the evidence for a role of ocular perfusion pressure in glaucomatous optic neuropathy.
60,61
To the best of our knowledge, this is the most comprehensive study modeling the sensitivity of the biomechanical environment within the ONH, in terms of parameters considered and responses examined. Understanding of ONH biomechanics requires parameterized models that incorporate a wide range of anatomic and material factors, pressures, and other boundary conditions. Similarly, it is necessary to study the effects of these factors on a wide range of responses. Not doing so risks missing important aspects of ONH biomechanics. We recognize that considering many responses can also be problematic, as it is possible for results to point to factors that are influential on those responses but that may not have a major role in the neuropathy. However, until the mechanistic link between ONH biomechanics and the neuropathy has been established, we believe that it is better to be comprehensive. We have demonstrated in this work that considering many responses is possible using PCA and archetypal analysis. Note that the use of PCA does not imply that the system biomechanics were linear. PCA can represent nonlinear relationships precisely. This is important because the relationships between responses as identified in this study were nonlinear, consistent with those reported elsewhere.
32,33,47
Archetypal analysis revealed a wide diversity of sensitivities to IOP and CSFP. Some ONHs were highly sensitive to one pressure and insensitive to the other. From a clinical perspective, a potentially troubling finding is that sometimes the pressure effects were mainly in the retrolaminar region (of IOP in archetype 3, and of CSFP in archetype 5). This means that the effects might be difficult to observe and measure, even with current swept-source optical coherence tomography systems.
Parametric modeling of the kind we present in this work, and which we have published elsewhere,
29,32 serves to obtain a general understanding of how all eyes work. These models are not intended to represent any specific eyes. There is value in pursuing specimen-specific models that can be inverse fit, or validated against experimental tests, which we have also done.
27,28,62 Specimen-specific models provide excellent information on the particular eyes, but generalizing to a population is problematic and can be highly misleading. We have illustrated potential problems with those generalizations and how parametric modeling can help prevent some of those misunderstandings.
58 Carefully done, parametric modeling helps provide fundamental new insight into the mechanical behavior of the posterior pole of the eye that would be otherwise unobtainable. A more detailed discussion of the role of parametric modeling in posterior pole biomechanics is outside the scope of this work, and is available elsewhere.
63
Peak strains predicted by the models in this study were slightly above 5%, which is similar to those predicted by comparable models of human
10,11,32–34,64 and monkey
58,65 LC, and also to some recent measurements in in vivo
56 and ex vivo
66 human and ex vivo porcine
67 eyes. For comparison with experiments it is important to consider that the strains predicted by our models assume the LC to be homogeneous. We, and others,
10,11,64 have followed this approach, as it is a reasonable approximation of the large-scale behavior of the tissues. As the resolving power of imaging technique increases, experimental studies of ONH biomechanics have reported higher levels of strain at the microscale within the LC, which sometimes exceeded 10%.
56,66–69 Elsewhere we studied the relationship between model detail and predicted LC strain by developing models with a detailed microarchitecture of the beams and pores of the LC.
70,71 We found that models with detailed LCs predicted higher strains, particularly in the pores adjacent to the sclera. However, when observed at a larger, mesoscale resolution, the models predicted LC strains between 2% and 4%, similar to the levels we reported here.
To compare with our previous studies and extend the lessons and predictions, we adopted the same model simplifications; that is, the geometries were axisymmetric and the mechanical properties were isotropic and linear. A thorough discussion of the limitations of this modeling approach can be found in our previous studies.
26,29,30,34,46,47,59 While these simplifications may not capture some of the complex behavior of the ONH, they provide a reasonable first approximation. We also aim to inspire others to do more comprehensive analysis of the powerful models they develop. Work is ongoing within our lab
70,71 and others
72–74 to create improved computational models that capture the anisotropy,
75–80 nonlinearity,
75,76,79,81,82 and inhomogeneity
79,80,83–85 of the ONH. Another limitation of this work is that the pressure variations were all within the normal range. Given the linear mechanical properties of the model, we find it best to limit the change in pressures to a small range. At elevated or abnormal pressures, the nonlinear material properties would more strongly influence the mechanical behavior of the ONH system. Finally, although we based the factor ranges on the literature and on reasonable assumptions, the choice of factor ranges may affect factor influences and outcome sensitivities. Hence, it is important to interpret the results as an estimate of the factor influences and not take the factor ranking as precise.
In conclusion, our models predicted that IOP and CSFP are the top and sixth most influential factors on the biomechanical environment within the ONH. IOP and CSFP may affect different aspects of ONH biomechanics, explaining why the overall influence of TLPD was substantially smaller than that of either IOP or CSFP. This suggests that TLPD alone will not be sufficient to predict biomechanically induced glaucomatous neuropathy. CON may drastically affect the responses relating to gross ONH geometry and thus should be accurately determined through experiments. Due to the substantial model simplifications, our results should be considered as an approximation to understand the complex biomechanical environment within the ONH under the simultaneous effects of IOP, CSFP, and BP.
The authors thank Jonathan L. Grimm for assisting with programming, modeling, and plotting.
Supported in part by National Institutes of Health Grants R01-EY023966, R01-EY025011, P30-EY008098, and T32-EY017271 (Bethesda, MD, USA) and the Eye and Ear Foundation (Pittsburgh, PA, USA) and Research to Prevent Blindness (New York, NY, USA).
Disclosure: Y. Hua, None; A.P. Voorhees, None; I.A. Sigal, None