Abstract
This work presents results from numerical simulations of optic nerve head’s (ONH) biomechanical behavior during exposure to elevated intraocular (IOP) and/or intracranial pressure (ICP) for ocular hypertension conditions. At the same time, a range of geometric and material properties of the eye structure and their interrelation with elevated IOP and ICP values are investigated. These simulations are performed on a generic model of the eye, which allows parametrical modification of geometric and material properties. Our main interest is in measuring ONH’s potential damage in ocular hypertension due to intracranial pressure. Simulation results indicate a significant role of ICP in post-laminar neural tissue failure and a possible role of central corneal thickness (CCT) and scleral modulus in clinical assessment and treatment of patients with ocular hypertension (OHT). Specifically, CCT was found to affect ONH at early stages of damage in ocular hypertension conditions, and high scleral modulus seems to result in reduced shear failure in lamina cribrosa in a similar OHT state. These findings suggest that CCT could be a risk factor for glaucoma in OHT patients at initial stage along with cornea stiffness.
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1 Introduction
Optic nerve head (ONH), cornea, and sclera biomechanical properties are postulated to play a role in a number of ophthalmic pathologies including glaucoma, which is the second most common disease that causes blindness worldwide [1]. Glaucoma is associated with a gradual damage of the optic nerve within the ONH, where the retinal ganglion cell axons and central retinal vein pass through a collagenous meshwork, called lamina cribrosa (LC) [2, 3]. LC is known to be the site of greatest susceptibility to glaucoma disease where retinal ganglion cell dysfunction occurs [4]. The retinal ganglion cell axons pass through LC, leave the eye as a post-laminar neural tissue (PLNT), and end up in the brain while being continuously surrounded by retrobulbar cerebrospinal fluid, which exerts pressure on them (intracranial pressure (ICP)), and meninges.
Experiments have shown that high intraocular pressure (IOP) causes the axonal bundles in the LC to bow posteriorly and shear [5]. IOP greatly affects the biomechanical environment within the ONH, and high IOP values cause tissue distortions leading to glaucomatous optic neuropathy [6, 7]; however, some people have no sign of glaucoma at elevated IOP values; this state is called ocular hypertension (OHT) [8]. Recent observational [9], retrospective [10], and interventional [11] studies reported that the ocular hypertensive subjects with elevated intraocular pressure (higher than 21 mmHg) but without glaucomatous optic nerve damage had an abnormally high cerebrospinal fluid pressure. We hypothesized that the abnormally high ICP, acting as a counter pressure across the lamina cribrosa, may compensate for the elevated IOP in OHT conditions.
Glaucoma is also related to the biomechanical properties of the cornea [12] particularly for OHT patients. Although the cornea is located far from LC, which is the primary location of interest for glaucoma, corneal biomechanical properties are relevant to the rigidity and thickness of the sclera, which in turn is believed to be one of the most influential factors in LC behavior [13]. Therefore, the importance of corneal biomechanical properties should not be underestimated. Our goal is to study the influence of intracranial pressure on ONH biomechanical environment in OHT patients. We have also included corneal geometric and material properties as potential factors leading to glaucoma, since central corneal thickness (CCT) was the most prone predictor for glaucoma risk assessment [14, 15] in patients with ocular hypertension. Corneal elasticity (CE) has been also shown to play a role in the interpretation of IOP, where the increased elasticity protects the eye from pressure surges [12].
Computational finite element eye models have been already successfully employed in a wide range of simulations and surgery training; see [16,17,18]. The novelty of this study is to use generic model to do parametric analysis, including cornea, and study the influence of intracranial pressure on optic nerve head biomechanics for ocular “hypertension” subjects using finite element analysis method. More specific to our field of study, computational finite element models have been used to study the biomechanical influence of IOP to ONH with regard to glaucoma [13, 19]. Hua et al. [20] have recently estimated the factors influencing ONH biomechanics. While IOP-induced mechanical strains on ONH have been properly characterized, the same cannot be said for ICP-induced strains on ONH, which is under-explored [21, 22]. A better understanding of IOP and its interrelations with ICP and corneal biomechanical properties is necessary in enhancing our predictions regarding glaucoma susceptibility. The contribution of this paper is twofold: (a) we characterized the effect of increased ICP and IOP on ONH’s biomechanical environment for OHT subjects, using Tresca failure criterion to check whether ICP compensates the adverse effect of IOP in lamina cribrosa, and (b) we performed a parametric study to assess the effect of corneal biomechanical properties, and their interrelation with ICP, in OHT conditions, since it was hypothesized that cornea characteristics can be of importance for hypertension subjects.
2 Material and methods
In our work, a generic geometric model of the eye was constructed to perform sensitivity analysis and identify the factors influencing lamina cribrosa, via a finite element analysis approach. The selected candidate factors were systematically varied using the statistical Taguchi method; see [23]. The ONH part of the baseline eye model is identical to the one presented in [24], whereas the anterior part was constructed on the basis of the corresponding image included in [25]. The employed ocular geometry along with the design of experiments is described in detail below.
2.1 Ocular geometry
Our study involves the comparison of a series of eyeball models with varying geometric and material properties where the finite element (FE) method is employed in their assessment. A three-dimensional eyeball (see Fig. 1) was constructed in SolidWorks 2017 (Dassault Systemes, SolidWorks Corporation, Concord, MA) using dimensions for its constituting components from pertinent literature [13, 25]. The complete set of employed dimensions and material properties along with source references are included in Table 1. This model was then imported to ANSYS 15 (ANSYS, Canonsburg, PA) and automatically meshed on the basis of its geometry and the employed analysis type. Two methods were used to verify our numerical results and establish convergence: error plot checking and mesh convergence. The ANSYS error plot was used to verify stress continuity and subsequently refine the mesh when this was not accomplished. For results in convergence, we checked normal stresses, as well as error plot in ONH region, and performed mesh refinements till peak stress deviation was lower than 1%. The final employed mesh comprises 955,000 nodes and 550,000 tetrahedral and hexahedral elements (lamina cribrosa). The procedure presented in [33] was also followed here: coarse elements were first generated, and the ONH region was subsequently manually refined till convergence was reached. Our results are comparable with the ones reported in [13, 25], which also use generic eye models.
Our eye model is an extended version of the ocular model developed by Leung et al. [25] since dura mater was included to study influence of ICP, and therefore, our model is anatomically more accurate. Scleral shell thickness of the globe is assumed to be 0.8 mm with 12-mm internal radius and attenuated tapering down to 0.4 mm at canal with an angle of 30° from the vertical axis (see Fig. 1). The eye globe and adipose tissue are assumed axisymmetric around the central axis of the LC. The adipose tissue is set to cover 140° of the sclera and is modeled with a thickness of 4.6 mm [31, 32].
Lamina cribrosa thickness is set to 0.3 mm while the anterior surface radius to 0.9 mm, as described in [13]. LC is modeled as a section of a spherical shell and concentric to scleral shell. Post-laminar neural tissue, i.e., the region beneath LC, is modeled using a taper angle of 80° from the horizontal axis [13]. The PLNT starts with a retinal shell thickness of 0.24 mm and ends up with 0.2 mm at the equator while following the contour extracted from image data published in [24].
The pia and dura mater thicknesses are assumed to be 0.06 and 0.255 mm, respectively [19]. The subarachnoid space geometry follows the same image data [24] with a thickness of 0.15 mm [19] between pia and dura mater. The elastic modulus of the uniform gap (subarachnoid) between pia and dura mater was not included in the analysis as it is generally considered extremely soft [34]. The central retinal artery is modeled according to pertinent literature [19] including the effect of blood pressure. The vessel is modeled as a tube with an external wall diameter of 0.18 mm and 0.05 mm for its thickness [19]. Finally, the cornea details are set according to mean population values [28] as follows: central corneal thickness at 0.5 mm, curvature radius at 7.8 mm, and diameter at 11 mm [28]. The angle between cornea central axis and ONH central axis is set to 165°, since the blind spot is 15° nasally from the fovea [35].
All tissues are assumed as an incompressible, isotropic, linearly elastic, and homogenous material. The surface interfaces of ONH, cornea, sclera, and adipose tissue were assumed to be fully adhered, hence deforming together. Therefore, a “bonded contact” between all relevant body faces was manually applied in ANSYS Workbench in a similar fashion to [25, 36], which makes the same assumption. The baseline material properties for each tissue are adopted from literature [13, 24, 30,31,32], i.e., 0.29 MPa for cornea, 3 MPa for pia mater, 0.03 MPa for prelaminar and post-laminar neural tissues, 0.047 MPa for adipose tissue, 9 MPa for dura mater, and 5 MPa for artery as shown in Table 1.
2.2 Design of experiments: description and methodology
A fractional factorial design method developed by Taguchi [23] was adopted to quantitatively analyze sensitivity of factors at two levels. The Taguchi’s method facilitates system performance optimization by identifying the most important control factors allowing the use of a reduced experimental data set without compromising the efficiency of the analysis.
Our eye model’s sensitivity to several factors including geometrical and material properties of its subcomponents was tested against elevated levels of ICP and IOP. Specifically, a two-level orthogonal matrix design (L16(2)14) with 14 factors was used, resulting in 16 different cases generated by Statistica (v13.3, StatSoft) software package. L16(2)14 is an orthogonal matrix design that can be represented as a two-dimensional array, where all the input factors appear in equal numbers in each vertical column and disperse evenly the pairwise combinations [37]. Here, 16 denotes the number of cases, 14 the number of factors, and 2 corresponds to the number of levels. This approach permits screening of a large number of factors and attaining good estimates of each factor’s effect with a reasonably small study case set.
A total of 14 input factors were studied as summarized in Table 2. The input factors are separated into two groups. The first group includes geometric factors, whereas the second one comprises material properties. The seven geometric factors are scleral thickness at canal (A), LC radius (B), LC thickness (C), pia mater thickness (D), dura mater thickness (E), central corneal thickness (F), and retinal thickness (G). The seven material properties are scleral modulus (H), LC modulus (I), prelaminar neural tissue modulus (J), pia mater modulus (K), dura mater modulus (L), corneal modulus (M), and post-laminar neural tissue modulus (N). The factors’ set was compiled to include the corneal geometric and material properties along with all other significant factors as reported in literature [24]. Each factor’s value range is defined within ± 20% of the corresponding baseline value. Note that we use factorial design with two levels for multiple factors to perform a screening test in which our major concern is to identify the important factors without any detailed analysis. Furthermore, for all factors, we avoid infeasible regions and we have a typical variation used in pertinent literature [13, 24].
2.3 Optic nerve damage prediction
As indicated in [5, 38], optic nerve damage is mostly linked to shear stresses. Specifically, experimental findings show that mechanical forces, and in particular shearing stresses at LC’s periphery, play a role in ONH damage [5]. In addition, computational results by Leung et al. [25] showed that Tresca criterion reasonably predicted the effect of ocular stiffening, due to aging, on optic nerve damages. The effect of radial oriented fibrils at LC’s periphery, which reinforce LC against transversal shear stresses, is widely studied by computational remodeling approach [39, 40]. Therefore, in our study, we are estimating ONH damage via calculation of peak maximum shear stress values in LC and PLNT. The influence of the selected 14 input factors, for the identified 16 case studies, is reflected to the predicted peak maximum shear stresses in the LC and PLNT as shown in Table 3. Nerve damage prediction was carried out by employing the classical shear Tresca failure criterion [25, 41]. More complex damage models that account for nerve fiber anisotropy, dependence on age, and time dependence could be added, but as a first approach, the Tresca criterion appears to be sufficient since it models the observed behavior; see [25]. When local maximum shear stress in LC exceeds a threshold, the nerve is categorized as damaged. In mild ocular hypertension (corneal moduli 0.17 MPa, scleral moduli 1.84 MPa and LC stiffness 0.12 MPa, IOP 21 mmHg), nerve damage is negligible [25]. The peak MSS in LC at mild ocular hypertension was computed at 0.0032 MPa (τmax); thus, we may set the Tresca criterion value (τc) slightly above this, i.e., 0.0035 MPa. LC shear failure corresponds to the number of nodes with MSS values higher than 0.0035 MPa and can be defined as the ratio of failure nodes over the total amount of nodes.
For the base model, an intraocular pressure of 15 mmHg is applied to the surface of the prelaminar neural tissue, sclera, and cornea. We also assume an ICP equal to 15 mmHg applied on the subarachnoid space [42] and constant arterial pressure of 55 mmHg at the vessel [43]; these values correspond to a healthy adult human.
3 Results
In this section, we present, in detail, the obtained computational results regarding the influence of ICP and corneal characteristics. The discussion begins with the effects of ICP variation, followed by the ones observed for variation in corneal geometry and material properties.
3.1 Effect of intracranial pressure
Table 3 clearly shows that, for all cases, shear stresses in a relatively stiff LC are considerably higher than corresponding values observed in a relatively soft PLNT. The peak MSS in LC ranges from 0.2205 to 0.5365 kPa, whereas in PLNT, it is generally much lower and varies from 0.0261 to 0.0476 kPa. Table 4 depicts collectively the results for the two factor value levels: Kn (n = 1, 2) corresponds to the average of eight values for each factor of the peak MSS for each factor level shown in Table 3. K1 represents the effect of the eight low-level (i.e., − 20%) values, while K2 represents the effect of eight high-level (i.e., + 20%) values for each factor. As an example, for input factor B (lamina cribrosa radius), K1 = 0.3879 is the average of the peak MSS values in LC corresponding to B = 0.76 in Table 3. Range value, R, is the difference between K1 and K2 for each factor. Large R values signify factors with great influence on the peak MSS in LC or PLNT. Figure 2 presents a graph depicting the percentage of LC’s volume subject to shear stresses above a certain value for each case in Table 3. This type of curve is helpful when computing the 95th percentile peak MSS. We should also note here that cases with a homogeneous distribution of MSS correspond to steep curves in the graph. Sensitivity analysis results are depicted in Fig. 3, where R values are plotted for each factor. Elastic moduli of LC and PLNT had the highest R values and, therefore, can be considered the most influential parameters among the selected factors. On the other hand, one may observe that although CCT is the sixth influential factor in LC, it comes second when considering PLNT shear stresses.
The relationship of peak MSS values to LC and PLNT moduli for two values of ICP and a constant IOP value (15 mmHg) is calculated and presented in Fig. 4 . As can be easily seen, increasing LC modulus elevates shear stresses in it, while, conversely, the increase of ICP has a beneficial effect on shear stresses. Specifically, the low ICP value of 7 mmHg induced higher shear stresses than the higher ICP of 15 mmHg (Fig. 4 a). Results from a recent computational study [19] are also indicating that ICP level affects the risk of high strains in LC and PLNT. For PLNT, the 15 mmHg ICP level induced extreme shear stresses exhibiting a more dominant effect than PLNT’s stiffness (see Fig. 3 b), which is consistent with findings in pertinent literature [24].
Glaucoma vision loss is also highly dependent on age and eye tissue hypertensiveness. Both IOP and elastic moduli of ocular tissues are positively correlated with age [44, 45]. Therefore, influence of IOP and ICP on LC shear failure is examined with increasing corneal, sclera, and LC moduli values (see Figs. 5 and 6). Calculated LC shear failure, using the shear failure criterion for ocular hypertension mentioned above, is depicted against varying IOP and ICP values in Fig. 5. Nerve damages increase with age due to increased stiffness of LC, sclera, and cornea. We vary the value of the elastic modulus of cornea (between 0.17 and 1.43 MPa), sclera (between 1.84 and 3.72 MPa), and lamina cribrosa (between 0.12 and 0.67 MPa) (Fig. 6) to study the effect of age stiffening [36, 44, 45]. These biomechanical ranges were adopted from experiments [36]. With a constant IOP level of 20 mmHg, when ICP level drops from 15 to 7 mmHg, LC shear failure increases from 17 to 48%. ICP seems to play the role of counter pressure to IOP in lamina cribrosa region. Abnormally low ICP (7 mmHg) induced higher translaminar pressure difference increasing LC shear failure. This is consistent with the observations of a prospective study [46], which found that cerebrospinal fluid pressure was significantly lower in glaucoma cases with normal IOP. A similar case-control study [10], including over 6000 subjects, compared ICP in patients with and without glaucoma and revealed that ICP was higher (12.6 ± 0.85 mmHg) in subjects with OHT than in age-matched control group (10.6 ± 0.81 mmHg).
3.2 Effect of corneal material and geometric properties
In this part of study, we examined shear failure for corneal thicknesses between 0.4 mm and 0.6 mm at a constant IOP value of 25 mmHg. At the same time, varying levels of LC Young’s modulus, LC radius at canal, sclera Young’s modulus, and sclera thickness were tested to establish the conditions revealing CCT’s role. LC shear failure value for each case was calculated, and results are summarized for all examined cases in Table 5. It is easy to see that CCT value affects LC shear failure significantly in the presence of the lower-valued LC modulus and the high-valued sclera modulus. Another interesting observation in the same table can be made for scleral stiffness’s effect on LS shear failure. When we consider a larger value for sclera’s modulus, the expected that shear failure percentage is significantly reduced to at least half the value attained with a softer sclera. Experimental studies [47] back up this evidence as they also reveal a beneficial effect of stiffened sclera in reducing LC strain at increased IOP. Finally, [48] reported that glaucomatous eyes appear to have thinner sclera when compared with normal eyes, and this is in agreement with our results, which show high LC shear failure in lower sclera thicknesses; see last two rows in Table 5.
To better illustrate the effect of the two CCT values (0.6 mm and 0.4 mm) on LC shear failure, we plot LC shear failure as a 3D surface with respect to sclera and lamina cribrosa moduli values (see Fig. 7a, b), which correspond to CCT values of 0.6 and 0.4 mm, respectively. Figure 7c, d depicts a top view of the corresponding (Fig. 7a, b, respectively) shear failure surface along with its isolines. In these figures, one may easily observe that the 10–70% isolines are shifted upwards for the larger CCT value and that the transition area between low and high failure rates is generally narrower when compared with the case of low-valued CCT. Hence, stiffer sclera and LC will generally protect the eye and especially for the case of a thicker cornea.
The isolines corresponding to 10%, 30%, and 70% of LC shear failure for both cases (CCT = 0.6 mm and CCT = 0.4 mm) are plotted side by side in Fig. 8. The green-marked areas in the subgraphs depict the difference between the same isolines for the two CCTs. One can observe that the deviation between the isolines diminishes as we approach high failure percentages, which indicated that CCT’s role is more prominent and protective at low shear failure values, i.e., when ONH is starting to get damaged (initial stage).
4 Discussion
One of the objectives of this study was to characterize the influence of intracranial pressure on the optic nerve head for ocular hypertensive subjects. Our results suggest that optic nerve damage decreases with high intracranial pressure (15 mmHg) (Figs. 4, 5, 6) across the laminar cribrosa in ocular hypertension while inducing extra shear stresses on post laminar neural tissue. Figure 5 indicates that the higher ICP value has a beneficial effect for the whole range of LC modulus values. In this case, high intracranial pressure may act as counter pressure across the lamina cribrosa that compensates the elevated intraocular pressure. This finding agrees with suggestions from a retrospective study [10]. In contrast to the protective role of “high” intracranial pressure, three recent studies suggested that abnormally low intracranial pressure may play a role in pathogenesis of glaucomatous optic nerve damages [46, 49, 50]. Interestingly, Fig. 5 is also indicating an increase in shear failure with low ICP. One may postulate that the compensation effect of ICP leads to normal translaminar pressure difference in the eye [10, 11], while abnormally high translaminar cribrosa pressure difference can lead to glaucomatous damage. If this is further verified, ocular hypertensive subjects with elevated translaminar cribrosa pressure could be treated by lowering the intraocular pressure. On the other hand, elevated levels of ICP induce extra stresses on PLNT (Fig. 4B), which is also consistent with observations from literature [19].
Glaucoma is positively correlated with IOP and age. Eye tissues stiffen with age and a positive correlation of eye’s elastic moduli with age has been established in [45]. Shear failure exhibits a decrease with increasing ICP values for ocular hypertensive subjects (corneal modulus 0.31 MPa, sclera’s elastic modulus 1.84 MPa and lamina cribrosa modulus 0.12 MPa) (Fig. 6). On the contrary, when LC, sclera and cornea stiffened together, the shear stress in LC slightly increased. In this range of higher-valued moduli, the ICP beneficial influence is eliminated and the estimated shear failure is even slightly higher when ICP increases. This suggests that in this area, shear failure is barely dependent on ICP values. This corroborates some studies reporting that aging would increase the shear stresses in the LC [25, 44, 45].
Brandt et al. [51] recruited 1636 patients and compared central corneal thicknesses in participants with and without glaucoma. They found out that patients with OHT had a thicker central cornea while cases with primary open-angle glaucoma exhibited thinner central corneas. Whereas studies by Johnson et al. [52], Whitacre et al. [53], and Argus et al. [54] suggest that thicker corneas may lead to IOP overestimation when measured with applanation tonometry, and OHT patients would be diagnosed with normal pressure, if corneal thickness was taken into account. Although the influence of scleral biomechanics is well established, the same cannot be said for cornea. Therefore, we tried to identify conditions in which cornea itself could be a risk factor in ocular hypertension. Specifically, we examined shear failure for corneal thicknesses between 0.4 mm and 0.6 mm at a constant IOP value of 25 mmHg. Based on our findings, a thicker CCT seems to play a protective role when it coexists with a generally stiff sclera and soft LC, and it could be the case that thicker corneas prolong glaucoma’s initial stage in OHT patients with increased IOP. Since sclera and LC are embedded in the eye, monitoring and characterization of the corneal thickness and elastic modulus might be practically infeasible. On the other hand, several in vivo corneal characterization methods are developed, including mechanical indentation testing device [55], dynamic testing [56], air jet indentation testing [57, 58], ultrasound elasticity microscope [59], and ocular response analyzer [60]. Available corneal elasticity measurement methodologies could be used in glaucoma risk assessment and disease treatment management.
4.1 Limitations of the study
Our model was analyzed with linearly elastic, homogeneous, and isotropic tissues and axisymmetric geometries, which may constitute an oversimplification, as recent studies on characterization of eye tissues suggest nonlinear responses [2, 61, 62]. Nevertheless, our results refer to the immediate and average response of ONH tissues without consideration of intricate tissues’ interrelations and material properties, which can justify this simplistic approach. In the same context, we acknowledge the fact that use of Tresca failure criterion will possibly omit biological and age-related axonal disruption. Another limitation of this study relates to the selection of a uniform range of variation (± 20%) for all geometric and material parameters’ values. This simplifying assumption may result in a slightly distorted image regarding the significance of some factor values, which may not differ that much from the considered base values. Finally, all outcomes are considered only in terms of shear stress, whereas first and third principal strains and stresses should be also considered.
5 Conclusion
In this work, an advanced 3D eyeball model was built and employed in the investigation of several factors’ contribution to optic nerve head damage under different levels of intraocular and intracranial pressure. A range of values for intraocular and intracranial pressures was utilized to quantify optic nerve head damage in lamina cribrosa for ocular hypertension subjects. Our results indicate that intracranial pressure induces a higher shear stress on post-laminar neural tissue which does not seem to be the general case for lamina cribrosa, where intracranial pressure seems to counter balance intraocular pressure for hypertension subjects. Further to this, variations in geometric and material characteristics of eye tissues and components, including the cornea, have been demonstrated to affect lamina cribrosa and post-laminar neural tissues. For the case of cornea, our findings indicate that a thicker cornea may play a protective role of optic nerve head damage at an early stage of glaucoma in ocular hypertension subjects. However, cornea is much less influential than tissues closer to the optic nerve, such as peripapillary sclera. Future work may include modeling with patient-specific geometry from optical coherence tomography images and inclusion of nonlinear material properties for eye tissues.
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This work is partially supported by the Nazarbayev University individual grants 481-2018 and 445-2019.
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Kharmyssov, C., Abdildin, Y.G. & Kostas, K.V. Optic nerve head damage relation to intracranial pressure and corneal properties of eye in glaucoma risk assessment. Med Biol Eng Comput 57, 1591–1603 (2019). https://doi.org/10.1007/s11517-019-01983-2
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DOI: https://doi.org/10.1007/s11517-019-01983-2