The Strain Response to Intraocular Pressure Decrease in the Lamina Cribrosa of Glaucoma Patients

Abstract

Objective:

To measure biomechanical strains in the lamina cribrosa (LC) of living human eyes with intraocular pressure lowering.

Design:

Cohort study.

Participants:

Glaucoma patients underwent imaging before and after laser suturelysis following trabeculectomy surgery (29 image pairs, 26 persons).

Intervention:

Non-invasive imaging of the eye.

Main Outcomes:

Strains in optic nerve head tissue and change in depth of the anterior border of the LC.

Results:

Intraocular pressure (IOP) decrease caused the LC to expand in thickness, anterior-posterior strain (E_zz) = 0.94% ± 1.2% (p = 0.0002) and to contract in radius, radial strain (E_rr) = −0.19% ± 0.33% (p = 0.004). The mean LC depth did not significantly change with IOP lowering: 1.33 ± 6.26 μm (p = 0.26). A larger IOP decrease produced a larger, more tensile E_zz (p < 0.0001), greater maximum principal strain (E_max) (p < 0.0001), and greater maximum shear strain (Γ_max) (p < 0.0001). Average LC depth change was associated with the maximum shear strain Γ_max and radial-circumferential shear strain (E_rθ) (p < 0.02), but was not significantly related to tensile or compressive strains. Analysis by clock hour showed that in temporal clock hours 3–6, a more anterior LC movement was associated with the more positive E_max and in clock hours 3, 5, 6 with more positive Γ_max. At 10 o’clock, a more posterior LC movement was related to more positive E_max (p < 0.004). Greater compliance (strain/ΔIOP) of E_max (p = 0.044), Γ_max (p = 0.052), and E_rθ (p = 0.02) were associated with thinner RNFL. Greater compliance of E_max (p = 0.041), Γ_max (p = 0.021), E_rθ (p = 0.024), and in-plane shear strain (E_rz) (p = 0.0069) were associated with more negative MD. Greater compliance of Γ_max (p = 0.055), E_rθ (p = 0.04), and E_rz (p = 0.015) were associated with lower VFI.

Conclusion:

With IOP lowering, the lamina cribrosa moves either into or out of the eye, but on average expands in thickness and contracts in radius. Shear strains are nearly as substantial as in-plane strains. Biomechanical strains are more compliant in eyes with greater glaucoma damage.

Trial Registration:

ClinicalTrials.gov Identifier: NCT03267849

Précis

The lamina cribrosa moves into or out of the eye with intraocular pressure decrease, but on average expands in thickness and contracts in radius. Biomechanical strains are more compliant in eyes with greater glaucoma damage.

INTRODUCTION

A major site of damage to retinal ganglion cell axons in glaucoma is the lamina cribrosa (LC) of the optic nerve head (ONH).^1–4 The biomechanical stress from intraocular pressure (IOP) produces strain in both the sclera and the ONH, leading to detrimental effects on axons, ONH astrocytes, and nutritional blood flow in the ONH.^5–9 The peripapillary sclera (PPS) has a circumferential pattern of collagen and elastin fibers and fibroblasts. This regional structural feature differs from the collagen structure elsewhere in sclera. It resists hoop stress, which acts along the circumference of the PPS and is perpendicular to its axial direction.^10–14 The collagen and elastin-containing LC beams are lined by astrocytes that course directly across the ONH opening.^15–19 Not only fibrous elements, but also the matrix of ONH and scleral connective tissues are important to their mechanical behavior.^20,21 The responses of sclera and ONH to the level of IOP are possible biomarkers and potential translational opportunities for glaucoma incidence and progression.²²

The structures of the sclera and ONH are remodeled in experimental monkey glaucoma^23–26 and human glaucoma eyes^27–29 with a decrease in the regularity of the circumferential PPS fiber pattern and with deeper and wider placement of ONH beams, in a dynamic process effected by resident fibroblasts and astrocytes.^30–34 The neurons, glia and fibroblasts of the ONH area are known to have mechanosensitive properties.^35–39 Regional differences^40–42 in connective tissue density and pore size within the LC and greater regional ONH strains^43–45 lead to selective death of retinal ganglion cell (RGC) axons in the upper and lower poles of the ONH.⁴ The interaction between PPS and ONH have been modeled to show how IOP-induced stress is translated.^46,47 Experimental alteration of sclera and ONH tissues have shown both detrimental^48,49 and beneficial effects.⁵⁰

In human eyes with glaucoma, the mechanical properties of the sclera have been reported to be stiffer in glaucoma eyes compared to non-glaucoma eyes by in vivo indirect measurements.^51–53 Experimental IOP elevation in monkeys produces a variably stiffer mechanical response in the sclera compared to controls.^54–56 Further estimates of scleral and ONH mechanics have been made by ex vivo inflation testing in animal^57–63 and human^64–68 eyes, commonly showing far less strain in the sclera than the ONH itself, and suggesting lower strain in glaucoma ONH. However, the differences between live and post mortem tissue in thickness and composition suggest the need for testing of living ONH.⁶⁹

Initial studies of ONH using optical coherence tomography (OCT) to estimate its biomechanical response to IOP change focused on movement of the easily identified anterior LC border, though initial studies used only single depth point measures⁷⁰ or produced a single-value shape index for the LC anterior border.⁷¹ LC depth was found to be greater with more severe glaucoma damage⁷², increased with acute IOP elevation in monkeys⁷³, and generally shallowed weeks to months after IOP lowering by glaucoma surgery.^74–76 IOP elevation by ophthalmodynamometry produced no significant LC depth change.⁷⁷ Our study after IOP-lowering by laser suturelysis following trabeculectomy found that the LC border could move either into the eye (toward the cornea) or outward (away from cornea), depending upon the degree of glaucoma damage.⁷⁸ Thus, LC depth may not indicate the vital relationship between IOP-related stress and strains within the LC.

We and others developed a method to estimate LC strains in living eyes using OCT and digital volume correlation (DVC) analysis of radial ONH images after IOP reduction by suturelysis, before and after trabeculectomy, and with acute IOP elevation.^79–87 Weeks after trabeculectomy with IOP lowering, Girard and co-workers reported a decrease in a measure called effective LC strain, but the degree of change was not associated with magnitude of IOP change and the posterior limits of the LC were not defined. Beotra et al.⁸¹ applied DVC to measure LC strains following acute IOP elevations estimated to be 35 mmHg and 45 mmHg by ophthalmodynamometer indentation of the sclera in normal, ocular hypertensive, and glaucoma subjects. The effective strain in ocular hypertensives was significantly smaller than in normals, but was not significantly different between normal and glaucoma eyes. Similarly, strain in selected OCT images of live monkey eyes have been presented, with 30 second IOP increase from 10 to 30 mmHg causing estimated 3.79% compressive strain in LC.⁸⁸

In the present study, we measured both LC anterior border displacement and the overall and regional strain fields of the defined LC volume in response to an IOP decrease 20 minutes after laser suturelysis. The LC depth change and LC strains were compared to the degree of IOP lowering and to the degree of glaucoma damage indicated by retinal nerve fiber layer (RNFL) thickness and visual field indices, mean deviation (MD), and visual field index (VFI). For the first time, we also investigated the relationship between LC depth change and the various types of LC strains, including tensile, compressive, and shear strains.

METHODS

Experimental subjects

This study was approved by the Institutional Review Board of the Johns Hopkins School of Medicine and written informed consent was obtained from patients prior to imaging. The study adheres to the tenets of the Declaration of Helsinki and can be found at ClinicalTrials.gov Identifier: NCT03267849. The eyes of 26 patients of the Wilmer Eye Institute with primary open angle glaucoma underwent imaging by spectral domain OCT (SD-OCT, Spectralis, Heidelberg Engineering, Heidelberg, Germany) immediately before and 20 minutes after laser suturelysis in the post-operative weeks after trabeculectomy. Their ages ranged from 53–86 years (mean: 67.9 ± 8.2 years, median: 67 years). One patient had suturelysis surgery in both the left and right eye, and two patients had repeat suturelysis in the same eye, which resulted in a total of n = 29 image pairs of 27 eyes from 26 patients. Inclusion of the small number of samples from the same persons did not substantively alter any of the analyses presented.

The thickness of the RNFL was measured by Cirrus OCT (Zeiss, Dublin, CA) and the visual field parameters, mean deviation (MD) and visual function index (VFI), were recorded from HFA 24–2 SITA Standard field tests (Zeiss, Dublin, CA) for each patient as part of routine diagnostic testing for glaucoma in an examination within 3 months of the suturelysis procedure. The stage of glaucoma damage of the 26 patient eyes varied from mild to severe, with MD ranging from −0.17 to −29.2 decibels (mean: −10.9 ± 9.05). Of the 27 eyes, 9 (9 patients) had mild glaucoma (MD > −6 decibels), 7 (6 patients) had moderate glaucoma (−12 < MD < −6 decibels), and 11 (11 patients) had severe glaucoma (MD < −12 decibels).

OCT Imaging

IOP was measured using an iCare tonometer (iCare Finland Oy, Espoo, Finland) immediately before each imaging session. The recorded IOP was the average of two mean measurements of 6 IOPs each. The baseline IOP of the patients before suturelysis ranged from 13–51 mmHg and the IOP decrease after suturelysis ranged from 2–45 mmHg (mean: 11.9 ± 8.9 mmHg). The iCare tonometer values were compared to Goldmann applanation tonometric values on each eye performed immediately before initial iCare measurement. There was no statistically significant pairwise mean difference between the iCare and Goldmann measurements (mean difference = 0.3 ± 3.9 mmHg, median difference = 0, paired t-test p = 0.71). Axial length was measured with the IOL Master instrument, which measures the distance from the corneal surface to the retinal pigment epithelium. This was performed in 28 lysis procedures (26 eyes from 25 patients). In 16 eyes of 15 persons, we also measured the axial length at the time of the second imaging after IOP lowering. For each imaging session, 24 radial SD-OCT scans were acquired in enhanced depth imaging, a variation on standard technique which uses a closer scanning position to improve depth resolution. The scans were 768 × 495 pixels in (R, Z) and centered on the ONH, with 7.5° between adjacent scans. The resolution in the anterior-posterior (Z) direction was constant at 3.87 μm/pixel and resolution in the radial (R) direction varied from 5.33 to 6.94 μm/pixel, as corrected by keratometry readings entered immediately prior to each image set. At least three sequential sets of images were taken at each imaging session, and the pair of images with the best contrast from baseline and post-IOP lowering sessions were chosen for analysis. Two sequential sets of images from the baseline session were used to estimate the DVC baseline and correlation errors, using the method developed in previous work.⁸⁰ Prior to DVC, the contrast of the OCT scans was enhanced by contrast-limited, adaptive piecewise histogram equalization (CLAHE) in FIJI (https:imageJ.net), an open source image processing platform. A gamma correction of 1.75 was applied to the image histogram to reduce noise and the settings were selected to minimize the baseline strain error.⁷ The enhanced images were then imported into MATLAB 2019a (Mathworks, Natick, MA) and reconstructed into a matrix of 8-bit intensity values for DVC.

Image Segmentation

On each of the 24 radial scans, a trained observer manually marked the termination of Bruch’s membrane on each side of the ONH, delineating the position of Bruch’s membrane opening (BMO). The observer also marked the anterior border of the LC at the baseline IOP using FIJI (Figure 1).^78,80 The manually marked positions were fit using piecewise linear interpolation due to the varied shape among eyes to generate a smooth boundary for each LC. The intra-observer and inter-observer reproducibility of the manual marking method were demonstrated in prior work.⁸⁹ The LC was defined as the region within the BMO delineating vertical lines and from the anterior LC border to 250 μm posterior to it, with the posterior limit represented by a curvilinear parallel to the anterior border (Figure 1).⁹⁰ This choice of a posterior LC limit was made because in most SD-OCT images there is no distinct change in contrast at the start of the myelin line, the actual posterior LC border. The choice of 250 μm thickness for the LC was based on histological measurements of the actual human LC⁹⁰ and is a conservative estimate designed to avoid inclusion of tissue posterior to the LC, even in eyes with thin LC as has been suggested in some glaucoma eyes.

Figure 1:

A: An OCT radial image after enhancement; B: Segmentation of LC (blue), and BMO. The division into 4 quadrants and into 12 clock hours is illustrated lower left and into central and peripheral LC is shown lower right. Right eye images were reversed left to right to present all data as left eyes; e.g., clock hour 3 represents a temporal region for both left and right eyes.

The LC volume was divided into a central and peripheral region with the central region diameter half of the BMO diameter. LC volume was also divided into 4 quadrants and into 12 clock hour regions (Figure 1) to analyze for the detailed relationships between strains and both LC depth change and degree of glaucoma damage (RNFL thickness). Each clock hour region consisted of 4 adjacent radial half scans extending only to the central point, without including any half scan in two adjacent clock hour data. The clock hours were defined starting from the superior axis, moving clockwise such that 3 o’clock coincided with the temporal axis, 6 o’clock with the inferior axis, and 9 o’clock with the nasal axis (all projected as left eyes, Figure 1).

DVC method to estimate LC strains and LC depth change

The details of the DVC method, DVC error estimations, and strain calculations were described in our previous publication.⁸⁰ In brief, the 3-dimensional images, reconstructed from the 24 radial scans acquired from before and after, were divided into overlapping sub-volumes surrounding points of a grid in (R, Z, Θ). For each sub-volume in the before (reference) image, the DVC algorithm searched the after image for the sub-volume with the best matching pattern of image intensity to calculate the displacement of the reference grid points in all 3 spatial dimensions.

We extended the Fast-Iterative DVC algorithm developed by Bar-Kochba et al.⁹¹ to calculate the 3-dimensional U_r, U_z, U_θ, representing radial, depth and circumferential displacements. The algorithm iteratively refines the size of the sub-volume from 256 × 256 × 32 to 2 × 2 × 1 in (R, Z, Θ) to better resolve large spatial variations in the displacements. The quality of the match of the sub-volumes in the 2 sets of images is given by the correlation coefficient. A low correlation coefficient indicates a poor match of the sub-volumes and usually occurs because of low contrast (featureless) or noise. Points with a correlation coefficient below a threshold of 0.055 were excluded. The percent area correlation was defined as the area of the radial scans with DVC correlation divided by the total area of the radial scans. Overlying blood vessels mask some areas of the LC, typically in the peripheral LC, so that the entire LC is not analyzable in all regions. The average percent area correlation of the LC with accurate DVC correlation over all 29 image sets was 58.56% ± 15.85%.

The change in LC depth was calculated as the displacement, U_z, relative to the displacement of a line connecting the two BMO points, averaged over all radial scans. While it is recognized that the BMO position also changes to some degree with IOP decrease, there is no other reference standard available in the image to estimate LC depth change, and this method has been widely used in this research area.

The components of the Green-Lagrange strain tensor, E_rr, E_θθ, E_zz, E_rθ, E_zθ, E_rz, were calculated by first smoothing the displacements, then calculating the gradient in a cylindrical coordinate system. For a given point in the LC, a positive (tensile) E_zz indicates an increase in thickness at that point, while a tensile E_rr or E_θθ denotes a lengthening in the radial or circumferential directions. The shear strains indicate a local shape distortion, where E_rθ distorts a circular cross-section into a rotated ellipse, E_rz transforms a right circular cylinder into an oblique cylinder, and E_zθ twists the cylinder. The E_zz, E_rr, and E_rz strains were used to calculate the maximum principal strain, E_max, and maximum shear strain, Γ_max, over all orientations in the RZ plane (plane of the radial scan). We calculated the E_max and Γ_max over all orientations in RZ rather than overall orientations in three-dimensions because the resolution in the Θ direction (scan direction) is lower than in the R and Z directions. Moreover, the uncertainties in the displacement and strains in the circumferential direction are nearly twice those in the R and Z directions.

For each eye, we calculated the baseline strain errors of the DVC calculations by performing a DVC analysis using 2 consecutive image volumes acquired at the same IOP. DVC correlation errors were calculated by numerically applying a rigid body displacement and triaxial strain to the image volume at the reference IOP, then applying DVC to the numerically deformed and reference volumes.⁸⁰ The difference between the applied displacement and the measured displacement was defined as the DVC correlation error. Baseline errors estimated the reproducibility between images, while DVC correlation errors estimated the accuracy of the DVC method given distortion to the image patterns caused by deformation but no imaging error. The DVC baseline and correlation errors for all displacement and strain components for the 29 image pairs are given in Supplement Tables S1, S2. The average baseline and correlation errors for the displacement, U_z, in the anterior-posterior direction were −0.04 ± 0.21 μm and 0.66 ± 0.12 μm, respectively, which were smaller than one pixel, the unit of data in such images. The average baseline and correlation errors for E_zz were 0.07% ± 0.12% and 0.47% ± 0.13%, respectively. We evaluated the repeatability of the DVC calculations for 3 patients by correlating 2 image volumes taken from 2 different imaging sessions, separated by 20 minutes. The average repeatability error for E_zz was 0.05%±0.09%, which was comparable to the average baseline error.

Statistical analysis

The primary outcomes were: LC depth change, the 6 strain components, and the two overall strain magnitudes, E_max and Γ_max. These were compared for the whole LC, for central and peripheral LC, for data divided into 4 quadrants (superior, inferior, nasal, temporal), and for each of the 12 clock hour regions. Linear regression was used to examine the relationships between IOP change and the average strains and the LC depth change. The compliance of the strain response and LC depth change were defined by dividing strains and LC depth change by the magnitude of IOP decrease in that eye. The relationship between the biomechanical outcomes and the structural and functional measures of glaucoma damage was examined by comparing the RNFL thickness and visual field status of each eye. There were no consistent differences in primary outcomes by age (Table 1). Nor were there differences by sex or race. To account for degree of IOP change when comparing strains or LC depth to degree of glaucoma damage, multivariable linear regression models were used in which strain or LC depth was the dependent variable, while IOP change and RNFL or MD or VFI were the independent variables. Linear regression was applied to determine the relationships between the compliance of both the strain response and the LC depth change with RNFL thickness, MD, or VFI. To investigate the relationship between the strain response, LC depth change, and regional glaucoma damage, the clock hour averaged strain responses and LC depth change were compared to the clock-hour RNFL thickness. A statistically significant result was defined as having p ≤ 0.05. Bonferroni corrections were applied as appropriate when multiple comparisons were made to the same outcome. For example, comparing strain outcomes at the 12 clock hour regions, we used the more stringent Bonferroni correction of p < 0.004 for statistical significance. One of the 29 patients did not have reliable RNFL measurements; thus only 28 samples were used to determine the relationship between strain compliance and RNFL thickness. For some clock hours, the average LC depth change and strains could not be calculated because DVC correlation did not reach the acceptable threshold of 0.055. The analysis for each clock hour had data from at least n = 27 samples from 24 patients. The average percent area correlation of the LC in the clock hours was 58.03% ± 22.84%. Clock hour 8 (inferior-nasal) had the lower percent area correlation 45.54% ± 19.34%, and clock hour 2 (superior-temporal) had the highest percent area correlation 73.95 % ± 19.85%.

Table 1:

Data are mean/standard deviation for 29 suturelysis procedures, IOP in mmHg, axial length in millimeters, field data in decibels, and retinal nerve fiber layer thickness (RNFL) in micrometers. Axial length and RNFL thickness were measured in 28 of the 29 procedures.

Age	67.2 ± 8.5
Sex	15M, 14 F
Baseline IOP	25.0 ± 8.7
Change IOP	−11.9 ± 8.9
Axial length	25.5 ± 1.3
MD field	−11.5 ± 8.9
VFI field	0.67 ± 0.28
RNFL thickness	63.0 ± 12.2

RESULTS

LC depth change with IOP decrease

The displacement of the LC surface relative to BMO was defined as positive if the LC moved out of the eye with IOP lowering and negative if it moved into the eye. Among all eyes, the mean LC depth did not significantly change with IOP lowering: 1.33 ± 6.26 μm (p = 0.26). The range of LC displacement was from +14.14 to −18.20 μm, indicating that the mean movement contained a mixture of eyes in which the LC went into the eye at lower IOP and eyes in which it moved outward on IOP lowering. The change in LC position was not significantly related to the magnitude of IOP lowering (regression R² = 0.027, p = 0.39). Likewise, the LC depth change was not related to visual field MD or VFI in multivariable analysis including IOP change (p = 0.52, 0.74, respectively). The compliance of LC depth change was defined by dividing its displacement by its IOP change. There was a tendency for LC compliance overall to be greater with thinner RNFL (regression R² = 0.13, p = 0.058), and in regional comparisons, both the inferior and nasal quadrants had greater LC compliance with thinner RNFL in those quadrants (regression R² = 0.14, p = 0.043, 0.026, respectively).

Strains with IOP decrease

IOP decrease produced uniformly tensile mean anterior-posterior strain, E_zz = 0.94% ± 1.2% (p = 0.0002) (Figure 2) and compressive radial strain E_rr = −0.19% ± 0.33% (p = 0.004), indicating that the LC on average expanded in thickness and contracted in radius (Table 2, Figure 3). The baseline and correlation errors for strains are shown in Supplemental Table S3, and all data given are for strains that exceeded both types of error. The central region did not significantly differ from the peripheral region in any overall mean strain value (paired t tests, p ≥ 0.50). There were no significant differences among the 4 quadrants in overall mean strain values (ANOVA by quadrant, p ≥ 0.68).

Figure 2:

The contour of local maximum principal strains, E_max, from DVC of a 12–6 o’clock radial scan.

Table 2:

LC strains with IOP decrease. P values for t tests for difference from no change.

	Strain Outcomes
	Mean	std	p-value
E zz	0.0095	0.012	0.00020
E rr	−0.0019	0.0033	0.0043
E θθ	−0.0021	0.0098	0.26
E rθ	0.0019	0.0055	0.072
E zθ	−0.0016	0.0057	0.15
E rz	0.0003	0.0047	0.73
E max	0.018	0.015	<0.0001
Γ max	0.015	0.011	<0.0001

Figure 3:

Overall mean E_zz and E_max, were significantly positive (tensile), E_rr was significantly negative (compressive), and the maximum shear strain was significantly positive with IOP decrease. * = p values <0.005.

A larger IOP decrease produced a larger, more tensile E_zz (p < 0.0001), greater E_max (p < 0.0001), and greater Γ_max (p < 0.0001, Table 3). The intercept, the predicted strain at 0 mmHg change from linear regression, was −0.13% for E_zz, which was comparable to our measurement of baseline error in sequential image sets at the same IOP for E_zz (−0.11% ± 0.14%).

Table 3:

Linear regression analysis comparing strain to IOP decrease.

	Strain at zero IOP	Change in strain per 10mmHg decrease	p-value	R2
E zz	−0.0013	0.009	<0.0001	0.45
E max	0.0027	0.013	<0.0001	0.57
Γ max	0.0041	0.0088	<0.0001	0.47

Strains with axial length

The baseline axial length was compared to each of the strain measures. Longer axial length was associated with greater compressive hoop strain, E_θθ (p = 0.008) and with greater in plane shear strain, E_rz (p = 0.02). The mean change in axial length for 16 eyes of 15 patients was not significantly greater than zero (−0.033 ± 0.074 mm, p = 0.11, paired t test). Due to the fact that the axial length as measured by the IOL Master includes change in choroidal thickness, and as previously published, IOP-lowering would lead to choroidal thickening by 3 μm/mm Hg IOP change,⁹² the average expected choroidal thickening for a mean IOP change of 11.9 mm Hg would be 0.036 mm, which is nearly identical to the mean axial length change measured here. As expected, we found that the change in axial length was highly associated with change in IOP (linear regression R² = 0.50, p = 0.0033) (Supplemental Figure S1). Therefore, we carried out further analyses using change in IOP as the operative variable representing these two highly correlated parameters.

Relation of strains to LC depth change

Average LC depth change was associated with shear strains, but was not significantly related to tensile or compressive strains (Supplemental Table S4). LC displacement into the eye was associated with larger maximum shear strain, Γ_max (p = 0.014) and with positive shear strain, E_rθ (p < 0.0001, Figure 4). The average LC depth change did not vary significantly with E_max, nor with the normal strains, E_zz, E_rr, and E_θθ.

Figure 4:

The more anterior the LC displacement change, the more positive the (A) shear strain, E_rθ (p < 0.0001) and (B) maximum shear strain, Γ_max (p = 0.014).

In comparisons of clock hour averaged LC depth change and strains, there was more anterior LC displacement (into the eye) with greater E_max in clock hours 3–6 (temporal and inferior regions; Figure 5), and E_rr in clock hours 4–5 (p < 0.004; Supplementary Tables S5 & S6). By contrast, more posterior LC displacement (out of the eye) was associated with greater normal strains, E_max in 10 o’clock (nasal region; Figure 5) and E_rr and E_zz in clock hours 10–11 (p < 0.004). Shear strains Γ_max and E_rθ followed a similar trend in the temporal and inferior regions. More anterior LC displacement was significantly associated with greater shear strains, Γ_max in clock hours 3, 5, 6 (Figure 5) and E_rθ in clock hours 2, 5, 7, 8 (p < 0.004).

Figure 5:

Significant relationships (colored clock hours) are indicated in inferior-temporal 3–6 clock hours between more anterior LC movement and positive (A) E_max and (B) Γ_max strains. At 10 o’clock, more posterior LC movement was related to more positive Emax strain (A).

Outcomes related to overall and regional glaucoma damage

The maximum principal strain, E_max, and the maximum shear strain, Γ_max, were significantly greater in eyes with lower mean RNFL thickness (p = 0.047, 0.037 in multivariable regression adjusting for IOP decrease). The effect of IOP decrease was nearly 3 times greater than the effect of RNFL thickness (Supplemental Table S7). The compliance of strain outcomes (strain/IOP decrease by eye) was compared to RNFL thickness, MD and VFI in linear regression models. Compliance of strains was greater with thinner RNFL for E_rθ (p = 0.018), Γ_max (p = 0.052) and E_max (p = 0.044; Figure 6). The compliance of E_rθ (p = 0.024), Γ_max (p = 0.021), E_max (p = 0.041), and E_rz (p = 0.0069; Supplemental Figures S2–S5) was greater with worse (more negative) MD. Lower VFI was associated with greater compliance of shear strains E_rθ (p = 0.040), Γ_max (p = 0.055), and E_rz (p = 0.015; Supplemental Figures S2, S4, S5). The compliance of LC depth change was not associated with MD, nor VFI.

Figure 6:

There was greater compliance, defined as strain divided by ΔIOP, with worse clinical glaucoma status. A: Greater compliance of E_max was associated with a thinner RNFL (p = 0.044) (n = 28, 25 patients), B: greater compliance of Γ_max was associated with more negative MD (p = 0.021) (n = 29, 26 patients), and C: greater compliance of E_rz was associated with lower VFI (p = 0.015), (Supplemental Tables S8–S10).

A detailed comparison of the regionally averaged compliance of clock hour strains yielded no statistically significant relationships when accounting for Bonferroni correction (p < 0.004) (Supplemental Tables S11 & S12).

DISCUSSION

There have been many publications on changes in anterior LC border position with change in IOP, induced either acutely or monitored after medium- to long-term change in IOP from glaucoma surgery. Since this parameter is relatively easy to identify in OCT images, initial studies marked one to 3 locations using BMO position as a reference. Later studies produced polynomial fits across the LC width or generated single indices of the 3-dimensional LC border shape. There was inconsistent movement of the LC border when even substantial increases in IOP were induced acutely by ophthalmodynamometry, while longer term observations indicated major displacements. These findings taken together seem to indicate that short-term measurements fail to detect movement due to resistance to biomechanical stress of the ONH region. Longer observations include not only short-term mechanical behavior, but remodeling of cellular and connective tissue ONH elements. The present experiments purposefully allowed 20 minutes after IOP lowering to capture the initial viscoelastic responses, without including remodeling events. We also constructed a 3-dimensional model of the LC border from 24 images, but did not reduce its structure to a single index, rather reporting its mean position and regional and clock hour behaviors.

Our data show that the LC anterior border can move either into or out of the eye with IOP decrease. This is intuitively puzzling, since we might expect that a lowering of the translaminar pressure gradient would always allow internal motion of the LC. However, our past research⁷⁸ found, as confirmed here, that the LC movement can be in either direction, but has net zero in mean displacement with the present conditions and methods, and depends upon various additional factors. More LC displacement into the eye was significantly associated with greater normal strains, E_rr, E_zz, and E_max, in clock hours 3–6 (temporal and inferior regions). By contrast, more posterior LC displacement out of the eye was associated with greater normal strains at 10 o’clock (nasal region) and 10–11 o’clock (E_rr, E_zz). This suggests that behavior of the ONH is not that of a regular structure with uniform behavior throughout its volume. We and others have proposed that this seemingly anomalous behavior is related to the dominance of the PPS hoop stress over the translaminar pressure gradient in many eyes. With lowered IOP, the reduction in PPS stress (outward) on the LC would in some eyes permit a bowing out of the eye. We plan to continue the present investigations on OCT imaging in living eyes with IOP change to measure PPS strains and to elucidate this hypothesis.

While the LC can move either into or out of the eye with IOP reduction, the measured LC strains were dominantly in one consistent direction for each strain component. For example, in the anterior—posterior axis, the E_zz strains were mainly positive or tensile, indicating that when IOP is lower, the LC increases its thickness by about 1% with the present IOP changes and duration, much like an accordion opening more. At the same time, the radial strain consistently decreased at lower IOP, as expected from the speculation above that the reduction in PPS hoop stress would lead to LC contraction. Surprisingly the mean maximum shear strain, Γ_max, was nearly as large as the maximum tensile strains E_max. The magnitude of LC strains reported here are within ranges estimated by others using different methods in human eyes. Our E_zz of 0.9% ± 1.2% was similar to that reported by Midgett et al⁸⁰ with similar IOP decreases following suturelysis (E_zz = 0.76% ± 0.24%). We calculated the effective strain to compare with previous studies of Girard and coworkers. Using the formula for effective strain given in Girard et al.⁸³ the average effective strain of the 29 image sets was 4.61% ± 3.0%, which was in line with average effective strain reported by Beotra et al.⁸¹ (3.96% from IOP elevation from approximately 15 to 45 mmHg), Wang et al.⁸⁴ (5.81% ± 2.07% from an IOP elevation of 21.13 ± 7.61 mmHg). Girard et al.⁸³ reported a higher effective strain (8.6%) from trabeculectomy. However, the strain measurements were made up to 50 days after trabeculectomy and can include the effects of remodeling.

The greater the IOP lowering, the greater were the strains, such as E_max and Γ_max. Linear regression showed that the strain intercept at no IOP change was comparable with the baseline errors calculated from two consecutive images in one imaging session and also the correlation error between two images from different imaging sessions. This confirms that DVC strain errors are low and validates the strain values. Given that IOP decrease was a dominant factor in strain responses, we calculated the compliance parameter, strain per mmHg IOP change for each eye, and compared it to clinical measures of glaucoma damage. In every strain measure that had a significant relationship to glaucoma damage, the compliance was greater with worse clinically determined damage. The compliance of E_max was greater with thinner RNFL and worse MD, the compliance of Γ_max and E_rθ were greater with worse RNFL, MD and VFI, and the compliance of E_rz was larger with worse MD and VFI.

These results may seem inconsistent with many past reports that the eye, the sclera, or the LC become stiffer or are stiffer than normal in glaucoma eyes. When examining past research suggesting glaucoma is associated with stiffer connective tissue, it is important to consider where and how past measurements were made. Often, the limitations of study in enucleated eyes of humans or monkey led to study only of the sclera in general and not the vital PPS or ONH area. Further, they often were limited to surface measurements, not through thickness assessments. In fact, it has only recently been possible to measure LC strains in living human eyes with glaucoma as performed here. We conducted ex vivo inflation tests of LC in normal and glaucoma donors and found that while mildly damaged eyes had stiffer strain responses than normals, strains for more damaged glaucoma eyes were larger than those with mild damage.⁴⁵ This is consistent with our finding in vivo that LC compliance was greater in those with more damage. Our further study of data from post mortem LCs found that their LC curvature in inflation testing was greater with greater damage, implying a more compliant response.⁹³ Both monkeys with chronic IOP elevation⁹⁴ and human glaucoma eyes⁹⁵ are reported to have thinner than normal LC, which would be more compliant all other factors being the same.

The relationship of LC depth change to shear strains is an intriguing finding in these data. Much attention has been placed on anterior—posterior tissue movements, but off-axis mechanical displacement could potentially be important in axon damage at the ONH. LC depth change was predictive of shear strains, E_rθ and Γ_max, but not normal strains. Although shear strains have not been reported by other groups in living patients in vivo, Yan et al.⁹⁶ proposed that shear stresses might be an important factor in the LC. They speculated that since IOP elevation results in LC displacement without the LC thickness change, shear may be the result. Midgett et al⁸⁰ found E_max and Γ_max were significantly greater with greater LC depth change in our initial series of in vivo OCT strain measurements. Quigley et al.⁹⁰ reported the LC in histological studies to develop a W-shape rather than the normal mild U-shape. Such longer-term remodeling may be more likely to generate shear strains.

There are multiple limitations of this study that should be considered. Our use of radial OCT images inevitably produced E_θθ, E_rθ, and E_zθ strains that were calculated with lower imaging resolution and higher error and uncertainty than the in-plane strains. To exclude these strain components, we chose to analyze the maximum tensile stress, E_max, and the maximum shear strain, Γ_max, in the plane of the radial scan rather than over all 3 dimensions. The resolution of SD-OCT is not sufficient to determine microstructural details, such as the dimensions of individual LC connective tissue beams, as we were able to do with post mortem eye evaluations by laser scanning microscopy.^44,93 This study only examined strains after suturelysis following glaucoma surgery with a 20-minute spacing between images. While we had a full range of glaucoma damage represented, it will be important to include both normal eyes and eyes with glaucoma who did not undergo surgery to broaden the generalizability of the findings. Further, we note that LC depth changes after suturelysis in a prior study were larger than those reported here. In that prior work, we included some rapidly spaced image pairs, while in other cases days to weeks separated the baseline and follow-up images, therefore including remodeling effects. We are now engaged in comparing longer term images of the persons included here to assess change over time. Finally, cross-sectional observations, as in this study, cannot determine whether the individuals and their present strains were the same at the onset of disease. This would permit differentiation of the two major potential explanations of these data: 1) more severe glaucoma-damaged persons are more damaged because their ONHs were more compliant at baseline, or 2) the more severely damaged eyes were normal in stiffness or stiffer at baseline and have become more compliant over time. We are designing a longitudinal study of ONH strains that can answer these questions by measuring strains over time.

In summary, we carried out detailed studies of change in the LC of glaucoma patients with short-term IOP lowering. The LC can move either into or out of the eye when IOP is reduced, and the change is related to the degree of IOP change. Strains within the LC are uniformly tensile at lower IOP and independent of the direction of LC border movement. The LC strains are greater in eyes with worse clinical measures of glaucoma damage. Shear strains are nearly as substantial as in-plane strains and were associated with movement of the LC anterior border.

Abbreviations:

LC

lamina cribrosa

ONH

optic nerve head

PPS

peripapillary sclera

SD-OCT

spectral domain optical coherence tomography

RNFL

retinal nerve fiber layer

MD

mean deviation

VFI

visual function index

IOP

intraocular pressure