Abstract

The lamina cribrosa (LC) is a connective tissue in the optic nerve head (ONH). The objective of this study was to measure the curvature and collagen microstructure of the human LC, compare the effects of glaucoma and glaucoma optic nerve damage, and investigate the relationship between the structure and pressure-induced strain response of the LC in glaucoma eyes. Previously, the posterior scleral cups of 10 normal eyes and 16 diagnosed glaucoma eyes were subjected to inflation testing with second harmonic generation (SHG) imaging of the LC and digital volume correlation (DVC) to calculate the strain field. In this study, we applied a custom microstructural analysis algorithm to the maximum intensity projection of SHG images to measure features of the LC beam and pore network. We also estimated the LC curvatures from the anterior surface of the DVC-correlated LC volume. Results showed that the LC in glaucoma eyes had larger curvatures p0.03), a smaller average pore area (p=0.001), greater beam tortuosity (p<0.0001), and more isotropic beam structure (p=0.01) than in normal eyes. The difference measured between glaucoma and normal eyes may indicate remodeling of the LC with glaucoma or baseline differences that contribute to the development of glaucomatous axonal damage.

1 Introduction

The lamina cribrosa (LC) is a connective tissue that forms part of the eye wall in the optic nerve head (ONH). The LC functions to support the capillaries, cells, and axonal structures of the ONH from the various loading conditions imposed by the intraocular pressure (IOP), intracranial pressure, and extraocular muscles [1]. The human LC is formed from a stack of cribriform plates composed of elastin, collagen types I and III, and various proteoglycans [2]. When viewed en face, the plates resemble a beam and pore network structure. Retinal ganglion cell axon injury has been shown to occur at the LC in human glaucoma eyes and in animal models of glaucoma with a prolonged increase in IOP [3]. The severity of axon damage in glaucoma is strongly associated with IOP, and higher IOP is associated with an increased prevalence of the disease [4,5].

The LC has been shown to remodel with glaucoma. The plate-like structure thins and becomes more curved with progressive axonal damage [6]. The collagen density in the LC beam decreases [7] and the pores may become smaller [8]. In the normal LC, axons and glial cells fill LC pores. However, Morrison et al. [9] found collagen types IV, I, and III in the LC pores of experimental glaucoma monkey eyes, and Hernandez et al. [10] also showed collagen type IV extending into the LC pores of moderately and severely damaged glaucoma human eyes. Ex vivo inflation studies, including those from our group, showed that the pressure-strain response of the LC was stiffer in glaucoma eyes [11] and in the eyes of older donors [12,13]. Therefore, the structure, curvature, and mechanical behavior of the LC are important aspects of glaucoma that may differ between diagnosed glaucoma eyes and normal eyes and with the severity of glaucomatous axon damage.

Previously, Ling et al. [14] developed a method to characterize the microstructure of the LC from second harmonic generation (SHG) images and applied the method to measure the LC beam and pore microstructure of normal human eyes, from donors with a wide range of ages, previously subjected to inflation testing by Midgett et al. [13] The results showed that the strain response of the LC to inflation was stiffer for microstructural features that indicated greater connective tissue density, wider beams, straighter beams, and greater beam connectivity. Other groups have measured strain in the LC using SHG imaging and digital volume correlation (DVC) [12,15,16]. Albon et al. [12] found a stiffer strain response with age in normal eyes. Sigal et al. [15] found significant amounts of in-plane LC stretch and compression when measuring LC deformation in two-dimensional (2D). Behkam et al. [16] measured significantly different shear strains between Hispanic, African-derived, and European-derived groups. In this study, we applied the method of Ling et al. [14] to characterize the beam and pore microstructure of the LC of glaucoma and age-matched normal eyes previously subjected to inflation testing by Midgett et al. [11] We also developed an automated method to estimate the LC curvature from the SHG image volumes. The LC curvature is challenging to measure. The deep position of the LC in the ONH beneath the prelaminar neural tissues and the thickness of the LC prevent optical methods, such as SHG, from imaging the full depth of the tissues. The surface of the LC is also irregularly shaped, and the LC curvature can exhibit large local variations. Prior OCT imaging studies reported surrogate measures of the LC curvature. For example, the LC curvature index is defined as the maximum depth of the anterior surface of the LC divided by the width of the Bruch's membrane opening times 100 [1719]. Girard and coworkers also defined an LC global shape by estimating the maximum and minimum curvatures of the LC anterior surface from radial curves produced by manually marking the LC anterior surface in radial cross sections passing through the center of the Bruch's membrane opening [20,21]. Sredar et al. [22] calculated the local mean curvature of the LC by fitting a thin-plate spline to manual markings of the anterior LC surface. For this study, we developed an automated method to estimate the curvature of the LC from a three-dimensional reconstruction of the LC volume obtained from the DVC of SHG images. The curvatures and microstructural features were analyzed for the effects of glaucoma diagnosis and the severity of axon damage in the optic nerve. We also investigated the relationships between the structural features and the strain response of glaucoma eyes and compared them to those of normal eyes.

2 Methods

2.1 Specimens and Specimen Preparation.

The specimens and specimen preparation method were described in detail in Midgett et al. [11]. Briefly, we received 10 eyes from 6 Caucasian donors with no history of glaucoma and 16 eyes from 8 Caucasian donors with glaucoma diagnosis within 24 h postmortem from National Disease Research Interchange, Eversight, and the Minnesota Lions Eye Bank (Table 1). The average age was 83.8 ± 6.1 years for normal eyes and 87.3 ± 5.4 years for glaucoma eyes. The optic nerve was cut 1 mm posterior to the sclera and used to qualitatively evaluate for axon loss by a glaucoma specialist (H.Q.) [4,2328]. We calculated the imaged LC thickness by counting the number of slices with visible LC signal and multiplying by the slice spacing (Table 1). Optic nerves with 25% or less axon loss were labeled as mildly damaged (GM), and those with greater than 25% axon loss were graded as more severely damaged (GS). Undamaged normal (NU) eyes were eyes with no history of glaucoma and with less than 10% optic nerve axon damage. Two out of 10 normal eyes had axonal damage in greater than 10% of the optic nerve and were labeled normal damaged (ND).

Table 1

Posterior sclera specimens from human donors with glaucoma and without glaucoma (normal)

System IDDiagnosisSexAge (year)GlaucomaEyeONH damageImaged LC thickness (μm)
H1482NormalMale88NoneLeftND215
H1487NormalFemale93NoneRightNU350
NoneLeftNU225
H1494NormalMale79NoneRightNU270
NoneLeftNU415
H1497NormalMale76NoneRightNU160
H1500NormalFemale83NoneRightND145
NoneLeftNU135
H1510NormalFemale84NoneRightNU255
NoneLeftNU185
H1501GlaucomaMale91POAGRightGS225
POAGLeftGM140
H1502GlaucomaFemale93ACGRightGM200
ACGLeftGS160
H1504GlaucomaMale86Pseudo-exfoliationRightGS150
Pseudo-exfoliationLeftGM140
H1505GlaucomaMale89UnknownRightGM250
UnknownLeftGM250
H1506GlaucomaMale76POAGRightGM275
POAGLeftGM315
H1507GlaucomaFemale85POAGRightGS220
POAGLeftGS230
H1508GlaucomaFemale92POAGRightGM260
POAGLeftGM215
H1509GlaucomaFemale86POAGRightGS240
POAGLeftUnknown265
System IDDiagnosisSexAge (year)GlaucomaEyeONH damageImaged LC thickness (μm)
H1482NormalMale88NoneLeftND215
H1487NormalFemale93NoneRightNU350
NoneLeftNU225
H1494NormalMale79NoneRightNU270
NoneLeftNU415
H1497NormalMale76NoneRightNU160
H1500NormalFemale83NoneRightND145
NoneLeftNU135
H1510NormalFemale84NoneRightNU255
NoneLeftNU185
H1501GlaucomaMale91POAGRightGS225
POAGLeftGM140
H1502GlaucomaFemale93ACGRightGM200
ACGLeftGS160
H1504GlaucomaMale86Pseudo-exfoliationRightGS150
Pseudo-exfoliationLeftGM140
H1505GlaucomaMale89UnknownRightGM250
UnknownLeftGM250
H1506GlaucomaMale76POAGRightGM275
POAGLeftGM315
H1507GlaucomaFemale85POAGRightGS220
POAGLeftGS230
H1508GlaucomaFemale92POAGRightGM260
POAGLeftGM215
H1509GlaucomaFemale86POAGRightGS240
POAGLeftUnknown265

The optic nerves of all specimens were examined, and the specimens were further classified as NU for undamaged normals with <10% axon loss, ND for damaged normals with >10% axon loss, GM for glaucomas with <25% axon loss, and GS for glaucomas with >25% axon loss. All eyes were cut flush with the posterior sclera and were imaged from the posterior cut surface. All specimens were of Caucasian descent. POAG = primary open angle glaucoma, ACG = angle closure glaucoma.

The posterior scleral shell was placed in a Zeiss 710 laser-scanning multiphoton microscope (LSM 710 NLO, Zeiss, Inc., Oberkochen, Germany) [11,13]. The tissue was pressured by a water column set first to a baseline pressure of 5 mmHg, then 10 mmHg, and 45 mmHg. The tissues were allowed to equilibrate for 25 min after each pressure increase before imaging to minimize the effects of tissue creep. The image volume consisting of a 2 × 2 tiled z-stack was acquired starting at 300 μm below the cut surface using a Chameleon Ultra-II laser tuned to 780 nm with a 390–410 nm bandpass filter for SHG. The z-slices were spaced 5 μm apart. The 512 × 512 pixels tiles were stitched together with a 15% overlap. Duplicate image volumes were acquired back-to-back and used for error analysis (Sec. 2.2). The SHG image volumes were subjected to an iterative deconvolution algorithm (Huygens Essentials, SVI, Hilversum, NL) to reduce blur and noise and to contrast-limited adaptive histogram equalization (CLAHE) [27] in FIJI [28] to bring out dark features.

2.2 Digital Volume Correlation.

The methods for DVC measurement of the displacement field, strain calculation, and error analysis were described in detail in previous works [11,13,14,29]. The Fast Iterative DVC algorithm by Bar-Kochba et al. [30] was used to calculate displacements from 5 to 10 mmHg and from 10 to 45 mmHg. The displacement fields from the two-pressure increments were summed to determine displacements from 5 to 45 mmHg. The displacement components were smoothed locally using linear interpolation functions as described in Midgett et al. [11] The components of the Green–Lagrange strain tensor were evaluated from the smoothed displacement components UX, UY, and UZ as
EXX=UXX+12((UXX)2+(UYX)2+(UZX)2)
(1)
EYY=UYY+12((UXY)2+(UYY)2+(UZY)2)
(2)
EXY=12(UXY+UYX+UXXUXY+UYXUYY+UZXUZY)
(3)
The specimens were oriented such that X corresponds with the nasal-temporal direction, and Y corresponds with the inferior–superior direction for both left and right eyes. The maximum principal strain Emax and maximum shear strain Γmax were calculated for the XY plane as
Emax=EXX+EYY2+(EXXEYY2)2+EXY2
(4)
Γmax=(EXXEYY2)2+EXY2
(5)
A coordinate transformation was used to calculate the cylindrical components of strain as
Err=EXXcos2θ+2EXYcosθsinθ+EYYsin2θ
(6)
Eθθ=EXXsin2θ2EXYcosθsinθ+EYYcos2θ
(7)
Erθ=(EYYEXX)cosθsinθEXY(sin2θcos2θ)
(8)

where Err is the radial strain, Eθθ is the circumferential strain, and Erθ is the shear strain in cylindrical coordinates. The orientation angle θ for a given point was determined by calculating the angle made by a line connecting the center of the central retinal artery and vein (CRAV) to the point with the X axis.

Digital volume correlation displacement and strain errors were calculated for each specimen using two sets of SHG z-stacks acquired back-to-back at 5 mmHG. The SHG z-stacks after contrast enhancement were imported into matlab 2019a (Mathworks, Natick, MA). A rigid body displacement and triaxial strain were applied to the second z-stack using the matlab function imwarp and DVC was applied to correlate the numerically deformed image volume with the undeformed volume. The absolute errors for displacement eUIj, and strain eEIJj for point j were defined as
eUIj=(UIjappUIj)2
(9)
eEIJj=(EIJjappEIJj)2
(10)

Regions with poor contrast and high DVC displacement errors were removed from the image volume by excluding points where the correlation coefficient was less than 0.001 and the absolute displacement error was greater than 2μm (1) pixel. For the LC, this mainly removed regions posterior to the cut surface of the LC and regions beyond the limit of laser penetration in the tissue. The remaining volume with accurate DVC displacements was used to calculate the strain field, the average DVC displacement and strain errors (Supplemental Materials of Midgett et al. [11]), and the curvature of the LC (Sec. 2.3). The LC was segmented by manually marking the boundary between the LC and peripapillary sclera (i.e., scleral canal) on the maximum intensity projection of the SHG image volume after contrast enhancement using FIJI [28]. The mask was extruded in z to segment the LC from the peripapillary sclera and the CRAV. The absolute displacement errors in the LC, averaged over all specimens were 0.79 ± 0.41 μm, 0.54 ± 0.34 μm, and 3.51 ± 2.30 μm for UX, UY, and UZ, respectively [11]. The average absolute strain errors were 0.27±0.27%,0.235±0.25%, and 0.15±0.15% for EXX, EYY, and EXY, respectively [11].

2.3 Curvature.

The SHG images had blurring in the z-direction that made it difficult to objectively mark the anterior surface of the LC directly in transverse sections (Fig. 1). Repeated markings were not reproducible. Therefore, we developed an automated method to approximate the curvature of the anterior LC surface using the volume with accurate DVC displacements (Sec. 2.2). The image volume for the LC with accurate DVC displacements was imported into matlab 2019a and used to estimate the LC curvatures (Fig. 1(a)). The anterior surface of the volume was created by identifying the most anterior Z position for all (X, Y) positions (Fig. 1(b)). The matlabcurve fitting toolbox was used to fit a fifth-order polynomial surface function Z=f(X,Y) to the anterior surface (Fig. 1(c)). Figure 1(d) shows a transverse section through the center of the SHG volume along the nasal-temporal axis for two glaucoma eyes and two normal eyes. The anterior-most points of the DVC volume with accurate correlations are shown in red, and the polynomial surface fit is shown in blue. The polynomial fit for all specimens smoothed out the local fluctuations of the points extracted from the DVC volume. A visual inspection of the nasal-temporal and inferior–superior sections (Fig. 1(d), Supplemental Figures S1–S3 available in the Supplemental Materials on the ASME Digital Collection) for all specimens showed that the polynomial fit provided a reasonable approximation of the anterior LC surface. The principal curvatures were calculated at every point of the polynomial surface using the matlab function surfature [31]. The maximum and minimum curvatures were defined as the largest and smallest principal curvature, respectively. The Gaussian curvature was calculated from the product of the maximum and minimum curvature, and the mean curvature was calculated by averaging the two.

Fig. 1
Schematic of the image processing steps to estimate the curvature of the LC, showing (a) a reconstruction of the LC volume with accurate DVC displacement correlation, and (b) the point cloud representing the most anterior surface of the LC volume with accurate DVC correlation. The blue areas represent steps in the surface at different Z depths. (c) A fifth-order polynomial surface was fit to the point cloud to calculate the principal curvatures. (d) The transverse view of the SHG image of the LC for two representative normal eyes (upper 2) and two glaucoma eyes (lower 2). The anterior most surface of DVC correlation (red), and the fifth-order polynomial fit to the surface (blue).
Fig. 1
Schematic of the image processing steps to estimate the curvature of the LC, showing (a) a reconstruction of the LC volume with accurate DVC displacement correlation, and (b) the point cloud representing the most anterior surface of the LC volume with accurate DVC correlation. The blue areas represent steps in the surface at different Z depths. (c) A fifth-order polynomial surface was fit to the point cloud to calculate the principal curvatures. (d) The transverse view of the SHG image of the LC for two representative normal eyes (upper 2) and two glaucoma eyes (lower 2). The anterior most surface of DVC correlation (red), and the fifth-order polynomial fit to the surface (blue).
Close modal

2.4 Microstructural Analysis.

The method developed by Ling et al. [14] was applied to the SHG images acquired at the baseline 5 mmHg pressure, to measure features of the beam and pore network structure of the LC of normal and glaucoma eyes. The LC of most of the glaucoma eyes was significantly more curved than the LC of normal eyes (Fig. 2). The middle z-slices for glaucoma eyes only contained a thin ring of the collagen network structure with many disconnected beams and open pores. These are discarded by the morphological analysis algorithm, which eliminated a large fraction of pores and beams in certain regions of the LC of many glaucoma eyes. Consequently, we analyzed the maximum intensity projection of the SHG images rather than individual z-slices so that we can calculate regional averages of the pore area fraction, beam connectivity, length, width, and anisotropy. However, the maximum intensity projection may underestimate the pore area more severely for glaucoma eyes with more curved LC than for normal eyes. Thus, we analyzed individual z-slices to calculate the average pore area in the LC. The large curvature of the glaucoma eyes caused most of the pores in the peripheral region to be excluded from the calculation in the middle z-slices because they were not fully enclosed by beams. The resulting average pore area was more representative of the central region of the LC for glaucoma eyes.

Fig. 2
SHG images of the LC acquired at three z-depths and a longitudinal section of the z-stack for a representative (a) glaucoma eye and (b) normal eye. The longitudinal sections show that the LC of the glaucoma eye resembled a curved shell while the LC of the normal eye resembled a plate. The large curvature of the LC of the glaucoma eye caused the middle z-slices to show a thin ring, which corresponds to the peripheral region of the LC.
Fig. 2
SHG images of the LC acquired at three z-depths and a longitudinal section of the z-stack for a representative (a) glaucoma eye and (b) normal eye. The longitudinal sections show that the LC of the glaucoma eye resembled a curved shell while the LC of the normal eye resembled a plate. The large curvature of the LC of the glaucoma eye caused the middle z-slices to show a thin ring, which corresponds to the peripheral region of the LC.
Close modal

A specimen-specific mask of the LC was created by manually marking points on the boundary between the LC and sclera and of the CRAV region in the maximum intensity projection as described in Sec. 2.2. The sclera is significantly denser in collagen than the LC and appears brighter in the SHG images. Therefore, the LC area in the maximum intensity projection excludes portions that may lie underneath the sclera when the scleral canal is at an angle. The area of the LC was estimated by fitting an ellipse to the marked points and calculating the area of the ellipse. For the microstructural analysis, regions with no visible beams were also marked manually and removed from the mask. A modified 2D Frangi filter developed by Campbell et al. [32] was applied to the maximum intensity projection to further enhance the contrast of the LC beams (Figs. 3(a) and 3(b)). The parameters of the 2D Frangi filter are given in the Supplemental Materials (Sec. S1) on the ASME Digital Collection.

Fig. 3
The image analysis for characterizing the microstructural features of the LC starts with (a) the maximum z-projection of the SHG image of the LC and surrounding peripapillary sclera after deconvolution to reduce noise and blur and contrast limited adaptive histogram equalization to bring out dark features. (b) The Frangi filter was applied to enhance the contrast of the beams. (c) The beam network was binarized and segmented from the adjoining peripapillary sclera using the Otsu thresholding method [33]. The custom algorithm by Ling et al. [14] was applied to (d) skeletonize the beam network and calculate microstructural features, such as the (e) nodes in the network where the beams intersect. The nodes are plotted here on the Frangi-filtered image and colored by quadrants. The green lines represent the boundaries dividing the CRAV region, central region, and peripheral regions of the LC.
Fig. 3
The image analysis for characterizing the microstructural features of the LC starts with (a) the maximum z-projection of the SHG image of the LC and surrounding peripapillary sclera after deconvolution to reduce noise and blur and contrast limited adaptive histogram equalization to bring out dark features. (b) The Frangi filter was applied to enhance the contrast of the beams. (c) The beam network was binarized and segmented from the adjoining peripapillary sclera using the Otsu thresholding method [33]. The custom algorithm by Ling et al. [14] was applied to (d) skeletonize the beam network and calculate microstructural features, such as the (e) nodes in the network where the beams intersect. The nodes are plotted here on the Frangi-filtered image and colored by quadrants. The green lines represent the boundaries dividing the CRAV region, central region, and peripheral regions of the LC.
Close modal

After the Frangi filter, the image was imported into matlab and the microstructural analysis function developed by Ling et al. [14]1 was applied to calculate the following features of the LC microstructure.

  • Pore area fraction: The total area of black pixels representing pores within the masked LC divided by the total area of the masked LC. Only pores fully enclosed by beams were included in the calculations.

  • Node density: The total number of nodes, defined as a junction of two or more LC beams, divided by the total area of the masked LC (Fig. 3(e)).

  • Connectivity: The average number of beam connections at a node.

  • Beam length: The average straight-line distance of a skeletonized collagen beam between two nodes.

  • Beam tortuosity: The contour length of the beam divided by its straight-line distance.

  • Beam orientation: The average orientation of the skeletonized collagen beams from π/2 to π/2 measured from the X-direction.

  • Anisotropy: The dispersion parameter of a semicircular von Mises probability density function fit to the orientation of the skeletonized LC beams. An anisotropy of 0 indicates a random distribution and infinity indicates perfect alignment along a dominant orientation.

  • Beam width: The width calculated at the midpoint of the beam.

  • Beam aspect ratio: The beam length divided by the beam width.

A similar procedure was applied to a subset of z-slices from SHG images after deconvolution and contrast enhancement to calculate the area of the LC pores. The substack of z-slices was selected so that a significant portion of the LC was visible in each z-slice. A slice-specific mask was created for every fifth z-slice of the substack by manually marking points on the boundary of regions with visible LC beams. A modified three-dimensional Frangi filter was applied to the z-stack to enhance the contrast of the beams. The enhanced image volume was imported into matlab and the microstructural analysis function was applied to each z-slice to identify the pores. The area of a pore was calculated by totaling the number of pixels in the pore times the spatial resolution of the pixels. The area of the pores was averaged for each z-slice, then averaged over all slices to calculate the average pore area. Only the pores fully enclosed by LC beams were used in the calculation, which meant that pores spanning multiple z-slices in the more highly curved regions of the LC were not included in the average pore area. As a result, the average pore area was excluded from regional comparisons.

2.5 Statistics.

The outcomes of the DVC calculations were the three in-plane strain components, Err, Eθθ,Erθ, the maximum principal strain Emax, and the maximum shear strains Γmax. The outcomes of the curvature calculations were the minimum and maximum curvatures, the mean curvature, and the Gaussian curvature. The outcomes of the microstructural analysis were the 10 microstructural features listed in Sec. 2.4. The outcomes were averaged over the LC volume for statistical analysis. DVC correlation was not possible for one LC from glaucoma as the 2 × 2 tiled z-stacks acquired at 45 mmHg failed to stitch together, and the specimen was excluded from analyses involving strains [11]. Generalized estimating equation (GEE) models were used to analyze the curvatures and microstructural features for the effect of glaucoma diagnosis (normal versus glaucoma) and the effects of axonal damage (NU, GM, and GS). We used the left and right eyes from the same donor, and GEE takes into account the correlation between measurements taken from the left and right eyes of a single donor.

To analyze regional variations, the LC was divided into eight regions. The regions were created by first diving the LC into four quadrants, superior (S), inferior (I), nasal (N), and temporal (T) using 45 deg and 135 deg lines passing through the center of the CRAV (Fig. 4). The quadrants were further divided at the midpoint between the center of the CRAV and the scleral canal opening to create four central regions and four peripheral regions. Regional averages were included in subsequent statistical analyses if the outcome variable could be calculated for at least 40% of the region [11]. Regions with accurate DVC displacement correlation for less than 40% of the volume of the region were excluded from regional analyses for strains. One LC from the normal group had accurate DVC displacement correlation in less than 50% of all regions. The specimen was excluded from regional analyses for strains. For regional measurements, all estimates and p-values were from linear mixed models with glaucoma group or structural parameter as the fixed effect. The models include donor as a random effect to account for the clustering of two eyes for a donor. The models also account for correlations among repeat measurements in different regions of a single eye. The repeat measurements were assumed to have an exchangeable correlation structure, in which any two regions have the same correlation. For some models with outcome change in radial strain in normal eyes, it was necessary to drop donor as a random effect for convergence of the model. Outliers within a group were excluded to improve the normality of model residuals. Outliers were defined as measurements less than the first quartile minus 1.5 times the interquartile range or greater than the third quartile plus 1.5 times the interquartile range. Comparisons were considered significant if the p-value was less than 0.05. All statistical analyses were performed using sas 9.4 (SAS Institute, Cary, NC).

Fig. 4
Regional division of the LC into four central regions, superior (S1), inferior (I1), nasal (N1), temporal (T1), and four peripheral regions, superior (S2), inferior (I2), nasal (N2), and temporal (T2)
Fig. 4
Regional division of the LC into four central regions, superior (S1), inferior (I1), nasal (N1), temporal (T1), and four peripheral regions, superior (S2), inferior (I2), nasal (N2), and temporal (T2)
Close modal

3 Results

3.1 Lamina Cribrosa Curvature.

The LC curvatures were calculated for n =16 glaucoma eyes and for n =9 out of 10 normal eyes from the image volume with accurate DVC displacements. One of the 10 normal eyes did not have accurate DVC displacement calculations in the LC and was excluded from the curvature calculations. The average maximum curvature of the LC of normal eyes (0.350 ± 0.312 mm–1) was 2.85 times larger than the average minimum curvature (Table 2). This resulted in an average Gaussian curvature of 0.0555 ± 0.0713 mm–2, and average mean curvature of 0.203 ± 0.175 mm–1, which corresponds to a mean radius of curvature of 4.93 ± 5.71 mm. The maximum, minimum, Gaussian, and mean curvatures of glaucoma eyes were 1.76 (p =0.03), 2.93 (p <0.0001), 3.55 (p =0.003), and 1.88 (p =0.01) times larger than normal eyes (Fig. 5). A more detailed comparison of the regionally averaged curvatures showed that all the curvature outcomes were significantly larger in glaucoma eyes than normal eyes (p0.005, Supplemental Table S1 available in the Supplemental Materials on the ASME Digital Collection).

Fig. 5
Box plots comparing the specimen-averaged (a) maximum curvature, (b) minimum curvature, (c)Gaussian curvature, and (d) mean curvature for the LC of normal (n = 9) and glaucoma (n = 16) eyes (Table2). The maximum (p = 0.03), minimum (p < 0.0001), Gaussian (p = 0.0003), and mean (p = 0.01) curvatures were significantly larger for glaucoma eyes than normal eyes. For all box plots shown here, the interior line indicates the median, the top, and bottom of the box plot denote the 25th and 75th percentile, respectively. The * indicates outliers, and the whiskers extend to the maximum and minimum values excluding outliers.
Fig. 5
Box plots comparing the specimen-averaged (a) maximum curvature, (b) minimum curvature, (c)Gaussian curvature, and (d) mean curvature for the LC of normal (n = 9) and glaucoma (n = 16) eyes (Table2). The maximum (p = 0.03), minimum (p < 0.0001), Gaussian (p = 0.0003), and mean (p = 0.01) curvatures were significantly larger for glaucoma eyes than normal eyes. For all box plots shown here, the interior line indicates the median, the top, and bottom of the box plot denote the 25th and 75th percentile, respectively. The * indicates outliers, and the whiskers extend to the maximum and minimum values excluding outliers.
Close modal
Table 2

Comparing the specimen-averaged curvature outcomes for the LC of normal (n =9, one eye did not have accurate DVC correlation) and glaucoma (n =16) eyes, showing the estimated mean, 95% confidence interval (CI), and p-value from GEE models

CurvatureGroupMean and 95%CIp-value
Gaussian (1/mm2)Normal0.0555(0.0006,0.110)0.0003
Glaucoma0.197(0.134,0.261)
Mean (1/mm)Normal0.203(0.077,0.329)0.01
Glaucoma0.381(0.320,0.441)
Maximum (1/mm)Normal0.350(0.123,0.576)0.03
Glaucoma0.617(0.519,0.715)
Minimum (1/mm)Normal0.123(0.070,0.176)< 0.0001
Glaucoma0.360(0.279,0.441)
CurvatureGroupMean and 95%CIp-value
Gaussian (1/mm2)Normal0.0555(0.0006,0.110)0.0003
Glaucoma0.197(0.134,0.261)
Mean (1/mm)Normal0.203(0.077,0.329)0.01
Glaucoma0.381(0.320,0.441)
Maximum (1/mm)Normal0.350(0.123,0.576)0.03
Glaucoma0.617(0.519,0.715)
Minimum (1/mm)Normal0.123(0.070,0.176)< 0.0001
Glaucoma0.360(0.279,0.441)

Note: Bold p-values indicate significance.

We next compared the effect of axon damage level on the specimen-averaged curvature outcomes (Supplemental Table S2 available in the Supplemental Materials). The Gaussian curvature (p =0.006) and the minimum curvature (p =0.0004) varied significantly between different damage groups. Pairwise comparisons showed that the Gaussian curvature of more GM glaucoma eyes was 3.34 times larger than that of NU eyes (p =0.015). The minimum curvature of the GM group was 2.82 times larger than that of the NU group (p =0.001, Fig. 6). None of the curvature outcomes differed between the more GS glaucoma and GM glaucoma groups. The Gaussian curvature for the GS group was borderline larger than the NU group (p =0.082).

Fig. 6
Box plots of the (a) Gaussian curvature and (b) minimum curvature comparing normal undamaged (n = 8), more GM glaucoma (n = 9), and more GS glaucoma (n = 6) groups. The Gaussian curvature (p = 0.015) and minimum curvature (p = 0.001) were significantly greater in the GM group than in the NU group.
Fig. 6
Box plots of the (a) Gaussian curvature and (b) minimum curvature comparing normal undamaged (n = 8), more GM glaucoma (n = 9), and more GS glaucoma (n = 6) groups. The Gaussian curvature (p = 0.015) and minimum curvature (p = 0.001) were significantly greater in the GM group than in the NU group.
Close modal

3.2 Lamina Cribrosa Microstructure.

A comparison of the specimen-averaged microstructural features of the LC (Table 3) of normal (n =10) and glaucoma eyes (n =16) showed that the tortuosity of the LC beams was 2.7% larger in glaucoma eyes, which indicates that the beams were slightly more curved (p <0.0001, Fig. 7(a)). The anisotropy of the LC beams was 35.8% lower in glaucoma eyes (0.74 ± 0.31) than in normal eyes (1.15 ± 0.32, p =0.01), which means that the LC beams were less aligned in glaucoma eyes (Fig. 7(b)). However, the dominant beam orientation did not differ between glaucoma and normal eyes and was on average within 4.5 deg–5.5 deg from the X (nasal-temporal) direction. The pore area fraction was nearly identical for both normal and glaucoma eyes (Fig. 7(c)). However, the average pore area was 20% smaller in glaucoma eyes (p =0.001, Fig. 7(d)). Analysis of the regionally averaged microstructural outcomes returned the same results (Supplemental Table S3 available in the Supplemental Materials).

Fig. 7
Box plots of the specimen-averaged (a) tortuosity and (b) anisotropy of the LC beams, and (c) pore area fraction and (d) average pore area comparing normal (n = 10) and glaucoma (n = 16) eyes (Table 3). The LC beams in glaucoma eyes were more curved (p < 0.0001) and less aligned (p = 0.01) than in normal eyes. Pore area fraction did not differ between normal and glaucoma eyes (p = 0.47). However, the average pore area was significantly smaller in glaucoma eyes than in normal eyes (p = 0.001).
Fig. 7
Box plots of the specimen-averaged (a) tortuosity and (b) anisotropy of the LC beams, and (c) pore area fraction and (d) average pore area comparing normal (n = 10) and glaucoma (n = 16) eyes (Table 3). The LC beams in glaucoma eyes were more curved (p < 0.0001) and less aligned (p = 0.01) than in normal eyes. Pore area fraction did not differ between normal and glaucoma eyes (p = 0.47). However, the average pore area was significantly smaller in glaucoma eyes than in normal eyes (p = 0.001).
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Table 3

Comparison of the specimen-averaged microstructural features of the LC between normal (n =10) and glaucoma eyes (n =16), showing the estimated mean, 95% CI, and p-value from GEE models

StructureGroupMean and 95%CIp-value
Pore area fractionNormal0.530 (0.515, 0.545)0.47
(μm2/μm2)Glaucoma0.522 (0.507, 0.537)
Node densityNormal1.03(0.85,1.20)×1040.97
(nodes/μm2)Glaucoma1.02(0.93,1.12)×104
ConnectivityNormal3.09 (3.07, 3.11)0.18
(beams/nodes)Glaucoma3.10 (3.09, 3.11)
Tortuosity (μm/μm)Normal1.12 (1.11, 1.14)<0.0001
Glaucoma1.15 (1.15, 1.16)
Beam length (μm)Normal62.96 (56.06, 69.85)0.40
Glaucoma59.63 (56.21, 63.06)
Beam width (μm)Normal30.52 (29.24, 31.79)0.21
Glaucoma31.37 (31.01, 31.73)
Beam aspect ratioNormal2.21 (2.03, 2.39)0.09
(μm/μm)Glaucoma2.04 (1.94, 2.13)
Orientation (deg)Normal4.41 (0.07, 8.76)0.63
Glaucoma5.59 (3.53, 7.65)
Anisotropy (μm/μm)Normal1.15 (0.92, 1.38)0.01
Glaucoma0.74 (0.56, 0.92)
Average pore area (μm2)Normal3.76(3.49,4.02)×1030.001
Glaucoma3.00(2.63,3.38)×103
StructureGroupMean and 95%CIp-value
Pore area fractionNormal0.530 (0.515, 0.545)0.47
(μm2/μm2)Glaucoma0.522 (0.507, 0.537)
Node densityNormal1.03(0.85,1.20)×1040.97
(nodes/μm2)Glaucoma1.02(0.93,1.12)×104
ConnectivityNormal3.09 (3.07, 3.11)0.18
(beams/nodes)Glaucoma3.10 (3.09, 3.11)
Tortuosity (μm/μm)Normal1.12 (1.11, 1.14)<0.0001
Glaucoma1.15 (1.15, 1.16)
Beam length (μm)Normal62.96 (56.06, 69.85)0.40
Glaucoma59.63 (56.21, 63.06)
Beam width (μm)Normal30.52 (29.24, 31.79)0.21
Glaucoma31.37 (31.01, 31.73)
Beam aspect ratioNormal2.21 (2.03, 2.39)0.09
(μm/μm)Glaucoma2.04 (1.94, 2.13)
Orientation (deg)Normal4.41 (0.07, 8.76)0.63
Glaucoma5.59 (3.53, 7.65)
Anisotropy (μm/μm)Normal1.15 (0.92, 1.38)0.01
Glaucoma0.74 (0.56, 0.92)
Average pore area (μm2)Normal3.76(3.49,4.02)×1030.001
Glaucoma3.00(2.63,3.38)×103

Note: Bold p-values indicate significance.

The beam tortuosity (p <0.0001), and average pore area (p =0.02) also differed significantly between the three damage groups (Fig. 8, Supplemental Table S4 available in the Supplemental Materials). The LC beams were significantly straighter in the NU group than in the GM and GS groups (p0.01), and the average pore area was significantly smaller in the GS than NU group. None of the microstructural features differed significantly between the GM and GS glaucoma damage groups.

Fig. 8
Box plots comparing the specimen-averaged (a) tortuosity, and (b) average pore area NU (n = 8), GM glaucoma (n = 9), and more GS glaucoma (n = 6) groups. The beam tortuosity was significantly lower in NU than in GM (p < 0.0001) and GS (p = 0.01). The average pore area was significantly smaller in GS than in NU (p = 0.04).
Fig. 8
Box plots comparing the specimen-averaged (a) tortuosity, and (b) average pore area NU (n = 8), GM glaucoma (n = 9), and more GS glaucoma (n = 6) groups. The beam tortuosity was significantly lower in NU than in GM (p < 0.0001) and GS (p = 0.01). The average pore area was significantly smaller in GS than in NU (p = 0.04).
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Table 4

Results of linear mixed models to investigate the relationship between regionally averaged curvature outcomes and microstructural features for the LC of glaucoma eyes, showing the number n of measurements, the estimated mean, 95% CI, and p-value

CurvatureStructurenChange in curvature and CIp-value
Gaussian curvaturePore area fraction (μm2/μm2)1171.23(1.04,0.0812)0.02
(1/mm2)Node density (nodes/μm2)1231.612(2.64,0.593)×1030.002
Mean curvaturePore area fraction (μm2/μm2)1172.04(0.602,3.47)0.006
(1/mm)Node density (nodes/μm2)1242.12(3.58,0.670)×1030.005
Maximum curvaturePore area fraction (μm2/μm2)1162.84(0.0015.68)0.05
(1/mm)Node density (nodes/μm2)1222.94(5.74,0.132)×1030.04
CurvatureStructurenChange in curvature and CIp-value
Gaussian curvaturePore area fraction (μm2/μm2)1171.23(1.04,0.0812)0.02
(1/mm2)Node density (nodes/μm2)1231.612(2.64,0.593)×1030.002
Mean curvaturePore area fraction (μm2/μm2)1172.04(0.602,3.47)0.006
(1/mm)Node density (nodes/μm2)1242.12(3.58,0.670)×1030.005
Maximum curvaturePore area fraction (μm2/μm2)1162.84(0.0015.68)0.05
(1/mm)Node density (nodes/μm2)1222.94(5.74,0.132)×1030.04

Note: Bold p-values indicate significance.

3.3 Regional Variations in Lamina Cribrosa Structure.

In glaucoma eyes, the Gaussian curvature, mean curvature, and maximum curvature were 1.9–2.7 times greater in the peripheral regions than in central regions (p <0.0001, Figs. 9(a) and 9(b), Supplemental Table S6 available in the Supplemental Materials). The peripheral regions of the LC also had a 2.8% higher pore area fraction (p =0.0002) and 15.2% lower node density (p <0.0001) than the central regions (Figs. 9(c) and 9(d)). The same differences were found for the LC of normal eyes (Supplemental Table S5 available in the Supplemental Materials). Moreover, the ratio of central to peripheral curvatures and microstructural features were not statistically different between normal and glaucoma eyes (Supplemental Table S7 available in the Supplemental Materials).

Fig. 9
Box plots comparing the (a) Gaussian curvature, (b) mean curvature, (c) pore area fraction, and (d) node density between the central and peripheral regions of the LC of glaucoma eyes. Linear mixed models showed that the peripheral regions had a higher Gaussian curvature and higher mean curvature (p < 0.0001), higher pore area fraction (p = 0.0002), and lower node density (p < 0.0001) than the central regions.
Fig. 9
Box plots comparing the (a) Gaussian curvature, (b) mean curvature, (c) pore area fraction, and (d) node density between the central and peripheral regions of the LC of glaucoma eyes. Linear mixed models showed that the peripheral regions had a higher Gaussian curvature and higher mean curvature (p < 0.0001), higher pore area fraction (p = 0.0002), and lower node density (p < 0.0001) than the central regions.
Close modal

Analysis of central glaucoma to central normal and peripheral glaucoma to peripheral normal showed the same relationships as the specimen averaged microstructural outcomes (Supplemental Tables S8 and S9 available in the Supplemental Materials). Comparing central regions in normal eyes to central regions in glaucoma eyes showed LC beams had higher tortuosity in glaucoma eyes (p =0.02), were more anisotropic in normal eyes (p =0.03), and all measures of curvature were greater in glaucoma eyes (p0.04). Comparing peripheral regions in normal eyes to peripheral regions in glaucoma eyes returned similar associations that were more significant. LC beams had higher tortuosity in glaucoma eyes (p =0.0005), were more anisotropic in normal eyes (p =0.0002), and Gaussian, mean, and maximum curvatures were greater in glaucoma eyes (p0.006).

3.4 Effects of Curvature on Microstructural Features.

Linear mixed models were applied to investigate the relationship between the regionally averaged curvatures and microstructural features of the LC. For normal eyes, larger Gaussian curvature, mean curvature, and maximum curvature were associated with greater pore area fraction (p0.02) (Supplemental Tables S10–13 available in the Supplemental Materials). For glaucoma eyes, larger Gaussian curvature, mean curvature, and maximum curvature were associated with greater pore area fraction (p0.05) and lower node density (p0.04) (Table 4, Supplemental Tables S10–S13 available in the Supplemental Materials on the ASME Digital Collection).

3.5 Effect of Lamina Cribrosa Structure on the Strain Response.

Linear mixed models were applied to analyze for associations between regionally averaged structural features and strain response of the LC to inflation from 5 to 45 mmHg (Supplemental Tables S14–S18 available in the Supplemental Materials on the ASME Digital Collection). The maximum principal strain Emax increased with increasing pore area fraction for both normal (p =0.02) and glaucoma eyes (p =0.001) at nearly the same slope (Figs. 10(a) and 10(b), Supplemental Table S14 available in the Supplemental Materials). Emax also increased with increasing Gaussian, mean, and maximum curvature for both normal (p0.002) and glaucoma eyes (p0.001). Similarly, Γmax increased with decreasing node density (p0.05) and with increasing maximum curvature (p0.05) for both normal and glaucoma eyes (Figs. 10(c) and 10(d)). There were additional significant relationships between strain and structure for glaucoma eyes that were not found in normal eyes. The Emax increased with decreasing node density (p =0.001). The Γmax increased with increased pore area fraction (p =0.0002) and with Gaussian and maximum curvatures (p0.003). The Err increased with increasing pore area fraction (p =0.02), and Eθθ increased with increasing maximum and minimum curvature (p0.03).

Fig. 10
Relationship between the regionally average Emax response to an IOP increase from 5 to 45 mmHg and pore area fraction, and the regionally averaged Γmax response and the maximum curvature. The Emax increases with increasing pore area fraction for (a) normal eyes (p = 0.02) and (b) for glaucoma eyes (p = 0.001). The Γmax increases with increasing maximum curvature for (c) normal (p = 0.05) and (d) glaucoma (p = 0.006) eyes. Also shown are a linear fit and associated R2 and 95% confidence bounds. The p-values are from linear mixed models.
Fig. 10
Relationship between the regionally average Emax response to an IOP increase from 5 to 45 mmHg and pore area fraction, and the regionally averaged Γmax response and the maximum curvature. The Emax increases with increasing pore area fraction for (a) normal eyes (p = 0.02) and (b) for glaucoma eyes (p = 0.001). The Γmax increases with increasing maximum curvature for (c) normal (p = 0.05) and (d) glaucoma (p = 0.006) eyes. Also shown are a linear fit and associated R2 and 95% confidence bounds. The p-values are from linear mixed models.
Close modal

4 Discussion

We analyzed SHG image volumes of the human LC of normal and glaucoma eyes with different levels of axonal damage to calculate the curvature and microstructural features of the LC. The maximum intensity projection was used to calculate the specimen-averaged and region-averaged pore area fraction, node density, beam connectivity, tortuosity, length, width, aspect ratio, orientation, and anisotropy. The maximum intensity projection can distort the features of the beam and pore microstructure, and the severity of the distortions depends on the curvature of the specimen. For example, the areas of the pores in highly curved regions may appear smaller in the maximum intensity projection. Thus, the individual z-slices were used to calculate the average pore area of the LC. However, using the z-slices also carries some important limitations. The large curvature of the glaucoma eyes caused most of the pores in the peripheral region to be excluded from the calculation because they were not fully enclosed by the beams. The average pore area calculated from the z-slices was more representative of the central region of the LC for glaucoma eyes. Using a plane tangent to the anterior LC surface to evaluate the beam and pore dimensions can address many of these limitations. In this study, the LC images were 5 μm apart in Z, while XY resolution was 2.78 μm/pixel. Defining a tangent surface would require interpolating image data between slices and would have primarily affected the glaucoma eyes. The interpolation method may affect the measurements for pore area and beam size, and more work is needed to develop this method.

We found that the LC curvatures of diagnosed glaucoma eyes were larger than those of age-matched normal eyes, which is consistent with clinical and histological findings of LC excavation in glaucoma patients [3436]. Lee et al. [37] reported that the average LC curvature index were significantly larger in primary open angle glaucoma (POAG) eyes than in the eyes of age-matched healthy subjects. Kadziauskienė et al. [38] showed using OCT imaging progressive flattening and shallowing of the LC in response to IOP-lowering after trabeculectomy over a period of 12 months. The larger curvature for glaucoma eyes measured here may have been caused by remodeling in response to the long-term elevation in IOP from glaucoma. Comparing the effects of axonal damage, we found that the LC curvatures of the undamaged normal group were smaller than the LC curvatures of the more mildly damaged group. The Gaussian curvature of the more mildly damaged group was on average 3.34 times larger than for the normal undamaged group. The curvature outcomes did not differ significantly between the two glaucoma damage groups. More specimens may be needed for these comparisons to be significant.

The microstructural analysis showed that the average pore area in the LC was smaller, the LC beams were slightly more curved, and the structure of the LC beams was more isotropic for glaucoma eyes than normal eyes. Comparing the different damage groups showed that damaged glaucoma eyes also had a smaller average pore area and more curved beams than undamaged normal eyes, but no significant differences were found between the mildly damaged and more severely damaged glaucoma groups. The sample size for the glaucoma groups may be too small to detect differences in the severity of glaucoma damage. Wang et al. [8] analyzed the visible portions of the LC of glaucoma patients using OCT and also found that the pore diameter was smaller and the beam width was larger in glaucoma eyes than in normal eyes. In contrast, Reynaud et al. [39] found in histological studies that pore diameter, connective tissue volume, and LC volume were larger in early experimental glaucoma monkey eyes than in control eyes. However, the connective tissue volume fraction was not different between early glaucoma and control eyes. We also did not find any differences in pore area fraction, which is the complement of the connective tissue fraction, between normal and glaucoma eyes. While the pore diameter and connective tissue volume were larger in early glaucoma eyes compared to control eyes in all animals, the eye-specific changes in the connective tissue volume fraction and beam diameter were variable, increasing for some animals and decreasing for others. Roberts et al. [40] also found in an early study that early glaucoma eyes had greater connective tissue volume but the same connective tissue volume fraction. Ivers et al. [41] imaged unilateral experimental monkey eyes longitudinally up to the development of early glaucoma and found that the increase in pore diameter was the earliest detected change in more than half of the early glaucoma eyes. The increase in pore diameter is consistent with the increased compliance of the LC in early glaucoma eyes [4244]. The human and monkey studies differed in age and glaucoma stage and are not directly comparable. However, we can speculate based on the results of our findings and those of early studies that the pore diameter increased in early glaucoma eyes, then decreased with the progression of glaucoma damage.

Previously, Midgett et al. [11] found that the LC area was significantly larger for glaucoma group than for the normal group. Altogether, these findings suggest that the larger LC of glaucoma eyes may have had a larger number of smaller pores, which would allow the pore area fraction of the glaucoma eyes to remain the same as those of normal eyes. Jonas et al. [45] previously showed that the number of pores increased with increasing LC area, but the average pore area did not vary significantly with LC area. Using the maximum intensity projection of the SHG images, we counted on average 152 ± 29 pores in glaucoma eyes and 130 ± 42 in normal eyes, but the difference was not statistically significant. The maximum intensity projection likely underestimated our pore count as it was lower than the 227 ± 36 pore count measured from SEM images of the human LC by Jonas et al. [45] Assuming no other differences, a larger LC would experience greater IOP-induced strains [14,46,47]. However, an LC microstructure with a larger number of smaller pores may be stiffer than one with a smaller number of large pores, which would compensate for the increased compliance of the larger LC area. The eyes in the glaucoma group may have had inherently a larger LC area, smaller pore area, and more isotropic beam arrangement. The net effect of these differences may have resulted in a stiffer LC and led to the development of glaucomatous axon damage [11]. Alternatively, the larger LC area and smaller pores area may have developed as a result of glaucoma-induced remodeling, where collagen types IV, I, and III infiltrate the pores after axonal loss [9,10].

The regional variation in the LC microstructure was similar in normal and glaucoma eyes. The pore area fraction was higher and the node density was lower in the peripheral regions compared to the central regions for both normal and glaucoma eyes. Previous studies also found lower connective tissue volume fraction in the peripheral compared to the central region of the LC for human and monkey eyes [45,48,49]. Furthermore, the ratio of the average pore area fraction and node density in the central region to their respective averages in the peripheral region did not differ between normal and glaucoma eyes. These findings together suggest that glaucoma-induced remodeling of the beam and pore microstructure may have occurred uniformly in the LC.

The maximum shear strain increased with the mean curvature for both glaucoma and normal eyes. Assuming no other differences, LCs with greater curvatures should have a more compliant strain response to pressure [47,50]. However, Midgett et al. [11] previously measured a stiffer (smaller) strain response to pressure for the mildly damaged glaucoma group than for the undamaged normal group, and the more severely damaged glaucoma eyes did not differ from undamaged normals. The stiffer strain response may be caused by the differences in the microstructural features measured here and by the mechanical properties of the beams. Computational modeling is needed to evaluate the effects of the measured differences in the beam and pore microstructure and mechanical properties of the beams on the IOP-induced strain response of the LC.

Several limitations should be considered regarding the methods used to calculate the LC curvature and microstructural features. The curvature was estimated by fitting a polynomial surface to the most anterior position of the LC volume with accurate DVC correlation. In a preliminary study, we manually marked points on transverse sections of the SHG images to calculate the curvature. However, the blurring of the SHG images in the z-direction made it challenging to consistently mark the pixel on the anterior surface. Using the most anterior points of the DVC volume with accurate displacement correlation provided an automated, fast, and objective method to identify the anterior surface in the SHG volume, but created local fluctuations that would have overestimated the local curvatures. Fitting a polynomial surface to the points smoothed out these spurious sharp features. A visual inspection of transverse sections along the nasal-temporal and inferior–superior axes of the specimens showed that the polynomial surface fit underestimated the local curvature in some areas and overestimated in others. However, it appears to provide a good representation of the anterior LC surface in the SHG images. The criteria we used for accurate DVC correlation carved out a 135–350 μm thick region of the LC. This falls in the lower end of the range of LC thicknesses reported in the histological study of Jonas and Holbach [51] for normal eyes and coincides with the average thickness measured by Jonas et al. [52] for glaucoma eyes. Thus, the curvatures reported here may represent the curvatures of the anterior LC surface for some eyes, particularly for glaucoma eyes with thinner LC, but not for others. LC thickness may also contribute to the different stiffness measurements between NU, GM, and GS groups measured by Midgett et al. [11] However, we did not find a correlation between imaged LC thickness and Γmax (Supplemental Figure S5 available in the Supplemental Materials on the ASME Digital Collection). The imaged LC thickness was influenced by the limit of laser penetration during imaging and how close the nerve was cut to the posterior LC, and may not represent the actual thickness of the LC in all eyes. We calculated the pore area fraction from the maximum intensity projection of the LC and the average pore area from the 2D z-slices of the LC. Wang et al. [53] found that the LC pores in glaucoma eyes took a more tortuous path through the LC than pores in normal eyes. Evaluating the pore area fraction from the maximum intensity projection may underestimate the pore area fraction in glaucoma eyes. Calculating the average pore area from the 2D z-slices may have also underestimated the pore area of LCs with larger curvature. The method to calculate the average pore area only considered pores that were fully enclosed by LC beams on a z-slice. These criteria excluded pores that spanned multiple z-slices in the more curved regions of the LC and would have affected the calculation of the average pore area in the peripheral region, with larger pores, more than in the central region. However, a Spearman correlation coefficients test using the specimen averaged average pore area showed that the average pore area did not vary significantly with the LC curvatures (Supplemental Table S19 available in the Supplemental Materials), and Wang et al. [8] previously also measured a smaller pore diameter in the LC of glaucoma eyes using OCT imaging.

The strain response of the LC was measured for enucleated eyes and may not be representative of the in vivo strain response to IOP elevation. We recently developed a method using spectral domain OCT (SD-OCT) and DVC to measure the in vivo strain response of the LC to IOP change [54] and are currently developing a method for microstructural analysis of the OCT image volume to calculate the LC microstructure. While most glaucoma eyes were from donors with primary open-angle glaucoma, one donor had angle closure glaucoma and one had pseudo-exfoliation glaucoma, which manifests from a systemic disorder of the extracellular matrix. The relationship between the connective tissue structures and strains in the LC may be different in eyes with pseudo-exfoliation glaucoma than open angle glaucoma and angle closure glaucoma. Previously, we analyzed the LC stains for the effects of glaucoma, including and excluding the eyes with pseudo-exfoliation glaucoma [11]. Excluding the two eyes with pseudo-exfoliation glaucoma increased the p-value for some comparisons and decreased the p-value for others, but did not change the overall conclusions of the analysis of LC strains. Finally, the sample size was small and included 10 normal eyes from six donors and 16 glaucoma eyes with different axonal damage levels from eight donors. A larger sample size is needed to detect significant differences in the LC curvatures and microstructural features between mild and severe glaucoma eyes.

5 Conclusions

The main findings of the study were as follows.

  • Curvature was significantly higher in glaucoma eyes than in normal eyes as measured by Gaussian, mean, and minimum curvature.

  • The LC of glaucoma eyes had a smaller average pore area, slightly more curved beams, and a more isotropic beam structure than the LC of normal eyes.

  • The LC of both glaucoma-damaged groups exhibited smaller average pore area, and more curved beams than the undamaged normal group, while only the more mildly damaged glaucoma group showed larger curvatures than the undamaged normal group.

  • The LC curvatures and pore area fraction were larger and the node density was smaller in the peripheral than central regions for both normal and glaucoma eyes. The ratio of the structural features in the peripheral regions to those in the central regions did not differ significantly between normal and glaucoma eyes.

  • For both glaucoma and normal eyes, a more compliant strain response to pressurization was measured for LCs with larger curvatures, greater pore area fraction, and lower node density.

We showed in this study and Midgett et al. [11] that the eyes in the glaucoma group had larger LC curvatures, a larger LC area, and greater axial length. All of these features should produce a more compliant strain response to inflation, yet Midgett et al. [11] measured a stiffer strain response to a 5–45 mmHg pressure increase for mildly damaged glaucoma eyes compared to undamaged normal eyes. These findings suggest that the stiffer strain response in the mildly damaged eyes may be caused in part by the smaller pore area, smaller beam aspect ratio, and more isotropic beam arrangement measured in this study. The mechanical properties of the beams and tissues within the pores can also affect the strain response of the LC to IOP. Further investigation is needed to determine whether these microstructural differences are the result of connective tissue remodeling during glaucoma progression and to evaluate their contribution to the stiffer strain response measured for the more mildly damaged glaucoma eyes.

Funding Data

  • Nicolas Gasquet and the Wilmer Biostatistics Core (Grant No. P30EY001765; Funder ID: 10.13039/100000053). (Core utilization is prioritized for investigators funded by R01 grants through NEI. All core users will cite grant P30EY001765, Wilmer Core Grant for vision research as a funding source.)

  • BrightFocus Foundation (Grant No. G2015132; Funder ID: 10.13039/100006312).

  • Johns Hopkins University (Grant No. Microscopy and Imaging Core Module and Wilmer Core Grant for Vision Research; Funder ID: 10.13039/100007880).

  • National Eye Institute (Grant Nos. EY01765 and EY02120; Funder ID: 10.13039/100000053).

  • National Science Foundation (Grant No. CMMI Award 1727104; Funder ID: 10.13039/100000001).

  • U.S. Public Health Service (Grant No. EY021500 and EY001765; Funder ID: 10.13039/100007197).

Conflict of Interest

The authors declare that they have no conflicts of interest.

Data Availability Statement

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

Footnotes

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Supplementary data