Effect of Corneal Stiffening on Goldmann Applanation Tonometry and Tono-Pen Measurements in Canine Eyes

Abstract

Purpose.: To experimentally examine the effect of increased corneal stiffness on Goldmann applanation tonometry (GAT) and Tono-Pen (Reichert, Inc., Depew, NY) measurements of intraocular pressure (IOP) in a canine eye model.

Methods.: Twenty globes were recovered from 10 dogs with no known diseases. For each dog, corneal stiffening was induced in one eye with glutaraldehyde/phosphate buffered saline (PBS) immersion while the other cornea was immersed in PBS only. Acoustic impedance was measured before and after treatment in all eyes. After treatment, IOP was measured by GAT and Tono-Pen at true pressures of 10, 15, 20, 30, and 40 mm Hg. The corneas were then dissected for uniaxial tensile testing. The GAT/Tono-Pen readings, corneal stiffness (measured by ultrasound and tensile tests), and corneal thickness were compared between the two groups. The correlations between GAT/Tono-Pen readings and corneal stiffness were evaluated.

Results.: Acoustic impedance significantly increased after glutaraldehyde treatment (P < 0.01). Secant modulus at 1% strain was significantly higher in corneas treated with glutaradehyde/PBS than those treated with PBS only (P < 0.01). GAT and Tono-Pen readings were significantly higher at all pressure levels (P < 0.001) in the eyes with corneal stiffening. Both corneal acoustic impedance and secant modulus were significantly correlated with GAT/Tono-Pen readings at all pressure levels (P < 0.01).

Conclusions.: This study provided experimental evidence that corneal stiffening significantly increases GAT and Tono-Pen readings in canine eyes. Noninvasive ultrasound measurement of acoustic impedance may be used to evaluate corneal stiffness and improve the accuracy of clinical measurements of IOP.

Intraocular pressure (IOP) is of fundamental importance in the management of glaucoma. Lowering IOP has long been the mainstay of glaucoma treatment, and accurate measurement of IOP is thus important. 

It is known that the measurement of the current clinical standard, Goldmann applanation tonometry (GAT), could deviate substantially from the true IOP depending on corneal properties. The potential inaccuracy is intrinsic to the design of the Goldmann tonometer, which assumes human corneas to be perfectly extensible (i.e., no resistance to deformation), infinitely thin, and completely dry. ¹ Variations of corneal thickness and stiffness could introduce clinically significant errors in IOP readings. Experimental and clinical data has clarified a positive correlation between central corneal thickness (CCT) and measured IOP. The measurement error was however inconsistently reported, with values ranging from 0.11 to 0.71 mm Hg per 10 μm deviation from the population mean of CCT. ^{2 –6} The difference in the correction algorithms may be related to different experimental conditions in the studies; however, it is generally acknowledged that corrections based solely on CCT are not sufficient because there are other influential confounding factors in IOP measurements, most notably corneal stiffness. Theoretical analysis suggested that the variance in corneal stiffness could potentially introduce larger errors in tonometric measurements ⁷ ; moreover, different corneal stiffness would result in different “slopes” necessary for correcting the effect of CCT. ⁷  

We have previously reported a correlation between GAT/Tono-Pen (Reichert, Inc., Depew, NY) readings and corneal secant modulus measured by uniaxial tensile tests on canine corneas. ⁸ The purpose of the present study was to test the hypothesis that an altered corneal stiffness directly leads to a change in GAT and Tono-Pen readings. In addition, we explored the potential of using a noninvasive ultrasound method to obtain an estimate of corneal stiffness which may be used for correcting clinical measurements of tonometry. 

Canine eyes were used in this study because of their availability immediately after euthanasia. This allowed for experimental measurements within a short postmortem time to minimize potential tissue degradation and hydration change. Canine eyes resemble human eyes in corneal thickness and radius of curvature although both parameters are slightly larger in the canine eye. The canine cornea has multiple layers including epithelium, stroma, Descemet's membrane, and endothelium, but the Bowman's membrane found in the human cornea is absent from the canine cornea. ⁹  

Corneal stiffening can be induced by corneal collagen cross-linking. Irradiation with ultraviolet light in the presence of photosensitizer has been reported to increase corneal stiffness. ^10,11 Corneal stiffening can also be achieved through chemical cross-linking using glutaraldehyde or other fixative agents. ^{11 –13} In the present study, we chose to use glutaraldehyde treatment because it does not require the removal of corneal epithelium which was useful for obtaining reliable GAT measurements. Our preliminary tests showed that glutaraldehyde penetration was sufficient without the removal of corneal epithelium when it was coadministered with benzalkonium chloride (BAK), which is known to facilitate transepithelial transport. ¹⁴ Glutaraldehyde treatment also provides an adjustable experimental procedure to achieve the desired extent of stiffening. ¹³  

Corneal stiffness was characterized first by an ultrasound method in the intact eye and then tensile tests in the dissected tissue strips. Our laboratory has shown that corneal acoustic impedance was correlated with corneal tangent or secant modulus. ¹⁵ The ultrasound method was thus used in the present study as a noninvasive measurement of the corneal stiffness. Direct measurement of corneal secant modulus was also carried out on dissected corneal strips using uniaxial tensile tests. 

Methods

Sample Preparation

Twenty fresh canine globes were obtained within 1 hour postmortem from 10 healthy dogs that were humanely euthanized for population control purposes at a local animal shelter. Globes from the same animal were randomly assigned into two groups: a control group and a corneal stiffening group. The eyes in the corneal stiffening group were treated with corneal immersion in a phosphate buffered saline (PBS) solution with 1% glutaraldehyde and 0.025% BAK for 1 hour. The glutaraldehyde concentration and the immersion time were chosen to induce a desired level of corneal stiffening based on initial tests. The sclera was not in contact with the solution during corneal treatment. Wet gauze was wrapped around the sclera to maintain its hydration during corneal treatment. For the control group, the corneas were immersed in PBS for 1 hour. CCT was measured by using an ultrasound pachymeter (DGH-550 PACHETTE 2; DGH Technology, Inc., Exton, PA) before and after the treatment. CCT was also checked after ultrasonic measurements and tonometric measurements. Three readings were recorded and the average was used for further analysis. Corneal stiffness was measured by using the ultrasound method before and after treatment in each eye. GAT and Tono-Pen measurements were collected after treatment at different controlled IOP levels. Uniaxial tensile tests were conducted on corneal strips prepared from all globes after the completions of the measurements mentioned above. All measurements were completed within 8 hours postmortem. Details of the ultrasound measurements, tonometric measurements, and tensile tests are elaborated below. 

Acoustic Impedance Measurements

Corneal acoustic impedance was measured in the intact globe before and after treatment for both control group and corneal stiffening groups, following the methods described previously. ¹⁵ Briefly, the globe was immersed in a saline bath and an unfocused ultrasound transducer (XMS-310; Panametrics-NDT, Waltham, MA) was used to measure the ultrasonic reflection from the cornea. Short-duration ultrasonic pulses were emitted along the optical axis of the eye and the reflected ultrasound signals were collected by the transducer. The position of the transducer was adjusted by using precision linear stages (1 μm step size; Newport 423 High-Performance Linear Stages; Newport, Irvine, CA) to ensure accurate alignment of the transducer with respect to the cornea by maximizing the amplitude of the reflected signals. The reflections were sampled by a digitizer (500MHz/8-bit; DP105; Acqiris, Monroe, NY) and stored for further analysis. The acoustic impedance of the cornea was determined from the amplitude of the ultrasound reflections from the cornea and the ultrasound reflection measured from a calibration sample (Soflens-59; Bausch & Lomb, Rochester, NY) with known acoustic properties, based on the following equation:  

 

where R is the reflection coefficient, A _s is the amplitude of the reflected ultrasound signal, A ₀ is the amplitude of the incident ultrasound signal, Z _w is the acoustic impedance of the coupling media (i.e., saline or aqueous humor), and Z _c is the acoustic impedance of the cornea. The amplitude of the ultrasonic reflection was adjusted for the curvature effect as described in a previous study. ¹⁶  

GAT and Tono-Pen Measurements

GAT measurements were performed in the treated globes using an experimental setup described previously. ^8,17,18 Briefly, the globe was placed in a holder padded with moistened gauze and affixed to a plastic plate that was mounted on the headset of a standard slit lamp (Topcon SL-2ED, Oakland, NJ). The IOP was controlled at 10, 15, 20, 30, and 40 mm Hg using a saline column and monitored by a pressure sensor that was connected to the anterior chamber. IOP was measured by using a Goldmann tonometer (AT900; Haag Streit, Koeniz, Switzerland) and Tono-Pen (Tono-Pen XL; Reichert, Inc.) at each pressure setting. Both GAT and Tono-Pen were calibrated before experiments. Each pressure measurement was repeated three times and the average was used for further analysis. 

Uniaxial Tensile Test of Corneal Strips

After completing the pressure measurements, the globes in both control group and cross-linking group were dissected and cornea strips (3.5 mm by 18 mm) were prepared along the nasal-temporal direction. Uniaxial tensile tests were performed on the corneal strips using a rheometric system analyzer (RSA-III; TA Instruments, New Castle, DE). The tissue strip was coupled between a motor and a transducer that measures the resultant force generated by sample deformation. The initial sample length between the two gripping jaws was approximately 10 mm. Sample width and thickness were measured by using a high resolution ultrasound imaging system (Vevo660; VisualSonics Inc., Toronto, Canada) and input into the rheometric system analyzer (RSA-III) control panel. A 55 MHz ultrasound scanning probe was used with an axial resolution of 30 μm and a lateral resolution of 62.5 μm. A preload of 20 mN was applied to each sample to precondition and flatten the tissue. The sample was then subject to a constant strain rate of 0.1% per second until strain reached approximately 6%. The stress-strain data were stored on the hard disc of the computer for further processing. The strain rate was selected from the typical values used in the literature. ^11,19,20 Secant modulus at 1% strain was calculated and used as the stiffness measure based on tensile tests in further analysis. 

Statistical Analysis

The CCT and acoustic impedance were summarized before and after the treatment for the control group and the corneal stiffening group. The after-treatment tensile modulus was summarized for both groups. The changes in CCT and corneal stiffness were tested using paired t test for each group and the difference between the two groups was tested using a mixed model to account for the dependency among observations in the same eye. GAT and Tono-Pen measurements were summarized as mean ± SD at each IOP level (10, 15, 20, 30, or 40 mm Hg) for each group. The differences in tonometric measurements were tested using a mixed model to account for the dependency of the measurements in the same eye. In both the control group and the corneal stiffening group, the correlations between GAT/Tono-Pen measurement and the corneal stiffness measurement (i.e., secant modulus or acoustic impedance) were evaluated at each IOP level by using Pearson correlation coefficients. The influence of CCT on the tonometric measurements was also explored using Pearson correlation at different IOP levels. Statistical software (SAS Version 9.12; SAS Institute Inc., Cary, NC) was used for all data analysis. 

Results

The mean CCT in the control group was 663.2 ± 53.7 μm before all measurements and 693.1 ± 47.9 μm after 1 hour immersion in PBS. The mean CCT in the corneal stiffening group was 659.9 ± 63.3 μm and 674.2 ± 49.9 μm, respectively. There was a small but statistically significant increase in CCT after treatment in both groups (P < 0.05, paired t test). No statistically significant difference was found in CCT between the control and the corneal stiffening group at baseline or after treatment (P = 0.90 and 0.40, two sample t test). 

The acoustic impedance (AI) in the control group was 1.71 ± 0.02 MPa · s/m at baseline and 1.71 ± 0.01 MPa · s/m after 1 hour immersion in PBS. The AI in the corneal stiffening group before and after treatment were 1.70 ± 0.02 MPa · s/m and 1.74 ± 0.02 MPa · s/m, respectively. No statistically significant difference was found in AI between the control and the corneal stiffening groups at baseline (P = 0.76, two sample t test). No significant change in acoustic impedance was found in the control group after PBS treatment (P = 0.10, paired t test). Acoustic impedance increased significantly in the corneal stiffening group after treatment (P < 0.001, paired t test), which was significantly higher than that in the posttreatment control group (P < 0.01, two sample t test). 

The mean GAT and Tono-Pen readings corresponding to various manometric IOPs (IOP_Man) are summarized in Table 1. The corneal stiffening group had statistically higher IOP measurements than the control group for both GAT and Tono-Pen measurements at IOP levels of 10, 15, 20, 30, and 40 mm Hg (P < 0.001). In the control group, both GAT and Tono-Pen underestimated the intraocular pressure while in the corneal stiffening group, both tonometric methods measured closer to the manometric pressure. 

Table 1.

 

GAT and Tono-Pen Readings at Various True IOP Levels in Canine Eyes

IOPMan (mm Hg)	GAT (mm Hg)		Tono-Pen (mm Hg)
	Control (n = 10)	Corneal Stiffening (n = 10)	Control	Corneal Stiffening (n = 10)
10	2.2 ± 1.0	10.1 ± 3.6	8.4 ± 1.2	13.8 ± 3.6
15	6.8 ± 1.4	15.6 ± 4.1	12.8 ± 1.4	17.9 ± 3.3
20	11.3 ± 1.5	21.1 ± 5.6	16.8 ± 1.6	22.3 ± 2.3
30	20.3 ± 1.5	30.7 ± 5.3	24.6 ± 2.1	30.0 ± 3.4
40	29.0 ± 1.8	40.7 ± 6.0	30.7 ± 2.2	37.2 ± 3.5

The stress-strain curves obtained from uniaxial tensile tests are plotted in Figure 1. Both groups showed typical nonlinearity. Secant modulus was calculated as the ratio of stress and strain at a given strain level. The mean secant modulus at 1% strain was 1.72 ± 0.41 MPa in the control group and 3.03 ± 0.61 MPa in the corneal stiffening group. The difference in secant modulus was statistically significant (P < 0.001). 

Figure 1.

 

The average stress-strain relationship for control and corneal stiffening groups.

The correlation between the GAT/Tono-Pen readings and the stiffness measurements was explored in the combined data set of the control and the corneal-stiffened eyes. A significant positive correlation was found between the GAT readings and the acoustic impedance at each pressure level (Fig. 2; R = 0.77, 0.77, 0.72, 0.73, and 0.77 for IOP_Man = 10, 15, 20, 30, and 40 mm Hg; P < 0.001). The slopes of the linear regression between GAT and acoustic impedance were 160.9, 180.3, 200.6, 209.8, and 247.2 mm Hg per MPa · s/m at 10, 15, 20, 30, and 40 mm Hg, respectively. Significant correlations were also found between the Tono-Pen readings and the acoustic impedance at all pressure levels (Fig. 3; R = 0.70, 0.69, 0.69, 0.79, and 0.60 for IOP_Man = 10, 15, 20, 30, and 40 mm Hg; P < 0.01). The slopes of the linear regression between Tono-Pen readings and acoustic impedance were smaller than the corresponding slopes between GAT and acoustic impedance, with values of 116.1, 108.3, 103.7, 135.1, and 115.1 mm Hg per MPa · s/m at 10, 15, 20, 30, and 40 mm Hg. 

Figure 2.

 

Scatter plots of GAT readings versus posttreatment corneal acoustic impedance at different levels of IOP_Man (, corneal stiffening; ▲, control).

Figure 3.

 

Scatter plots of Tono-Pen readings versus posttreatment corneal acoustic impedance at different levels of IOP_Man (, corneal stiffening; ▲, control).

The GAT readings were found to be significantly correlated with the secant modulus (Fig. 4; R = 0.87, 0.89, 0.83, 0.85, and 0.86 for IOP_Man = 10, 15, 20, 30, and 40 mm Hg; P < 0.001). The slopes of the linear regression between GAT and secant modulus were 4.9, 5.7, 6.3, 6.7, and 7.6 mm Hg/MPa at 10, 15, 20, 30, and 40 mm Hg. There was also a significant correlation between the Tono-Pen readings and the secant modulus (Fig. 5; R = 0.73, 0.78, 0.81, 0.82, and 0.75 for IOP_Man = 10, 15, 20, 30, and 40 mm Hg; P < 0.001). The slopes of the linear regression between Tono-Pen readings and secant modulus were smaller than the corresponding slopes between GAT and secant modulus, with values of 3.3, 3.3, 3.3, 3.8, and 3.9 mm Hg/MPa at 10, 15, 20, 30, and 40 mm Hg. 

Figure 4.

 

Scatter plots of GAT readings versus posttreatment corneal secant modulus at 1% strain at different levels of IOP_Man (, corneal stiffening; ▲, control).

Figure 5.

 

The scatter plots of Tono-Pen readings versus posttreatment corneal secant modulus at 1% strain at different levels of IOP_Man (, corneal stiffening; ▲, control).

The acoustic impedance was significantly correlated with the secant modulus in the measured canine corneas (Fig. 6; R = 0.80; P < 0.001). 

Figure 6.

 

Linear correlation between posttreatment corneal acoustic impedance and secant modulus at 1% strain.

No correlation was found between the GAT readings and CCT (Fig. 7; R = −0.02, 0.04, −0.01, 0.01, and 0.02; P = 0.94, 0.86, 0.98, 0.96, and 0.93 for IOP_Man = 10, 15, 20, 30, and 40 mm Hg, respectively). There was also no correlation between the Tono-Pen readings and CCT (Fig. 8; R = 0.11, 0.03, 0.01, 0.15, and 0.12; P = 0.64, 0.89, 0.98, 0.52, and 0.6, respectively). 

Figure 7.

 

Scatter plots of GAT readings versus posttreatment CCT at different levels of IOP_Man (, corneal stiffening; ▲, control).

Figure 8.

 

Scatter plots of Tono-Pen readings versus posttreatment CCT at different levels of IOP_Man (, corneal stiffening; ▲, control).

Discussion

The primary finding of the present study was that corneal stiffening significantly increased GAT and Tono-Pen readings in the canine eyes. In the normal canine eyes, GAT and Tono-Pen both underestimated IOP. For example, the average GAT reading was 6.8 mm Hg at a true pressure of 15 mm Hg and the underestimation was more pronounced at higher pressures. This level of underestimation by GAT was reported in a previous study on porcine eyes. ¹⁸ The potential factors underlying this large underestimation were discussed in our previous publication. ⁸ Primarily, GAT is calibrated to the dimensions and properties of the human eye. After corneal stiffening through chemical cross-linking, GAT reading was increased to 15.6 mm Hg, considerably closer to the true pressure of (i.e., 15 mm Hg). A similar increase in Tono-Pen readings was also found. 

Uniaxial tensile tests showed that the glutaraldehyde-treated corneas had a significantly higher secant modulus than those in the control group (3.03 ± 0.61 MPa vs. 1.72 ± 0.41 MPa). In this study, we found the secant modulus in the control dog corneas (n = 10) was from 1.15 to 2.53 MPa. This range (i.e., 2.53–1.15 = 1.38 MPa) was comparable to the difference between the control and glutaraldehyde-stiffened dog corneas (i.e., 3.03–1.72 = 1.31 MPa). Cartwright et al. ²¹ reported that the stiffness of the human cornea doubled between the ages of 20 and 100 years. In the present study, glutaraldehyde treatment increased corneal stiffness by a factor of approximately 1.8, which was comparable to the age-related stiffening in human corneas. Our laboratory recently performed mechanical testing on several human corneas (n = 8, unpublished data, 2011) following the same protocol described in this article and found that the 1% secant modulus ranged from 1.70 to 3.15 MPa. Therefore, the glutaraldehyde treatment used in the present study appeared to induce a corneal stiffness change that is within the physiological variance of corneal stiffness. Future studies are needed to fully characterize the range of corneal stiffness in both normal and diseased human eyes. 

The ultrasound method also detected significantly higher acoustic impedance in the stiffened corneas. The strong correlation between corneal acoustic impedance and secant modulus (Fig. 6), previously reported by our laboratory, ¹⁵ was confirmed in the present study. Importantly, we found a strong correlation between acoustic impedance and GAT/Tono-Pen readings, suggesting that the measurement of acoustic impedance may serve as a noninvasive approach to estimate corneal stiffness and guide the clinical interpretation of IOP measurements using these tonometric methods. For instance, a higher than normal acoustic impedance measurement may suggest the possibility of overestimation of IOP using GAT. However, corneal stiffness alone is not sufficient in calibrating GAT or Tono-Pen readings, because other parameters such as corneal thickness, curvature, as well as the interactions between corneal properties and the true pressure could all affect tonometric readings. It is noted that the linear regression slopes between acoustic impedance and tonometric errors were dependent on the true pressure. This pressure dependence, reflecting the nonlinear nature of corneal biomechanics, makes correction algorithms based on a single factor likely unattainable. More sophisticated algorithms incorporating several factors may be needed to predict true pressures from tonometric measurements. A possible approach could be to optimize the true pressure estimates from patient-specific computational models of clinical GAT measurement that incorporate nonlinear corneal responses and fit the predicted GAT readings, as well as corneal thickness, curvature, and stiffness to the measured data. 

Our results showed that an increase of corneal modulus from 1.72 to 3.03 MPa was associated with an increase of GAT readings from 6.8 to 15.6 mm Hg (an 8.8 mm Hg increase) when the true IOP was 15 mm Hg. A previous analytical model suggested an increase of GAT readings by 17 mm Hg when corneal modulus increased from 0.1 to 0.9 MPa. ⁷ The current experimental data agreed qualitatively with the theoretical prediction confirming that a clinically significant difference in GAT readings could result from plausible individual difference in corneal stiffness. The model however assumed linear isotropic mechanical properties of the cornea while in reality the cornea is nonlinearly viscoelastic and has strong anisotropy due to the preferential collagen fiber alignment in the direction parallel to the surface. These limitations of the analytical model may explain the quantitative difference in the predicted errors when compared with the experimental results found in this study. Future efforts are needed to develop theoretical models that can more accurately represent corneal biomechanical characteristics that are relevant in GAT measurements. 

In the present study, no statistically significant correlation was observed between CCT and GAT/Tono-Pen readings at any pressure level (Figs. 7, 8). Although this result was possibly due to the small sample size, the undetectable correlation with CCT contrasted with the strong correlation with corneal stiffness and indicated that the effect of corneal stiffness may be greater than CCT within clinically relevant ranges of each parameter. Future studies are needed to further elucidate the effects of CCT and corneal stiffness on tonometric measurements of the human eye and the interactions of these parameters in a larger sample size. 

Our results showed that Tono-Pen also underestimated IOP in control canine eyes but the underestimation was smaller compared with GAT. For example, at a true IOP of 15 mm Hg, the average underestimation was 2.3 mm Hg. This result was consistent with previous reports that Tono-Pen was relatively reliable for canines at normal pressure levels. ²² Our results also showed that Tono-Pen readings were significantly higher in the eyes with stiffened corneas, indicating the effect of corneal stiffness on Tono-Pen measurements. The smaller slopes of the linear regressions between Tono-Pen readings and secant modulus suggest that corneal stiffness may have less influence on Tono-Pen than GAT. 

The limitations of the present study are as follows. First, the experimental setup in the present study adopted an “open stock” system to maintain the IOP level while in the living eye the applanation procedure may induce a significant IOP rise. The “open stock” system was helpful in studying the relationship between equilibrium pressures and their tonometric readings. ²³ The results of this study therefore should be interpreted with the understanding of potentially more complicated processes in actual clinical situations. ⁵ Second, corneal curvature was not measured. Although it is unlikely that corneal curvature was significantly different between the two groups before treatment, it could be differentially altered during treatment. Previous analytical and numerical models suggested that corneal curvature had a much smaller influence on tonometric readings than corneal thickness and stiffness. ^7,24 Therefore, the main outcome of the present study will likely remain the same if the information of the curvature is made available. Third, canine eyes were used in the present study. Although sharing similar corneal thickness, canine corneas differ from human corneas in microstructure and biomechanical properties. Future studies are needed to investigate the effect of altered corneal stiffness on tonometric errors in human eyes. 

In summary, the present study found a significant increase in both GAT and Tono-Pen measurements of IOP in canine eyes with stiffened corneas. These results provide experimental evidence to support the hypothesis that corneal stiffness significantly influences tonometric readings. The GAT/Tono-Pen errors appeared to be correlated with the corneal tensile modulus. Corneal acoustic impedance may be used as a surrogate for corneal tensile modulus and provide a noninvasive method for estimating tonometric errors associated with abnormal corneal stiffness. 

Footnotes

 Supported by the American Health Assistance Foundation–National Glaucoma Research.

Footnotes

 Disclosure: J. Tang, None; X. Pan, None; P.A. Weber, None; J. Liu, None