# Goldmann Tonometry and Corneal Biomechanics
## 4 Discussion  
The purpose of the present work was to test the hypothesis that corneal stiffness and thickness are correlated to errors in IOP measured indirectly by GAT, as compared to the true IOP invasively detected using a pressure transducer. The experimental tests were performed on enucleated pig eyes, chosen for their similarity to human eyes both from the anatomical and mechanical point of view [59], also in the studies of glaucoma associated diseases [58; 60; 61; 62]. ANOVA tests demonstrated that the values of IOP are significantly affected by the instrument used to measure it, therefore deviations of GIOP from TIOP can be attributed to the use of GAT. Although we applied ANOVA test to our two groups of data (GIOP and TIOP) even if none of the two were normally distributed, it should be recalled that ANOVA test remains a valid statistical procedure even under non-normality [63]. GAT in most measurement underestimated IOP measured by the transducer, and the average difference as evaluated by Bland-Altman plots is roughly 8 mmHg. The Bland-Altman plot is the elective method to put in evidence differences in measurements between two  
Figure 6: (a) Stress-strain curves for untreated corneas obtained from the average data in Table 3 using the shell theory; (b) secant elastic modulus, E, for the applied pressures during inflation tests. Error bars in (b) are standard deviations. \begin{table}
\begin{tabular}{c c} \hline \hline
**IOP Interval (mmHg)** & **Pearson Correlation** \\ \hline
1–35 & \(-\)0.10 \\
1–12 & 0.09 \\
13–21 & \(-\)0.41 \\
22–35 & \(-\)0.29 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Pearson correlation indexes between delta-pressure and corneal stiffness, \(E\), for different pressure ranges. instruments. Being such difference roughly constant throughout the whole pressure range, we conclude that GAT underestimated IOP for any level of pressure in our enucleated eyes. Figure 4a shows an increase in delta-pressure with pressure which is not in contrast with Figure 5a, being variables on the \(x\)-axis different in the two figures. Inflation tests confirmed the non-linear mechanical behavior with large data dispersion typical of porcine corneas [53] and other soft biological tissues. The average values of apex displacement reported in Table 4 are very similar to values measured by [PERSON] and [PERSON] [64] in human corneas, but lower than those measured by [PERSON] et al. [65]. The difference may be attributed to corneal viscoelasticity. Our data and those of [PERSON] and [PERSON] [64] were obtained under quasi-static conditions, whereas [PERSON] et al. [65] applied pressures at variable rates from 3.7 to 37.5 mmHg/min. Furthermore, our pressure ranges are much more similar to those of [PERSON] and [PERSON] [64] and in the physiological range. A weak negative correlation was found between delta-pressure and corneal stiffness, \(E\). Even more importantly, the negative correlation becomes stronger if we look at physiologic or high values of pressure, where it would be important not to underestimate the IOP. For very high values of IOP, the increase in \(E\) (Figure 6b) may compensate the errors in GAT (last bar in Figure 4a). In the interval 0-12 mmHg no correlation could be found between delta-pressure and \(E\), we attribute this result to the hypotonic state of eyes. Such pressure ranges are never met in vivo, though, and were measured in our excised eyes which become hypotonic soon after the animal death and need volume infusion to regain tone. As the GAT is usually calibrated to work with a range of \"normal\" stiffnesses, our results suggest that GAT introduces larger errors for softer than normal corneas. As a support to this consideration, [PERSON] et al. [66] reported thin cornea and low corneal hysteresis as main risk factors for glaucomatous visual field progression in eyes with well-controlled IOP.