# Goldmann Tonometry and Corneal Biomechanics
## 3 Results  
### Tonometry Results  
For each of the 49 pig eyes, we obtained a few couples of measurements of IOP by the two instruments, for a total of 126 measurements. The values of IOP increase with volume increase for both the instruments, with a trend line for GIOP lower than TIOP, as shown in Figure 3a. Lower GIOP values are also evident from Figure 3b, in which GIOP is plotted versus TIOP, and most of the experimental points are below the first quadrant bisector. Figure 2: Scheme of the inflation tests experimental setup used to evaluate corneal stiffness. Tables 1 and 2 summarize results of normality test (Shapiro-Wilk) and significance test (\(t\)-test or Mann-Whitney test) for the five groups of data in Figure 4a. Delta-pressure values of 4-7 mmHg are the most frequent (30%), followed by the intervals 8-11 and 12-15 mmHg (both 20%), as Figure 4b illustrates. \(t\)-test was applied to normal distributions, Mann-Whitney test otherwise. Given the presence of consistent differences in IOP measured by the two instruments, we applied a two-way ANOVA test to our data. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Delta-Pressure (mmHg)** & **Normal Distribution** & **N** \\ \hline
0–7 & No & 32 \\
8–14 & No & 37 \\
15–21 & No & 22 \\
22–28 & Yes & 18 \\
29–35 & Yes & 17 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Shapiro-Wilk test results on the difference between transducer intraocular pressure and Goldmann intraocular pressure (delta-pressure) grouped in five intervals. Figure 3: **(a)** Intraocular pressure, IOP, resulting from discrete volume infusions of 0, 100, 200, 300, 400, and 550 \(\mu\)L. Filled symbols and continuous line are the transducer intraocular pressure, TIOP, data and TIOP trendline, respectively. Empty symbols and dashed line are Goldmann intraocular pressure data, GIOP, and GIOP trendline, respectively. **(b)** GIOP as a function of TIOP measured in the same pig eye. The line represents the first quadrant bisector. First, we grouped our data by volume infusion to test whether only volume infusion had an influence on the measured IOP, or the instrument too, or the combination of volume infusion and instrument. Of the total 126 measurements, 78 were relative to 0 mL infusion, 66 to 100 mL, 52 to 200 mL, 30 to 300 mL, 18 to 400 mL, and eight to 500 mL. The \(p\)-value resulted less than 0.001 for both volume infusion and instrument, whereas the combination of instrument and volume infusion resulted in a \(p\)-value of 0.51. Therefore, we conclude that both volume infusion and instrument affect the measurement but not the combination of the two. We also applied two-way ANOVA to data organized by pressure level. Data were divided by five groups identified by the mean pressure of pressure ranges in Table 1, i.e., 4, 11, 18, 25, and 32 mmHg. This time we tested whether the pressure level or the instrument had an influence on IOP measurement. Again, the \(p\)-value was less than 0.001 for both pressure level and instrument. The combination of instrument and pressure level resulted in a \(p\)-value of 0.004, so this time also the combination of the two variables had an effect on IOP. We finally applied Bland-Altman analysis to our data to evaluate more deeply the differences in IOP measured by the two instruments. Figure 5a reports the difference in IOP measurements, delta-pressure, as a function of the average of the two measurements, average. Being most points between the two dashed lines, which represent the confidence lines, the two methods give congruent results, apart from an error. A positive mean value of delta-pressure of 7.8 mmHg is calculated (thick horizontal line in Figure 5a). No trend in delta-pressure with pressure can be observed from Figure 5a. Although delta-pressure for the average lower than 10 mmHg seems lower than for the higher average, Figure 5b shows that such values are on the contrary very high (about 200%) when considered as percentage values (Bland-Altman PI plot, Figure 5b).