**Purpose**:
We evaluate solutions for an applanating surface modification to the Goldmann tonometer prism, which substantially negates the errors due to patient variability in biomechanics.

**Methods**:
A modified Goldmann or correcting applanation tonometry surface (CATS) prism is presented which was optimized to minimize the intraocular pressure (IOP) error due to corneal thickness, stiffness, curvature, and tear film. Mathematical modeling with finite element analysis (FEA) and manometric IOP referenced cadaver eyes were used to optimize and validate the design.

**Results**:
Mathematical modeling of the optimized CATS prism indicates an approximate 50% reduction in each of the corneal biomechanical and tear film errors. Manometric IOP referenced pressure in cadaveric eyes demonstrates substantial equivalence to GAT in nominal eyes with the CATS prism as predicted by modeling theory.

**Conclusion**:
A CATS modified Goldmann prism is theoretically able to significantly improve the accuracy of IOP measurement without changing Goldmann measurement technique or interpretation. Clinical validation is needed but the analysis indicates a reduction in CCT error alone to less than ±2 mm Hg using the CATS prism in 100% of a standard population compared to only 54% less than ±2 mm Hg error with the present Goldmann prism.

**Translational Relevance**:
This article presents an easily adopted novel approach and critical design parameters to improve the accuracy of a Goldmann applanating tonometer.

^{1,2}Glaucoma alone is a chronic and potentially debilitating disease requiring lifelong treatment. This disease currently affects 2.2 million Americans, with 3.3 million more expected by the year 2020. Glaucoma is now the leading cause of blindness in the aging Hispanic and African American populations, and nearly three times as common in African Americans as in White Americans. Worldwide, there were 60.5 million people with various types of glaucoma in 2010; this figure is expected to increase to 79.6 million by 2020.

^{3}Patients still go blind and suffer significant debilitating vision loss from glaucoma due to misdiagnosis and mismanagement.

^{4}

^{5,6}Numerous significant errors in the GAT IOP measurements (mm Hg) have been described previously. Those errors are due to patient variability in corneal thickness (±7 mm Hg), corneal rigidity (±8 mm Hg), corneal curvature (±2 mm Hg), and corneal tear film (±5 mm Hg).

^{7–9}The combined errors of patient variable parameters are potentially sight threatening to a large population of patients, such as those with glaucoma or undiagnosed ocular hypertension from other causes, yet currently this is the best method we have clinically. Despite the inherent shortcomings identified in the GAT, nothing has improved upon its accuracy, cost-effectiveness, and ease of use. This problem was brought into the spotlight by the findings of the Ocular Hypertension Treatment Study (OHTS), which noted that pressure readings tend to be overestimated in thick, and underestimated in thinner, corneas. These errors lead to a misdiagnosis of glaucoma.

^{10}Since the OHTS findings, the standard of practice has changed to include a measurement of central corneal thickness (CCT) with a nomogram to correct the pressure for the CCT. Additionally, the effects of laser-assisted in situ keratomileusis (LASIK) surgery render accurate IOP measurement by the GAT problematic.

^{11}The CCT correction has been partially effective but unreliable due to the other potential corneal biomechanical and tear film errors. Attempts were made to measure and quantify the various error components to correct the GAT measurement and yield a standard IOP reading comparable between patients.

^{12}However, the process in practice is error prone and cumbersome, leading to very limited clinical adoption with the exception of CCT. Other direct measurements of IOP that potentially reduce error have been developed, such as the dynamic contour tonometer (DCT) which provides for a constant appositional force of 1 g on a concave surface, which contains a central miniaturized piezoresistive pressure sensor. This device is very similar to a tonopen tonometer but adds the constant 1 g of force which partially negates biomechanical errors by allowing the corneal deformation force to be partly resisted by the portion of the contact surface that does not measure IOP. The DCT similar to the error correcting noncontact ocular response analyzer (ORA) is not widely used and has had minimal clinical acceptance for routine IOP measurement.

^{8}The cornea is assumed by the Imbert-Fick principle to be an infinitely thin membrane that by definition has no shear rigidity, only strength in tension.

^{5,8}The “rigidity” of the cornea also is affected by the corneal curvature. A steeply curved cornea must be “bent” more to applanate against the tonometer prism overestimating the IOP. Conversely a flat cornea, such as in someone who has had LASIK, underestimates the IOP. Also, the intrinsic material property of the cornea (the modulus of elasticity – both Young's and shear) greatly affect the “rigidity” of the cornea.

^{13–15}All of these rigidity-affecting components together increase the force on the tonometer prism, which is attributed to IOP but, in fact, have no direct relation to IOP, hence the error. Finally, attraction created by the surface tension in the tear film (which also is extremely variable in patients) was theorized to negate much of the “rigidity” error.

^{16,17}However, no clinical quantification of this highly variable attractive capillary force has been demonstrated in its effect on IOP.

^{7,9,10,12}In these patients, the variability in each of these parameters induces significant individual and combined error in GAT IOP measurement, as mentioned previously.

^{7–9}Even the errors due to corneal thickness alone, which is but a fraction of the total error, are sight threatening.

^{10}For this reason, CCT correction was adopted as a standard of practice.

^{10}Although several other separate measurements and error corrections were proposed, they have been too cumbersome to be adopted clinically.

^{12}The CATS tonometer prism, illustrated in Figures 1 and 2, can significantly reduce all of the identified measurement errors using the exact same measurement apparatus (with a modified prism), practitioner protocol, and measurement technique without calculations, increased time, and at minimal cost.

^{5}the force to pressure conversion assumes that the IOP is uniquely responsible for the force required to applanate the cornea force.

^{18,19}In reality, the structure of the eye contributes significantly to the applanation force.

^{7–10}Moreover, its contribution will vary based on the specimen. It is known that the measured IOP is affected by material properties and geometry of the eye.

^{7,8,12–14}

*F*, is a linear function of the IOP,

*P*. The reaction force also depends on the force to deform the cornea tissue,

*T*, and the cross-sectional contact area of the tonometer surface,

*A*. In this study, the normal IOP,

*P*

_{0}, was 16.0 mm Hg.

*δ*. In this study, the modeled cornea had a spherical radius of 7.800 mm, and the tonometer had a cylindrical radius of 1.53 mm. This resulted in the maximum displacement of 0.147 mm, and the maximum contact area was 7.354 mm

^{2}. The calculation of the contact area,

*A*, as a function of the spherical radius of the cornea,

*R*, and the vertical displacement,

*δ*, is shown in Equation 2.

*P*, is a linear function of the reaction force. It also depends on a calibration reaction force

_{GAT}*F*(

*P*), which is compared to the normal cornea

*F*

_{550}(

*P*

_{0}), where the 550 refers to the nominal 550 μm CCT, and

*P*

_{0}is the nominal IOP. This is shown in Equation 3.

^{14,21–25}

^{14,21,25}The material properties were determined via analyses of finite element simulations. The effects of the various geometric aspects of the cornea were measured and studied in previous studies. Since the published corneal material properties vary widely, the specific properties were chosen to approximate known reactions to GAT diagnostics. The force required for applanation of a normal cornea under normal conditions was set near 1.6 g. The cornea was allowed to contribute only 30% of this applanation force under nominal conditions, with the rest coming from the IOP. The finite element mesh density was set so that the perimeter of the applanation area would be precise to within 30 μm, but with a measurement tolerance of no finer than 0.1 g. A nominal cornea has a CCT of 550 μm, central radius of curvature of 7.8 mm,

*P*value of 0.82, and width of 11.0 mm. The

*P*value is a metric of eccentricity of an ellipsoid. A sphere has a

*P*value of 1. A prolate ellipsoid, such as the human cornea, has a

*P*value less than 1.

^{16,17}The attractive force created by the fluid bridge and associated surface tension of the tear film between the tonometer prism and cornea is reduced in the mathematical model by increasing the contact angle between the cornea and contacting prism in the region of the tear film meniscus with the CATS Tonometer prism. (Fig. 1)

^{26}Three eyes were individually measured five times with each prism at each of the following nine intracameral pressures (0, 5, 10, 15, 20, 25, 30, 40, 50 mm Hg). Each measurement was rotated counterclockwise 90° from a standard reference axis to account for any astigmatic errors. For example, three cadaver eyes were tested four times (alternately rotating 90°) at a 5 mm Hg intracameral pressure using the GAT and the CATS prisms. A randomization occurred to determine which tonometer prism was used first.

^{27}The cadaver eyes were used on the day of arrival and within hours postmortem. The eyes, ages of the cadavers, and cause of death were recorded. Eyes with a history or evidence of previous anterior segment intraocular surgery (except cataract) or corneal abnormalities were excluded.

^{7}The simulated sensitivity of each prisms' IOP measurement to modulus of elasticity is shown in Figure 11. Again, the shallower slope indicates that the CATS prism is less sensitive to this source of error. Finite element analysis of the CATS prism indicates a maximum IOP measurement error of ±2 mm Hg maximum error due to variations of corneal Young's modulus compared to ±8 mm Hg error with the standard GAT prism.

^{8}The design also was analyzed for a reduction in corneal curvature error dependence. The design effectively reduced the corneal curvature error from ±2.5 mm Hg with the GAT prism to ±1.5 mm Hg with the CATS prism.

^{16,17}The CATS prism effectively minimized the contribution from capillary tear film adhesion by decreasing the radius of curvature of the CATS surface where the tear film bridged between the two solids prism surface and cornea. The calculated attractive force created by the fluid bridge and associated surface tension of the tear film between the tonometer prism and cornea is reduced approximately 45% for the CATS prism compared to that of the standard GAT. This is achieved by increasing the contact angle between the cornea and contact surface, as illustrated in Figure 12. The range of values shown for the GAT and CATS prisms is due to variations in cornea geometry. This reduction in average attractive force is equivalent to a reduction of IOP measurement error of approximately 1.5 mm Hg.

^{7–9}Even the errors due to corneal thickness alone, which is but a fraction of the total error, were shown to be potentially sight threatening.

^{10}For this reason, CCT correction has been adopted as a standard of practice.

^{10}Although several other separate measurements and error corrections were proposed, they have been too cumbersome to be adopted clinically.

^{12}

^{7}The most common recognized error is that due to CCT at a published ±7 mm Hg, which is but a small portion of the total possible error. The effect of an error corrected IOP on clinical decisions can be profound. For example, if we only consider corneal thickness GAT error at ±7 mm Hg over a standard distribution of varying thicknesses: The average CCT is approximately 556 ± 40 μm standard deviation.

^{10}Using this distribution, the percentage of people who's IOP error is greater than ±2 mm Hg translates to 46% of all patients with significant IOP error from CCT alone. Using the CATS tonometer, the number of patients in which the IOP error is greater than ± 2 mm Hg drops to 0%. The CATS tonometer prism may negate the need for pachymetry measurement and CCT correction.

^{28}The mathematical modeling predicted this bias and the cadaver eye study and preliminary clinical evaluation also indicated this bias. Therefore, to make it equivocal to the GAT prism for an average eye with nominal error characteristics, the decision was made also to include this bias in the CATS prism. This bias equalization in the design means that a nominal eye with average corneal thickness, average corneal rigidity, and average corneal curvature will measure the same IOP with the GAT and CATS prisms. However, The CATS measurements will differ significantly from GAT as the error parameters vary from average, which is significant in likely greater than 50% of the population.

^{7–10,12}

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