purpose. For diagnostic purposes and for follow-up after treatment, it is important to have simple and reliable methods for measuring intraocular pressure (IOP). The purpose of this study was to develop a new applanation method for IOP measurement that uses combined continuous force and area measurement and to develop and evaluate an applanation resonator sensor (ARS) tonometer based on that method.

methods. The tonometer was developed and evaluated in an in vitro porcine eye model, in which enucleated eyes were pressurized with a saline column. A model assuming that the applanation principle is valid over a certain interval of contact area was proposed. Continuous contact area was measured with a resonator sensor device, and contact force was measured with a force transducer, both mounted together in one probe. Reference IOP was measured in the vitreous chamber (IOP_{VC}) with a standard fluid pressure transducer.

results. An optimization algorithm determined the applanation interval that was optimal for calculating IOP_{ARS}. The corresponding time interval was 30 ± 3 to 77 ± 4 ms (mean ± SD, *n* = 418) after initial contact. The proposed model showed a degree of explanation of *R* ^{2 [supi]} = 0.991 (*n* = 410, six eyes), corresponding to a correlation of *r* = 0.995 (*n* = 410) between IOP_{ARS} and IOP_{VC}. The within-eyes precision (i.e., 95% confidence interval for the residuals between IOP_{ARS} and IOP_{VC}) was ± 1.8 mm Hg (*n* = 410, six eyes).

conclusions. In this study, the ARS method for measuring IOP was evaluated in an in vitro porcine eye model and showed high precision. The ARS method is, to the authors’ knowledge, the first to combine simultaneous, continuous sampling of both parameters included in the applanation principle: force and area. Consequently, there is a potential for reducing errors in clinical IOP tonometry.

^{ 1 }All treatment so far has been intended to reduce IOP. Therefore, it is important for diagnostic purposes and for follow-up after treatment to have simple and reliable methods for measuring IOP, because tonometry is a standard procedure in all examinations of the eye.

^{ 2 }For IOP measurement the applanation principle is generally described through the Imbert-Fick law

^{ 2 }by contact force (

*F*

_{C}) and area of contact (

*A*) (equation 1) .

^{ 2 }Thus, IOP is calculated from a one-point reading of area and force.

^{ 3 }The sensor is based on a piezoelectric element that is set to vibrate at its resonance frequency. It has been shown

^{ 3 }that when the sensor is applied against the cornea, the frequency shift is proportional to the contact area. By using a constant force and frequency shift (i.e., contact area) measure, IOP can be calculated according to equation 1 . The study

^{ 3 }demonstrated that the resonator sensor principle can be used to measure IOP in a physical model. As with GAT, the calculation of IOP is based on a one-point reading of area and force. That study,

^{ 3 }as well as a later study,

^{ 4 }showed an IOP measurement variation related to differences between eyes. In the latter study, normalization of frequency shift was shown to reduce between-eye variability, and a further development toward a method that incorporates a self-calibration, similar to the normalization, was suggested.

_{ARS}measurement was based on a resonator sensor element for measuring the contact area between the sensor and cornea, and a force transducer for measuring the contact force (Fig. 1) . The area measuring device consisted of a rod-shaped (23 × 5 × 1 mm) piezoelectric element made of lead zirconate titanate (PZT). A PZT pick-up (5 × 5 × 1 mm) was glued on the center of the PZT element. A feedback circuit processed the signal from the pick-up and powered the PZT element to sustain the oscillations in the resonance frequency. A plastic piece (Duro; E Wiberger, Molndal, Sweden), used for contact against the cornea, was glued onto one end of the PZT element. The contact surface of the piece is convex, with a radius of curvature of ρ = 7 mm. The resonance frequency depends on the geometry and material properties of the PZT element and contact piece, the suspension of the element, and the frequency characteristics of the feedback circuit.

^{ 5 }When the sensor is brought in contact with the cornea, the acoustic impedance of the cornea mechanically loads the sensor and a new oscillating system is formed with a new resonance frequency. Because the degree of load on the resonance system depends on the contact area, the resonance frequency of the system is related to the contact area between sensor and cornea.

^{ 3 }The frequency of oscillation can be used for area measurement. The principle and theory of the resonator sensor system have been described earlier.

^{ 3 }

^{ 5 }

^{ 6 }The force transducer (PS-05 kDa; Kyowa, Tokyo, Japan) and the resonator element were mounted in a sensor module consisting of a cylindrical aluminum case (Fig. 1) .

^{ 3 }

^{ 5 }In designing a model for the current ARS probe we therefore assumed that frequency (

*f*) changes proportionally to contact area

*(A)*

*f*

_{0}as the resonance frequency of unloaded sensor and

*C*

_{ARS}being a sensor-specific proportionality constant. Equations 1 and 2 yield

_{VC}) during applanation was measured with a standard monitoring kit (BD Biosciences, Lincoln Park, NJ). The vertical position of the sensor was measured with an inductive position transducer

^{ 6 }placed at the lever. Indentation (

*L*) was defined as the position change after contact (Fig. 2) . Maximum indentation was set so that the force at full indentation was between 40 and 50 mN at an IOP of 10 mm Hg, which resulted in a maximum indentation ranging from 1.20 to 1.63 mm. Frequency, pressure, force, and position data were sampled with a data acquisition card (DAQCard 1200; National Instrument, Inc., Austin, TX). The sampling rate was set to 1000 Hz, and recording time was set to 15 seconds.

^{ 7 }Six eyes were used for evaluation of the sensor’s ability to measure IOP. One eye was used for evaluation of off-center positioning dependence of the sensor. After IOP measurement was completed, the equatorial diameter of the eyeball (∅

_{eye}) and corneal diameter, (∅

_{cornea}) were measured with a vernier caliper. The cornea was then removed from the eye and the corneal thickness,

*T*

_{cornea}, was measured with a micrometer. Anatomic measurements are found in Table 1 .

^{ 5 }Briefly, the eyes were mounted firmly in a Petri dish with agar solution (15 g/L) that covered the eye approximately 50%. A winged, thin-walled cannula of dimensions 0.8 × 19 mm (Terumo Corp., Tokyo, Japan) was introduced through the side of the eyeball into approximately the middle of the vitreous chamber. The interface between the cannula and the tissue was sealed with cyanoacrylate adhesive (True Bond; Pro-Gruppen AB, Stockholm, Sweden) to avoid leakage.

^{ 8 }The cannula was connected to a saline column consisting of PVC tubing, a three-way stopcock, and, at the distal end, a partially saline-filled syringe open to air. The syringe was movable and mounted on a stable stand. The eye was pressurized for 10 seconds by opening it to the saline column. The pressure level was calculated from the measured height of the saline column. Just before measurement the stopcock was closed to create a closed system that approximated the normal state of the eye.

^{ 8 }To account for the continuous pressure decline after the stopcock was closed, IOP

_{VC}was defined as the mean monitored pressure in the interval 1.0 to 0.5 seconds before ARS contact. To avoid drying of the cornea, the eye was moistened before every pressurization with room temperature saline. To simulate blinking, the saline was applied to the eye with one sweep of a very soft goat hair brush (Kreatima 922; Schormdanner Pinsel, Nürnberg, Germany).

*f*

_{0}) for each measurement was determined as the mean frequency in the interval 1.0 to 0.5 seconds before contact. The force-frequency and position-frequency analyses focuses on an interval in the initial phase of applanation (Fig. 2) . The frequency interval is described by a starting offset

*f*

_{start}=

*f*

_{0}−

*f*

_{1}and an ending offset

*f*

_{end}=

*f*

_{0}−

*f*

_{2}(Figs. 2 3) . The interval length was defined as

*f*

_{interval}=

*f*

_{1}−

*f*

_{2}. To optimize the frequency interval, an algorithm stepped through all combinations of start points and interval lengths (50 <

*f*

_{start}< 250 Hz; 50 <

*f*

_{interval}< 500 Hz), increasing with steps of 10 Hz. Using linear regression, we applied the model of equation 5 to the force and frequency data of the chosen frequency interval from all measurements. The precision of the model according to equation 5 was interpreted from the SD of the residuals. Optimal frequency interval was determined as the frequency interval that produced the lowest SD.

*P*< 0.05 was considered statistically significant. Within each eye, the replicate observations on each IOP level were based on independent measurements of both IOP

_{VC}and

*dF*

_{C}/

*df*and were regarded as independent measurements in the analysis. Terms used in the equations are listed and defined in

^{Appendix 1}.

*f*

_{1}=

*f*

_{0}−

*f*

_{start}and

*f*

_{2}=

*f*

_{0}−

*f*

_{end}. The force,

*F*

_{C}, was plotted against the frequency and

*dF*

_{C}/

*df*was calculated as the slope of a linear regression in the selected interval (Fig. 3) .

*f*

_{start}= 150 and

*f*

_{end}= 470 Hz (Fig. 2) . This frequency interval was then used in the analysis throughout this study. The corresponding indentations for the frequency interval were between

*L*

_{1}= 0.19 ± 0.02 mm (

*n*= 418) and

*L*

_{2}= 0.49 ± 0.02 mm (

*n*= 418; Fig. 2 ). The number of measurements (

*n*= 418) originated from 6 eyes × 7 IOP levels × 10 repetitions. Two measurements were omitted during experiments because of operator error. The corresponding time interval after initial contact was

*t*

_{1}= 30 ± 3 (

*n*= 418) to

*t*

_{2}= 77 ± 4 ms (

*n*= 418; Fig. 2 ).

*n*= 418), put together, showed that the residuals were normally distributed (

*P*> 0.20,

*n*= 19,959) around zero. The number of samples (

*n*= 19,959) originated from 418 measurement series, with interval length varying between 36 and 57 samples in each measurement series. This means that the relationship between frequency and indentation was linear in the frequency shift interval from 150 to 470 Hz below the unloaded frequency. The linear relationship in that interval can be described by

_{ fL }) was determined for each measurement series. There was a significant but low correlation between α

_{ fL }and IOP

_{VC}(

*r*= 0.47,

*n*= 418). The linear relationship was described by α

_{ fL }= −2.30 IOP + 1152, resulting in a 6% variation over the 10- to 40-mm Hg interval. SD of the residuals was 44 Hz/mm (

*n*= 418).

^{(Appendix 2)}, the measured indentation interval (

*L*= 0.19–0.49 mm) and radius of corneal curvature approximated with human corneal curvature (

*R*= 7.5 mm)

^{ 9 }

*dA/dL*was nearly constant, with a range from 22.77 to 22.80 mm

^{2}/mm.

^{(Appendix 2)}the area interval used was approximately 4.3 to 11.2 mm

^{2}. From these convex areas, the effective area normal to the axial direction can be calculated to 4.3 to 11.0 mm

^{2}.

*dF*/

*df*

*dF*

_{C}/

*df*and IOP

_{VC}, based on the model of equation 5 and eye number as a categorical factor (GLM analysis), was

*R*

^{2}= 0.987 (

*n*= 418, Table 2 ). Residual analysis from the linear fit showed a standard deviation of 1.14 mm Hg (

*n*= 418) and that the deviations were not normally distributed (

*P*< 0.001,

*n*= 418). Exclusion of eight observations and a subsequent GLM analysis on the reduced data set yielded

*R*

^{2}= 0.991 (

*n*= 410, Table 2 ) and showed that the residuals were normally distributed (

*P*= 0.16,

*n*= 410). The reduced set (

*n*= 410) was used in the subsequent analysis. The residuals of the excluded observations all exceeded 3 SD of the normally distributed residuals of the reduced data set.

^{ 10 }The mean of the residuals was 0.00 mm Hg (

*n*= 410), with a standard deviation of 0.94 mm Hg (

*n*= 410), indicating that the 95% confidence interval for the residuals between IOP

_{ARS}and IOP

_{VC}was ± 1.8 mm Hg. The GLM analysis also showed that the systematic contributions from the eyes were −0.71, −0.21, 0.61, −0.14, 0.34, and 0.11 mm Hg (

*n*= 410) for the six eyes. Predicted IOP

_{ARS}data are plotted against IOP

_{VC}in Figure 4 . Table 3 shows that there was no clear trend regarding the standard deviation of the residuals in relation to IOP.

*R*

^{2}and reduced the residual standard deviation moderately (Table 2) . The analysis of individual eyes (Table 4) showed that the variation in slope (β

_{1}) was less than ±6%, compared with the GLM analysis (Table 2) . The 95% confidence intervals for the individual slopes did not all overlap (Table 4) , indicating differences between eyes.

*dF*

_{C}/

*df*, a linear regression model including IOP

_{VC}and corneal thickness was used:

_{Const}= −0.0161, β

_{VC}= −0.00351, and β

_{CT}= 0.0312,

*n*= 410, six eyes) which means that

*dF*

_{C}/

*df*was dependent on both IOP

_{VC}and

*T*

_{cornea}.

*dF*

_{C}/

*df*(equation 8) , translates to a contribution of 0.75 mm Hg to IOP

_{ARS}for a 10% change in corneal thickness.

_{VC}= 20.4 ± 0.1 mm Hg (

*n*= 50). IOP

_{ARS}, calculated from measured

*dF*

_{C}/

*df*and the linear model with coefficient according to Table 2 , second row, varied between 20.7 and 24.6 mm Hg (mean,

*n*= 10). The coordinates (

*X*,

*Y*) describe the off-center position of the eye. IOP

_{ARS}for two off-center positions, IOP

_{ARS}(−1,0) = 21.3 (

*n*= 10) and IOP

_{ARS}(0,1) = 21.3 (

*n*= 10), corresponded well to the center position IOP

_{ARS}(0,0) = 20.7 (

*n*= 10). Measurements from two positions, IOP

_{ARS}(1,0) = 23.8 (

*n*= 10) and IOP

_{ARS}(0,−1) = 24.6 (

*n*= 10) deviated significantly from the center measurement (ANOVA post hoc,

*n*= 50).

^{ 3 }

^{ 4 }

*f*

_{0}– 150) to (

*f*

_{0}– 470) Hz. Furthermore, because the relationship between change in contact area and change in indentation,

*dA/dL*, was shown to be nearly constant, we can conclude that, within the chosen interval, a change in indentation corresponds to a linear change in area. This supports the hypothesis that a change in contact area, within this interval, corresponds linearly to a change in resonance frequency.

^{ 3 }

^{ 4 }of ARS probes for IOP measurement have been based on a constant-force method and area measurement with the ARS probe. Those studies showed a high reproducibility within each eye, but clear differences between eyes. The Imbert-Fick law assumes that the cornea is infinitely thin, perfectly elastic, and perfectly flexible and that the only force acting against it is the pressure of the applanated surface.

^{ 7 }None of these assumptions is true. The cornea is not a membrane without thickness, and it offers resistance to indentation, varying with its curvature and thickness and the presence or absence of corneal edema. The surface of the cornea is covered with a liquid film. Therefore, during the applanation of the cornea, capillary attraction or repulsion forces between the contact piece and the cornea interfere with the measurement.

^{ 2 }The force term depends on the width of the ring (i.e., the amount of fluid).

^{ 2 }Thus, there are forces unrelated to IOP that are present, and the magnitude of the forces is dependent on properties that differ from eye to eye and even from measurement to measurement. In Eklund et al.

^{ 3 }it was shown that the correlation between reference IOP and IOP

_{ARS}was

*r*= 0.92 (

*n*= 360, six eyes together) for the constant-force ARS method. By the same calculation, the present study with a model based on the continuous force and area measurement showed a corresponding correlation of

*r*= 0.99 (

*n*= 410, six eyes together). The eye-dependent variation in proportionality coefficient (β

_{1}) was –25% to +16% (calculated from Table 1 in Ref.

^{ 3 }) for the constant-force study and less than ±6% in the present study. This shows that the intereye variation was much less with the new method. One explanation for the improvement is that the differential force–area method is not sensitive to constant-force terms, because it analyzes the change in force over an area interval and is therefore unaffected by any constant terms.

_{eye}= 24 mm and ∅

_{cornea}= 12 mm).

^{ 11 }This supports the use of an in vitro porcine eye model for a first evaluation of new tonometers. However, factors such as scleral rigidity, ocular curvature, and pressure–volume relationships, all vary between species, and tonometers must be calibrated for each species.

^{ 12 }

^{ 13 }to affect IOP measurement performed with the applanation method. The corneal thickness of the eyes of the Landrace pigs used in this study varied between 0.80 and 0.90 mm, thicker than the cornea of a normal human eye (

*T*

_{human =}0.534 mm).

^{ 13 }Ideally, for an applanation method, the cornea should be as thin as possible, indicating that the accuracy for an in vitro human eye should be better than the results of this study. Because of differences in corneal thickness, both the frequency interval and the coefficients of the model have to be optimized and reestimated for use in humans. Although only a small number of eyes were studied, there was a significant dependence of the ARS method on cornea thickness. This dependence, however, was less than the sensitivity to corneal thickness shown with GAT in healthy eyes (1.1 ± 0.6 mm Hg for a 10% change in corneal thickness).

^{ 13 }Further studies are needed to determine fully the relationship between corneal thickness and accuracy of IOP

_{ARS}.

_{VC}. We therefore cannot draw conclusions about overall accuracy in this type of study. Because the mean deviation is zero, the within-eye precision is described by the variation of the residuals. The overall SD of the residuals in this study was 0.93 mm Hg. This is in parity with the results of Schmidt

^{ 14 }for GAT on four fresh enucleated human eyes (residual SD = 0.85 mm Hg,

*n*= 20, calculated from Table 2 in Ref.

^{ 14 }). The quadratic and cubic models did not produce any substantial improvement in the precision of the method. For simplicity and robustness, we therefore choose and recommend the linear model (equation 5) .

^{ 3 }was effectively reduced with the current method, which showed an approximately similar precision at all pressure levels (Table 3) . The main difficulty with the previous ARS method was that it used constant force and measured the resultant contact area. The contact area was therefore inversely proportional to IOP (equation 1) which resulted in small areas of contact and a decrease in resolution at high pressures.

^{ 3 }This problem was solved with the new method, which uses the same contact area interval, independent of IOP. Similar to GAT, this leads to a measured force that is directly proportional to the IOP at all pressure levels. In addition, the area interval used in the new ARS method (4.3–11.0 mm

^{2}) is close to the interval for which Goldmann

^{ 2 }(4.9–12.6 mm

^{2}, calculated from contact diameters of 2.5–4 mm) suggested that the Imbert-Fick law is valid.

^{ 15 }With the GAT, the standard contact area guarantees that the displaced volume is small, and the pressure in the eye will be elevated only slightly.

^{ 15 }For indentation–applanation methods with constant area and guard ring (Tono-Pen; Mentor, Norwell, MA) there is no control of the indentation and volume displacement. The area measurement of the ARS method and choice of area interval for analysis based on that measurement ensures that the indentation, as in the Goldmann method, is standardized (

*L*

_{2}≈ 0.49 mm). Thus, the scleral rigidity-related IOP-increase during measurement is controlled and should be approximately the same for all measurements.

^{ 4 }off-center alignment was acknowledged as a source of error with the ARS. The study with an ARS mounted in a biomicroscope indicated that the maximum off-center alignment was approximately 1 mm. It also showed that this sensitivity could be reduced with a convex contact surface. The results of the present study showed that a 1-mm off-center alignment could result in a 4-mm Hg overestimation of the IOP

_{ARS}at the 20-mm Hg level. Although the current tip was smaller and may be easier to apply at the center, this has to be taken into consideration in the future development of the ARS system.

^{ 16 }

_{cornea}, corneal diameter

_{eye}, equatorial diameter of the eyeball

*A*, contact area between sensor and cornea

_{ fL }, proportionality constant between frequency shift and indentation

*C*

_{ARS}proportionality constant between frequency shift and area

*f*, frequency

*f*

_{0}, frequency of unloaded sensor

*f*

_{1}, frequency of starting offset for interval used in analysis

*f*

_{2}, frequency of end offset for interval used in analysis

*f*

_{start},

*f*

_{0}–

*f*

_{1}

*f*

_{end},

*f*

_{0}–

*f*

_{2}

*f*

_{interval},

*f*

_{start}–

*f*

_{ end }

*F*

_{C}, contact force

_{ARS}, IOP measured with the ARS

_{VC}, IOP measured in vitreous chamber

*L*, indentation of the cornea

*L*

_{1}, indentation at beginning of the interval used in the analysis

*L*

_{2}, indentation at the end of the interval used in the analysis

*r*, correlation coefficient

*R*, corneal radius of curvature

*R*

^{2}, degree of explanation for a model

*t*, time references to initial contact

*t*

_{1}, starting time for interval used in analysis

*t*

_{2}, end time for interval used in the analysis

*T*

_{cornea}, corneal thickness

*T*

_{human}, corneal thickness of human eye

*a*)

^{ 17 }:

*b*and

*c*can be expressed as

*A*) as a function of indentation (

*L*). The differentiation in equation A6 produces the relationship between change in indentation and change in area

**Figure 1.**

**Figure 1.**

**Figure 2.**

**Figure 2.**

Eye | ⊘_{eye} | ⊘_{cornea} | T _{cornea} |
---|---|---|---|

1 | 24.0 | 14.5 | 0.81 |

2 | 23.5 | 14.6 | 0.86 |

3 | 24.8 | 15.5 | 0.84 |

4 | 24.6 | 15.5 | 0.85 |

5 | 23.8 | 15.8 | 0.90 |

6 | 24.4 | 15.2 | 0.85 |

7 | 23.3 | 14.3 | 0.90 |

**Figure 3.**

**Figure 3.**

Model | β_{0} | β_{1} | β_{2} | β_{3} | R ^{2} | SD Residual | n |
---|---|---|---|---|---|---|---|

Linear^{*} | 3.36 | −284 | 0.987 | 1.14 | 418 | ||

Linear | 3.18 | −283 | 0.991 | 0.94 | 410 | ||

Quadratic | 4.56 | −242 | 267 | 0.992 | 0.89 | 410 | |

Cubic | 5.53 | −187 | 1080 | 3520 | 0.992 | 0.88 | 410 |

**Figure 4.**

**Figure 4.**

IOP Level (mm Hg) | Mean Residuals (mm Hg) | SD (mmHg) | n |
---|---|---|---|

10 | 0.33 | 1.00 | 58 |

15 | −0.08 | 0.69 | 59 |

20 | −0.37 | 0.69 | 59 |

25 | −0.15 | 0.74 | 60 |

30 | −0.41 | 0.86 | 60 |

35 | 0.00 | 1.04 | 59 |

40 | 0.74 | 0.98 | 55 |

Eye | β_{0} | β_{1} | β_{1 95%} Lower^{*} | β_{1 95%} Upper^{*} | R ^{2} | SD Residuals | n |
---|---|---|---|---|---|---|---|

1 | 2.71 | −280 | −286 | −274 | 0.99 | 0.88 | 69 |

2 | 3.30 | −279 | −282 | −275 | 1.00 | 0.57 | 69 |

3 | 2.61 | −298 | −303 | −293 | 1.00 | 0.72 | 70 |

4 | 2.93 | −284 | −289 | −279 | 1.00 | 0.73 | 70 |

5 | 4.86 | −265 | −273 | −257 | 0.99 | 1.18 | 65 |

6 | 2.49 | −293 | −301 | −286 | 0.99 | 1.04 | 67 |

**Figure 5.**

**Figure 5.**