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Development and Validation of a Correction Equation for Corvis Tonometry
Akram Joda1, Mir Mohi Sefat Shervin2, Daniel Kook3, Ahmed Elshiekh1,4*
1School of Engineering, University of Liverpool, Liverpool L69 3GH, UK
2Smile Eyes Clinic, Munich, Germany
3Department of Ophthalmology, Ludwig-Maximilians-University, Munich, Germany
4NIHR Biomedical Research Centre for Ophthalmology, Moorfields Eye Hospital NHS Foundation
Trust and UCL Institute of Ophthalmology, UK
* Corresponding author
Proprietary interest statement - nil
Financial Disclosures
This work was partly funded by Oculus Optikgeräte GmbH, Wetzlar, Germany
Keywords: tonometry; cornea; ocular biomechanics; intraocular pressure
Author for correspondence:
Ahmed Elsheikh, School of Engineering, University of Liverpool, Liverpool L69 3GH, UK
elsheikh@liv.ac.uk, Tel: +44-151-7944848
Number of words: 3295
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Abstract:
Purpose:
This study uses numerical analysis and validation against clinical data to develop a method to
correct intraocular pressure (IOP) measurements obtained using the Corvis ST Tonometer (CVS)
for the effects of central corneal thickness (CCT), central radius of corneal curvature (R) and age.
Materials and Methods:
Numerical analysis based on the finite element method was conducted to simulate the effect of
tonometric air pressure on the intact eye globe. The analyses considered eyes with wide variations
in IOP (10 to 30 mmHg), CCT (445 to 645 microns), R (7.2 to 8.4 mm), shape factor, P (0.6 to 1)
and age (30 to 90 years). In each case, corneal deformation was predicted and used to estimate the
IOP measurement by Corvis (CVS-IOP). Analysis of the results led to an algorithm relating
estimates of true IOP as a function of CVS-IOP, CCT and age. All other parameters had negligible
effect on eye deformation under air pressure and have therefore been omitted from the algorithm.
The models have been validated in two steps. First, the output of four models representing 4 eyes
with wide variations in IOP, CCT and age was compared to the eye deformation measured with the
CVS. Second, predictions of corrected IOP, as obtained by applying the algorithm to a clinical
dataset involving 634 patients, were assessed for their association with the cornea stiffness
parameters; CCT and age.
Results:
In four cases with wide variations in IOP, CCT and age, model predictions of the maximum apical
deformation under air pressure and the time to first applanation were within ±8.0% and ±1.5% of the
Corvis data. Analysis of CVS-IOP measurements within the 634-large clinical dataset showed
strong correlation with CCT (3.06 mmHg/100 microns, r2 = 0.204) and weaker correlation with age
(0.24 mmHg/decade, r2 = 0.009). Applying the algorithm to IOP measurements resulted in IOP
estimations that became less correlated with both CCT (0.04 mmHg/100 micros, r2 = 0.005) and age
(0.09 mmHg/decade, r2 = 0.002).
Conclusions:
CCT accounted for the majority of variance in CVS-IOP, while age and R had a much smaller effect.
The IOP correction process developed in this study was successful in reducing reliance of IOP
measurements on both corneal thickness and curvature in a healthy European population.
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Introduction
Glaucoma is a group of diseases that can lead to optic nerve damage and irreversible loss of vision.
60 million people worldwide are affected by glaucoma; the second most-common cause of
blindness [1]. The diseases are associated with an elevated intraocular pressure (IOP), the accurate
determination of which is important for the effective management of glaucoma. The most-commonly
used method to measure IOP, and the reference standard in tonometry, is the Goldmann
applanation tonometer (GAT) [2]. The method, which determines IOP by measuring the force
required to applanate a certain area of the central cornea, has been found to be affected by corneal
stiffness parameters including the central corneal thickness (CCT), the mechanical properties of
corneal tissue and corneal curvature [3–7]. As a result, several correction equations have been
developed to compensate for the effect of stiffness and hence obtain a more accurate estimate of
the true IOP [5,8–10].
Over the past five decades several other tonometers have been developed including those that still
rely on contact techniques (most notably the Rebound Tonometer and the Dynamic Contour
Tonometer) and non-contact techniques that use an air-puff to indent the cornea. The advantages
of non-contact tonometers over contact tonometers include their relative ease of use and less-
invasive operation. However, non-contact tonometers, which are similar to contact tonometers in
that they apply a mechanical force and correlate the resulting deformation to the value of IOP, have
also been found to be influenced by corneal stiffness parameters, and in particular corneal
thickness, curvature and mechanical properties [11–13]. Additionally, as non-contact tonometers
have traditionally been known to be less reliable than contact methods, their use has been mainly in
clinics, leaving hospital applications to be dominated by contact tonometers.
However, this trend is changing with the emergence of reliable non-contact tonometers such as the
Ocular Response Analyzer, which has been shown to provide close results to GAT and other
contact devices such as the Dynamic Contour Tonometer. More recently, a non-contact tonometer,
the Corvis ST (Corneal Visualization Scheimpflug Technology), has been developed by OCULUS
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Optikgeräte, Inc. (Wetzlar, Germany) [14]. The Corvis relies on high-precision, ultra-high-speed,
Scheimpflug technology to monitor corneal deformation under air puff and produce a wide range of
tomography and deformation parameters, which have the potential to enable accurate estimates of
both corneal stiffness and IOP.
This paper presents a parametric study of the Corvis procedure to determine the effect of the main
stiffness parameters; corneal thickness, curvature, shape factor and the tissue’s material properties,
on IOP measurements. The study uses nonlinear finite element simulations of the air pressure
application on the eye as applied by the Corvis. Analysis of the results allowed developmed of a
closed-form algorithm providing estimates of IOP with significantly reduced correlation with the
stiffness parameters. Successful validation of the equation has been carried out using a clinical
dataset of 634 healthy eyes.
Methods
The finite element (FE) software ABAQUS 6.13 (Dassault Systèmes Simulia Corp.,Rhode Island,
USA) was used to model the Corvis ST testing procedure. In order to ensure accurate
representation of in-vivo conditions, the FE models adopted the following features from previous
work [15–17]:
Full representation of the human eye’s outer tunic with consideration of cornea’s and sclera’s
thickness variation;
Representation of the eye’s internal fluids; the aqueous and the vitreous;
Stress-free form of the eye globe (under zero IOP);
Regional variation of sclera’s mechanical properties; and
Dynamic representation of the Corvis air pressure.
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The models employed 10952 fifteen-noded elements organised in 25 element rings in the cornea,
124 element rings in the sclera and 1 element layer (Figure 1). This high mesh density allowed
smooth representation of ocular topography and thickness variation.
Third-order, hyperelastic Ogden models were used to represent the ocular tissue’s mechanical
behaviour and its variation with age [18,19]. Scleral regional variation in stiffness and its gradual
reduction from the limbus towards the optic nerve was incorporated in the models [15].
To prevent the models from rigid-body motion, all nodes along the equator were restrained in the
anterior-posterior direction (z-direction), and corneal apex and posterior pole nodes were restrained
in both the superior-inferior and temporal-nasal directions. To account for the aqueous’ and vitreous’
incompressible behaviour, the ocular globe models were filled with an incompressible fluid with a
density of 1000 kg/m3 [20].
Before conducting the study, the stress-free configuration for each model was obtained while
following an iterative procedure explained in [16]. Two subsequent steps were then adopted in the
simulations. First, the models started from their stress-free configurations and the IOP was applied
gradually as a pressure increase in the internal incompressible fluid up to the desired level. In the
second step, space- and time-varying external air pressure was applied on the anterior surface of
the cornea. The spatial distribution of the air pressure (Figure 2a) was obtained from [12] and the
time variation was obtained from data acquired from the device manufacturers (Figure 2b). The
maximum air pressure that Corvis produces is about 180 mmHg and that was found by the
manufacturer to be reduced by approximately 50% as the air puff reached the cornea’s anterior
surface.
In the Corvis device, successive images are taken by the device’s Scheimpflug camera during the
30 ms duration of the air-puff. The images are analysed by an integrated computer to determine
IOP and several other parameters including corneal pachymetry, apical deformation, first and
second applanation time (A1, A2-time), first and second applanation length (A1, A2 length), velocity
of corneal apex at first and second applanation (A1, A2 velocity), highest concavity time (HC time),
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and the distance between the two peaks at the point of highest concavity (Figure 3). The IOP is
measured in Corvis (CVS-IOP) as a function of the time to the first applanation event (A1-time), or
when the cornea starts to change its shape from convex to concave. Once the A1-time is known,
the external pressure acting on the cornea at that time (AP1) is measured and the IOP estimate is
calculated as a function of AP1. This process was replicated in the analysis of the FE model results
to determine AP1 and hence estimate CVS-IOP.
Parametric Study
The numerical models were used in a parametric study to quantify the effect of parameters with
potential considerable influence on CVS-IOP measurements. The parameters included the true IOP
in addition to the main stiffness parameters of the cornea, namely the thickness, curvature and
shape factor. Age was introduced for its known effect on the stress-strain behaviour of the tissue,
and it was therefore used as a parameter controlling the mechanical stiffness of both the cornea
and sclera [19,21,22]. In the study, IOP was varied from 10 to 30 mmHg in steps of 5 mmHg, central
corneal thickness (CCT) from 445 to 645 μm in steps of 50 μm, age from 30 to 90 years in steps of
10 years, central radius of anterior curvature (R) from 7.2 to 8.4 mm in steps of 0.3 mm and corneal
anterior shape factors (P) of 0.6, 0.71, 0.82 and 1. These values were compatible with the ranges of
variation reported in earlier clinical studies [23–27].
The total number of models in the parametric study was 1575. In each model specific values of
CCT, R, P, age and IOP were used. The analysis step of the air puff application was dynamic and
consisted of 300 pressure increments (time step = 0.0001s) covering the 0.03 s of the Corvis
procedure. The coordinates of corneal anterior nodes were extracted at each time step using a
Python code, and a MATLAB code (MathWorks, MA) was used to determine the point of
applanation (A1-time), the external pressure at this point (AP1) and hence IOP estimate as a
product of AP1 and a calibration factor provided by Oculus.
The results of the parametric study were used to analyse the effect of CCT, R, P and age on the
CVS-IOP estimates, and to develop an algorithm relating estimates of true IOP to both the
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measured CVS-IOP and the cornea’s stiffness parameters. Following development, the algorithm
was validated in a clinical dataset by testing its effect on the strength of association between IOP
estimates and the stiffness parameters considered. This validation exercise was preceeded by a
short comparative study where the match between the output of 4 models of four randomly-selected
eyes with wide variations in IOP, CCT and age was assessed in detail against the Corvis output for
the same eyes.
Validation clinical dataset
A clinical dataset was collected at Smile Eyes Clinics in Munich, Germany, and used in an exercise
to assess the success of the IOP algorithm developed in this study in reducing association between
IOP measurments and the cornea’s stiffness parameters. The dataset involved 634 eyes of 317
healthy participants with no pathological conditions. All patients signed a written informed consent
form. The study was approved by the local institutional review board and adhered to the tenets of
the Declaration of Helsinki. For each participant, CCT, IOP, apical deformation, A1 time and AP1
were measured by the Corvis. All measurements were performed by the same investigator (SM).
Mean, standard deviation and range of measurements are presented in Table 1.
Results
Validation of numerical results
In order to validate the numerical simulations of the Corvis procedure, the numerical results of four
models representing four randomly-selected eyes with wide variations in IOP, CCT, R and age were
considered in detail. Table 2 shows part of the Corvis output for the four eyes where the mean
values of three measurements are presented.
An eye-specific model was generated for each eye based on the CCT and R values, and the
material properties for the cornea and sclera were assumed to follow the association identified in
earlier work between stress-strain behaviour and age [15,18,19]. Constant values of the shape
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factor, axial length and sclera diameter of 0.82, 23.7 mm and 23.0 mm, respectively, were assumed
since they were not measured clinically and were found numerically to have a negligible effect on
IOP estimations.
The four models were analysed and their output compared to Corvis parameters. Figure 4 shows a
selection of the comparisons held, which concentrate on two parameters with good repeatability and
direct relevance to corneal stiffness [28]; namely the maximum apical deformation and the first
applanation time (A1-time). The comparisons demonstrated a close match between the numerical
predictions and the Corvis output with the differences remaining below ±8% in all cases.
Parametric Study
The numerical results illustrate a clear effect of increased CCT (from 445 μm to 645 μm) in
decreasing maximum apical displacement by 37% and increasing A1-time by 14% on average,
Figure 5a. Similarly, an increase in age from 30 to 90 years (and hence increased material stiffness)
was associated with an average decrease in corneal displacement of 27% and a slight increase in
A1-time of 4%, Figure 5b. Moreover, an increase in true IOP from 10 to 30 mmHg led to an average
reduction in apical displacement of 47% and an average increase in A1-time of 48% (Figure 5c).
Changes in corneal curvature and shape factor within the considered range led to only slight
changes in corneal deformation and A1-time that were <3% as shown in Figures 5d & e. The results
show that the apical deformation and applanation time are associated with changes in CCT, IOP
and age, while variations in corneal curvature parameters (R and P) have only negligible effects on
corneal deformation behaviour.
Further, the influence of true IOP, CCT, age, R and P on estimated CVS-IOP is presented in Figure
6 (a-d). The results demonstrate that CVS-IOP is strongly associated with (or strongly influenced by)
CCT, correlated with age but with weaker association, while it is almost independent of variations in
R and P. These results illustrate that for the IOP to be estimated with reduced influence of corneal
stiffness, consideration must be made of variations in CCT and age.
IOP Correction algorithm
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The parametric study predictions of CVS-IOP and the input parameters of true IOP, CCT and age
were used to develop equation (1) linking the four parameters together and providing estimates of
IOP that were less affected by the stiffness parameters than CVS-IOP. Values of the equation’s
parameters were obtained using the least squares method by minimising the sum of squared errors
between predicted and corrected IOP (Σ(IOPc – CVS-IOP)2). The resulting equation has the form:
IOPc = (CCCT1 x CCVS-IOP + CCCT2) x Cage + C (1)
where CCCT1, CCCT2 are parameters representing the effect of variation in CCT (mm);
CCCT1 = 4.67 x 10-7 x CCT2 – 7.8 x 10-4 x CCT + 0.63
CCCT2 = -1.73 x 10-5 x CCT2 + 2.02 x 10-3 x CCT – 0.97
CCVS-IOP represents effect of variation in measured CVS-IOP (mmHg) = 10 + (CVS-IOP + 1.16) /
0.389
Cage denotes effect of variation in age (years) = -2.01 x 10-5 x age2 + 1.3 x 10-3 x age + 1.00
C = 1.50 mmHg
Figure 7a shows the difference between the corrected IOP and CVS-IOP increasing mainly with
CCT but also with CVS-IOP and age. Without compensating for CCT and age variation, CVS-IOP
had a predicted measurement error as high as 10 mmHg when CCT = 645 μm and age > 60 years.
After IOP correction, the error in IOP reduced in most cases to below 1 mmHg (Figure 7b).
Correction Equation Assessment using Clinical Data
The clinical dataset described above was used to evaluate the effectiveness of the correction
algorithm in reducing reliance of IOP on the cornea’s stiffness parameters. Figure 8a presents
uncorrected CVS-IOP versus CCT, where strong association was evident from the regression and
gradient of the trend line (r2 = 0.204, slope = 0.0306 mmHg/µm). Figure 8b shows the results after
applying equation (1), leading to a reduction in r2 to 0.004 and the gradient to -0.0035 mmHg/µm.
Meanwhile, the mean CVS-IOP increased slightly from 14.45±2.83 mmHg before correction to
14.92±2.40 mmHg after correction. Similar to the numerical results, CVS-IOP was found to be
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correlated weakly with age (Figure 9a). Using Equation (1), the coefficient of determination was
reduced from 0.009 to 0.0005 and the gradient from 0.024 to 0.0043 mmHg/year.
Discussion
The study evaluated the effect of major corneal stiffness parameters on the IOP measurements by
the Corvis. The Corvis has a number of unique features over other tonometers. First, it is able to
measure corneal thickness directly without a need for a separate device, making it possible to
directly correct for the effect of CCT on IOP. CCT measurements by the Corvis were found to have
good repeatability and accuracy compared to ultrasound pachymetry [28,30]. Second, the several
deformation parameters the device collects may make it possible to quantify corneal material
behaviour, which could then be considered in the further correction of IOP measurements.
In this paper, the effect on CVS-IOP measurements of both corneal geometric stiffness parameters
(CCT, R, P) and material stiffness (while assuming correlation with age [19,21,22]) has been
quantified. The results demonstrated clear effect of CCT on CVS-IOP, a relatively smaller effect of
material behaviour (as it varies with age) and almost no influence of R or P. Similar results were
obtained for GAT-IOP which, while being different in the nature of the force applied on the cornea,
still applies a mechanical force and correlates the resulting corneal deformation to the value of IOP
[9,32–34].
The development of a correction algorithm for CVS-IOP relied initially on numerical simulation that is
representative of the eye’s geometric and material characteristics and the Corvis procedure.
Numerical simulation was found to be a reliable tool in modelling the cornea’s response to
mechanical loads such as those applied by tonometers. Similar earlier work has led to a number of
correction equations for GAT and ORA, which were later successfully validated clinically [12,35,36].
The numerical simulations of the Corvis procedure were first validated against clinical results
obtained in-vivo for four randomly-selected eyes with wide variations in CVS-IOP, age and CCT.
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The close match between the numerical and clinical results, including the values of central
displacement and A1-time, demonstrated the reliability of the simulations and their ability to
accurately model the Corvis procedure. Subsequently, a parametric study considering wide ranges
of variation in CCT, R, P, age and true IOP was conducted. The study provided confirmation that
the A1-time is strongly correlated with IOP, CCT and age. Using the least squares method, an
algorithm quantifying the correlation of CVS-IOP with CCT and age was developed and proposed
as a means to provide estimates of IOP that were less affected by variations in corneal mechanical
stiffness.
The correction algorithm was tested against a clinical dataset of 634 healthy eyes. Uncorrected
CVS-IOP measurements were significantly correlated with CCT (r2 = 0.204, slope = 0.0306
mmHg/µm) and less correlated with age (r2 = 0.009, slope = 0.024 mmHg/year). Introducing the
correction algorithm reduced the dependency of CVS-IOP on both CCT (r2=0.004, slope = -0.0035
mmHg/µm) and age (r2 = 0.0005, slope = 0.0043 mmHg/year) considerably.
The correction algorithm presented in this paper offers a novel, simple, yet effective, method to
obtain IOP estimates that are less affected by the main corneal stiffness parameters, removing
dependency on a major error source and producing more reliable IOP estimates for glaucoma
management.
Acknowledgements:
The research was partially supported by the National Institute for Health Research (NIHR)
Biomedical Research Centre based at Moorfields Eye Hospital NHS Foundation Trust and UCL
Institute of Ophthalmology (AE). The views expressed are those of the author(s) and not necessarily
those of the NHS, the NIHR or the Department of Health of the United Kingdom.
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Figure captions
Figure 1 Computational mesh of the whole eye model (a) and Von mises stress distribution at the
highest concavity (b).
Figure 2 Spatial distribution (a) and time variation (b) of air pressure on the cornea’s surface. In (b)
thick black line represents air-puff produced at the device piston and grey line represents the
pressure acting on the cornea’s surface.
Figure 3 Example of a Corvis measurement showing the deformed cornea at the highest concavity.
Figure 4 Comparison of numerical predictions with clinical measurements of (a) the maximum apical
deformation and (b) the first applanation time (A1-time).
Figure 5 Relationships between maximum apical deformation and A1-time and (a) age, (b) CCT, (c)
true IOP, (d) radius of curvature and (e) shape factor.
Figure 6 CVS-IOP as a function (a) age, (b) CCT, (c) radius of curvature, and (d) shape factor.
Figure 7 Difference between the (a) true IOP and CVS-IOP and (b) true IOP and IOPc for different
true IOP levels, CCT values and ages.
Figure 8 Association between CVS-IOP measurement and CCT, (a) before correction and (b) after
correction.
Figure 9 Association between IOP measurements and age, (a) before correction and (b) after
correction.
18
Table 1 Details of the clinical dataset
Parameter
CCT (µm)
CVS-IOP (mm Hg)
Age (years)
Mean ± SD
537.3±41.8
14.5±2.8
40.0±11.6
Range
404 – 650
6.5 – 35.5
21 – 83
Table 2 Mean Corvis output for four cases considered in a validation study of numerical results
Case #
CVS-IOP (mm Hg)
CCT(µm)
Age (year)
R (mm)
Case 1
17.3
581
68
7.82
Case 2
15.3
529
58
7.29
Case 3
11.3
537
31
7.55
Case 4
12.3
554
46
7.28
19
(a)
(b)
Figure 1 Computational mesh of the whole eye model (a) and Von mises stress distribution at the
highest concavity
(a)
(b)
Figure 2 Spatial distribution (a) and time variation (b) of air pressure on the cornea’s surface. In (b)
thick black line represents air-puff produced at the device piston and grey line represents the
pressure acting on the cornea’s surface
20
Figure 3 Example of a Corvis measurement showing the deformed cornea at the highest concavity
(a)
(b)
Figure 4 Comparison of numerical predictions with clinical measurements of (a) the
maximum apical deformation and (b) the first applanation time (A1-time)
21
(a)
(b)
(c)
(d)
(e)
Figure 5 Relationships between maximum apical deformation and A1-time and (a) age, (b) CCT, (c)
true IOP, (d) radius of curvature and (e) shape factor
22
(a)
(b)
(c)
(d)
Figure 6 CVS-IOP as a function (a) age, (b) CCT, (c) radius of curvature, and (d) shape factor
23
(a)
(b)
Figure 7 Difference between the (a) true IOP and uncorrected CVS-IOP and (b) true IOP
and corrected CVS-IOP for different true IOP levels, CCT values and ages
24
(a)
(b)
Figure 8 Association between CVS-IOP measurement and CCT, (a) before correction and (b) after
correction.
(a)
(b)
Figure 9 Association between IOP measurements and age, (a) before correction and (b) after correction
