Repeatability and reproducibility of corneal biomechanical parameters derived from Corvis ST

Abstract

Introduction:

The aim of this study was to evaluate repeatability and reproducibility of newly calculated biomechanical parameters of the cornea, developed by our research group.

Methods:

One eye from each of the 23 healthy subjects was measured three times consecutively, three times at different daytimes and on three different days. The within-subject standard deviation and coefficient of variation, as well as the intraclass correlation coefficient, were calculated for every parameter in each group.

Results:

Excellent repeatability and reproducibility (coefficient of variation < 5%, intraclass correlation coefficient > 0.75) was found for corrected values measured at A1, HC, and A2 time points (2nd A2 Time, 2nd A1 Time, 2nd HC Time, 2nd HC Def Amp and 2nd A1 Def Amp). Corneal-specific stiffness parameters, which showed good repeatability and reliability, were DA_cor (coefficient of variation = 4.02%, intraclass correlation coefficient = 0.919), KcLinear (coefficient of variation = 4.03%, intraclass correlation coefficient = 0.895), areaForceCornea (coefficient of variation = 3.34%, intraclass correlation coefficient = 0.853) and E2 (coefficient of variation = 4.1%, intraclass correlation coefficient = 0.78). Overall, most parameters fell into the category of good reliability (high intraclass correlation coefficient) and poor reproducibility (low coefficient of variation), including all the parameters describing extraocular deformation (DA_ext, AEPvED, AUC EDef, areaForceExtra, Kg and μg). Comparing the coefficient of variation values for intrasession, intersession and daytime measurements, there were no indices for diurnal changes.

Conclusion:

Most parameters showed good repeatability and reliability. The extraocular stiffness parameters showed poor reproducibility. KcLinear can serve as a very reliable and repeatable indicator of corneal stiffness.

Keywords

Corvis ST cornea biomechanics reproducibility

Introduction

The cornea accounts for about two-thirds of the refractive power of the eye. Small changes in its properties can have a big impact on eyesight, which is best illustrated by pathologies such as keratoconus, as well as outcomes of refractive surgical procedures.

The Corvis ST is a non-contact applanation tonometer paired with a high-speed Scheimpflug camera (4330 frames/sec), enabling real-time assessment of the corneal response to the air puff.^1,2

Several studies showed varying repeatability of the parameters reported by the Corvis device.^3–7 As software update parameters were introduced in 2016,^8,9 there has been an attempt at creating reference values in the healthy population stratified by age.⁸

Prior to assessing the clinical significance and interpreting the causal relationships among the myriad of parameters the Corvis device produces with each measurement, one must make sure that these are reproducible and reliable. Until now, this was not performed in healthy Caucasian controls for the parameters developed by Sinha Roy et al.¹⁰ and Matalia et al.¹¹

New parameters

Currently, rather than measuring the intrinsic elastic properties of the cornea, applanation tonometers provide information on the geometric deformation of the cornea.¹² In other words, they cannot be interpreted as biomechanical parameters of the cornea.¹³ Moreover, the air puff used in the measurement process not only deforms the cornea but also the eye globe in total, including scleral and extraorbital tissues, such as muscles and fat.¹⁰

Our research group found a way to isolate the corneal contribution to overall applanation and by computational modelling characterize the viscoelastic behaviour of the cornea. The total displacement amplitude was mathematically considered as a sum of corneal deformation and the extraocular tissue deformation. By analysing the displacement of the corneal edge and the apex separately through time in sequential image frames, the different components could be discerned.¹¹

A finite element approach was previously used to retrieve elastic corneal properties by analysing pre- and postoperative corneal elevation maps in patients undergoing LASIK (laser-assisted in situ keratomileusis)¹⁴ and to estimate both elastic and viscoelastic properties of the cornea based on air-puff applanation.¹⁵

A composite viscoelastic model^11,16 was used to estimate the different stiffness components after separating the different deformation curves (u1, u2, u3)

F_{a i r - p u f f} (t) = K c \times u 2 (t) + K g \times u 3 (t) + μ g \times (\frac{d u 3 (t)}{d t})

By solving this equation, it was possible to obtain four different indices of corneal biomechanical properties, two for the cornea and two for extraocular tissue.^11,16

In the above equation, Kc (linear) is the corneal stiffness assuming a linear elastic response, reflecting the instantaneous elastic response;^11,16 Kc (mean) is the corneal stiffness assuming a nonlinear response, reflecting a nonlinear response to increasing strain;^11,16 Kg is the extraocular tissue stiffness;^11,16 and μg is the extraocular tissue viscosity.^11,16

The cornea has viscoelastic¹⁷ rather than linear elastic properties, and its response is thus dependent on the duration and intensity of applied stress.¹⁸ This is how two different Kc parameters provide information on different aspects of elasticity and viscosity.

The Corvis ST corneal hysteresis (CCH), as in the Ocular Response Analyzer,¹⁹ was defined as the difference between the flattening applanation pressures at A1 and A2.¹¹

The main goal of this study is to evaluate the repeatability and reproducibility of these newly calculated values. By identifying the most reliable parameters, it will be possible to further investigate their relation to corneal biomechanics and their relation to ocular pathologies.

A summary of all newly assessed parameters can be found in Table 1.

Table 1.

Biomechanical parameters developed and calculated by our research group

Parameter	Meaning
CCH_mmHg_(CCH)	Corvis ST corneal hysteresis
AreaUnderDeformation-AmplitudeCurve (mm/ms) (AUC DefAmp)	Whole area under deformation per ms
AreaUnderCorneal DeformationCurve (mm/ms) (AUC CDef)	Part of whole area under deformation contributed by corneal movement per ms
AreaUnderExtra_ocularTissueDeformationCurve (mm/ms) (AUC EDef)	Part of whole area under deformation contributed by the movement extraocular tissue per ms
AreaEnclosedPressureVsExtra_ocularTissueDeformation (AEPvED)	‘Area enclosed by the hysteresis curve equivalent formed by applied pressure and whole-eye movement waveform’
AreaEnclosedPressureVs CornealDeformation (AEDvCD)	‘Area enclosed by the hysteresis curve equivalent formed by applied pressure and deflection waveform’
IOP_mmHg_(2nd IOP)	Intraocular pressure
CCT_microMeter_(2nd CCT)	Central corneal thickness
DeformationAmplitude_mm_(2nd HC Def Amp)	Maximum deformation of the anterior corneal apex
Applanation1Time_ms_(2nd A1 Time)	Time of first applanation
Applanation2Time_ms_(2nd A2 Time)	Time of second applanation
HighestConcavityTime_ms_(2nd HC Time)	Time of highest concavity
Applanation1Deformation Amplitude_mm_(2nd A1 Def Amp)	Deformation amplitude at time point of first applanation (A1)
Applanation2Deformation Amplitude_mm_(2nd A2 Def Amp)	Deformation amplitude at time point of second applanation (A2)
Beta	Coefficient describing the rate of increase in corneal stiffness with increasing applanation force
Alpha	Coefficient describing the rate of increase in corneal stiffness with increasing applanation force
Kg (N/m)	Extraocular tissue stiffness
µg (Pa/s)	Extraocular tissue viscosity
KcMeanArith (N/m)	Mean corneal stiffness over a range of air-puff pressures from 0 to 180 mmHg
KcLinear (N/m)	Mean corneal stiffness using a linear viscoelastic model, which assumes a linear elastic response
KcMeanTime (N/m)	Arithmetic mean of Kc values at three different time points (t1, t2, t3 – as defined by Matalia et al.¹¹)
RMSErrorForce	Root mean square error for force
DA_cor	Corneal deformation amplitude
DA_ext	Deformation amplitude of extraocular tissue
DA_cor_by_DA_ext	DA_cor divided by DA_ext
areaForceCornea	‘Area enclosed by the force curve acting on the corneal area calculated with respect to time’
areaForceExtra	‘Area enclosed by the force curve acting on the extra-corneal area calculated with respect to time’
areaForceCornea2extra (AreaFC2e)	areaForceCornea divided by areaForceExtra
meanForceCornea2extra (MeanFC2e)	‘Ratio of mean force applied during corneal deformation (deflection amplitude) to extra-corneal deformation (whole-eye movement amplitude)’
maxForceCornea2extra (MaxFC2e)	‘Ratio of max force applied during corneal deformation (deflection amplitude) to extra-corneal deformation (whole-eye movement amplitude)’
kcAtMaxForceByKg	Corneal stiffness at max force divided by extraocular tissue stiffness
kcMeanArithByKg	Mean corneal stiffness over a range of air-puff pressures from 0 to 180 mmHg divided by extraocular stiffness
KcMeanTime_by_kg	Arithmetic mean Kc value using three different time points (t1, t2, t3 – as defined by Matalia et al.¹¹) divided by extraocular stiffness
E1 (kPa)	KcMeanArith divided by Pachy
E2 (kPa)	KcLinear divided by Pachy
E3 (kPa)	KcMeanTime divided by Pachy

Methods

Twenty-three healthy subjects (6 males and 17 females) with a mean age of 31.83 ± 12.3 years were included in the study. Three groups of triplicate measurements were obtained for each subject: consecutive (intrasession), on three different days (daytime), and during a single day at three different daytimes (intersession). Only one eye per patient was analysed. All measurements were obtained in automatic mode, eliminating inter-observer bias. The three datasets were analysed separately and compared.

Exclusion criteria were hyperopia or myopia >2 dpt, corneal astigmatism >1.5 dpt, previous eye surgery of any kind, abnormal anatomical findings in any segment of the eye, keratoconus/keratoglobus and corneal degeneration.

Approval for this retrospective observational study was received from the medical ethics committee II, University of Heidelberg, Germany, in Mannheim in August 2016 (registration number: 2016-842R-MA).

Statistical analysis

Reliability of measurement was expressed for each parameter in terms of the coefficient of variation (CV). First, the subject mean (mean (w)) and standard deviation (SD (w)) were obtained by calculating these values for each triplicate measurement and then by taking the average of those values. The CV is a ratio of SD (w) and mean (w) and is expressed in percentage. A CV of 5% was set as the upper threshold for good reliability.

Reliability was further assessed using the intraclass correlation coefficient (ICC) for averaged measurements, which relates the error of measurement to overall variability. A high ICC means the error of measurement is low compared to the population variance, which allows for distinction between patients. Parameters with an average ICC >0.90 were considered to have excellent reliability, an ICC between 0.90 and 0.75 indicated good reliability and an ICC <0.75 indicated poor reliability.

In the intrasession measurement group, the CV was used as an estimate for the measurement error. If the ICC was low, and the CV also low, then the error was small, confirming low reliability of the parameter. If the CV, however, was high, the measurement error was deemed high. By subsequently comparing the intrasession with the intersession CV, it was established whether the measurement itself influences the parameter. Parameters with good intrasession reproducibility and reliability were compared with the daytime group, with a daytime CV of >5% indicating possible diurnal changes.

In our study, a coefficient of variation (CV) <5% was considered to display good reliability. Precision and the coefficient of repeatability (CR) were also calculated by multiplying SD (w) by 1.96 and 2.77, respectively. Precision and CR are reported in the same units as the assessed parameter itself. All calculations were performed in Microsoft Office Excel 2016 and SPSS v25.0 for Windows.

Results

Original parameters

The original parameters showed overall good repeatability, with A1 length and A2 length showing a higher CV of 6.4% and 8.2%, respectively. This group showed excellent reliability with an averaged ICC of >0.9, except A1 length, A2 length and HC time (ICC < 0.75). The same poor intersession and daytime repeatability (high CV) was observed for A1 and A2 lengths (Figure 1).

Software update parameters

The 2016 software update parameters showed similarly good repeatability and reliability, with deflection area, deflection length and dArc length parameters, showing overall poor repeatability. Exceptions are A1 Deflection Length (CV = 2.84%, ICC = 0.872), HC Deflection Area (CV = 3.6%, ICC = 0.916) and HC dArc Length (CV = 4.08%, ICC = 0.948).

Stratified by time point of their calculation, variables measured at the time of the second applanation (A2) showed the highest variability as compared to time points A1 and HC.

The following parameters had high reliability (high ICC) values at poor repeatability (high CV), suggesting high measurement error in relation to population variance: A1 Deflection Area (CV = 5.62%, ICC = 0.821), A2 Deflection Area (CV = 7.76%, ICC = 0.807), Maximum dArc Length (CV = 5.1%, ICC = 0.799) and ARTh (CV = 6.11%, ICC = 0.755).

Across measurement sessions, Maximum dArc Length showed lower variability in the daytime and intersession group, suggesting that the act of measurement itself might influence this parameter. ARTh had low variability only in the intersession group, implying it might need longer than a day to recover.

The following parameters had low reliability (low ICC) at good repeatability (low CV): A1 Deformation Amplitude (CV = 3.08%, ICC = 0.721), HC Time (CV = 1.16%, ICC = 0.698), Time of Whole Eye Movement (CV = 1.8%, ICC = 0.629), and Time of Maximum Deflection Amplitude (CV = 2.8%, ICC = 0.211). Their population variance might thus be too high to differentiate between individuals (Figure 2).

Modified viscoelastic model parameters

Good reliability and excellent reliability (CV < 5%, ICC > 0.9) were found for only two parameters: 2nd CCT (CV = 0.81%, ICC = 0.992) and DA_cor (CV = 4.02%, ICC = 0.919). They were followed closely by KcLinear (CV = 4.03%, ICC = 0.895). Their intrasession characteristics are summarized in Table 2.

Table 2.

Novel viscoelastic corneal parameters showing good to excellent reliability

Parameters	Mean	SD (w)	CV (%)	Average ICC	95% CI		p value
2nd CCT	553.453	4.461	0.81	0.992	0.987	0.996	<0.001
DA_cor	0.001	0	4.02	0.919	0.861	0.955	<0.001
KcLinear	115.003	4.637	4.03	0.895	0.82	0.942	<0.001

SD: standard deviation; CV: coefficient of variation; ICC: intraclass correlation coefficient; CI: confidence interval; CCT: central corneal thickness.

Excellent repeatability and reliability (CV < 5%, ICC > 0.75) was found for corrected values measured at A1, HC and A2 time points (2nd A2 Time, 2nd A1 Time, 2nd HC Time, 2nd HC Def Amp and 2nd A1 Def Amp).

Corneal-specific stiffness parameters, which showed good repeatability and reliability, were DA_cor (CV = 4.02%, ICC = 0.919), KcLinear (CV = 4.03%, ICC = 0.895), areaForceCornea (CV = 3.34%, ICC = 0.853) and E2 (CV = 4.1%, ICC = 0.78).

The following corneal-specific parameters had high reliability (high ICC) values at poor repeatability, suggesting high measurement error in relation to population variance (high CV): CCH (CV = 40.45%, ICC = 0.847), KcMeanArith (CV = 5.51%, ICC = 0.877), KcMeanTime (CV = 5.8%, ICC = 0.873), AEDvCD (CV = 22.72%, ICC = 0.857) and AUC CDef (CV = 7.1%, ICC = 0.856). Repeatability did not fall below 5% in any of the measurement sessions, implying an absence in diurnal changes or error related to consecutive measuring. The same was true for following parameters relating different elasticity components: DA_cor_by_DA_ext (CV = 12.08%, ICC = 0.92), AreaFC2e (CV = 21.87%, ICC = 0.851), MaxFC2e (CV = 16.56%, ICC = 0.844) and MeanFC2e (CV = 17.73%, ICC = 0.811). There was no repeatability improvement in different measurement sessions.

A constellation for low reliability (low ICC) and good repeatability (low CV) was not found. Overall, most parameters fell into the category of good reliability (high ICC) and poor reproducibility (low CV), including all the parameters describing extraocular deformation (DA_ext, AEPvED, AUC EDef, areaForceExtra, Kg, μg). None of the parameters showed diurnal changes, as indicated by an increase in CV for the daytime measurement session (Figure 3).

Discussion

In the standard parameters, poor repeatability was found for HC time, and good repeatability for A1 and A2 velocity, as opposed to a previous study,⁴ whereas good reliability was confirmed for intraocular pressure (IOP) and CCT.^4,6,19

The differences in findings might have arisen due to the variation in populations observed, with respect to age and sex homogeneity of the samples. As previously reported,⁵ overall good reproducibility was found for the newer parameters, even though Bak-Nielsen et al.⁴ had varying results. In this study, we saw poor reproducibility only for dArc length and deflection length parameters.

One of the latest additions to the set of parameters as reported by the Corvis is the Corneal Biomechanical Index (CBI), which was developed as a means of detecting keratoconic eyes.⁸ Even though the CBI was previously described as a descriptor of overall corneal biomechanical stability,⁸ it was among the biggest outliers in our study with a CV of 55.4%. The value is supposed to be between 0 and 1, with 1 indicating an unstable cornea.²⁰ This might mean the device needs a more comprehensive built-in scan quality assessment tool. As a result, software update parameters were introduced in 2016,^8,9 where there has been an attempt at creating reference values in the healthy population stratified by age.⁸

As a descriptor of reproducibility, the CV is a dimensionless measure of data spread and can thus be used to compare parameters measured on completely different scales. When paired with the ICC as a reliability parameter, one can isolate parameters with overall good repeatability and reliability.

This was the case for only three of the new parameters, two of them describing the isolated corneal response to the applanation: DA_cor (corneal deformation amplitude) and KcLinear (mean corneal stiffness using a linear viscoelastic model, assuming a linear elastic response). These parameters with excellent reliability and repeatability should be further examined in a clinical context.

The introduction of the Corvis ST corneal hysteresis (mmHg), an analogy to the CH in the Ocular Response Analyzer,¹⁹ is an attempt at measuring hysteresis. This is an inherent property of viscoelastic tissues and reflects the difference between the inward and outward movement behaviour.²¹ We found good reliability (high ICC) at poor repeatability (high CV) of the newly measured parameter, implying there was high measurement error in relation to population variance. Finding a parameter with lower intra-patient variance and a reduced measurement error might provide more accurate estimates of corneal hysteresis. It could however also be that the error is related to a specific age group, meaning studies on a bigger population sample are needed. The same was found for extraocular stiffness and viscosity parameters.

It is evident from older and newer studies that the sclera influences the corneal biomechanic response.^22,23 The value of the newly acquired parameters lies in the fact that the extraocular and corneal stiffness parameters were obtained without any assumptions made beforehand.^11,16 Of the four new stiffness parameters, only KcLinear showed good reliability and repeatability, hinting at the possibility that there possibly exist confounding factors influencing the other three, such as age, corneal thickness, IOP or precision of measurement beyond the scope of the machine’s built-in quality control.

An obvious limitation of the study is the low number of healthy subjects, due to the impracticalities of measuring throughout the whole day. Further studies with a larger number of healthy subjects would shed more light on subpopulation-specific variability.

A valuable extension of the study, as previously done for old parameters,^8,24 would be to examine metrics and establish reference values for KcLinear and areaForceCornea in a large population. Furthermore, models which assess topographic stress response differences across the cornea could be more useful in a more detailed characterization of its biomechanical properties and aid in the detection of abnormalities.¹² It is evident that the IOP and CCT have a significant impact when it comes to measuring biomechanical indices,^8,12 also specifically for the Corvis tonometer.²⁴ It would therefore be of interest to investigate the new parameters in a population stratified by IOP and CCT measures.

Supplemental Material

Tables_3-14 – Supplemental material for Repeatability and reproducibility of corneal biomechanical parameters derived from Corvis ST

Supplemental material, Tables_3-14 for Repeatability and reproducibility of corneal biomechanical parameters derived from Corvis ST by Nermin Serbecic, Sven Beutelspacher, Lovro Markovic, Abhijit Sina Roy and Rohit Shetty in European Journal of Ophthalmology

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Supplemental material

Supplemental material for this article is available online.

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