Journal of Refractive Surgery

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Can the Corvis ST Estimate Corneal Viscoelasticity?

Ahmed Abass, PhD; Cynthia J. Roberts, PhD; Bernardo Lopes, MD; Ashkan Eliasy, MEng; Riccardo Vinciguerra, MD; Renato Ambrósio Jr, MD, PhD; Paolo Vinciguerra, MD; Ahmed Elsheikh, PhD

Abstract

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Abstract

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We have read with interest the article by Francis et al in the November 2019 issue titled “Corneal Viscous Properties Cannot Be Determined From Air-Puff Applanation,”1 where the Corvis ST (Oculus Optikgeräte GmbH) output for 312 healthy eyes, 107 fellow eyes of patients with keratoconus, and 289 keratoconic eyes was fitted to mathematical models to assess whether the cornea's viscous properties can be measured with an air-puff. Although we agree with many of the study's findings as reported in the article, we would like to use this opportunity to discuss some aspects of the study that generated flaws, including the lack of validation, and present our views on the central question of the study.

First, about the analysis method. We agree with the authors' assertion that “two classes of mathematical approaches are available for the calculation of biomechanical properties from the deformation amplitude: rheological closed-form analytical and inverse finite element methods. The rheological models are simpler, computationally non-intensive, and fast.” Although these statements are correct, they do not present a balanced assessment of the two approaches and lack appreciation of the shortfalls of closed-form analysis, in comparison to inverse finite element analysis. Closed-form analysis requires the essential introduction of simplifications, and these will affect the results, which is why validation is required. Because this form of analysis was selected for the study, a detailed assessment of their approximations, and the subsequent effect on study outcomes, should have been included. A validation study of the reliability of the closed-form analysis should also have been presented. Without these two critical components, it is impossible to assess the applicability of the analysis results.

We also would like to note a few apparent omissions that may have affected the results. These include the inertia or the mass force, which would be difficult to justify ignoring given the dynamic nature of the air puff excitation, especially when the main objective is to assess viscous response. Further, the primary input to the model, Fair-puff, was not given in the article. When we searched the previous publication2 as the authors instructed, we noticed that the authors calculated the cross-sectional area of the air-puff with a diameter d as πd2, not πd2/4. If the cross-sectional area was wrongly estimated four times greater, the force also must have been estimated four times more prominent. This would undoubtedly affect the results.

Our second point is about the method adopted to estimate corneal viscoelasticity. Viscoelasticity is time-dependent elasticity, which shows in four different ways in mechanical behavior. These are (1) creep (gradual growth in deformation under a constant load), (2) stress-relaxation (gradual reduction in stress under a constant deformation), (3) loading or strain rate dependency (producing higher stiffness under faster loads or faster deformation), and (4) hysteresis (difference in behavior between those experienced under loading and unloading).

With air-puff devices such as the Corvis ST and the Ocular Response Analyzer (ORA) (Reichert Technologies), creep and stress-relaxation cannot be measured because the devices are not designed to apply a constant load or a constant deformation in any stage of the air-puff application. On the other hand, the loading or strain rate dependency means that the corneal material behavior that applies is specific to the loading or strain rate of the air-puff device. This means that if we were to determine corneal viscoelasticity through the loading or strain rate dependency route, the device would have to apply different loading rates or strain rates. However, because this is out of the scope of the current devices, this route is also not feasible.

The remaining sign of viscoelasticity is the hysteresis, which can be easily determined from the pressure-deflection behavior recorded by both the Corvis ST and the ORA, and this in our view is the most straightforward route that could be taken to determine corneal viscoelasticity. This route had been adopted by the ORA and resulted in the corneal hysteresis parameter denoting the difference between applanation pressures recorded during the loading and unloading stages.3 This parameter was used in earlier studies to show significant differences between keratoconic and healthy corneas.4 Another parameter (the hysteresis loop area) based on the ORA output developed by Hallahan al5 was also successful in differentiating keratoconic and healthy corneas.

We would like to make a further point concerning the study methodology. Although we agree with using one eye from normal and keratoconic patients, the inclusion of the “107 fellow eyes of patients with asymmetric keratoconus as a subset of 107 of 289 patients with keratoconus” is confusing because this is not clear. We may assume these have normal topography. In fact, the normal topography eyes from patients presenting with very asymmetric ectasia have been extensively studied for enhancing ectasia detection.6 Considering these cases as keratoconus is not in full agreement with the current concepts that keratoconus is a bilateral but asymmetric disease, and that ectasia may occur unilaterally secondary to biomechanical impact from the environment.

Any computational approach to modeling corneal behavior requires validation to demonstrate that appropriate assumptions have been made and the results are sound. Without validation, the results cannot be meaningfully interpreted. The unknown error of fit may be acceptable or, alternatively, large. This remains unknown for the current study.

Ahmed Abass, PhD
Cynthia J. Roberts, PhD
Bernardo Lopes, MD
Ashkan Eliasy, MEng
Riccardo Vinciguerra, MD
Renato Ambrósio, Jr., MD, PhD
Paolo Vinciguerra, MD
Ahmed Elsheikh, PhD
Liverpool, United Kingdom

References

  1. Francis M, Matalia H, Nuijts RMMA, Haex B, Shetty R, Sinha Roy A. Corneal viscous properties cannot be determined from air-puff applanation. J Refract Surg. 2019;35(11):730–736. doi:10.3928/1081597X-20191010-03 [CrossRef]
  2. Francis M, Pahuja N, Shroff R, et al. Waveform analysis of deformation amplitude and deflection amplitude in normal, suspect, and keratoconic eyes. J Cataract Refract Surg. 2017;43(10):1271–1280. doi:10.1016/j.jcrs.2017.10.012 [CrossRef]
  3. Dupps WJ Jr, . Hysteresis: new mechanospeak for the ophthalmologist. J Cataract Refract Surg. 2007;33(9):1499–1501. doi:10.1016/j.jcrs.2007.07.008 [CrossRef]
  4. Gkika M, Labiris G, Giarmoukakis A, Koutsogianni A, Kozobolis V. Evaluation of corneal hysteresis and corneal resistance factor after corneal cross-linking for keratoconus. Graefes Arch Clin Exp Ophthalmol. 2012;250(4):565–573. doi:10.1007/s00417-011-1897-0 [CrossRef]
  5. Hallahan KM, Sinha Roy A, Ambrosio R Jr, Salomao M, Dupps WJ Jr, . Discriminant value of custom ocular response analyzer waveform derivatives in keratoconus. Ophthalmology. 2014;121(2):459–468. doi:10.1016/j.ophtha.2013.09.013 [CrossRef]
  6. Ambrósio R Jr, Lopes BT, Faria-Correia F, et al. Integration of Scheimpflug-based corneal tomography and biomechanical assessments for enhancing ectasia detection. J Refract Surg. 2017;33(7):434–443. doi:10.3928/1081597X-20170426-02 [CrossRef]

Reply

We greatly appreciate the letter to the editor by Abass et al on our recent study.1 We request the authors to refer to another recent publication,2 where closed-form analyses and inverse modeling were linked retrospectively to show that preoperative closed-form stiffness and inverse modeling (with added corneal and extracorneal masses) were excellent predictors of postoperative stiffness. This is by itself a strong validation of the relationship between the two forms of analyses applied to prediction of biomechanical outcomes of refractive surgery.2 We agree that further studies with large sample sizes and longer follow-up are warranted.

The Fair-puff was patient-specific and derived from the Corvis ST (Oculus Optikgeräte GmbH) exported comma separated value files. These files are readily available from any Corvis ST device without any manufacturer restrictions. We thank the authors here because the numeral 4 was missed in the text.3 This was simply a typographical error in the article. The actual formula used was πd2/4.3 Therefore, the results from our earlier study3 and this one1 remained unchanged.

We agree with the fundamentals of corneal deformation regarding creep, hysteresis, and stress relaxation. However, we have also stated in our study that modulating the air-puff force or time scale of the applanation could elicit a “true” viscoelastic behavior and be successfully analyzed by closed-form and inverse models.1 We would like to refrain from making comparisons with the Ocular Response Analyzer (ORA) (Reichert Technologies) because the ORA does not report deformation and, to date, no quantitative relationship between the ORA signals and deformation due to applanation has been established. So, all discussions related to this subject will be merely speculative.

The selection of the patient groups was based on a prior study.2 In earlier studies, the authors have used the classification of very asymmetric ectasia for these eyes and our classification was essentially the same. The authors also comment on error of fit. We have presented the mean root mean square error of the model prediction of Fair-puff in our earlier study, which was 0.4% of the maximum Fair-puff.2,3 With the two-compartment model of elastic and viscous components of corneal deformation, the error of fit did not change from the previous study. Hence, the conclusions of the current study could be related to our earlier findings with the same level of accuracy.

Mathew Francis, MTech
Himanshu Matalia, MD
Rudy M.M.A. Nuijts, MD, PhD
Bart Haex, PhD
Rohit Shetty, MD, PhD, FRCS
Abhijit Sinha Roy, PhD
Bangalore, India

References

  1. Francis M, Matalia H, Nuijts RMMA, Haex B, Shetty R, Sinha Roy A. Corneal viscous properties cannot be determined from air-puff applanation. J Refract Surg. 2019;35(11):730–736. doi:10.3928/1081597X-20191010-03 [CrossRef]
  2. Francis M, Khamar P, Shetty R, et al. In vivo prediction of air-puff induced corneal deformation using LASIK, SMILE, and PRK finite element simulations. Invest Ophthalmol Vis Sci. 2018;59(13):5320–5328. doi:10.1167/iovs.18-2470 [CrossRef]
  3. Francis M, Pahuja N, Shroff R, et al. Waveform analysis of deformation amplitude and deflection amplitude in normal, suspect, and keratoconic eyes. J Cataract Refract Surg. 2017;43(10):1271–1280. doi:10.1016/j.jcrs.2017.10.012 [CrossRef]
Authors

Drs. Ambrósio, PVinciguerra, RVinciguerra, Roberts, and Elsheikh are consultants for Oculus Optikgeräte GmbH. Dr. Elsheikh has received research funding from Oculus Optikgeräte GmbH. The remaining authors have no financial or proprietary interest in the materials presented herein.

10.3928/1081597X-20200212-04

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