Comparing the Performance of Stress-Strain Index Versions 1 and 2 in Normal and Keratoconus Patients

Abstract

Purpose: The purpose of this study was to compare the performance of the Stress-Strain Index versions 1 and 2 (SSI and SSI2) in healthy patients and patients with keratoconus (KC).

Methods: Fifty-two healthy and 104 KC eyes were examined using Scheimpflug-based tomography and air-puff tonometry (Pentacam and Corvis). Correlations between both versions of SSI and age, thinnest pachymetry, and tomographic parameters were assessed. To discriminate KC eyes from healthy eyes, receiver operating characteristic curves were generated to calculate the area under the curve (AUC) for both versions of SSI and compared with a Delong test.

Results: Both versions of SSI showed statistical differences between the healthy group and the group of patients with KC (all P < 0.001). In the healthy group, significant correlations were found between both versions of SSI and age, K₁, K₂, and K_max, between SSI and average relational thickness (ART) Max (R² = 0.23) and between SSI2 and Belin A (R² = 0.08). In the KC group, significant correlations were found between both versions of SSI and all tomographic parameters (all P < 0.01, except for SSI2 with age P = 0.346); the R² values in SSI2 were consistently higher than in SSI. AUC for SSI and SSI2 when comparing normal and KC eyes was 0.772 and 0.740, respectively (P = 0.468).

Conclusions: Both versions of SSI correlated with tomographic parameters describing KC severity, but correlations were higher for SSI2 and were not affected by age. Both versions demonstrated the same diagnostic ability for KC.

Translational Relevance: Both versions of SSI are not interchangeable, SSI2 may be preferred to depict the corneal stiffness.

Introduction

Keratoconus (KC) is a bilateral corneal biomechanical disorder characterized by local biomechanical weakness and corneal thinning.¹ This can result in increased myopia, irregular astigmatism, corneal scarring, hydrops, and vision impairment.² The management of KC involves early diagnosis, timely treatment of progressive cases, and long-term follow-up, which can be achieved through the measurement of corneal tomography,³ as well as corneal biomechanics. 

In vivo measurements of corneal biomechanics can be done using commercially available devices, such as the Ocular Response Analyzer (ORA; Reichert, NY, USA), the relatively new Brillouin Optical Scanning System (BOSS; Intelon Optics, Boston, MA, USA), and the Corneal Visualization Scheimpflug Technology (Corvis ST, Oculus Optikgeräte, Wetzlar, Germany). In previous studies, corneal hysteresis (CH) and corneal resistance factor (CRF), two parameters generated by ORA, have shown a low ability to discriminate early-stage KC from healthy eyes.^4,5 BOSS, which uses Brillouin microscopy,^6–8 measures the longitudinal modulus, which does not correlate directly with the tangent modulus that represents corneal stiffness.⁹ Moreover, it has a lengthy acquisition time and is sensitive to environmental conditions, limiting clinical applicability in its current form, although it exhibits high repeatability and the ability to differentiate between healthy patients and patients with KC.¹⁰ 

By combining a high-speed Scheimpflug imaging camera with an air-puff tonometer, Corvis ST generates a series of Scheimpflug-based images of the cornea in different stages of deformation. By analyzing these images, various parameters have been proposed to describe the dynamic corneal response (DCR) as a means to evaluate corneal biomechanics. One of these parameters, called the Stress-Strain Index (SSI), is based on a finite element analysis of the human eye to derive the material stiffness of the cornea and can be used to follow-up the progression of KC.^11,12 Recently, a second version of the parameter was introduced, called SSI2. Whereas both versions of SSI were developed using results of numerical models simulating the action of the air-puff on corneas with different dimensions and material properties, SSI2 used many more models, covering more dimensional parameters and more variations in each parameter.¹³ 

The aim of this study is to compare the performance of SSI and SSI2 in healthy patients and patients with KC, to determine their clinical applicability, functions, and scope. 

Methods

The Intelligent Computer Analysis of Keratoconus Evolution (iCAKE) project is a prospective, longitudinal, observational study and was designed and carried out in compliance with the tenets of the Declaration of Helsinki. This study was approved by the Ethical Committee of the Antwerp University Hospital in the framework of the iCake study. Data were collected at the Antwerp University Hospital, where enrollment started in May 2017 and ended in September 2020. All included patients signed an informed consent form prior to their examination. 

Patient Inclusion and Exclusion Criteria

This study included a control group and a KC group. For both groups, only one eye per person was randomly included in this study for analysis. Prior to the examination, patients were asked to discontinue soft and rigid gas-permeable contact lenses wear for at least 2 weeks. 

For the healthy control group, the inclusion criteria comprised the absence of ocular diseases, except myopia and/or astigmatism, and no systemic abnormalities. The exclusion criteria included a history of ocular surgery (e.g. blepharoplasty and laser vision correction), any congenital eye disease, and pregnancy or breastfeeding. 

Patients with KC, aged 12 to 45 years at baseline, were diagnosed by a corneal specialist (author C.K.). The diagnosis typically required two typical signs of KC on Scheimpflug tomography in Pentacam (Oculus Optikgeräte, Wetzlar, Germany, software version 1.26r26), such as abnormal corneal thickness distribution and thinnest pachymetry, abnormal posterior elevation, skewed asymmetric bowtie/inferior steepening [SAB/IS] or increased inferior steepness, and/ or one classic slit lamp finding (Fleischer ring, Vogt striae, or central thinning). The sample included untreated patients with KC within the spectrum of severity, from forme fruste KC (FFKC) — defined as the contralateral eye without clinical or tomographic signs of an eye diagnosed as KC — to severe cases. Systemic disease (except allergies), ocular comorbidities, or surgeries (including corneal cross-linking [CXL]), and corneal scarring were considered exclusion criteria. Systemic drug therapy was not considered an exclusion criterion unless it was known to induce corneal changes. 

Scheimpflug-Based Tomography

The corneal tomography measurements were obtained using a Pentacam HR. The following parameters were recorded: K₁, K₂, K_max, difference between K_max values in the inferior and superior areas at 3 mm from the corneal apex (IS value), corneal apex/thinnest pachymetry, and six parameters describing anterior surface asymmetry (including Index of Surface Variance [ISV], Index of Vertical Asymmetry [IVA], Keratoconus Index [KI], Central Keratoconus Index [CKI], Index of Horizontal Asymmetry [IHA], and Index of Height Decentration [IHD]). Furthermore, the values of “A,” “B,” and “C” were read from the Belin ABCD staging, where “A” and “B” stood for the anterior and posterior radius of curvature for a 3.0 mm zone centered on the thinnest point and “C” stood for the thinnest pachymetry. “D” related to corrected distance visual acuity (CDVA), was not included in current analysis. Finally, the minimum/ maximum/ average Ambrósio relational thickness (ART Min/Max/Avg) were analyzed as well. 

High-Speed Dynamic Scheimpflug Imaging Air-Puff Device

Following the tomography measurements, the corneal biomechanics were measured by Corvis ST (software version 1.6r2543) and only measurements with an acceptable quality (“OK” with no eyelashes covered in the videos) were included in analysis. Following internal extensive testing of SSI, it was decided to develop a new version of the parameter that would represent better the material behavior of corneal tissue in both healthy and KC eyes. Like SSI, SSI2 was based on numerical modelling, but these models included not only healthy cases (like SSI) but also KC cases with wide variations in cone location, size, and height. As a result, SSI2 was found to be better able to simulate the stiffening caused by CXL and stiffness deterioration associated with KC progression. The values of SSI and SSI2 were recorded.¹¹ 

Statistical Analysis

The statistical analysis was performed in SPSS (version 29; IBM, Armonk, NY, USA) and R (version 4.3.1; R Foundation for Statistical Computing, Vienna, Austria; https://www.R-project.org/). The normality of the data was verified using the Shapiro-Wilk test. Descriptive statistics were presented as mean ± standard deviation. For continuous variables, analyses of Student’s t-test and Mann-Whitney U test were conducted to analyze the differences between the groups. Simple linear regression analyses were performed to evaluate the relationships between the two versions of SSI with age, corneal pachymetry, and corneal tomographic parameters. Correlations were categorized based on the R² as follows: very weak (R² ≤ 0.19), weak (0.2 ≤ R² ≤ 0.39), moderate (0.4 ≤ R² ≤ 0.59), strong (0.6 ≤ R² ≤ 0.79), and very strong (R² ≥ 0.8). Receiver operating characteristic (ROC) curves and area under the curve (AUC) were used to assess the accuracy of the two versions of SSI in diagnosing KC, as well as the corresponding optimal cutoff values, sensitivity, and specificity of these two parameters. An AUC value of 1.00 indicates perfect discriminatory power, whereas 0.50 or lower indicates that the evaluated parameter has no diagnostic use. Delong's test was used to compare the AUC between two versions of SSI. A value of P < 0.05 was considered statistically significant for all tests. 

Results

Demographics and Comparisons

This prospective study included 52 healthy eyes from 52 healthy patients and 104 KC eyes from 104 patients with KC. The basic demographic information and comparisons between the healthy and KC groups are shown in Table 1. All parameters were significantly different between the two groups (P < 0.001). 

Table 1.

 

Basic Demographic Information

 

Simple Linear Regression Analyses

Although a significant linear relationship existed between SSI and SSI2 in the healthy and KC groups (Fig. 1A), and the value of R² was higher in the KC group (R² = 0.34) than in the healthy group (R² = 0.21), the Bland-Altman analyses between the two versions of SSI showed that the 95% lower/upper limits of agreement (LoA) ranged from −0.42 to 0.25 in the healthy group (Fig. 1B) and from −0.39 to 0.26 in the KC group (Fig. 1C), which showed that two versions of SSI were not interchangeable. 

Figure 1.

 

The correlations between both versions of SSI in the healthy and KC groups (A); the Bland-Altman analyses between both versions of SSI in the healthy (B) and KC (C) groups. KC, keratoconus; SSI, the Stress-Strain Index.

Basic Parameters

As shown in Figure 2 and Supplementary Materials A, the healthy group demonstrated significant linear relationship between both versions of SSI and age (R² = 0.75 and 0.10, respectively), K₁ (R² = 0.10 and 0.09), K₂ (R² = 0.13 and 0.21), and K_max (R² = 0.12 and 0.16). In the KC group, a significant correlation was only found between SSI and age (R² = 0.32, P < 0.001) but not between SSI2 and age (P = 0.346). In contrast, significant correlations were found between both versions of SSI and thinnest pachymetry, K₁, K₂, and K_max (all P values < 0.01): the values of R² in SSI2 (ranged between 0.17 and 0.35) were all higher than in SSI (range = 0.09 to 0.24). 

Figure 2.

 

The correlations between both versions of SSI and basic parameters in the healthy and KC groups. K, keratometry; KC, keratoconus; Pachy Min, corneal thinnest pachymetry; SSI, the Stress-Strain Index.

Ambrósio/ Belin Diagnostic and Staging Parameters

As shown in Figure 3 and Supplementary Materials B, in the healthy group, significant correlations were only found between SSI and ART Max (R² = 0.23, P < 0.001). Whereas in the KC group, all parameters showed significant correlations with both versions of SSI (all P values < 0.01); R² values for SSI2 were higher than those for SSI. 

Figure 3.

 

The correlations between both versions of SSI and Ambrósio/ Belin diagnostic and staging parameters in the healthy and KC groups. ART Max, Maximum Ambrósio relational thickness; KC, keratoconus; SSI, the Stress-Strain Index.

Six Anterior Surface Asymmetry Parameters

The P values indicated no statistically significant relationships between both versions of SSI and the six anterior surface asymmetry parameters in the healthy group (Fig. 4 and Supplementary Materials C). In the KC group, all the correlations with these 6 parameters were negative and statistically significant: the values of R² ranged between 0.12 and 0.35 for SSI, whereas they were relatively higher in SSI2 (range = 0.13 to 0.41). 

Figure 4.

 

The correlations between both versions of SSI and six anterior surface asymmetry parameters in the healthy and KC groups. CKI, Center Keratoconus Index; IHA, Index of vertical Asymmetry; IHD, Index of Height Decentration; ISV, Index of Surface Variance; IVA, Index of Vertical Asymmetry; KC, keratoconus; KI, Keratoconus Index; SSI, the Stress-Strain Index.

Diagnostic Analyses of SSI and SSI2

The ability of SSI and SSI2 to distinguish KC eyes from healthy eyes is assessed in Table 2. SSI shows higher sensitivity, whereas SSI2 has higher specificity. The AUC of SSI and SSI2 was 0.772 and 0.740, respectively. The Delong's test showed no significant difference between the two AUCs (P = 0.468). 

Table 2.

 

The Diagnostic Ability of SSI Version 1 and Version 2

 

Discussion

This study assessed the performance of two versions of SSI in healthy eyes and KC eyes. Our findings revealed that the two versions of SSI have comparable diagnostic ability for discriminating KC eyes from healthy eyes. In KC eyes, fair correlations were observed between the two SSI versions, as well as significant correlations between the two versions of SSI and the examined tomographic parameters, but with higher correlations obtained for SSI2. Meanwhile, in healthy eyes, similar correlations existed, albeit weaker. The two versions of SSI also correlated with each other in healthy eyes but may not be interchangeable. 

To characterize corneal stiffness in vivo using the Corvis ST, DCR parameters have been developed, including the stiffness parameter at first applanation (SP-A1), the deformation amplitude ratio (DA ratio) at 1 and 2 mm, and others. Subsequently, comprehensive parameters derived from these DCRs have been introduced using artificial intelligence (AI). These include the Corvis Biomechanical Index (CBI), designed for early KC diagnosis, and its linear transformation, the Corvis Biomechanical Factor (CBiF),¹⁴ intended for KC grading. 

In contrast to the DCR parameters, which are often affected by intraocular pressure (IOP) and corneal pachymetry,¹⁵ the SSI was developed to characterize the cornea’s material stiffness. Hence, it tries to show no significant correlation with IOP and corneal pachymetry but a positive correlation with age.¹¹ Recently, the SSI was updated to SSI2 to optimize the parameter’s applicability, making the index less dependent on IOP and corneal pachymetry.¹³ 

In agreement with the study detailing the SSI development,¹¹ this work identified a significant positive correlation between SSI2 and age in healthy eyes group, but not in the KC group. This discrepancy may arise from the fact that, in healthy eyes, corneal material stiffness typically increases with age, whereas in KC eyes, the stiffness changes with the progression of the disease over a small age range. Therefore, it is anticipated that the correlation between SSI2 and age in KC eyes would be weaker and possibly nonsignificant. As expected, the correlations between the two versions of SSI and corneal thinnest pachymetry were not significant in the healthy group, but showed significant, but weak, positive correlations in the KC group (R² of 0.09 and 0.17 in SSI and SSI2, respectively). This weak correlation is likely associated with the decreased corneal material stiffness that coincides with corneal thinning. 

The assessment of biomechanical properties plays an important role in the KC diagnosis,¹⁶ thus the diagnostic ability of both versions of SSI was tested in the current patient cohort. Although both SSI and SSI2 exhibited comparable diagnostic ability, their performance differed significantly, with SSI demonstrating high sensitivity, whereas SSI2, conversely, exhibited high specificity. In contrast, a recent study by Miao et al., conducted on a Chinese population, reported a limited diagnostic efficacy for SSI, especially in FFKC eyes (AUC = 0.572), whereas SSI2 achieved an AUC of 0.915 in the same FFKC sample.¹⁷ Our previous work using SSI showed no statistical difference between normal, FFKC or early KC (EKC) eyes, but significant differences with advanced KC eyes.^18,19 This finding was later confirmed by Padmanabhan et al.²⁰ Borderie et al. also found statistical differences between healthy eyes and KC eyes, but did not stage the patients with KC.²¹ Although all these studies demonstrated the diagnostic ability of SSI for advanced KC, the diagnostic ability of both versions of SSI for early-stage KC remains to be confirmed due to the lack of consensus in the literature on the definition of FFKC, subclinical KC, and EKC.^22,23 

Whereas KC starts with a localized decrease in corneal stiffness,²⁴ SSI describes the stiffness of the entire cornea and was as such not originally designed to diagnose KC. Recently, SSI maps that show corneal stiffness distribution across the corneal surface were proposed²⁵; those highlighted the regions with a localized decrease in stiffness and can be used for early-stage KC diagnosis. Such maps can also be created using SSI2, but these still require further investigation. 

This work also investigated the relationship between both versions of SSI and diverse tomographic parameters that represent KC severity. All these parameters, including the Belin ABC staging system, are inversely correlated with both versions of SSI in the KC group. This suggests that both versions of the SSI, which reflect corneal material stiffness properties, are related to topographic parameters that reflect KC severity. Furthermore, the correlation coefficients were slightly higher for SSI2, suggesting that this parameter may better capture KC staging and progression. Based on these correlations, SSI2 may be more appropriate for staging KC and assessing KC progression as it seems to reflect better the biomechanical changes underlying KC. 

There are some limitations of our study, one of which is that a limited number of patients with KC in the early stage were included, precluding the division into KC stage subgroups in the analysis. This may be due to the fact that we excluded patients with a history of contact lenses wearing. Further investigations should involve a larger cohort of patients with early-stage KC, possibly including the patients who have contact lenses wearing history after the sufficient discontinuing wearing time, for a more comprehensive evaluation of SSI and SSI2 ability in early KC diagnosis. In addition, there was an important difference in the male-female balance between the healthy and KC groups, which may have affected the group comparisons. 

Our findings indicate that in KC eyes there are moderate correlations between the two versions of SSI and the tomographic parameters describing the severity of KC. In all comparisons, the R² values were higher for SSI2 than for SSI. SSI2 was also less affected by age than SSI, which is expected in a KC population. This indicates that the two versions of SSI are not interchangeable, and a potential advantage of SSI2 in KC staging that should be verified in future studies. Both versions of SSI exhibited comparable ability in diagnosing KC. 

Acknowledgments

Supported in part by a research grant by the Flemish Government Agency for Innovation by Science and Technology (No. TBM-T000416N) and the Sichuan Provincial Department of Science and Technology (No. 2024YFFK0302). 

Disclosure: N.-J. Lu, None; M. Jiménez-García, None; A. Elsheikh, Oculus, Wetzlar, Germany (C); A. Makarem, None; C. Koppen, None; J.J. Rozema, None