Staging of Keratoconus Indices Based on Localized Corneal Biomechanics Stress–Strain Index Map

Abstract

Purpose

To assess Stress–Strain Index (SSI) map parameters and to establish a new corneal-biomechanics-based staging (CBBS) system and the diurnal variation of SSI.

Design

Hospital-based cross-sectional study.

Subjects

Seventy-eight keratoconus subjects.

Methods

A total of 78 keratoconus (KC) subjects were included in this study. All subjects had corneal tomography (Pentacam HR, Oculus) and biomechanical measurements (Corvis ST, Oculus) 5 times a day, which were at 8:30, 11:30, 14:30, 17:30, and 20:30. Stress–Strain Index value was obtained from Corvis ST, and SSI map parameters were derived from a customized SSI map generator (Matlab runtime 9.8). An analysis of variance was used to compare the SSI map parameters among varying stages of KC groups. The best performing parameters according to the Youden index were subsequently used to create the CBBS system. Cohen κ statistics and contingency tables were used to compare CBBS and topographic KC classification (TKC) systems.

Main Outcome Measures

Stress–Strain Index map parameters were used for analysis: mean inside cone SSI, mean outside cone SSI, minimum SSI, and maximum SSI.

Results

Significant diurnal variations were observed in mean inside cone SSI (F = 5.536, P < 0.001) and Min SSI (F = 6.031, P < 0.001) without any clinical significance. Mean inside cone SSI had the highest area under the curve value and sensitivity among the 3 KC stages and was used to establish the CBBS system. Cohen κ statistics (0.652, P < 0.001) and contingency tables (76.9% KC eyes were of the same stage) showed good agreement between CBBS and TKC systems.

Conclusions

A new corneal-biomechanics-based KC staging system was established on the basis of localized corneal biomechanics (mean inside cone SSI). There was no clinically significant diurnal variation in localized corneal biomechanics based on SSI map parameters.

Financial Disclosure(s)

The authors have no proprietary or commercial interest in any materials discussed in this article.

Keratoconus (KC) is a bilateral, progressive corneal ectasia characterized by thinning and protrusion of the cornea that can lead to irregular astigmatism and visual impairment.^1,2 Assessing the severity of KC is one of the vital steps taken in selecting treatment methods. Traditional staging strategy mainly relies on corneal topography and tomography.³ However, some researchers indicated that corneal morphological changes in KC are secondary to corneal biomechanical changes,⁴ and therefore, it may be necessary to grade KC based on corneal biomechanics.

The corneal visualization Scheimpflug technology device (Corvis ST) is widely used for corneal biomechanical assessment5, 6, 7, 8 and has been used in KC staging.9, 10, 11 However, traditional Corvis ST parameters assess biomechanical behavior but do not directly measure corneal stiffness.¹² When evaluating corneal biomechanics, pachymetry, geometry, and intraocular pressure (IOP) must be considered.13, 14, 15 The Stress–Strain Index (SSI) is the first in vivo biomechanical metric from Corvis ST that is independent of pachymetry and IOP.¹⁶ Several studies have highlighted the asymmetric spatial distribution of microstructure and biomechanics in KC.17, 18, 19 A local reduction in elastic modulus within the pathologic area is an early sign of KC.⁴ However, the SSI value represents an overall rather than a localized biomechanical parameter. Recently, Eliasy et al¹⁶ developed an SSI map to characterize the regional distribution of corneal biomechanics.²⁰ Thus, localized corneal biomechanical parameters based on SSI maps may be more effective for KC staging. Diurnal variations of some anatomic and physiological parameters, such as corneal thickness, IOP, and axial length, have been detected in both healthy^21,22 and KC²³ eyes. Knowledge about the diurnal variations of these parameters is crucial for clinical practice. Until recently, no study has explored the daily fluctuations of Corvis ST parameters and SSI map parameters, and we believe it is necessary to quantify these diurnal variations before using the stiffness parameters in clinical practice. Thus, the aim of this study was twofold: to determine the diurnal variation of SSI map parameters and to establish a new KC staging system based on SSI map parameters.

Methods

Study Population

A total of 78 KC subjects who had visited the Eye Institute and Department of Ophthalmology at the Eye & ENT Hospital, Fudan University, were included in this study. The study was conducted under the Declaration of Helsinki and approved by the Ethics Committee of the Eye & ENT Hospital, Fudan University. Written informed consent was obtained from every subject before enrolling in the study.

The diagnosis of KC was based on the following criteria: (1) history of vision loss; (2) ≥1 of the following biomicroscopic signs: Vogt striae, Fleischer ring, or focal stromal thinning; and (3) the presence of ≥1 tomographic abnormality: maximum keratometry >47.2 D, an I–S value at 6 mm >1.4, or a KISA% index >100%. The exclusion criteria included (1) a history of ocular surgery (such as refractive surgery or corneal cross-linking); (2) a history of ocular trauma; (3) other ocular diseases (such as corneal ulcer, corneal ectasia, or glaucoma); (4) systemic diseases that affect corneal biomechanics (such as diabetes, connective tissue disease, etc.); (5) pregnancy or menstruation; (6) recent use of drugs that affect corneal biomechanics (such as prostaglandins); (7) recent wearing of contact lenses (soft contact lens within 1 week, Rigid Gas Permeable Contact Lens within 1 month, or orthokeratology within 3 months); and (8) inability to cooperate to complete the eye examination.

Stress–Strain Index Map Parameters

Stress–Strain Index value was obtained from Corvis ST. It was generated by numerical modeling based on finite element models of entire eye globe.¹⁶ The single overall value of SSI was converted into a 2-dimensional biomechanical distribution map based on the collagen fibril density distribution by finite-element–based numerical modeling method.²⁴ It relied on the proven theory that the corneal biomechanical distribution is related to collagen fibril density distribution.²⁵ A special algorithm was used to determine the collagen fibril density distribution of KC by characterizing the size,²⁶ center,²⁶ and the fibril density²⁷ of the area of pathology. In this study, the SSI value and corneal elevation data from Pentacam HR were input into a customized SSI map generator (Matlab runtime 9.8) to generate an SSI map and related parameters. Two patient-specific, 3-dimensional finite element models of the whole eye were developed. Model 1 was composed of homogeneous material, and its stiffness at all locations was determined by SSI values obtained through in vivo Corvis ST.²⁸ Model 2 uses an anisotropic material whose average distribution of stiffness follows the distribution pattern of corneal fibril density. To obtain the specific stiffness of each integration point of model 2, an inverse analysis process was carried out. This procedure assumes an initial stiffness value, taking care that the ratio between these stiffness values matches the fiber content ratio at the same location, and then compares the corneal apex displacement between models 1 and 2. The stiffness value of model 2 was adjusted by the same percentage of the difference in the displacement of the vertices of models 1 and 2, and this was repeated until the matching state was reached according to the objective function described as follows:

Root-mean-squared error $=\sqrt{\frac{{\sum }_{i=1}^{\mathrm{n}}{\left({\sigma }_{i\text{model}1}-{\sigma }_{i\text{model}2}\right)}^2}{\mathrm{n}}}$

$\sigma$ represents the displacement at the apical displacement, i denotes the different IOP application steps, and n signifies the total number of IOP steps.

When the root-mean-squared error was at its minimum, the corresponding distribution of SSI throughout the numerical model was considered to represent the SSI map of the cornea.²⁸

The following SSI map parameters were used for analysis: (1) mean inside cone SSI; (2) mean outside cone SSI; (3) minimum SSI (Min SSI); and (4) maximum SSI (Max SSI). Figure 1 indicates the representative case of the SSI map in different grades of KC.

Figure 1.

Representative case of Stress–Strain Index (SSI) map in the keratoconus eye. A, Mild. B, Moderate. C, Severe.

Study Procedure

Subjects were screened according to their prior medical history and slitlamp and fundus examination. Manifest refraction and best-corrected visual acuity were assessed by an experienced ophthalmologist. All subjects had corneal tomography (Pentacam HR, Oculus) and biomechanical measurements (Corvis ST, Oculus) 5 times a day, which were at 8:30 (session 1), 11:30 (session 2), 14:30 (session 3), 17:30 (session 4), and 20:30 (session 5). Biomechanically corrected IOP (bIOP), Kmax, central corneal thickness (CCT), and thinnest corneal thickness (TCT) were recorded. In each measurement session, 3 consecutive scans were obtained by one experienced operator. Corneal biomechanical measurement was performed last in each eye to avoid corneal deformation interfering with the accuracy of other measurements. Participants were asked to blink at intervals to stable tear film during measurements. At least 1 minute was left between consecutive Corvis ST measurements to allow the cornea to restore its normal shape. All measurements were taken without pupillary dilation in a dark room. Only measurements with an “OK” quality were used in the analysis.

Statistical Analysis

A random eye was selected for analysis for bilateral KC subjects, and only the KC eye was included in subjects with monocular KC. Statistical analyses were conducted using SPSS 25 (IBM SPSS Statistics for Windows, Version 25.0.0, IBM). All data were normal distribution by the Kolmogorov-Smirnov test. Measurement data were presented as mean ± standard deviation.

The mean value of 3 consecutive measurements was calculated for each subject at each measurement session. A one-way repeated-measures analysis of variance was used to investigate the diurnal variation of SSI map parameters, bIOP, Kmax, CCT, and TCT. The sphericity assumption for repeated-measures analysis of variance was confirmed using the Mauchly sphericity test. A Greenhouse–Geisser correction was applied when sphericity was violated. Post hoc tests with Bonferroni correction were conducted for significant effects. For parameters showing significant diurnal variation, the average daily value for each subject was calculated as the mean across all sessions. The amplitude of change was determined by calculating the difference between the average daily value and the value at each session.

All subjects were then divided into mild topographic KC classification (TKC) (TKC1 and 1–2), moderate (TKC 2 and 2–3), and severe (TKC 3, 3–4 and 4) groups based on TKC from Pentacam HR.^29,30 Analysis of variance was conducted to compare SSI map parameters across 3 groups with different KC stages. Post hoc tests with Bonferroni correction were applied when significant effects were detected. Boxplots were used to illustrate the distribution and comparison of SSI map parameters across the 3 KC groups. The parameter with the least overlap was selected to establish the new KC staging system.

To determine the cut-off values for the KC classification within the KC staging system, the receiver operating characteristic curve was used. Sensitivity and specificity were evaluated using the Youden index. Additionally, the DeLong test was used to assess the area under the curve values for specific parameters in terms of their classification performance.^31,32 An internal validation was carried out using a leave-one-out cross-validation procedure. In this approach, each subject was iteratively excluded from the data set and used as an independent validation case, whereas the remaining subjects were used to compute the receiver operating characteristic curve and determine the optimal threshold. This process was repeated until every subject had served as the validation case once. The leave-one-out cross-validation approach minimizes overfitting and provides a robust, unbiased estimation of model performance. This procedure was repeated 10 times, and the averaged performance metrics were computed. Cohen κ statistics were calculated to compare the new KC staging system with the TKC system.³³ Contingency tables were also constructed to show the staging distributions between the new KC staging system and the TKC system.

Results

Seventy-eight KC subjects (28 women) with a mean age of 25.82 ± 6.30 years were included in this study. Subjective refraction sphere, spherical equivalent, and best-corrected visual acuity had significant differences among the 3 KC groups (P all < 0.05). However, there were no significant differences in gender, age, and subjective refraction cylinder (P all > 0.05). More details about basic demographic and refractive information are provided in Table 1

Table 1.

Basic Demographic and Refractive Data of the Study Population

Parameters	Overall	Mild (a)(n = 18)	Moderate (b)(n = 30)	Severe (c)(n = 30)	P Value
Gender (F/M)	28/50	8/10	14/16	6/24	0.068
Ages (yrs)	25.82 ± 6.30	25.88 ± 5.74	25.08 ± 7.22	26.83 ± 5.51	0.756
Subjective refraction sphere (D)	–5.95 ± 3.77	–4.23 ± 1.66	–6.85 ± 4.28	–6.19 ± 3.99	0.044 (a,b: 0.017; a,c: 0.047)
Subjective refraction cylinder (D)	–3.67 ± 2.04	–3.14 ± 2.01	–3.86 ± 1.75	–3.85 ± 2.44	0.109
SE (D)	–7.19 ± 4.27	–4.68 ± 2.17	–8.43 ± 4.55	–7.62 ± 4.49	0.012 (a,b: 0.005; a,c: 0.014)
BCVA (LogMAR)	0.33 ± 0.35	0.16 ± 0.15	0.35 ± 0.37	0.46 ± 0.39	0.016 (a,b: 0.049; a,c: 0.005)

BCVA = best-corrected visual acuity; D = diopters; LogMAR = logarithm of the minimum angle of resolution; SE = Spherical equivalent.

Diurnal Variation of the Ocular Biometric Parameters

The Kmax was maintained during all measurement sessions (F = 1.127, P = 0.293). However, there were differences in CCT (F = 2.64, P = 0.034), TCT (F = 10.518, P < 0.001), and bIOP (F = 4.118, P = 0.003) over time (Table 2). Bonferroni adjustment for multiple comparisons shows that CCT measures were significantly different between sessions 1 and 3 (P = 0.008), 1 and 4 (P = 0.008), and 2 and 4 (P = 0.008). The TCT measured at session 1 was significantly higher than the TCT at all subsequent visits (P < 0.001 for all). Biomechanically corrected IOP also showed a daily fluctuation pattern (P = 0.003).

Table 2.

Diurnal Variation of the Ocular Biometric Parameters

Parameters	Mean ± SD (95% CI)					F	η2	P Value
	1	2	3	4	5
Kmax (D)	62.64 ± 9.85 (60.22,65.07)	62.48 ± 9.52 (62.48,64.82)	62.61 ± 10.00 (60.15,65.07)	62.79 ± 9.83 (60.37,65.21)	62.67 ± 10.07 (60.19,65.14)	1.127	0.015	0.293
CCT (μm)	448.36 ± 40.82 (438.32,458.39)	448.09 ± 41.87 (437.80,458.38)	445.26 ± 39.65 (435.52,455.01)	445.08 ± 41.53 (434.87,455.29)	446.83 ± 40.10 (436.83,456.55)	2.64	0.038	0.034 (1,3:0.008;1:4:0.002:2,4:0.037)
TCT (μm)	441.22 ± 44.25 (430.34,452.09)	434.84 ± 43.62 (424.12,445.57)	432.42 ± 42.74 (421.92,442.94)	433.63 ± 42.67 (423.14,444.12)	433.52 ± 43.34 (422.86,444.17)	10.518	0.123	<0.001 (1,2;1,3;1,4;1,5 all <0.001)
bIOP (mmHg)	14.42 ± 2.03 (13.92,14.92)	14.47 ± 1.92 (14.00,14.95)	14.11 ± 2.08 (13.59,14.62)	14.39 ± 2.19 (13.85,14.93)	13.89 ± 2.13 (13.37,14.41)	4.118	0.059	0.003 (1,5:0.003;2,3:0.016;2,5:0.002;4,5:0.005)
SSI	0.73 ± 0.20 (0.68,0.78)	0.73 ± 0.20 (0.68,0.78)	0.71 ± 0.19 (0.66,0.76)	0.72 ± 0.22 (0.67,0.78)	0.70 ± 0.19 (0.65,0.74)	2.055	0.03	0.087
Mean inside cone SSI	0.58 ± 0.11 (0.55,0.61)	0.58 ± 0.11 (0.55,0.60)	0.57 ± 0.10 (0.54,0.60)	0.57 ± 0.11 (0.54,0.60)	0.57 ± 0.10 (0.54,0.59)	5.536	0.081	0.001 (1,3:0.012,1,4:0.032;1,5:0.004)
Mean outside cone SSI	1.00 ± 0.06 (0.98,1.01)	1.00 ± 0.07 (0.98,1.01)	0.99 ± 0.06 (0.98,1.01)	1.00 ± 0.07 (0.98,1.01)	0.98 ± 0.07 (0.97,1.00)	1.575	0.024	0.198
Min SSI	0.40 ± 0.12 (0.37,0.44)	0.40 ± 0.12 (0.37,0.43)	0.40 ± 0.12 (0.37,0.43)	0.39 ± 0.12 (0.36,0.42)	0.39 ± 0.12 (0.36,0.42)	6.031	0.087	<0.001 (1,4:0.001,1,5:0.01)
Max SSI	1.51 ± 0.10 (1.49,1.54)	1.51 ± 0.10 (1.48,1.54)	1.50 ± 0.09 (1.48,1.52)	1.51 ± 0.10 (1.49,1.54)	1.49 ± 0.10 (1.47,1.52)	1.817	0.028	0.126

bIOP = biomechanically corrected intraocular pressure; CCT = central corneal thickness; CI = confidence interval; D = diopters; Max SSI = maximum Stress–Strain Index; Min SSI = minimum Stress–Strain Index; Kmax = maximum keratometry; SD = standard deviation; SSI = Stress–Strain Index; TCT = thinnest corneal thickness.

8:30 (session 1), 11:30 (session 2), 14:30 (session 3), 17:30 (session 4), and 20:30 (session 5).

Diurnal Variation of the SSI Map Parameters

Significant diurnal variation was found in mean inside cone SSI (F = 5.536, P < 0.001) and Min SSI (F = 6.031, P < 0.001) but not in SSI (F = 2.055, P = 0.087), mean outside cone SSI (F = 1.575, P = 0.198), and Max SSI (F = 1.817, P = 0.126) (Table 2; Fig 2). The amplitudes of change of mean inside cone SSI were 0.01 ± 0.01, 0.01 ± 0.01, 0.01 ± 0.01, 0.01 ± 0.01, 0.02 ± 0.02. For Min SSI, amplitudes of change were 0.01 ± 0.01, 0.01 ± 0.01, 0.01 ± 0.01, 0.01 ± 0.01, and 0.01 ± 0.01. Bonferroni adjustment for multiple comparisons shows that the mean inside cone SSI, which was observed at session 1 (8:30), was significantly higher than the mean inside cone SSI at all other sessions except session 2 (11:30) (P all < 0.05). The Min SSI measured at session 1 (8:30) was also significantly higher than the Min SSI at session 4 (17:30) and 5 (20:30) (P all ≤ 0.01). However, other paired session measurements of mean inside cone SSI and Min SSI showed no significant differences (P > 0.05). These are really small values and would not have any clinical relevance.

Figure 2.

Diurnal variation of Stress–Strain Index (SSI) (A), Mean inside cone SSI (B), Mean outside cone SSI (C), Min SSI (D), and Max SSI (E). ∗P ≤ 0.05, ∗∗P ≤ 0.01, ∗∗∗P ≤ 0.001. Max SSI = maximum SSI; Min SSI = minimum SSI.

Corneal-Biomechanics-Based Staging System Building

Given that all SSI map parameters have no clinically significant diurnal variation, the average daily value of SSI map parameters was used to compare 3 KC groups. There were statistically significant differences in SSI, mean inside cone SSI, and Min SSI among the varying severity of KC groups (P all < 0.001), whereas there were no significant differences in mean outside cone SSI (P = 0.624) and Max SSI (P = 0.244) (Table 3). Bonferroni post hoc test showed significant differences in mean inside cone SSI and Min SSI between all pairs (P all < 0.001) and in SSI between all pairs except for moderate with severe groups (P > 0.05) (Table 3). Boxplots showed the distribution of each SSI map parameter among the 3 groups (Fig 3).

Table 3.

SSI and SSI Map Parameters among Various Stages of KC

	Mean ± SD (95% CI)
	Mild (a)	Moderate (b)	Severe (c)	P Value
SSI	0.88 ± 0.13 (0.81–0.95)	0.70 ± 0.19 (0.61–0.78)	0.62 ± 0.15 (0.56–0.68)	<0.001 (a,b: 0.002; a,c: <0.001)
Mean inside cone SSI	0.71 ± 0.06 (0.67–0.74)	0.57 ± 0.06 (0.55–0.60)	0.49 ± 0.05 (0.47–0.51)	<0.001 (all pairs: <0.001)
Mean outside cone SSI	1.00 ± 0.05 (0.97–1.03)	0.98 ± 0.07 (0.95–1.01)	1.00 ± 0.06 (0.97–1.02)	0.626
Min SSI	0.54 ± 0.08 (0.50–0.58)	0.40 ± 0.08 (0.36–0.44)	0.31 ± 0.07 (0.28–0.34)	<0.001 (all pairs: <0.001)
Max SSI	1.49 ± 0.07 (1.45–1.53)	1.49 ± 0.10 (1.45–1.53)	1.53 ± 0.09 (1.49–1.56)	0.244

CI = confidence interval; KC = keratoconus; Max SSI = maximum Stress–Strain Index; Min SSI = minimum Stress–Strain Index; SD = standard deviation; SSI = Stress–Strain Index.

Figure 3.

Boxplots of Stress–Strain Index (SSI) (A), Mean inside cone SSI (B), Mean outside cone SSI (C), Min SSI (D), and Max SSI (E) among mild, moderate, and severe keratoconus (KC) subgroups. The blue dotted line represents the cutoff line for mild/moderate stage, whereas the black dotted line represents the cutoff line for moderate–severe stage. ∗P ≤ 0.05, ∗∗P ≤ 0.01, ∗∗∗P ≤ 0.001. Max SSI = maximum Stress–Strain Index; Min SSI = minimum Stress–Strain Index.

Compared with SSI, mean inside cone SSI and Min SSI presented smaller overlap among the 3 groups (Fig 3). Moreover, the overlap in these 2 parameters between mild and moderate KC groups was smaller than between moderate and severe KC groups. Table 4 shows the classification performance of various SSI map values across different grades of KC, based on which the most suitable classification for the corneal-biomechanics-based staging (CBBS) system was determined. Consequently, the mean inside cone SSI was selected because it exhibited the highest area under the curve value and sensitivity. The cutoff values of the 3 stages were 0.54 and 0.64. The resulting mean inside cone SSI area under the curve was 0.83 (95% confidence interval: 0.72–0.91), demonstrating stable predictive performance across folds (Table 5). These findings confirm that overfitting is unlikely and that the CBBS model maintains good internal validity.

Table 4.

Comparison of the AUC between the Indices of the SSI Map Parameter

Parameter		Mild/Moderate	Moderate/Severe
SSI	AUC (95% CI)	0.85 (0.74–0.93)	0.66 (0.51–0.75)
	Cutoff value	0.76	0.63
	Sensitivity (%)	73.96	66.38
	Specificity (%)	79.86	66.34
Mean inside cone SSI	AUC (95% CI)	0.97 (0.92–0.99)	0.84 (0.74–0.91)
	Cutoff value	0.64	0.54
	Sensitivity (%)	87.26	83.30
	Specificity (%)	97.76	74.40
Mean outside cone SSI	AUC (95% CI)	0.66 (0.49–0.77)	0.58 (0.43–0.68)
	Cutoff value	0.99	0.95
	Sensitivity (%)	67.58	61.92
	Specificity (%)	62.08	60.44
Min SSI	AUC (95% CI)	0.90 (0.81–0.96)	0.81 (0.70–0.89)
	Cutoff value	0.46	0.32
	Sensitivity (%)	76.72	66.04
	Specificity (%)	90.82	85.92
Max SSI	AUC (95% CI)	0.58 (0.41–0.70)	0.62 (0.47–0.71)
	Cutoff value	1.49	1.45
	Sensitivity (%)	61.08	62.80
	Specificity (%)	62.78	66.48

AUC = area under the curve; CI = confidence interval; Max SSI = maximum Stress–Strain Index; Min SSI = minimum Stress–Strain Index; SSI = Stress–Strain Index.

Bold values represent the best-performing SSI map parameter.

Table 5.

Comparison of the AUC between the Indices of the SSI Map Parameter Using LOOCV

Parameter		Mild/Moderate	Moderate/Severe
SSI	AUC (95% CI)	0.77 (0.63–0.87)	0.77 (0.65–0.87)
	Cutoff value	0.80	0.62
	Sensitivity (%)	61.22	71.15
	Specificity (%)	79.31	71.43
Mean inside cone SSI	AUC (95% CI)	0.83 (0.72–0.91)	0.79 (0.66–0.81)
	Cutoff value	0.71	0.56
	Sensitivity (%)	73.47	71.62
	Specificity (%)	82.76	74.36
Mean outside cone SSI	AUC (95% CI)	0.66 (0.50–0.78)	0.57 (0.44–0.70)
	Cutoff value	1	1
	Sensitivity (%)	48.98	61.54
	Specificity (%)	89.66	52.56
Min SSI	AUC (95% CI)	0.71 (0.56–0.83)	0.69 (0.55–0.82)
	Cutoff value	0.64	0.4
	Sensitivity (%)	65.31	50
	Specificity (%)	72.41	87.18
Max SSI	AUC (95% CI)	0.60 (0.44–0.74)	0.61 (0.47–0.74)
	Cutoff value	1.49	1.45
	Sensitivity (%)	48.98	64.1
	Specificity (%)	75.86	59.49

AUC = area under the curve; CI = confidence interval; LOOCV = leave-one-out cross-validation; Max SSI = maximum Stress–Strain Index; Min SSI = minimum Stress–Strain Index; SSI = Stress–Strain Index.

Bold values represent the best-performing SSI map parameter.

Staging System Distributions and Comparisons

The distribution of each parameter from the current new staging system was assessed. On the basis of cross-tabulation, the distribution of the staging system was compared with that of the CBBS KC staging system and TKC system. Of the KC eyes, 76.9% were of the same stage using the CBBS and TKC systems, whereas 10.3% and 12.8% of KC eyes had higher or lower CBBS staging than TKC staging, respectively (Fig 4). Cohen κ was 0.652 (P < 0.001), indicating a good agreement between the CBBS and TKC systems.

Figure 4.

Keratoconus (KC) group staging distribution in the topographic KC classification (TKC) and corneal-biomechanics-based staging system (CBBS).

Discussion

This study characterizes the diurnal variation of localized corneal biomechanics in KC eyes by SSI map parameters. Stress–Strain Index map is a novel method for characterizing the corneal biomechanics distribution. Diurnal variation was observed only in mean inside cone SSI and Min SSI, but not in mean outside cone SSI, Max SSI, and overall SSI. Previous studies have also proved that corneal biomechanics was stable throughout the day in healthy eyes using ORA,³³ air-puff optical coherence elastography³⁴ and a corneal indentation device,⁴ which were consistent with the results of outside cone area in this study. It is reported that the microstructural alterations of corneal tissue in the cone area, such as the density and orientation of collagen fibrils, are mainly related to the biomechanical weakening.²⁷ These alterations will mainly occur inside the cone area in KC eyes. There is evidence that the area outside the cone maintained almost the same microstructure as healthy corneas.²⁷ Thus, the different distribution patterns of collagen fibers inside the cone and outside the cone may result in different patterns of diurnal variation. However, the amplitudes of change of mean inside cone SSI and Min SSI (0.01–0.02) across all measurement sessions were so small that they did not meet the clinical significance. The confounded effects of IOP on corneal elasticity derived from optical coherence elastography and corneal tangent modulus derived from corneal indentation device should be considered, because the cornea is a nonlinear viscoelastic tissue.¹² In other words, these corneal stiffness parameters would be altered with a change of the load (IOP).¹² Stress–Strain Index is a standard mechanical metric reflecting the overall stress–strain curve, which was free of the influences of IOP.¹⁶ Although the P value revealed statistical significance, the correlation coefficients were low (r < 0.25) between bIOP and SSI map parameters in this study. Thus, we did not consider the confounded effects of IOP in this study.

This study showed that with higher stages of KC, the SSI, mean inside cone SSI, and Min SSI decreased in magnitude. It indicated that corneal stiffness became lower with KC progression. Mean inside cone SSI and Min SSI had smaller overlaps in the 3 KC groups than the overall SSI. Consistent with this study, Padmanabhan et al³⁴ also found a large overlap of SSI among various KC stages (TKC system). There was a viewpoint that the biomechanical modification of KC is localized—concentrated in the cone—rather than a uniform weakening.⁴ The localized corneal biomechanical parameters, mean inside cone SSI, and Min SSI were more in line with the local lesions of KC than the overall parameter, SSI.

There are several KC staging systems used in clinical practice. Amsler-Krumeich staging system³⁵ and TKC system³⁶ have an intuitive staging strategy. Belin and Duncan³⁷ developed the ABCD system with a focus on the anterior and posterior radii of curvature in the 3.0 mm zone centered on the thinnest point of the cornea, TCT, and visual acuity. Because the technology of measurement continues to advance, researchers introduced the cornea’s higher order aberrations,³⁸ corneal biomechanics,³⁹ and corneal OCT measurement parameters⁴⁰ into KC staging systems. Corneal biomechanical decompensation may precede changes in the posterior corneal curvature,⁴¹ and hence, adding corneal biomechanics to KC staging systems may be more effective. To establish a more concise and effective staging system based on corneal biomechanics, we used mean inside cone SSI to build the new CBBS system. This system agreed well with the TKC system (with agreement in 76.9% of KC eyes and with a Cohen κ parameter of 0.652). Make a further comparison with the ABCD system, as shown in Figure 5, each heatmap illustrates the distribution of cases across ABCD levels (A0–A4, B0–B4, C0–C4, and D0–D4) versus CBBS grades (mild, moderate, and severe). The results demonstrate a consistent trend—higher ABCD grades are associated with higher CBBS grades, confirming good correlation and construct validity of the new system. For parameter A (anterior curvature), the lower levels (A0–A1) mainly cluster around mild, the medium levels (A2–A3) tend to group toward moderate, and A4 has the highest proportion in severe (Severe = 23). The B parameter classification is in the same direction as the severity of CBBS, and the proportion of moderate to severe cases corresponding to B4 has significantly increased. The proportion of moderate to severe cases for C2 was the highest, suggesting that this parameter becomes significantly correlated with more severe CBBS levels once it reaches the 2 level. D2 peaks in moderate–severe, whereas D0–D1 remain largely mild. The monotonic relationship of the ABCD levels rising toward the moderate–severe aggregation in CBBS is most significant for A4, B4, C2, and D2. This supports the validity of the CBBS classification. A4 corresponds to severe = 23/78, whereas A0–A1 mainly fall into mild, which is consistent with the biological weakening of the disease from the early stage to the progressive stage. The peak rows of different parameters are not exactly the same, suggesting that CBBS can capture complementary information from multiple biological mechanical characteristics. Flockerzi et al³⁹ introduced the Corvis biomechanical factor into the ABCD system to combine tomography with biomechanics in a system called the ABCDE system. However, the ABCDE system produces 5 independent staging parameters, which makes it challenging to assess the overall severity of KC. Among these parameters, “E” tends to indicate more advanced stages compared with “A” and “C”, reflecting localized biomechanical weakening that contributes to tomographic alterations. However, this trend was not found in this study. This may be attributed to the fact that the TKC system is a comprehensive result based on multiple topographic parameters, whereas each independent classification of the ABCD system is based on one simple parameter. The CBI β is a linear combination of biomechanical and thickness-related parameters derived from Corvis ST,¹¹ with strong correlation between CBI β and ABC grading parameters in the KC group, but all of which reflect the overall biomechanical properties. Nevertheless, the CBBS system based on mean inside cone SSI is a rich supplement to traditional staging strategies. It is not only instrumental in KC staging but may also be conducive to efficacy evaluation for corneal cross-linking.

Figure 5.

Comparison of corneal-biomechanics-based staging system (CBBS) classification with Belin ABCD grading system across different severity groups. Comparison between CBBS and Belin A grading (A). Distribution of CBBS classifications relative to Belin B grading (B). Comparison with Belin C grading (C). Comparison with Belin D grading (D).

Unlike other staging systems, the CBBS system does not include the healthy eye (staging 0). The generation strategy of the SSI map for healthy eyes and KC eyes is different. It is assumed that there is a strong consistency in biomechanical distribution in healthy corneas with little variation between individuals.²⁴ In other words, as long as the value of SSI is the same, the values of other SSI map parameters are also the same. It has been proven that SSI lacks the ability to discriminate KC eyes from healthy eyes.⁴² However, the aim of the CBBS staging is to further refine the staging system rather than to diagnose KC. Another limitation is that CBBS lacks staging ability for forme fruste KC (FFKC). Mean inside cone SSI describes the biomechanics of the cone area, which is delineated on the basis of topographic information. However, FFKC has the normal topography,⁴³ so that it is impossible to delineate the cone zone. Although Min SSI may be a potential indicator for FFKC staging, KKFC subjects were not included in this study. Future studies should focus on biomechanical classification for FFKC.

Conclusion

In summary, there was no clinically significant diurnal variation in localized corneal biomechanics based on SSI map parameters. Mean inside cone SSI had the largest difference among various KC stages, and this parameter was used to propose a new corneal-biomechanics-based KC staging system. This KC staging system is a promising addition to existing KC staging systems and has strong potential for improved KC management and progression monitoring.

Manuscript no. XOPS-D-25-00686.