Stromal mechanical anisotropy of the SMILE lenticule shows no detectable association with postoperative refractive error

Abstract

Background

Small-incision lenticule extraction (SMILE) removes an intrastromal lenticule whose stiffness differs between corneal meridians, producing measurable stromal mechanical anisotropy. Whether this meridional anisotropy biases postoperative refractive or astigmatic outcomes—and could therefore guide individualized treatment—remains unestablished. We tested whether lenticule mechanical anisotropy is associated with axis-specific astigmatic error, using an orthogonal negative control to guard against spurious correlation.

Methods

In this prospective consecutive cohort, 282 patients undergoing SMILE for the correction of myopia or myopic astigmatism were enrolled, and 279 right eyes with complete 3-month follow-up were analyzed. Excised lenticules underwent orientation-registered biaxial mechanical testing to derive the meridional anisotropy index A_mech = (E_SI − E_NT)/(E_SI + E_NT) and the mean tangent modulus Ē. The pre-specified primary outcome was the association between A_mech and the on-axis astigmatic power-vector error (ΔJ₀); the association between A_mech and the orthogonal oblique error (ΔJ₄₅)—onto which a true meridional effect should not project—served as a pre-specified negative control. The mean modulus was related to spherical-equivalent error (ΔM). Associations were assessed by Spearman correlation and refractive predictability by attempted-versus-achieved analysis.

Results

Refractive outcomes were excellent (spherical-equivalent error + 0.29 ± 0.39 D; 99.3% within ± 1.00 D; attempted-versus-achieved R² = 0.918). The primary association between A_mech and ΔJ₀ was null (ρ = +0.054, P = 0.365), and the orthogonal negative control was likewise null (A_mech–ΔJ₄₅ ρ = +0.033, P = 0.587), indicating the absence—rather than masking—of an axis-specific signal. The mean modulus showed only a borderline relation to ΔM (ρ = +0.117, P = 0.050), and the residual astigmatic vector was centred near the origin (ΔJ₀ +0.03 ± 0.15 D, ΔJ₄₅ −0.02 ± 0.11 D).

Conclusions

Although SMILE lenticules exhibit reproducible meridional mechanical anisotropy, this property did not translate into detectable axis-specific or magnitude-related refractive error in this cohort. The concordant null finding in the orthogonal negative control supports the interpretation that no measurable axis-specific signal was present, rather than a meridian-independent analytical artifact. Lenticule-derived biomechanical metrics therefore appear unlikely, by themselves, to meaningfully refine refractive accuracy through individualized treatment planning in this setting. These conclusions are limited to the ex vivo lenticule-derived metrics evaluated here and should not be generalized to all corneal biomechanical measurements or to their established role in ectasia risk assessment.

Background

Myopia is among the most common ocular conditions worldwide, and its global prevalence is projected to rise substantially over the coming decades [1], sustaining a large and continuing demand for corneal refractive surgery. Corneal biomechanics has become a focus of interest in keratorefractive surgery, because the cornea’s mechanical response to tissue removal is thought to shape both its safety and its optical outcome [2]. Within this interest, two distinct clinical aspirations can be distinguished. The first, and the better established, is preoperative risk assessment: by identifying corneas with weak mechanical reserve, biomechanical evaluation aims to screen out eyes predisposed to post-refractive ectasia, operating at the level of patient selection [3–5]. The second is more speculative: that preoperative mechanical measurement might be used to individualise the ablation—adjusting treatment to a given cornea’s mechanical behaviour in order to improve refractive accuracy [6, 7]. Whereas the screening role is supported by clinical experience, the design role rests on an untested premise, namely that corneal mechanical properties are stably and substantially associated with postoperative refractive error.

Testing that premise has been difficult, in part because the corneal stroma is not readily accessible for direct mechanical characterisation in vivo. Small-incision lenticule extraction (SMILE) [8, 9] offers an unusual opportunity in this respect: the procedure removes an intact intrastromal lenticule that can be retrieved and subjected to direct mechanical testing [10–12]. However, the extracted lenticule represents the removed stromal tissue rather than the residual stromal bed that remains after surgery, and its relationship to postoperative whole-corneal biomechanical behavior is therefore indirect. Biaxial tensile testing of such lenticules has shown that the corneal stroma is mechanically anisotropic, with the tangent modulus differing between orthogonal meridians [13, 14]. This directional behaviour has a structural basis: X-ray scattering studies of the human cornea have shown that stromal collagen lamellae are not randomly arranged but adopt preferred orientations, with central fibrils running predominantly along the orthogonal nasal–temporal and superior–inferior meridians [15, 16]. Crucially, when the lenticule’s orientation is registered to the corneal meridians, this directional stiffness can be expressed as a signed quantity along the 90°/180° axis—the same axis described by the J₀ component of the refractive power vector. Mechanical anisotropy and astigmatic error are therefore geometrically comparable in a common double-angle coordinate frame, although this directional correspondence does not by itself imply physiological equivalence or causality. The oblique (J₄₅) component, for which the meridional measurement carries no information, therefore provides a natural negative control. Because the SMILE lenticule is mechanically anisotropic, its removal could theoretically induce meridian-dependent, asymmetric stress redistribution within the residual stromal bed. Such an effect, if present, would be expected to manifest primarily as co-axial astigmatic error in the J₀ component rather than as oblique J₄₅ error.

On this basis, if lenticule-derived biomechanical properties are to inform individualized treatment design, directional stromal anisotropy would be expected to show an association with axis-specific astigmatic error, while overall stromal stiffness might relate to the spherical-equivalent outcome. The present study tested these expectations in a large series of myopic SMILE eyes by relating the biaxial mechanical properties of the extracted lenticule to the 3-month postoperative refractive error, decomposed into power vectors, with the oblique astigmatic component pre-specified as a negative control. By examining both the astigmatic and the spherical-equivalent dimensions, the study aimed to determine whether lenticule-derived biomechanics carries information of the kind that an individualized-design strategy would require, and thereby to clarify the potential clinical relevance of these metrics in SMILE.

Methods

Study design and participants

The study was approved by the Ethics Committee of Shanxi Aier Eye Hospital (approval EYESX-20240415-04) and performed in accordance with the Declaration of Helsinki. All personal identifiers were removed and replaced with unique study codes, the identification linkage file was stored separately from the analytical database, and all data were fully de-identified prior to analysis.

This prospective consecutive cohort enrolled 282 eligible patients who underwent small-incision lenticule extraction (SMILE) between June 2025 and December 2025 for the correction of myopia or myopic astigmatism, with a planned target of emmetropia (plano) in every eye. Three patients did not attend the 3-month postoperative examination and were excluded, leaving 279 right eyes for final analysis. To avoid inter-eye correlation, only the right eye of each patient was included. Refractive outcomes were evaluated at the single postoperative time point of 3 months; eyes without a 3-month examination were not analysed. Because the intended postoperative refraction was plano in all eyes, the postoperative manifest refraction was taken to represent the refractive error directly.

Surgical procedure

All SMILE procedures were performed using the VisuMax 500 femtosecond laser system (Carl Zeiss Meditec, Jena, Germany) by the same experienced surgeon. The cap thickness was 120 μm in all eyes. The optical zone was individualized between 6.0 and 7.0 mm according to preoperative refraction and corneal thickness, and the cap diameter was set as the optical zone plus 1.0 mm. The programmed spherical correction magnitude followed our institutional nomogram and was set at 118% of the manifest spherical refractive error to compensate for expected undercorrection. Cylindrical correction followed the standard manufacturer algorithm, with no additional cylinder-specific or axis-specific nomogram adjustment. After completion of the laser cuts, the anterior and posterior lenticule interfaces were fully separated before extraction. The lenticule was then gently removed with minimal traction, and care was taken to avoid excessive stretching or forceful extraction from residual adhesions before biomechanical testing.

Biaxial mechanical testing

The extracted refractive lenticule of each eye was subjected to planar biaxial tensile testing using a BioTester 5000 biaxial testing system (CellScale Biomaterials Testing, Waterloo, Canada) equipped with a 5-N load cell. The load cell was calibrated before testing sessions according to the manufacturer’s instructions. Each lenticule was marked at the 12 o’clock position before extraction so that its orientation could be registered to the corneal meridians, and was immediately placed in Optisol-GS after removal. Specimens were tested within 2 h of extraction.

During testing, the lenticule was immersed in lactated Ringer’s solution at room temperature (22–24 °C) to maintain hydration. The central 4 × 4 mm region was mounted with four sets of BioRakes. The superior–inferior (SI) meridian corresponded to the 12-to-6 o’clock direction and the nasal–temporal (NT) meridian to the 3-to-9 o’clock direction, allowing the tangent modulus to be resolved along the vertical (90°) and horizontal (180°) meridians.

After seven preconditioning cycles using an 80 μm displacement (approximately 2% engineering strain), quasi-static loading was performed at 10 μm/s. Engineering stress was calculated as σ = F/(t·w), where F is the force along the corresponding loading direction, t is the central lenticule thickness from the SMILE surgical plan, and w is the specimen width. Engineering strain was calculated from BioRake clamp displacement relative to the gauge length.

The tangent modulus was evaluated at a fixed engineering stress of 0.03 MPa, which was selected as a physiologically relevant sampling stress within the stable portion of the stress–strain curve rather than as a direct simulation of in vivo intraocular pressure. A fixed-stress reference was used instead of a fixed-strain reference because the zero-strain reference of thin hydrated collagenous tissue can be affected by fibril crimp and viscoelastic settling. Local slopes were obtained after Savitzky–Golay smoothing by least-squares linear fitting over the 0.025–0.035 MPa stress interval; all local fits had R² > 0.99. The tangent modulus of each meridian (E_SI and E_NT) was recorded. Mechanical anisotropy was expressed as a signed index, A_mech = (E_SI − E_NT) / (E_SI + E_NT), with positive values indicating a stiffer vertical meridian; overall stiffness was summarized as the mean tangent modulus E̅ = (E_SI + E_NT) / 2. Because the two meridians correspond to the 90°/180° axis, A_mech is geometrically aligned with the J₀ power-vector component but carries no directional information about the oblique 45°/135° axes represented by J₄₅.

Because each lenticule was destructively tested once, formal repeat testing of study specimens was not performed. All measurements were performed by the same trained operator using the same device, standardized mounting procedure, hydration conditions, loading protocol, and data-processing workflow to minimize procedural variability. The paired SI and NT measurements were acquired simultaneously under identical testing conditions, which reduces the influence of common systematic errors on the anisotropy index.

Refractive assessment and vector analysis

Preoperative and 3-month postoperative manifest refractions were recorded as sphere, cylinder and axis, and cylinder notation was harmonised to negative-cylinder convention. Each refraction was decomposed into Thibos power vectors [17]: M = S + C/2, J₀ = −(C/2)·cos(2α) and J₄₅ = −(C/2)·sin(2α). The spherical-equivalent error was defined as the postoperative M (ΔM) and the astigmatic error as the postoperative power-vector pair (ΔJ₀, ΔJ₄₅); ΔJ₀ is the component co-axial with the mechanical measurement, whereas ΔJ₄₅ served as a pre-specified negative control. Astigmatic outcomes were additionally summarised by Alpins vector analysis [18, 19] (TIA, DV, CI, IOS, ME, AE), computed over eyes with astigmatism to correct (TIA > 0).

Statistical analysis

Statistical analyses were performed using Python 3 (SciPy and statsmodels libraries) and GraphPad Prism (version 11). The primary analysis evaluated the association between mechanical anisotropy (A_mech) and the co-axial astigmatic error (ΔJ₀), with the oblique component (ΔJ₄₅) serving as a pre-specified negative control. Associations were quantified using Spearman rank correlation with bootstrap 95% confidence intervals (5000 resamples) and multivariable linear regression adjusted for age and sex. For the secondary analysis of spherical-equivalent error (ΔM), multivariable linear regression was performed with age, sex, mean tangent modulus, and preoperative spherical equivalent as covariates; collinearity was assessed using variance inflation factors, and model assumptions were evaluated using residual-versus-fitted plots and Q–Q plots of residuals. Regression estimates are reported as unstandardized coefficients with 95% confidence intervals. A pre-specified sensitivity analysis repeated the primary correlation in subgroups stratified by increasing levels of preoperative astigmatism. As an effect-size sensitivity statement, the final analyzable sample of 279 eyes provided 80% power at a two-sided α of 0.05 to detect a small correlation of approximately |ρ| ≥ 0.17. This threshold was interpreted as a small effect size and as the lower bound of associations likely to be clinically relevant for refractive predictability. Graphs were prepared using GraphPad Prism.

Results

Cohort and mechanical characteristics

Of the 282 consecutively enrolled patients, 3 did not attend the 3-month postoperative examination and were excluded, leaving 279 right eyes for analysis. The analyzed eyes had a mean age of 23.8 ± 6.1 years (190 male, 89 female) and a mean preoperative spherical equivalent of − 4.80 ± 1.36 D (Table 1). The tangent modulus was higher in the SI than in the NT meridian (E_SI 2.59 ± 0.70 vs. E_NT 2.21 ± 0.51 MPa; Wilcoxon signed-rank P < 0.001), so that the anisotropy index was positive on average (A_mech + 0.07 ± 0.13) and 74.6% of eyes showed a stiffer vertical meridian. A reproducible directional anisotropy was therefore present at the lenticule level.

Table 1.

Baseline patient, refractive and mechanical characteristics (279 right eyes)

Characteristic	Mean ± SD	Range
Right eyes, n	279	—
Age, years	23.8 ± 6.1	17 to 42
Sex, male / female (n)	190 / 89	—
Preoperative spherical equivalent, D	−4.80 ± 1.36	−8.00 to − 0.75
Preoperative refractive cylinder, D	0.86 ± 0.58	0.00 to 3.25
Tangent modulus, SI meridian (ESI), MPa	2.59 ± 0.70	1.19 to 5.56
Tangent modulus, NT meridian (ENT), MPa	2.21 ± 0.51	1.18 to 3.76
Mean tangent modulus (), MPa	2.40 ± 0.52	1.39 to 3.90
Mechanical anisotropy index (A_mech)	+ 0.07 ± 0.13	−0.37 to 0.47
Lenticule thickness, µm	108.6 ± 19.0	55 to 147
Residual stromal bed thickness, µm	441.1 ± 30.2	397 to 551
Optical zone, mm	6.55 ± 0.23	6.00 to 7.00

SI, superior–inferior; NT, nasal–temporal

Refractive and astigmatic outcomes

At 3 months the mean spherical-equivalent error was + 0.29 ± 0.39 D, with 69.2% of eyes within ± 0.50 D and 99.3% within ± 1.00 D of the plano target (Table 2). Astigmatic outcomes were favourable: the mean postoperative refractive cylinder was 0.31 ± 0.22 D, 92.1% of eyes had ≤ 0.50 D of residual cylinder, and the residual astigmatic vector was centred near the origin (ΔJ₀ +0.03 ± 0.15 D, ΔJ₄₅ −0.02 ± 0.11 D; Fig. 1D). Among the 261 eyes with astigmatism to correct, the difference vector was 0.31 ± 0.22 D and the correction index 1.07 ± 0.52, with an angle of error of + 0.8 ± 17.3°, indicating minimal systematic over- or under-correction and no systematic axis offset. Attempted spherical-equivalent correction was expressed as a positive correction magnitude. The attempted-versus-achieved spherical-equivalent correction demonstrated excellent linear predictability (R² = 0.918), with a slope of 0.925 (95% CI, 0.892 to 0.958) and an intercept of + 0.651 D (95% CI, + 0.488 to + 0.815 D; Fig. 2).

Table 2.

Refractive and astigmatic outcomes at 3 months

Outcome at 3 months	Value
Postoperative spherical equivalent, D (mean ± SD)	+ 0.29 ± 0.39
Eyes within ± 0.50 D of target, %	69.2
Eyes within ± 1.00 D of target, %	99.3
Postoperative refractive cylinder, D (mean ± SD)	0.31 ± 0.22
Eyes with cylinder ≤ 0.50 D, %	92.1
On-axis astigmatic error ΔJ0, D (mean ± SD)	+ 0.03 ± 0.15
Oblique astigmatic error ΔJ45, D (mean ± SD)	−0.02 ± 0.11
Target induced astigmatism (TIA), D ¹	0.86 ± 0.58
Difference vector (DV), D ¹	0.31 ± 0.22
Correction index (CI) ¹	1.07 ± 0.52
Index of success (IOS) ¹	0.50 ± 0.57
Magnitude of error (ME), D ¹	−0.01 ± 0.28
Angle of error (AE), degrees ¹	+ 0.8 ± 17.3

¹ Alpins vector parameters summarised over the 261 eyes with preoperative astigmatism (TIA > 0)

Fig. 1.

Associations between lenticule-derived biomechanical metrics and postoperative refractive error. (A) Primary association between mechanical anisotropy index (A_mech) and on-axis astigmatic error (ΔJ₀). (B) Negative-control association between A_mech and oblique astigmatic error (ΔJ₄₅). (C) Mean tangent modulus (E̅) versus spherical-equivalent error (ΔM). (D) Double-angle plot of residual astigmatic error showing a centroid near the origin. Shaded bands in panels A–C represent 95% confidence intervals of the fitted regression lines. All panels include 279 right eyes

Fig. 2.

Attempted versus achieved spherical-equivalent correction in 279 eyes. Attempted correction was expressed as a positive spherical-equivalent correction magnitude. The dashed line represents the intended outcome (y = x), and the solid line represents the least-squares regression line. The shaded band represents the 95% confidence interval of the fitted regression line. The regression equation, R², and sample size are shown in the plot. The regression slope below unity with a positive intercept reflects mild relative undercorrection at higher attempted corrections

Primary analysis: mechanical anisotropy and astigmatic error

Mechanical anisotropy was not associated with the co-axial astigmatic error: the correlation between A_mech and ΔJ₀ was negligible and non-significant (ρ = +0.054, 95% CI − 0.065 to + 0.175, P = 0.365; Fig. 1A; Table 3). The negative-control association with the oblique component ΔJ₄₅ was likewise null (ρ = +0.033, P = 0.587; Fig. 1B). The null result for ΔJ₀ was not attributable to insufficient power, as the cohort could detect |ρ| ≥ 0.17 and the observed estimate was well below this threshold; A_mech remained unrelated to ΔJ₀ after adjustment for age and sex (β = +0.034, P = 0.640). In the pre-specified sensitivity analysis, restricting the cohort to eyes with larger preoperative astigmatism produced a consistently positive but non-significant trend (≥ 0.75 D: ρ = +0.11, P = 0.18, n = 166; ≥1.00 D: ρ = +0.14, P = 0.11, n = 130; ≥1.50 D: ρ = +0.24, P = 0.12, n = 42), which should be regarded as hypothesis-generating only. Visual inspection of the scatterplots did not suggest that the null findings were driven by a single extreme observation or an obvious outlier cluster.

Table 3.

Associations between lenticule mechanical properties and postoperative refractive error

Association	ρ or β	n	95% CI	P
A_mech vs. ΔJ0 (primary)	+ 0.054	279	−0.065 to + 0.175	0.365
A_mech vs. ΔJ45 (negative control)	+ 0.033	279	−0.083 to + 0.148	0.587
vs. ΔM (SE error)	+ 0.117	279	−0.002 to + 0.236	0.050
ΔJ0 ~ A_mech (adj. age, sex) ²	+ 0.034	279	−0.108 to + 0.176	0.640
ΔM ~ E̅ (adj. age, sex, preop SE) ²	+ 0.054	279	−0.034 to + 0.141	0.231
ΔM ~ preoperative SE (same model) ²	+ 0.069	279	+ 0.035 to + 0.102	< 0.001

ρ values are Spearman rank correlation coefficients with bootstrap 95% confidence intervals. β values are unstandardized coefficients from multivariable linear regression models. The ΔJ₀ model was adjusted for age and sex; the ΔM model was adjusted for age, sex, mean tangent modulus, and preoperative spherical equivalent. Variance inflation factors were < 1.3 in all multivariable models

Secondary analysis: stiffness and spherical-equivalent error

Findings were similar in the spherical-equivalent dimension. Mean tangent modulus showed only a weak univariate association with ΔM (ρ = +0.117, P = 0.050), and in a multivariable model including age, sex, mean modulus and preoperative spherical equivalent, mean modulus carried no independent association (β = +0.054, P = 0.231; Table 3). The only independent predictor of ΔM was the preoperative spherical equivalent itself (β = +0.069, standardised β = +0.239, P < 0.001), reflecting the well-recognised tendency toward slight undercorrection at higher attempted corrections. The NT-meridian modulus, which reached significance univariately (ρ = +0.151, P = 0.011), likewise lost significance after adjustment for preoperative refraction (P = 0.109). Model diagnostics did not suggest that the null findings were driven by major assumption violations. Visual inspection of residual-versus-fitted plots and normal Q–Q plots showed no major systematic residual pattern or marked departure from approximate normality, and multicollinearity was minimal in the multivariable models, with all variance inflation factors < 1.3.

Discussion

The aspiration to use corneal biomechanics for individualised treatment design presupposes that the mechanical properties of a given cornea carry usable information about its refractive response to surgery. Until now that premise had been pursued largely through patient-specific computational simulation, in which an assumed mechanical behaviour is used to predict post-surgical shape [20, 21]; it had not been tested directly against clinical outcomes using measured tissue mechanics. The present study provides such a direct test using ex vivo lenticule-derived biomechanical measurements, and the results did not support an independent predictive association. In a large, single-eye series of myopic SMILE eyes, the directional mechanical anisotropy of the extracted lenticule showed no detectable association with the co-axial astigmatic refractive error, and the pre-specified oblique negative control was likewise null; the same held in the spherical-equivalent dimension, where overall stromal stiffness carried no independent association with the SE error once the attempted correction was accounted for, the only independent predictor being the preoperative spherical equivalent itself. The weak univariate association seen for mean tangent modulus disappeared after adjustment for preoperative spherical equivalent and may therefore reflect shared association with preoperative refractive magnitude or tissue-removal depth rather than an independent mechanical effect on refractive outcome. The convergence of these two methodologically independent lines of analysis—the axis-resolved astigmatic vector (ΔJ₀) and the spherical-equivalent magnitude (ΔM)—is what gives the conclusion its weight: within the resolution and power of this study, the ex vivo mechanical properties of the excised lenticule did not provide clinically meaningful independent predictive information for early postoperative refractive error. Importantly, this null is informative rather than merely absent: it was obtained in a cohort powered to detect a small correlation of approximately |ρ| ≥ 0.17, with a pre-specified negative control that behaved as expected. Associations smaller than this detectable threshold would explain only a very small proportion of refractive-error variability and, in isolation, would be unlikely to provide a clinically useful basis for individualized treatment adjustment. At the same time, the present analysis was designed to test pre-specified monotonic and linear associations between lenticule-derived biomechanical metrics and postoperative refractive error. Therefore, nonlinear, threshold-dependent, interaction, or subgroup-specific effects cannot be excluded and should be investigated in larger cohorts with pre-specified nonlinear or interaction modeling. This possibility is also consistent with the exploratory, non-significant positive trend observed in the higher-astigmatism subgroups; however, these subgroup analyses were underpowered, particularly for eyes with preoperative cylinder ≥ 1.50 D, and should therefore be interpreted as hypothesis-generating rather than confirmatory.

Several factors plausibly account for this dissociation. The tissue tested is the anterior-to-mid stromal lenticule, whereas the postoperative refraction is governed by the retained residual stromal bed; the mechanical behaviour of the lenticule need not represent that of the residual bed, so the inference from one to the other is indirect [22, 23]. Postoperative wound healing and epithelial remodelling may further attenuate or mask any stromal-level mechanical difference, leaving little imprint on the refractive outcome [24, 25]. The 0.25 D resolution of subjective refraction imposes a measurement floor that can obscure effects of smaller magnitude [26]. Finally, and most decisively, the spherical-equivalent predictability of SMILE is already very high in this cohort (99.3% within ± 1.00 D; Fig. 2), so the surgery leaves little residual error variance for any mechanical predictor to explain.

These findings help clarify, but should not overextend, the clinical interpretation of corneal biomechanics in refractive surgery. The present data do not show that corneal biomechanics as a whole are unrelated to postoperative refractive outcomes; rather, they indicate that the specific ex vivo lenticule-derived metrics measured here did not provide independent predictive information for 3-month refractive error after SMILE. This distinction is important because the postoperative corneal response is governed not only by the extracted lenticule but also by the retained residual stromal bed, epithelial remodeling, wound healing, and patient-specific biomechanical behavior in vivo. Accordingly, the proposal that preoperative mechanical measurement of the excised-lenticule type evaluated here might be used to individualise SMILE treatment parameters is not supported by the present data. This does not diminish the established value of corneal biomechanical assessment in refractive surgery, particularly for preoperative ectasia risk screening and patient selection. Thus, in this setting, lenticule-derived biomechanical assessment appears more appropriately positioned as a mechanistic research tool and risk-contextualizing measurement than as a determinant of individualized SMILE treatment parameters.

A strength of this study is the pre-specified oblique negative control. Because the meridional mechanical measurement carries no information about the 45°/135° axis, the residual ΔJ₄₅ error was expected to be unrelated to A_mech; this expectation was met (ρ = +0.033, P = 0.587). This supports the absence of a meridian-independent systematic bias, such as axis misregistration or coordinate-frame error, and strengthens the internal validity of the primary ΔJ₀ analysis. Because both the primary and negative-control analyses were null, however, this result should be interpreted as supportive evidence against systematic bias rather than as proof that no small axis-specific effect exists. Further strengths include orientation-registered biaxial testing in the same coordinate frame as the astigmatic vector, the single-eye design avoiding inter-eye correlation, and a sample adequately powered to detect at least small-to-moderate correlations.

Limitations should be acknowledged. The mechanical indices derive from the excised lenticule rather than the residual stromal bed, and the relationship between the two warrants dedicated study. Refractive error was assessed by subjective manifest refraction, whose 0.25 D clinical resolution may underestimate small associations. In addition, refractive error alone may not capture subtle structural or optical effects potentially related to postoperative biomechanical response. Corneal topography, anterior-segment or Scheimpflug tomography, and corneal higher-order aberration analysis may provide more sensitive structural and optical endpoints, including anterior or posterior corneal shape and optical aberrations [27]. Epithelial thickness mapping may also detect compensatory epithelial remodeling that is not fully reflected in subjective refraction [24, 25]. These considerations may be particularly relevant in the high-astigmatism subgroup, where an underpowered positive trend cannot exclude a true effect; larger studies enriched for high astigmatism are warranted to test for such nonlinear or subgroup-specific associations. Follow-up was limited to 3 months, so the present findings apply to early postoperative refractive outcomes only. Longer-term residual stromal remodeling, epithelial compensation, wound-healing responses, and biomechanical adaptation may continue beyond this time point and could influence later corneal shape or refractive stability. Longer follow-up studies are therefore needed to determine whether lenticule-derived biomechanical metrics are associated with long-term remodeling or refractive stability. Comparison with previously reported SMILE refractive-outcome series is also warranted [28, 29]. More broadly, emerging in-vivo biomechanical techniques—including Brillouin optical microscopy and dynamic Scheimpflug-based analysis—may eventually permit measurement of corneal biomechanics in the living eye, including the residual stromal bed, offering a more direct test of the relationships examined here than excised-tissue testing allows [30–32].

Conclusions

In conclusion, within the resolution and power of this study, the directional and overall mechanical properties of the excised SMILE lenticule showed no detectable, clinically meaningful association with 3-month postoperative refractive error in either the astigmatic or spherical-equivalent dimension, while the surgery itself was highly predictable. This finding should be interpreted specifically in relation to the ex vivo lenticule-derived anisotropy and stiffness metrics evaluated here. Because the extracted lenticule may not fully represent the residual stromal bed or the biomechanical behavior of the postoperative cornea in vivo, these results should not be generalized to all corneal biomechanical measurements. On present evidence, the lenticule-derived metrics assessed in this study appear unlikely, by themselves, to guide individualized SMILE treatment planning for early refractive accuracy, whereas broader corneal biomechanical assessment remains important for preoperative risk evaluation and patient selection.

Abbreviations

SMILE

Small-incision lenticule extraction

A_mech

Mechanical anisotropy index

E_SI

Tangent modulus, superior–inferior meridian

E_NT

Tangent modulus, nasal–temporal meridian

E̅

Mean tangent modulus

ΔM

Spherical-equivalent refractive error

ΔJ₀

On-axis astigmatic error (power vector)

ΔJ₄₅

Oblique astigmatic error (power vector)

TIA

Target induced astigmatism

DV

Difference vector

CI

Correction index

IOS

Index of success

ME

Magnitude of error

AE

Angle of error

Author contributions

PH conceived and designed the study, performed the statistical analysis, prepared the figures, and drafted the manuscript. PC performed quality control of the clinical data. LZ and YS collected the clinical data. HQ performed the biomechanical measurements. WC provided guidance on the biomechanical testing, and XL performed quality control of the biomechanical data. QZ supervised the study and critically revised the manuscript for important intellectual content. All authors read and approved the final manuscript.

Funding

This study was supported by the Aier Eye Hospital Group Research Fund (grant no. AGK2309D06) and the Shanxi Aier Eye Hospital Research Fund (grant no. AS-YB202401). The funders had no role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Data availability

Due to privacy and ethical restrictions, the data are not publicly available. The de-identified datasets supporting the findings of this study are available from the corresponding author upon reasonable request.

Declarations

Ethics approval and consent to participate

The study was approved by the Ethics Committee of Shanxi Aier Eye Hospital (approval EYESX-20240415-04) and performed in accordance with the Declaration of Helsinki. All personal identifiers were removed and replaced with unique study codes, the identification linkage file was stored separately from the analytical database, and all data were fully de-identified prior to analysis. Written informed consent was obtained from all participants. The institutional review board approval and the participant consent also covered the retention and biomechanical testing of the excised refractive lenticules.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.