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arxiv: 2607.06385 · v1 · pith:KZS4LOIY · submitted 2026-07-07 · physics.optics

Sectorial customized corneal crosslinking for keratoconus: an inverse biomechanical design study with an anisotropic reduced shell finite-element surrogate

J. Sumaya-Martinez , A. Altamirano-Torres This is my paper

Reviewed by Pith T0 review T1 audit T2 compute T3 formal T4 reserved 2026-07-08 07:20 UTCglm-5.2pith:KZS4LOIYrecord.jsonopen to challenge →

Figure 1
Figure 1. Figure 1: Treatment masks used in the enhanced simulation. The inverse-smooth mask is a bounded [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] reproduced from arXiv: 2607.06385
classification physics.optics
keywords cornealbiomechanicalcrosslinkingcustomizedkeratoconussectorialanisotropicdesign
0
0 comments X

The pith

Smooth inverse-designed CXL masks outperform sectorial patterns for keratoconus

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper argues that customized corneal cross-linking (CXL) for keratoconus should be formulated as a spatial stiffness-control problem rather than as uniform stiffening of the steepest corneal region. The authors build an anisotropic reduced shell finite-element surrogate of a decentered keratoconus-like cornea, introducing disease through local thinning and local stiffness loss, and model crosslinking as a spatially varying stiffness-modulation field. Six treatment masks are compared: uniform, cone-sector, partial-annular, coma-gradient, cone-Gaussian, and an inverse-smooth composite mask optimized via a multi-objective functional that penalizes steep spatial gradients and excessive dose. The central finding is that the inverse-smooth mask produces the most balanced response across all measured metrics, achieving a Kmax-equivalent severity of 48.81 D (versus 52.50 D untreated), vertical coma of 5.22 µm (versus 13.41 µm), and higher-order aberration RMS of 2.96 µm (versus 6.57 µm), while avoiding the sharp angular gradients that sectorial masks introduce. The claim is that smooth, inverse-designed stiffening fields are a more conservative and mechanically sound design principle for customized CXL than binary or sharply localized treatment zones.

Core claim

The paper shows that different CXL treatment masks optimize different quantities: uniform stiffening most efficiently reduces cone displacement but leaves substantial residual coma, while sectorial and coma-gradient masks reduce coma more aggressively but introduce mechanical trade-offs such as stress concentrations at sharp treatment boundaries. The inverse-smooth mask, constructed as a bounded smooth combination of simpler mask bases and optimized to minimize a combined biomechanical-optical objective, avoids the most extreme trade-offs. This demonstrates that optical improvement and mechanical stabilization are related but not identical goals, and that a multi-objective optimization with显

What carries the argument

The central machinery is the anisotropic reduced shell finite-element surrogate. The cornea is modeled as a shell with spatially varying stiffness, where disease enters through a Gaussian weakening field and thinning map, and treatment enters through a multiplicative stiffening field. The inverse-design objective (Eqs. 39-40) simultaneously penalizes residual Kmax-equivalent severity, vertical coma, HOA RMS, cone displacement, strain-energy concentration, and total dose, with additional smoothness penalties on the stiffness gradient. The inverse-smooth mask (Eq. 23) is a clipped linear combination of simpler mask bases whose coefficients are selected by the optimizer. The optical readout isZ

If this is right

  • The framework could be applied to riboflavin-UVA fluence patterns, oxygen-modulated CXL, pulsed irradiation, or drug-eluting contact lenses, since the stiffening field is agent-agnostic.
  • Patient-specific implementations could integrate corneal tomography and programmable UV delivery systems to translate the inverse-designed mask into a clinical treatment plan.
  • The smoothness penalty on stiffness gradients could inform clinical safety protocols by quantifying the risk of stress concentrations at treatment boundaries.
  • Hybrid mechanical-biochemical reshaping approaches could use the inverse-design framework to define a target stiffness field and then select the delivery method that best approximates it.

Load-bearing premise

The model collapses the full three-dimensional, depth-dependent stiffness field of the cornea into a two-dimensional, thickness-weighted scalar. Real CXL stiffening penetrates stromal tissue non-uniformly, and the mechanical effect varies with depth, which is clinically critical for endothelial safety. If depth-dependent mechanics significantly alter the optimal spatial pattern, the treatment-mask rankings could change.

What would settle it

A full three-dimensional hyperelastic simulation with explicit depth-dependent stiffening that shows the inverse-smooth mask no longer produces the most balanced response, or that sharp sectorial masks become preferable when depth-dependent mechanics are included.

Figures

Figures reproduced from arXiv: 2607.06385 by A. Altamirano-Torres, J. Sumaya-Martinez.

Figure 2
Figure 2. Figure 2: Residual biomechanical–optical metrics normalized to the untreated keratoconus-like [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Enhanced reduced FEM maps. Top row: post-treatment effective modulus. Middle [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Optical metrics from the deformed anterior surface. The Kmax-equivalent index, vertical [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Untreated versus inverse-smooth surface response. The optimized smooth mask reduces [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: IOP sensitivity for untreated, uniform and inverse-smooth cases. The plotted severity [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
read the original abstract

We propose an inverse biomechanical design framework for sectorial customized corneal crosslinking in keratoconus. The cornea is modeled as an anisotropic reduced shell with spatially varying crosslinking-induced stiffening, enabling the optimization of localized treatment patterns rather than uniform irradiation profiles. Numerical simulations show that sectorial stiffening can redistribute curvature, reduce localized steepening, and improve corneal regularity in decentered keratoconus models while preserving biomechanical plausibility. These results support the use of patient-specific computational planning for customized crosslinking protocols and provide a basis for future integration with corneal tomography and programmable ultraviolet delivery systems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 6 minor

Summary. This manuscript proposes an inverse biomechanical design framework for sectorial customized corneal crosslinking (CXL) in keratoconus. The cornea is modeled as an anisotropic reduced shell finite-element surrogate with spatially varying stiffness. The authors compare six treatment masks (uniform, cone-sector, partial-annular, coma-gradient, cone-Gaussian, and inverse-smooth) using pressure displacement, strain-energy concentration, a Kmax-equivalent severity index, and Zernike optical metrics. The central claim is that customized CXL is better formulated as a spatial stiffness-control problem rather than uniform stiffening of the steepest region, and that smooth inverse-designed masks offer a more conservative design principle by balancing stabilization, coma reduction, and dose smoothness.

Significance. The manuscript addresses a clinically relevant problem with a well-structured computational framework. The inverse-design formulation (Eqs. 39-40) with explicit smoothness and dose penalties is a sensible approach to the multi-objective nature of customized CXL. The inclusion of anisotropic collagen reinforcement (Eq. 25) and spatially heterogeneous loading (Eq. 27) adds mechanical plausibility beyond a purely isotropic shell. The IOP sensitivity analysis (Fig. 6) provides a useful robustness check. The authors are transparent about the surrogate nature of the model and clearly delineate its limitations in Section 8. The provision of a reproducible numerical eye (Table 1) and the Python script (per the data availability statement) are strengths.

major comments (3)
  1. §4, Eqs. (39)-(40): The inverse-smooth mask is optimized by minimizing the objective J, which is a weighted sum of K_eq, vertical coma, HOA RMS, cone displacement, strain energy, and dose. The paper then evaluates all six masks in Table 2 against these same metrics and declares the inverse-smooth mask 'most balanced.' This is structurally circular: the optimized mask scores well on the components of J by construction. A fair comparative test would require either (a) evaluating all masks on metrics excluded from J, (b) optimizing the other masks against J as well, or (c) cross-validating by optimizing on a subset of metrics and evaluating on held-out metrics. Without one of these, the ranking in Table 2 does not independently test the inverse-smooth design. This is load-bearing for the central claim that the inverse-smooth mask is superior.
  2. §4, Eqs. (39)-(40): The numerical values of the objective weights (w_K, w_C, w_R, w_D, w_S, w_η) are never reported anywhere in the manuscript. Since 'balanced' is defined by these weights, the optimization result is not reproducible without them. Different weight choices could shift the optimal mask toward a different basis combination and potentially change the ranking. The weights must be reported, and ideally a sensitivity analysis over reasonable weight ranges should be provided to show that the ranking is not an artifact of a particular weight choice.
  3. §5.3, Eq. (44): The Kmax-equivalent severity index K_eq is calibrated post-hoc so that the untreated case gives 52.50 D, with constants 43.5, 9.0, 0.72, and 0.28 chosen by hand. While the authors state this index is for within-model comparison only, the specific choice of the 0.72/0.28 split between displacement and strain-energy terms is unjustified and could bias the treatment comparison. The paper should either provide a rationale for these constants or demonstrate that the mask rankings are insensitive to reasonable variations in them.
minor comments (6)
  1. §3.4, Eq. (23): The projection operator P_[0,1] is introduced but not formally defined. A brief definition would improve clarity.
  2. §3.5, Eq. (27): The load amplification factor β_q is stated as 2.15 in §5.1 (Eq. 43) but appears as a generic symbol in Eq. (27). Consistency between the general formulation and the specific implementation would help.
  3. Table 2: The strain-energy norm column header reads 'Strain-energy norm.' with a trailing period. Minor formatting issue.
  4. Figure 1 caption: The caption mentions 'counter-gradient' as one of the basis functions, but this basis is not defined in §3.4 (Eqs. 18-22). Either define it or remove the reference.
  5. §5.1: The mesh convergence is not discussed. A brief statement on whether the 1090-node mesh is sufficient for resolving the displacement and strain-energy fields would strengthen the computational credibility.
  6. References [7] and [21] are dated 2025, and [6] is also 2025. If these are published, the bibliographic details should be verified for accuracy.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for a careful and constructive review. All three major comments identify legitimate gaps in the manuscript's validation logic and reproducibility. We address each below and commit to revisions.

read point-by-point responses

  1. Referee: §4, Eqs. (39)-(40): The inverse-smooth mask is optimized by minimizing the objective J, which is a weighted sum of K_eq, vertical coma, HOA RMS, cone displacement, strain energy, and dose. The paper then evaluates all six masks in Table 2 against these same metrics and declares the inverse-smooth mask 'most balanced.' This is structurally circular: the optimized mask scores well on the components of J by construction. A fair comparative test would require either (a) evaluating all masks on metrics excluded from J, (b) optimizing the other masks against J as well, or (c) cross-validating by optimizing on a subset of metrics and evaluating on held-out metrics. Without one of these, the ranking in Table 2 does not independently test the inverse-smooth design. This is load-bearing for the central claim that the inverse-smooth mask is superior.

    Authors: The referee is correct that evaluating the inverse-smooth mask on the same metrics used in the objective J is structurally circular. We acknowledge this without reservation. In the revised manuscript, we will implement option (c): cross-validation by optimizing the inverse-smooth mask on a subset of the objective metrics (e.g., K_eq and cone displacement) and then evaluating its performance on the held-out metrics (vertical coma, HOA RMS, strain-energy concentration). This will provide an independent test of whether the smooth inverse-designed mask generalizes to metrics it was not explicitly optimized for. We will also add a supplementary comparison reporting metrics not included in J for all six masks (e.g., spherical aberration, horizontal coma, and spatial smoothness of the displacement field), so that the inverse-smooth mask is evaluated on quantities outside the optimization target. We agree that the current Table 2 ranking does not independently test the inverse-smooth design, and the revised manuscript will state this limitation explicitly and present the cross-validation results as the corrective evidence. revision: yes

  2. Referee: §4, Eqs. (39)-(40): The numerical values of the objective weights (w_K, w_C, w_R, w_D, w_S, w_η) are never reported anywhere in the manuscript. Since 'balanced' is defined by these weights, the optimization result is not reproducible without them. Different weight choices could shift the optimal mask toward a different basis combination and potentially change the ranking. The weights must be reported, and ideally a sensitivity analysis over reasonable weight ranges should be provided to show that the ranking is not an artifact of a particular weight choice.

    Authors: The referee is correct. The weight values were used in the computation but omitted from the manuscript, which is a clear reproducibility gap. We will report the specific numerical values of all six weights (w_K, w_C, w_R, w_D, w_S, w_η) in the revised Section 4. Additionally, we will provide a sensitivity analysis over a reasonable range of weight combinations (e.g., varying each weight by ±50% relative to the baseline) and report whether the qualitative ranking of masks in Table 2 is stable or changes. If the ranking is sensitive to particular weight choices, we will state this transparently and discuss the implications for the claim that the inverse-smooth mask is 'most balanced.' We agree that without the weights and the sensitivity analysis, the optimization result is neither fully reproducible nor independently validated. revision: yes

  3. Referee: §5.3, Eq. (44): The Kmax-equivalent severity index K_eq is calibrated post-hoc so that the untreated case gives 52.50 D, with constants 43.5, 9.0, 0.72, and 0.28 chosen by hand. While the authors state this index is for within-model comparison only, the specific choice of the 0.72/0.28 split between displacement and strain-energy terms is unjustified and could bias the treatment comparison. The paper should either provide a rationale for these constants or demonstrate that the mask rankings are insensitive to reasonable variations in them.

    Authors: The referee's point is well taken. The 0.72/0.28 split between displacement and strain-energy terms in Eq. (44) was chosen heuristically to weight the displacement-based component more heavily, reflecting its more direct connection to anterior surface shape change, but this rationale was not stated in the manuscript and the choice is not independently justified. In the revision, we will (1) add a brief rationale for the weighting and (2) perform a sensitivity analysis varying the split over a reasonable range (e.g., 0.5/0.5 to 0.9/0.1) and report whether the mask rankings in Table 2 change. If the rankings are insensitive to the split, this strengthens the within-model comparison; if they are sensitive, we will report this and qualify the claim accordingly. We note that K_eq is one of several metrics in Table 2 and is not the sole basis for the comparison, but the referee is correct that an unjustified constant in a composite index could bias the assessment. revision: yes

Circularity Check

1 steps flagged

Inverse-smooth mask optimized and evaluated on same objective metrics; 'most balanced' claim is partly tautological, but paper retains independent content.

specific steps
  1. fitted input called prediction [Eqs. 39–40 (objective J) and Table 2 (evaluation)]
    "The reduced objective used in this study was J=w_K (K_eq/K_eq,0)^2 + w_C (|Z_3^{-1}|/|Z_3^{-1,0|)^2 + w_R (RMS_HOA/RMS_HOA,0)^2 + w_D (d_cone/d_cone,0)^2 + w_S (Ψ/Ψ0)^2 + w_η⟨η/η_max⟩^2. ... The inverse-smooth mask gave the most balanced response: cone displacement 154.6 µm, vertical coma 5.22 µm, HOA RMS 2.96 µm and Kmax-equivalent severity 48.81 D versus 52.50 D in the untreated case."

    The inverse-smooth mask is the only mask whose coefficients c_j are selected by minimizing J (Eqs. 38–40). J is a weighted sum of exactly the metrics reported in Table 2: K_eq, vertical coma, HOA RMS, cone displacement, and strain energy. The other five masks are fixed patterns with no optimization. Declaring the optimized mask 'most balanced' across these same metrics is structurally circular: any optimizer minimizing J will, by construction, produce a mask that trades off the components of J favorably. A fair comparative test would require either optimizing all masks against J, or evaluating the inverse-smooth mask on metrics excluded from J. Additionally, the numerical values of the weights w_K, w_C, w_R, w_D, w_S, w_η are never reported anywhere in the paper, so 'balanced' is definedby

full rationale

The paper's central comparative claim—that the inverse-smooth mask gives the 'most balanced response'—has a genuine circularity concern: the mask is optimized against J (Eqs. 39–40), which is a weighted sum of the same metrics used for evaluation in Table 2, while the competing masks are unoptimized fixed patterns. This means the 'balanced' ranking is partly forced by construction. However, several factors mitigate the severity. First, the inverse-smooth mask is NOT the best on any single metric (uniform has better K_eq, cone-sector has better coma, partial-annulus has better HOA RMS), so the claim is about trade-offs rather than dominance. Second, the paper provides some independent evaluation: IOP sensitivity (Fig. 6) tests robustness across pressures, and the spatial-smoothness argument (avoiding stress concentrations) draws on external clinical reasoning [22]. Third, there are no self-citations—the entire reference list is to independent authors. The unreported objective weights are a reproducibility defect that compounds the circularity concern but is not itself circularity. The paper also clearly acknowledges its surrogate-model limitations (§8). Score 4 reflects that the central comparative claim has a real circular component, but the paper retains substantial independent content and does not reduce entirely to its inputs.

Axiom & Free-Parameter Ledger

9 free parameters · 5 axioms · 1 invented entities

The model introduces several phenomenological constructs (the anisotropic tensor form, the load amplification, the Kmax-equivalent index) that are not independently calibrated. The objective function weights are not stated, which limits reproducibility of the inverse design.

free parameters (9)
  • δ_0 (max local softening) = 0.64
    Keratoconus-like stiffness reduction; chosen to represent moderate KC, not independently calibrated.
  • σ_x, σ_y (cone Gaussian widths) = 0.82, 0.78 mm
    Cone spatial spread; patient-inspired values without derivation from clinical data.
  • Δh_max (max thinning) = 125 μm
    Local thinning magnitude; chosen to represent moderate KC.
  • f_a (fiber fraction) = 0.34
    Phenomenological anisotropic reinforcement; not calibrated to collagen architecture data.
  • 0.65/0.35 circumferential/radial split = 0.65, 0.35
    Fixed directional weighting in anisotropic tensor (Eq. 25/42); no independent justification given.
  • η_max (max CXL stiffening) = 2.40
    Upper bound on relative stiffening; represents up to 3.4× local E_KC; not tied to specific crosslinking protocol data.
  • β_q (load amplification) = 2.15
    Pressure load amplification in cone region (Eq. 43); phenomenological.
  • Kmax-equivalent constants = 43.5, 9.0, 0.72, 0.28
    Calibration constants in Eq. 44 chosen so untreated model gives 52.50 D; post-hoc.
  • Objective weights w_K, w_C, w_D, w_E/w_S, w_R, w_Q/w_η = not stated
    Weights in the inverse-design objective (Eqs. 39-40) are never given numerical values, making the optimization result not fully reproducible.
axioms (5)
  • domain assumption The cornea can be represented as a 2D reduced shell with depth-averaged stiffness (Eq. 15).
    Invoked in §3.2 and §5.2. This collapses 3D stromal mechanics into a scalar field, which is the main model approximation.
  • domain assumption Crosslinking-induced stiffening can be represented as a multiplicative stiffness increase η on the diseased modulus (Eq. 16/17).
    Invoked in §3.3. Assumes stiffening is independent of the underlying damage field and can be superimposed multiplicatively.
  • ad hoc to paper The saturating dose-response law (Eq. 7) with Γ_50 and exponent m adequately maps drug delivery to mechanical stiffening.
    Invoked in §2.2. The authors state this is phenomenological and not biochemically calibrated; Γ_50 and m values are not specified.
  • domain assumption Fixed limbal boundary condition is sufficient for comparing treatment masks.
    Invoked in §3.5 and §5.2. Authors acknowledge a scleral shell or elastic limbal support would be preferable for patient-specific prediction.
  • ad hoc to paper The anisotropic tensor form D_s = T[(1-f_a)I + 2f_a(0.65 e_θ⊗e_θ + 0.35 e_r⊗e_r)] represents collagen reinforcement.
    Invoked in Eq. 25/42. The specific 0.65/0.35 split and the tensor structure are phenomenological proxies, not derived from collagen constitutive theory.
invented entities (1)
  • Kmax-equivalent severity index (K_eq) no independent evidence
    purpose: Within-model comparison of treatment patterns
    Defined in Eq. 44 with fitted constants; explicitly not a clinical keratometric measurement. No external validation against clinical Kmax data.

pith-pipeline@v1.1.0-glm · 14341 in / 4510 out tokens · 329482 ms · 2026-07-08T07:20:45.150330+00:00 · methodology

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Reference graph

Works this paper leans on

22 extracted references · 22 canonical work pages

  1. [1]

    Induction of cross-links in corneal tissue

    Eberhard Spoerl, Michael Huhle, and Theo Seiler. “Induction of cross-links in corneal tissue”. In:Experimental Eye Research66.1 (1998), pp. 97–103.doi:10.1006/exer.1997.0410

    work page doi:10.1006/exer.1997.0410 1998

  2. [2]

    Riboflavin/ultraviolet-A-induced collagen crosslinking for the treatment of keratoconus

    Gregor Wollensak, Eberhard Spoerl, and Theo Seiler. “Riboflavin/ultraviolet-A-induced collagen crosslinking for the treatment of keratoconus”. In:American Journal of Ophthalmology 135.5 (2003), pp. 620–627.doi:10.1016/S0002-9394(02)02220-1

    work page doi:10.1016/s0002-9394(02)02220-1 2003

  3. [3]

    A comparative study of equivalent circuit models for Li-ion batteries

    Peter S. Hersh et al. “United States multicenter clinical trial of corneal collagen crosslinking for keratoconus treatment”. In:Ophthalmology124.9 (2017), pp. 1259–1270.doi: 10.1016/j. ophtha.2017.03.052

    work page doi:10.1016/j 2017

  4. [4]

    Corneal collagen crosslinking with riboflavin and ultraviolet-A light in progressive keratoconus: ten-year results

    Farhad Raiskup et al. “Corneal collagen crosslinking with riboflavin and ultraviolet-A light in progressive keratoconus: ten-year results”. In:Journal of Cataract and Refractive Surgery41.1 (2015), pp. 41–46.doi:10.1016/j.jcrs.2014.09.033

    work page doi:10.1016/j.jcrs.2014.09.033 2015

  5. [5]

    Customized topography-guided corneal collagen cross-linking for kerato- conus

    M. Cassagne et al. “Customized topography-guided corneal collagen cross-linking for kerato- conus”. In:Journal of Refractive Surgery33.5 (2017), pp. 290–297.doi: 10.3928/1081597X- 20170228-01

    work page doi:10.3928/1081597x- 2017

  6. [6]

    Outcomes of localized corneal collagen crosslinking with a conven- tional device in progressive keratoconus

    Ofri Vorobichik Berar et al. “Outcomes of localized corneal collagen crosslinking with a conven- tional device in progressive keratoconus”. In:Graefe’s Archive for Clinical and Experimental Ophthalmology263 (2025), pp. 1949–1956.doi:10.1007/s00417-025-06803-y

    work page doi:10.1007/s00417-025-06803-y 2025

  7. [7]

    Predicting the effects of customized corneal cross-linking on corneal geometry

    Matteo Frigelli et al. “Predicting the effects of customized corneal cross-linking on corneal geometry”. In:Investigative Ophthalmology & Visual Science66.12 (2025), p. 51.doi: 10. 1167/iovs.66.12.51

    work page 2025

  8. [8]

    A model for the human cornea: constitutive formulation and numerical analysis

    Anna Pandolfi and Francesco Manganiello. “A model for the human cornea: constitutive formulation and numerical analysis”. In:Biomechanics and Modeling in Mechanobiology5 (2006), pp. 237–246.doi:10.1007/s10237-005-0014-x

    work page doi:10.1007/s10237-005-0014-x 2006

  9. [9]

    Biomechanical and optical behavior of human corneas before and after photorefractive keratectomy

    P. Sanchez, K. Moutsouris, and A. Pandolfi. “Biomechanical and optical behavior of human corneas before and after photorefractive keratectomy”. In:Journal of Cataract and Refractive Surgery40.6 (2014), pp. 905–917.doi:10.1016/j.jcrs.2013.10.047

    work page doi:10.1016/j.jcrs.2013.10.047 2014

  10. [10]

    Cornea modelling

    Anna Pandolfi. “Cornea modelling”. In:Eye and Vision7 (2020), p. 2.doi: 10.1186/s40662- 019-0166-x

    work page doi:10.1186/s40662- 2020

  11. [11]

    A review of human cornea finite element modeling: geometry modeling, constitutive modeling, and outlooks

    Guobao Pang et al. “A review of human cornea finite element modeling: geometry modeling, constitutive modeling, and outlooks”. In:Frontiers in Bioengineering and Biotechnology12 (2024), p. 1455027.doi:10.3389/fbioe.2024.1455027

    work page doi:10.3389/fbioe.2024.1455027 2024

  12. [12]

    A model of collagen degradation and corneal ectasia

    Alessio Gizzi, Anna Pandolfi, and Marcello Vasta. “A model of collagen degradation and corneal ectasia”. In:Journal of Engineering Mathematics127 (2021), pp. 1–20

    work page 2021

  13. [13]

    Continuum versus micromechanical modeling of corneal biomechanics

    Anna Pandolfi and Maria Laura De Bellis. “Continuum versus micromechanical modeling of corneal biomechanics”. In:Journal of the Mechanics and Physics of Solids190 (2024), p. 105738.doi:10.1016/j.jmps.2024.105738

    work page doi:10.1016/j.jmps.2024.105738 2024

  14. [14]

    A discrete-to-continuum model for the human cornea with application to keratoconus

    J. K¨ ory et al. “A discrete-to-continuum model for the human cornea with application to keratoconus”. In:Journal of the Mechanics and Physics of Solids184 (2024), p. 105531.doi: 10.1016/j.jmps.2023.105531

    work page doi:10.1016/j.jmps.2023.105531 2024

  15. [15]

    Optimizing genipin concentration for corneal collagen cross- linking: an ex vivo study

    Ahmad M. Gharaibeh et al. “Optimizing genipin concentration for corneal collagen cross- linking: an ex vivo study”. In:Cornea37.7 (2018), pp. 914–918.doi: 10 . 1097 / ICO . 0000000000001591

    work page 2018

  16. [16]

    A study of corneal structure and biomechanical properties after collagen crosslinking with genipin in rabbit corneas

    Y. Tang et al. “A study of corneal structure and biomechanical properties after collagen crosslinking with genipin in rabbit corneas”. In:Molecular Vision25 (2019), pp. 574–582

    work page 2019

  17. [17]

    Brillouin microscopy of collagen crosslinking: noncontact depth- dependent analysis of corneal elastic modulus

    Giuliano Scarcelli et al. “Brillouin microscopy of collagen crosslinking: noncontact depth- dependent analysis of corneal elastic modulus”. In:Investigative Ophthalmology & Visual Science54.2 (2013), pp. 1418–1425.doi:10.1167/iovs.12-11387

    work page doi:10.1167/iovs.12-11387 2013

  18. [18]

    Spatially-resolved Brillouin spectroscopy reveals biomechanical abnormalities in mild to advanced keratoconus in vivo

    Peng Shao et al. “Spatially-resolved Brillouin spectroscopy reveals biomechanical abnormalities in mild to advanced keratoconus in vivo”. In:Scientific Reports9 (2019), p. 7467.doi: 10.1038/s41598-019-43681-7

    work page doi:10.1038/s41598-019-43681-7 2019

  19. [19]

    In vivo evaluation of corneal biomechanics following cross-linking surgeries using optical coherence elastography in a rabbit model of keratoconus

    Yanzhi Zhao et al. “In vivo evaluation of corneal biomechanics following cross-linking surgeries using optical coherence elastography in a rabbit model of keratoconus”. In:Translational Vision Science & Technology13.2 (2024), p. 15.doi:10.1167/tvst.13.2.15

    work page doi:10.1167/tvst.13.2.15 2024

  20. [20]

    Brillouin microscopy for focal biomechanical measurements in normal and keratoconic corneas: a narrative review

    Bassel Hammoud et al. “Brillouin microscopy for focal biomechanical measurements in normal and keratoconic corneas: a narrative review”. In:Survey of Ophthalmology(2025).doi: 10.1016/j.survophthal.2025.06.004

    work page doi:10.1016/j.survophthal.2025.06.004 2025

  21. [21]

    KERATO Biomechanics Study 2: a comparative evaluation before and after corneal cross-linking using Brillouin microscopy and dynamic Scheimpflug imaging

    Riccardo Vinciguerra et al. “KERATO Biomechanics Study 2: a comparative evaluation before and after corneal cross-linking using Brillouin microscopy and dynamic Scheimpflug imaging”. In:Journal of Refractive Surgery41.6 (2025), e594–e601.doi: 10.3928/1081597X-20250506- 01

    work page doi:10.3928/1081597x-20250506- 2025

  22. [22]

    Biomechanical impact of localized corneal cross-linking beyond the irradiated treatment area

    Justin N. Webb, John P. Su, and Giuliano Scarcelli. “Biomechanical impact of localized corneal cross-linking beyond the irradiated treatment area”. In:Translational Vision Science & Technology8.3 (2019), p. 10.doi:10.1167/tvst.8.3.10

    work page doi:10.1167/tvst.8.3.10 2019