Advanced Corneal Thickness Variation Simulation — Myopic Only + Volumes (FIXED)

Standard Mode: Uses average corneal parameters (K = 43.0 D, Q = -0.2) for quick calculations. Ideal for routine screening and patient education.

📊 About the Standard Mode

This mode calculates the residual corneal thickness after refractive surgery using population-average corneal parameters. It supports PRK, LASIK, and KLEX/SMILE.

Key Parameters Used

Mean corneal radius: 7.8 mm (K = 43.0 D)
Asphericity (Q): -0.2 (prolate)
Keratometric index: n = 1.3375 (for K readings)
Stromal index: n = 1.376 (optical calculations)
Posterior radius: 6.7 mm

Clinical Guidelines

PRK epithelium removal: 50 µm
LASIK flap thickness: 100–140 µm (typical)
Optical zone: 6.0–7.0 mm (standard)
Minimum safe residual bed: 300 µm (PRK), 250–300 µm (LASIK)
PTA: < 40% recommended

⚡ Vertex Distance Settings

Vertex distance [mm]:

🛡️ Safety Limit Settings

Minimum residual posterior wall [µm]:

Sphere (spectacles) [D]:

Cylinder (spectacles) [D]:

Axis [°]:

Optical zone diameter [mm]:

Central corneal thickness at apex [µm]:

Flap thickness (LASIK) / Cap thickness (KLEX/SMILE) [µm]:

Custom Mode: Allows specification of patient-specific corneal parameters including preoperative keratometry and asphericity. Ideal for complex cases and research applications.

🔬 About the Custom Mode

This advanced mode enables precise calculations using patient-specific parameters. You can input the actual preoperative keratometry and asphericity values, and specify the target postoperative asphericity for customized ablation profiles.

Additional Custom Parameters

Preoperative keratometry (K): Mean corneal power in diopters
Preoperative Q1/Q2: Asphericity on K1/K2 (−1 to +1)
Target postoperative Q: Desired asphericity after surgery

Radius from K:
R (mm) = (n − 1) × 1000 / K, with n = 1.3375 (keratometric index)

Note: Optical calculations use n = 1.376 (stromal index)

🎯 Custom Corneal Parameters

Preoperative mean K [D]:

Preoperative Q1 (along K1):

Preoperative Q2 (along K2):

Target postoperative Q:

🔧 Posterior Corneal Parameters (Advanced)

Posterior R1 (K1) [mm]:

Posterior R2 (K2) [mm]:

Posterior Q1 (K1):

Posterior Q2 (K2):

⚡ Vertex Distance Settings

Vertex distance [mm]:

🛡️ Safety Limit Settings

Minimum residual posterior wall [µm]:

Sphere (spectacles) [D]:

Cylinder (spectacles) [D]:

Axis [°]:

Optical zone diameter [mm]:

Central corneal thickness at apex [µm]:

Flap thickness (LASIK) / Cap thickness (KLEX/SMILE) [µm]:

📈 Calculation Results

⚠️ Clinical Disclaimer:

This simulator is an educational and research tool. All surgical decisions must be based on comprehensive clinical examination, actual patient measurements, and professional judgment. Individual variations in corneal biomechanics, healing response, and other factors significantly influence surgical outcomes.

📚 References

Gatinel D, Weyhausen A, Bischoff M. The Percent Volume Altered in Correction of Myopia and Myopic Astigmatism With PRK, LASIK, and SMILE. J Refract Surg. 2020 Dec 1;36(12):844-850.

Gatinel D, Saad A, Binder PS. Comparison of the effect of LASIK parameters on the percent tissue altered (1-dimensional metric) versus percent volume altered (3-dimensional metric). J Cataract Refract Surg. 2018 Jul;44(7):897-904.

Gatinel D, Hoang-Xuan T, Azar DT. Three-dimensional representation and qualitative comparisons of the amount of tissue ablation to treat mixed and compound astigmatism. J Cataract Refract Surg. 2002 Nov;28(11):2026-34.

Gatinel D, Hoang-Xuan T, Azar DT. Volume estimation of excimer laser tissue ablation for correction of spherical myopia and hyperopia. Invest Ophthalmol Vis Sci. 2002 May;43(5):1445-9.

Santhiago MR, et al. Role of percent tissue altered on ectasia after LASIK in eyes with suspicious topography. J Refract Surg. 2015 Apr;31(4):258-65.

🔎 Technical Appendix — Variables, Surfaces, Areas & Volumes (with Plain-English Notes)

This appendix mirrors the exact computations used by the simulator above, including constants, units, and numerical integration over the treatment zone. It is designed so that a non-specialist can follow along while preserving scientific accuracy. Aligned with code

Mental map. Think of the cornea like a shallow bowl. We describe its shape with a height function (the "sag") over the pupil plane, then:

Area ≈ the size of the patch we treat (mm²).
Thickness (µm/mm) = how much tissue we remove at each point.
Volume (mm³) = area × thickness, summed over the whole patch.

1) Symbols & Units (⇄ code variable names)

Symbol	Code name	Unit	Meaning
S, C, AX	Ssp, Csp, AX	D, D, °	Spectacle prescription (sphere, cylinder, axis).
v	vertex	mm	Vertex distance (glasses → cornea), typ. 12 mm.
ZO	ZO	mm	Optical zone diameter (defines the treatment patch Ω).
CT (CCT)	CT_um	µm	Central corneal thickness at apex (total, includes epithelium).
CST	—	µm	Central stromal thickness at apex (CST = CCT − 50 µm; epithelium assumed 50 µm uniform for references).
FLAP/CAP	CAP_um	µm	Flap/cap thickness (LASIK/KLEX).
n_K, n_stroma	N_KERATO, N_STROMA	—	Keratometric and stromal indices: 1.3375 and 1.376.
337.5, 376	K_CONST, K_OPTICAL	—	1000×(n-1) for K and optical calculations.
R₁, R₂	R1_i, R2_i	mm	Pre-op anterior radii (flat/steep meridians K1/K2).
R′	R_f	mm	Target spherical radius post-op (inside Ω).
Q	Q_PRE, Q_POST	—	Asphericity (pre, post).
r_x, r_y	r_x, r_y	mm	Semi‑axes of Ω (ellipse) or radius if circle.
R_back, Q_back	R_BACK, Q_BACK	mm, —	Posterior conic: 6.7 mm, -0.4 (fixed in Standard mode).
R_1,post, R_2,post	R1_BACK, R2_BACK	mm	Posterior radii along K1/K2 (Custom mode; defaults 6.7 mm).
Q_1,post, Q_2,post	Q1_BACK, Q2_BACK	—	Posterior asphericities along K1/K2 (Custom mode; defaults −0.4).
50 µm	EPI_SHIFT_MM	mm	Epithelium thickness = 0.05 mm (used for stromal references).

2) From spectacles to the corneal plane

$ F_{\text{cor}} \;=\; \frac{F}{\,1 - (v/1000)\,F\,} $

In words: we correct for the glasses‑to‑cornea distance so that the optical power we use matches the corneal plane (not the spectacle plane).

What the code does

S_cor = specToCor(Ssp, v)
C_cor = specToCor(Ssp + Csp, v) − S_cor

3) Keratometry ↔ Radius

$ R\,[\text{mm}] \;=\; \frac{337.5}{K\,[\text{D}]} $

In words: the corneal "K" reading is a power; converting to radius (mm) lets us write the corneal shape as a height (sag) function.

4) Pre-operative anterior shape (biconic)

$ z_{\text{pre}}(x,y) \;=\; \frac{x^2}{R_1\!\left(1+\sqrt{1-(1+Q_1)\,\frac{x^2}{R_1^2}}\right)} \;+\; \frac{y^2}{R_2\!\left(1+\sqrt{1-(1+Q_2)\,\frac{y^2}{R_2^2}}\right)} $

In words: the cornea can differ along K1 (flatter) and K2 (steeper) not only in radius but also in asphericity; we therefore use Q1 along K1 and Q2 along K2 in the separable biconic sag.

5) Post-op spherical target and boundary continuity

$ R' \;=\; \frac{K_{\text{optical}}}{\,K_{\text{optical}}/R_1 \;+\; S_{\text{cor}}\,} \quad\text{(target spherical radius)} $

In words: we adjust the flat‑meridian optical power by the intended spherical correction; the result is converted back to a radius.

$ z_{\text{post}}^*(x,y) = z_{\text{biconic}}(x,y; R',R',Q_{\text{post}}),\qquad \text{offset} = z_{\text{pre}}(0,r_y) - z_{\text{post}}^*(0,r_y),\\ z_{\text{post}} = z_{\text{post}}^* + \text{offset}\ \text{inside } \Omega,\quad z_{\text{post}} = z_{\text{pre}}\ \text{outside } \Omega $

In words: we make the post‑op surface meet the pre‑op surface smoothly at the edge of the treatment zone (no step at the border).

6) Treatment zone Ω — ellipse vs circle

$ r_y = \frac{ZO}{2}, \qquad r_x = r_y\sqrt{ \frac{1/R_2 - 1/R'}{\,1/R_1 - 1/R'\,} } $

In words: the treated patch is an ellipse aligned with K1/K2 (or a circle if spherical correction ≈ 0). Its size sets the area over which we integrate volumes.

Note: The display includes a gentle transition along K1 in the "pure cylinder" case, but this transition is not counted in volumes.

7) Local ablation (depth removed)

$ \text{abl}(x,y)\ [\mu\text{m}] \;=\; \max\!\Big(0,\ \big[z_{\text{pre}}(x,y)-z_{\text{post}}(x,y)\big]\times 1000\Big) $

In words: at each point we compare the pre‑op anterior stromal shape and the post‑op anterior stromal shape; positive differences are tissue removed. Epithelium (PRK) and flap/cap (LASIK/KLEX) are handled separately (50 µm epithelial shift and an added lamellar term for LASIK). Central ablation is the value at (0,0).

8) Posterior surface and stromal thickness under Ω (customizable)

$ z_{\text{back}}(x,y) \;=\; z_{\text{biconic,sep}}\!\big(x,y;\ R_{1,\text{post}}, R_{2,\text{post}}, Q_{1,\text{post}}, Q_{2,\text{post}}\big) \;+\; \text{back\_offset} $

In words: the posterior surface is modeled as a separable biconic aligned with K1/K2 (flat/steep meridians). If no custom values are provided, we use the population defaults (R = 6.7 mm, Q = −0.4 on both meridians). The constant back_offset is chosen so that the central stromal thickness equals CT − 50 µm (epithelium removed).

$ \text{back\_offset} \;=\; \big[z_{\text{pre}}(0,0) + (CT/1000 - 0.05)\big] \;-\; z_{\text{back,raw}}(0,0)\,, \quad\text{so that}\quad T(0,0) = CT/1000 - 0.05. $

$ T(x,y) \;=\; z_{\text{back}}(x,y) \;-\; z^{\text{st}}_{\text{pre}}(x,y) $

In words: stromal thickness is the gap between the posterior surface and the pre-op anterior stromal surface at each location. This definition excludes the epithelium by construction (50 µm are removed in PRK, or are lamellar in LASIK/KLEX).

9) Areas & Volumes — how the integrals are computed

Plain English: We cover Ω with tiny squares of side dx = dy (in mm). For each square inside Ω, we multiply its area (mm²) by the local thickness (mm) and add them up. This "sum of little blocks" is what mathematicians call a numerical integral (Riemann sum).

$ A_{\Omega} \;\approx\; \sum_{\,(x,y)\in\Omega}\ dx\,dy \quad(\text{intuitively } \pi r_x r_y) $

$ V_{\text{abl}} \,[\text{mm}^3] \;=\; \iint_{\Omega} \frac{\text{abl}(x,y)}{1000}\,dx\,dy \;\approx\; \sum\frac{\text{abl}_{ij}}{1000}\,dx\,dy $

$ V_{\text{lam,LASIK}} \;=\; A_{\Omega}\ \max\!\big(0,\ \tfrac{CAP}{1000} - 0.05\big),\qquad V_{\text{total,LASIK}} \;=\; V_{\text{abl}} + V_{\text{lam,LASIK}} $

$ V_{\text{stroma},\Omega} \;=\; \iint_{\Omega} T(x,y)\,dx\,dy \;\approx\; \sum T_{ij}\,dx\,dy $

10) PVA (Percent Volume Altered)

$ \text{PVA}_{1D,\text{PRK}}(\%) \;=\; 100\ \frac{V_{\text{abl}}}{A_{\Omega}\,CCT_{\text{mm}}},\qquad \text{PVA}_{1D,\text{LASIK}}(\%) \;=\; 100\ \frac{V_{\text{total,LASIK}}}{A_{\Omega}\,CCT_{\text{mm}}} $

$ \text{PVA}_{3D,\text{PRK}}(\%) \;=\; 100\ \frac{V_{\text{abl}}}{V_{\text{stroma},\Omega}},\qquad \text{PVA}_{3D,\text{LASIK}}(\%) \;=\; 100\ \frac{V_{\text{total,LASIK}}}{V_{\text{stroma},\Omega}} $

In words:
• 1D uses a "slab" reference: A_Ω × CCT_apex, where CCT_apex is the single central (apical) thickness value entered in the UI (not a map and not necessarily the thinnest point).
• 3D uses the actual stromal volume under Ω, i.e., the integral of local stromal thickness T(x,y) between posterior surface and pre‑op anterior stroma.
3D is geometrically faithful; 1D is a quick approximation that assumes uniform thickness across Ω.
If desired, the 'slab' thickness could be switched to the thinnest pachymetry (TCT), but this is not what the current UI does.

11) PTA (for LASIK) — what it is and why it differs

$ \text{PTA}(\%) \;=\; 100\ \frac{CAP + \text{ablation at the center}}{CCT_{\mu m}} $

In words: PTA is 1-dimensional and central (it uses the central ablation depth). PVA-1D uses the mean ablation over Ω, so for myopic corrections we usually have PVA_1D < PTA.

12) Quick checklist (what each calculation is doing)

Convert prescription to the corneal plane → get S_cor, C_cor.
Split mean K into K1/K2 → get R1_i, R2_i (flat/steep radii).
Compute target spherical radius $R'$ from R1_i and S_cor.
Define Ω (ellipse or circle) from ZO, R1_i, R2_i, R'.
Enforce border continuity → compute offset.
Map ablation $\text{abl}(x,y)$ and integrate to get volumes.
Build posterior surface and integrate stromal thickness under Ω.
Compute PVA (1D & 3D) and compare to PTA.

All constants, equations and numerical choices above (indices, posterior conic, epithelium = 50 µm, ellipse geometry, integrals) match the simulator's code exactly. This appendix is intentionally educational while remaining faithful to the implementation. Source-aligned

Advanced Corneal Thickness Variation Simulationafter Refractive Surgery

📊 About the Standard Mode

Key Parameters Used

Clinical Guidelines

⚡ Vertex Distance Settings

🛡️ Safety Limit Settings

🔬 About the Custom Mode

Additional Custom Parameters

🎯 Custom Corneal Parameters

🔧 Posterior Corneal Parameters (Advanced)

⚡ Vertex Distance Settings

🛡️ Safety Limit Settings

📈 Calculation Results

📚 References

🔎 Technical Appendix — Variables, Surfaces, Areas & Volumes (with Plain-English Notes)

1) Symbols & Units (⇄ code variable names)

2) From spectacles to the corneal plane

3) Keratometry ↔ Radius

4) Pre-operative anterior shape (biconic)

5) Post-op spherical target and boundary continuity

6) Treatment zone Ω — ellipse vs circle

7) Local ablation (depth removed)

8) Posterior surface and stromal thickness under Ω (customizable)

9) Areas & Volumes — how the integrals are computed

10) PVA (Percent Volume Altered)

11) PTA (for LASIK) — what it is and why it differs

12) Quick checklist (what each calculation is doing)

Advanced Corneal Thickness Variation Simulation
after Refractive Surgery