Pachymetric Progression Index (PPI) & Thinnest Point Displacement: Early Ectasia Screening Before Refractive Surgery

In over $85\%$ of keratoconic eyes, the point of minimal corneal thickness (Thinnest Point) does NOT coincide with the geometric center or pupil center; it is displaced inferotemporally by $0.8\text{ to } 1.8\ \text{mm}$:

$$\vec{d}_{\text{displacement}} = \sqrt{(x_{\text{thinnest}} - x_{\text{apex}})^2 + (y_{\text{thinnest}} - y_{\text{apex}})^2} > 0.80\ \text{mm} \implies \text{Strong Suspicion of Ectasia}$$

A patient with $CCT = 535\ \mu\text{m}$ may have a thinnest point of only $470\ \mu\text{m}$ tucked inferotemporally. If a surgeon ablates based on central CCT, the residual stromal bed over the cone will collapse.

The Corneal Thickness Spatial Profile (CTSP) graphs mean corneal thickness as a function of distance from the thinnest point along 22 concentric rings ($0\text{ to } 9\ \text{mm}$):

$$PPI_{\text{meridian}} = \frac{\text{Thickness}_{\text{ring}} - \text{Thickness}_{\text{thinnest}}}{\text{Distance}_{\text{ring}}} \implies PPI_{\text{max}} > 1.45 \implies \text{Pathologic Thinning Rate}$$

Keratoconic profiles plunge below the normal normative bell-curve confidence intervals, indicating that stroma is thinning at an accelerated rate toward the apex.

Combining absolute thinnest point ($TP$) with the maximum pachymetric progression rate yields the Ambrósio Relational Thickness maximum ($ART_{\text{max}}$):

$$ART_{\text{max}} = \frac{\text{Thinnest Point Thickness } (\mu\text{m})}{PPI_{\text{max}}} \implies \begin{cases} > 410\ \mu\text{m}: & \text{Normal Cornea} \\ 339\text{--}410\ \mu\text{m}: & \text{Borderline Suspicious} \\ < 339\ \mu\text{m}: & \text{Keratoconus Ectasia Risk} \end{cases}$$