Understanding SIA Centroid

Why Your Toric Calculator Might Be Wrong

1 What Happens at the Incision

A standard 2.2 mm temporal CCI flattens the cornea at the incision meridian.

Flattening at 180° → steepening at 90° (with-the-rule astigmatism)
But the exact amount and axis vary from eye to eye
Wound healing, tissue elasticity, and geometry all differ

2 Measuring SIA: What You Get

SIA = Post-op K values − Pre-op K values

But SIA is a VECTOR — it has magnitude AND direction.

  Axis convention: Astigmatism axes range from 0° to 180° only (not 360°). Diagrams below use 360° for visual clarity.

Four patients, same temporal incision:

Patient	SIA Magnitude	SIA Axis	Comment
A	0.40 D	180°	Classic horizontal flattening
B	0.30 D	170°	Slightly off-axis
C	0.50 D	155°	Oblique — drifted 25°
D	0.20 D	85°	Perpendicular to incision!

3 Arithmetic Mean vs. Centroid

Step 1: Four SIA vectors — different lengths, different directions

4 SIA vectors with different magnitudes and directions

Step 2: The Mean (WRONG) — add lengths, divide by 4, ignore direction

Arithmetic mean calculation — lengths added, divided by 4, direction ignored

Step 3: The Centroid (CORRECT) — chain vectors head-to-tail, find resultant, divide by 4

Centroid calculation — vectors chained head-to-tail, resultant divided by 4

Step 4: The Comparison — Mean (green circle) vs. Centroid (blue arrow)

Mean vs Centroid comparison — green circle much larger than blue centroid arrow

4 Beyond the Centroid — 3 Deeper Problems with SIA

(Wendelstein)

Problem 1: The Vector Mismatch

SIA is a vector (magnitude + direction)
But toric calculators only accept a single number — no axis input for SIA
The calculator assumes SIA acts perpendicular to the incision meridian
In reality, SIA direction varies from eye to eye
This is a fundamental simplification that adds uncertainty

Problem 2: Surface ≠ Optics

SIA is measured on the corneal SURFACE (via keratometry: pre-op vs post-op K)
But the optical outcome depends on more than surface astigmatism — the crystalline lens is removed and replaced
Corneal surface SIA may not equal the actual refractive change
Measuring SIA via refraction would be more accurate but is unreliable in practice
This means we’re correcting based on a measurement that may not reflect the true optical effect

Problem 3: The scatter is larger than the effect

Wendelstein et al. (JCRS 2023, 498 eyes, superior incision):
Centroid SIA = 0.26–0.34 D, but SD = ±0.37–0.42 D
The standard deviation is LARGER than the centroid itself. This means the scatter of individual measurements exceeds the systematic effect you’re trying to measure.
For temporal incisions it’s even worse: centroid ~0.10 D vs SD ~0.40 D
Consequence: personalizing your SIA risks OVERFITTING to noise

Side note: Some modern toric formulas (Barrett, EVO, Kane) use built-in regressions (e.g., Abulafia-Koch, Homburg-Adelaide) that account for SIA alongside many other factors — without requiring you to personalize it.

When the incision cuts the cornea, 3 things can happen:

Only the magnitude of astigmatism changes
Only the axis rotates
Both change simultaneously

Effects 2 and 3 happen far more frequently than most surgeons assume.

Source: Wendelstein JR et al. "Characteristics of surgically induced astigmatism after standardized microincisional cataract surgery with a superior limbal incision." JCRS 2023;49(10):1025-1035.

5 Why This Matters for Toric IOL Calculation

Every toric calculator asks: "What is your SIA?"

If you enter 0.50 D (arithmetic mean):

→ Calculator thinks your incision RELIABLY induces 0.50 D
→ It reduces toric correction by 0.50 D at the incision meridian
→ But your incision does NOT reliably do this!
→ Result: You’re ADDING error, not removing it.

If you enter 0.10 D (centroid):

→ Calculator makes a tiny, accurate adjustment
→ Matches reality. Honest and correct.

6 What to Do in Practice

Enter 0.10 D (or zero) in your toric calculator.

Barrett Toric Calculator already defaults to 0.10 D — trust it.
If you want precision: calculate your personal centroid from ≥50 cases.
Do NOT use the arithmetic mean of your SIA measurements.

Formula for centroid:

x = magnitude × cos(2 × axis) → average all x values
y = magnitude × sin(2 × axis) → average all y values
Centroid magnitude = √(x̄² + ȳ²)

7 The Punchline

"The biggest SIA mistake isn't not measuring it.
It's measuring it wrong — using the mean instead of the centroid —
and confidently entering the wrong number."

★ Quick Reference

Concept	Value	Use it?
Arithmetic mean SIA	~0.30–0.50 D	NO — ignores direction
Centroid (vector mean)	~0.05–0.15 D	YES — true systematic effect
Barrett Toric default	0.10 D	YES — evidence-based
If unsure, enter	0.10 D (or 0)	YES — better than guessing high

Prepared for Dr. Lorenz Kuske · April 2026 · learnabouteyes.com
Sources: Wendelstein et al., JCRS 2023; Koch DD et al., JCRS 2012; Barrett Toric Calculator; Lahood CRSToday 2023