SRK/T (Sanders-Retzlaff-Kraff/Theoretical) Formula -CEW

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====== SRK/T (Sanders-Retzlaff-Kraff/Theoretical) Formula ======

The SRK/T is a third-generation IOL power calculation formula combining theoretical optics with empirical regression optimization, published by Retzlaff, Sanders, and Kraff in 1990.

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===== Input Variables =====

  * **K** = average keratometry (diopters)
  * **AL** = axial length (mm)
  * **A** = IOL A-constant

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===== Step 1: Corneal Radius of Curvature =====
Calculate the corneal radius of curvature  
$$ r = 337.5 / K $$

r= corneal radius\\
where 337.5 is the keratometric index converting K (diopters) to corneal radius (mm).

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===== Step 2: Corrected Axial Length (LCOR) =====

If AL ≤ 24.2:

LCOR = AL

If AL > 24.2:

$$ LCOR = -3.446 + 1.716 × AL - 0.0237 × AL² $$

This regression-based correction adjusts for the relationship between measured and optical axial length, incorporating a retinal thickness factor.

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===== Step 3: Computed Corneal Width (Cw) =====
Corneal Width is derived from the corneal radius
$$ Cw = -5.40948 + 0.58412 × LCOR + 0.098 × K $$

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===== Step 4: Corneal Height (H) =====

Using the Pythagorean theorem applied to corneal dome geometry:

$$ H = r - \sqrt{r^2 - \left( \frac{Cw}{2} \right)^2}* $$

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===== Step 5: Estimated Postoperative ACD =====

The A-constant is converted to an ACD estimate and combined with corneal height:

ACDconst = 0.62467 × A - 68.747

Offset = ACDconst - 3.336

ACDest = H + Offset

Thus: 

$$ ACDest = H + ACDconst -3.336 $$

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===== Step 6: Retinal Thickness and Optical Axial Length =====
Retinal thickness (Rethick) and optical axial length (LOPT) are calculated:
  - $$ Rethick = 0.65696 - 0.02029 × AL $$
  - $$ LOPT = AL + Rethick $$

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===== Step 7: IOL Emmetropic Power =====

The IOL power for emmetropia is calculated using a modified vergence formula:

$$ \text{IOL}{\text{emme}} = \frac{1000 \times na \left( na \times r - nc \times L{OPT} \right)}{\left( L{OPT} - ACD{est} \right) \times \left( na \times r - nc \times ACD{est} \right)} $$


where:

  * **na** = refractive index of aqueous/vitreous (1.336)
  * **nc** = corneal refractive index (1.333)

===== Step 8: Refraction Correction =====

To target a specific postoperative refraction (**REF**) rather than emmetropia:

$$ \text{IOL}{\text{power}} = \text{IOL}{\text{emme}} - \frac{\text{REF}}{1 - 0.012 \times \text{REF}} \times \frac{1000 \times na}{\left( L{OPT} - ACD{est} \right)^2 \times \left( \frac{na \times r}{na \times r - nc \times ACD{est}} \right)^{-1}} $$

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===== Key Design Features =====

  * Corneal refractive index, retinal thickness correction, and ACD prediction were **interactively optimized** using regression on 1,677 posterior chamber lens cases
  * Can use either the **SRK A-constant** or a direct ACD estimate as input
  * The **T2 modification** (Sheard et al., 2010) later addressed nonphysiologic behavior in the corneal height calculation step

=====Reference=====
[[https://docs.eyefixer.org/Cataract/IOL%20Calculations/Development%20of%20the%20SRK_T%20intraocular%20lens%20implant%20power%20calculation%20formula.pdf|Development of the SRK/T intraocular lens implant power calculation formula. Retzlaff et al. J Cataract Refract Surg. 1990;16:333-339]]

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