(MERIDIONAL ANALYSIS))
CONCEPT
With this formula we can calculate the power of the THORIC IOL to be implanted as well as the expected refraction.
Holladay's formula I is used to calculate the power in the orthogonal meridians.
CALCULATION
1. CALCULATE IOL THORIC CHARACTERISTICS TO REACH EMETROPIA
The following steps must be followed for its calculation:
a. CALCULATE THE S.I.R.C.
Obtained by following Holladay's recommendations.
The cylinder must be at Negative
SSIRC / CSIRC X ESIRC (Sphere Cylinder Axis)
S1 / C1 X E1
b. GET CORNEAL POWER.
The sphero-cylindrical power of the cornea is obtained through keratometry.
S2 = MaxK
C2 = MinK- MaxK
E2 = Meridian of MinK
S2 / C2 X E2
c. PREDICTING THE RESULTING CORNEAL CYLINDER AFTER SURGERY (SIRC + CORNEA)
The two cylinders are combined according to the Holladay method.
α = A2 -A1
2 = arctan ((C2 * SIN2α) / (C1 + (C2 * COS2α)))
θ = (2 + 180) / 2
SC = (C1 * SIN2θ) + (C2 * SIN2 (α - θ))
S3 = S1 + S2 + SC
C3 = C1 + C2 - (2 * SC)
A3 = A1 + θ
In this way we obtain the sphero-cylindrical refraction after combining the SIRC and the preoperative keratometry data: S3 / C3 X E3
The cylinder must be negative, if not, the transposition must be carried out.
Therefore the corneal meridional power in the plane of the cornea is as follows:
- Flattest Meridian (Flat): (S3 + C3) @ A3 with radius rflat = (0.3375 / (S3 + C3)) * 1000
- Sharpest Meridian (Steep): S3 @ (180 - A3) with radius rsteep = (0.3375 / S3) * 1000
The mean of the radii is: rmean = 0.50 * (rsteep + rflat)
d. DETERMINE THE SOUTHERN POTENCY OF THE IOL IN THE 2 MERIDIANS (STEEP AND FLAT)
If we do not know the ACD, it must be calculated according to Holladay's formula:
ACD = ELPHolladay + SF
ELPHolladay = (0.56 + rmedia) - ((rmedia2) - (AG2 / 4)) 1/2
AG is the corneal width and depends on the ALX. Is calculated:
AG = (12.5 * ALXCorrected) / 23.45
The result cannot be greater than 13.50, if so AG = 13.50.
The power to reach emmetropia will be for the acute meridian (steep):
LIONumerator = 1336 * (((1.336 * rsteep) / 0.3333) - ALXCorrected))
LIODenominator = (Corrected ALX- ACD) * (((1.336 * rsteep) / 0.3333) - ACD)
LIOSteep = IOLNumerator / IOLDenominator
The power to reach emmetropia will be for the flat meridian:
LIONumerator = 1336 * (((1.336 * rflat) / 0.3333) - ALXCorrected))
LIODenominator = (Corrected ALX- ACD) * (((1.336 * rflat) / 0.3333) - ACD)
LIOFlat = IOLNumerator / IOLDenominator
e. DETERMINE THE POWER OF THE TORIC IOL
Once the data of the orthogonal, flat and acute meridians are known, the power of the toric IOL necessary to reach emmetropia is (IN THE IOL PLANE and with the CYLINDER -):
Sphere = LIOSteep
Cylinder = LIOFlat - LIOSteep
Axis = A3
LIONecearia = LIOSteep / (LIOFlat - LIOSteep) * A3
2. CALCULATE THE RESULTING REFRACTION WHEN IMPLEMENTING A THORIC IOL OF CERTAIN CHARACTERISTICS
Given an IOL with the following refractive characteristics:
SLIO / CLIO X ELIO
How it is intended to place the axis of the IOL on the same meridian as the patient's astigmatism:
ELIO = A3
The following steps must be followed for its calculation:
a. VERIFY THAT THE CYLINDER IS NEGATIVE
b. CALCULATE SOUTHERN POWER IN THE IOL PLANE
The spherical equivalent will be:
EELIO = SLIO + (0.50 * CLIO)
The acute meridian (Steep):
LIOSteep = SLIO @ (180 - ELIO)
The flat meridian (Flat):
LIOFlat = (SLIO - CLIO) @ ELIO
With these data we can calculate rsteep and rflat.
c. CALCULATE THE EXPECTED REFRACTION IN EACH MERIDIAN (STEEP AND FLAT) USING THE HOLLADAY FORMULA I
In the acute meridian or steep it will be:
RXNumerator = (1336 * ((1.336 * rsteep) - (0.3333 * Fixed ALX))) - (LIOSteep * (Fixed ALX- ACD) * ((1.336 * rsteep) - (0.3333 * ACD)))
RXDenominator = 1.336 * ((dVertice * (1.336 * rsteep- 0.3333 * ALXCorrected)) + ALXCorrected * rsteep) - ((0.001 * LIOSteep) * (ALXCorrected - ACD) * (dVertice * (1.336 * rsteep) + 0.3333 * ACD * rsteep));
RXsteep = RXNumerator / RXDenominator
In the flat meridian it will be:
RXNumerator = (1336 * ((1.336 * rflat) - (0.3333 * Fixed ALX))) - (LIOFlat * (Fixed ALX- ACD) * ((1.336 * rflat) - (0.3333 * ACD)))
RXDenominator = 1.336 * ((dVertice * (1.336 * rflat- 0.3333 * ALXCorrected)) + ALXCorrected * rflat) - ((0.001 * LIOFlat) * (ALXCorrected - ACD) * (dVertice * (1.336 * rflat - 0.3333 * ACD) ACD * rflat));
RXflat = RXNumerator / RXDenominator
d. TRANSFER THE SPHERO-CYLINDRICAL REFRACTION
RX Sphere = RXsteep
RXCilindro = RXflat - RXsteep
Axis RX = A3
BIBLIOGRAPHY
1. Meridional analysis for calculating the expected spherocylindrical refraction in eyes witn toric intraocular lenses, Han Bor Fam, Kooi Ling Lim, BOptom, J Cataract Refract Surg 2007;33:2072-2076.
2. Calculating the surgically induced refractive change following ocular surgery, Holladay JT, Cravy TV, Koch DD, J Cataract Refract Surg 1992;18:429-443.