The Haigis Formula

The Haigis formula is the simplest thin lens formula possible. The ELP (= d value) is predicted using a multiple regression taking ACD and AL as inputs.

def Haigis(AL, R, ACD,a0,a1,a2,power): 
    n = 1.336 
    nc = 1.3315 
    dx = 0.012 
    d = a0 + a1*ACD + a2*AL 
    R = R/1000 
    AL = AL/1000 
    d = d/1000 
    Dc = (nc - 1)/(R) 
    qnum = n * (n - power * (AL - d)) 
    qdenum = n * (AL - d) + d * (n - power *(AL-d)) 
    q = qnum / qdenum 
    SEpred = round((q - Dc) / (1 + dx*(q - Dc)),3) 
    return SEpred

Optimizing the Haigis Formula

The Haigis formula can be single-optimized (A0 acts like a "potentiometer" or variable resistor, like the A constant in SRK/T, until a mean prediction error equal to zero is reached) or triple-optimized.

The Haigis triple-optimization is in fact a complete retraining of the formula. The perfect d value is back-calculated for each eye of the dataset. This is the d value giving the real postoperative spherical equivalent when using the biometric values and the implanted IOL power in thin lens equations.

A multiple regression takes ACD and AL as inputs, then allows fitting to predict this "perfect" d value. Et voilà : the intercept is a0, the ACD coefficient is a1, and the AL coefficient is a2.

Back-calculation of the d value

You can back-calculate the d value for a given eye with the following function (As expected you'll need the postoperative SE, ARC, AL and the implanted IOL power).

# AL, R in meters 
def solve_d_Haigis(AL, R, power, Rx): 
    n = 1.336 
    nc = 1.3315 
    dx = 0.012 
    Dc = (nc - 1) / R 
    z = Dc + Rx/(1-Rx*dx) 
    b = -power * (AL + n/z) 
    c = (n * (AL - n/z) + power * AL * n/z) 
    d = (1 / (2*power)) * (-b - np.sqrt(b**2 - 4 * power * c) ) 
    return d

From :  W.Haigis. "The Haigis formula", in Intraocular Lens Power Calculation, H. John Shammas, Chapter 5, edited by  Slack Incorporated, 2004.

# Example : 

val = solve_d_Haigis(0.024, 0.0075, 21, -2) 
print(val) 

#output : 0.005461457048808832

The output of this function is in meters : multiply by 1000 before fitting your regression.

Like this :

from sklearn.linear_model import LinearRegression
df['d_Haigis'] = df['d_Haigis'] * 1000
lin = LinearRegression()
lin.fit(df[['ACD','AL']], df['d_Haigis'])
lin.intercept_

# output : 
# -0.07756916259537494

This is your a0 value !

lin.coef_

# output : 
# array([0.39819972, 0.16012471])

And the coefficients are a1 and a2, respectively. What a beautifully simple formula! Genius.

Let's dive into the details :-)

The SRK/T Formula

Published in 1990 by Sanders, Retzlaff and Kraff, the SRK/T (1,2) has long been the favourite IOL calculation method among ophthalmologists, and is still extremely popular.

In this formula, the axial length is slightly modified before being used to predict the lens position. It allows to lower its impact on lens position prediction for high AL values.

def setLCOR(LA): 
	if LA <= 24.2: 
    	LCOR = LA 
    else: 
    	LCOR = -3.446 + (1.715 * LA) - (0.0237* (LA**2))
    return LCOR

To be more precise, the modified AL value (LCOR) is used, with the K value, to predict the Corneal Width (Cw). Cw and R are then used to calculate H, which is added to the transformed A constant to give the ELP.  

Cw = -5.40948 + (0.58412 * LCOR) + (0.098 * K)

def setH(r, Cw):
    x = r**2 - (Cw**2 / 4.0) 
    if x < 0: 
    	x = 0 
    else: 
    	pass 
    H = r - math.sqrt(x) 
    return H

The influence of the AL value on lens position has a ceiling...

... and the predACD value has a strange relationship with the anterior corneal radius value :

This is because the value entered in the square root of the formula allowing the calculation of H is set to zero when negative (3) !

Let's use a 3D representation :

Also, note that the AL value used in the optical equation is modified by adding a theoretical Retinal Thickness (RETHICK) value to it. RETHICK is itself a function of AL.

RETHICK = 0.65696 - 0.02029*LA 

This is the final SRK/T function :

def SRKT_SE(LA, r, aconst, power):
    # a keratometric index value of 1.3375 is used to compute the ACD via the Cw value
    # but : a keratometric index value of 1.333 is used as the real keratometric index in the optical calculation ! (cf ncml value)
    K = 337.5/r 
    V = 12.0 
    na = 1.336 
    nc = 1.333 
    ncml = 0.333
    # the SRK A constant is modified to represent a physical offset
    ACDconst = 0.62467 * aconst - 68.747 
    offset = ACDconst - 3.336
    # The eye-specific lens position is calculated
    LCOR = setLCOR(LA) 
    Cw = -5.40948 + (0.58412 * LCOR) + (0.098 * K) 
    H = setH(r, Cw) 
    # The ELP is added to the modified A constant
    ACDest = H + offset 
    # The optical AL is equal to AL + retinal thickness
    RETHICK = 0.65696 - 0.02029*LA 
    LOPT = LA + RETHICK 
    # the thin lens calculation is finally done
    num = 1000 * na * (na *r - ncml * LOPT)- power * (LOPT-ACDest) * (na * r - ncml * ACDest) 
    denum = na * (V*(na * r - ncml * LOPT) + LOPT * r) - 0.001 * power * (LOPT-ACDest) * (V * (na * r - ncml * ACDest) + ACDest * r) 
    SEpred = num/denum 
    return round(SEpred,3)

The Hoffer Q Formula

The Hoffer Q formula (4-7) is the most difficult, among the third generations formulas, to code correctly. The AL value is used to generate 3 other values, which are used along with the K value to calculate the lens position. pACD + 0.05 is added to the predicted value. K is calculated using a keratometric index of 1.3375. The original K and AL values are used in the optical equations.

def defMG(LA): 
    if LA <= 23.0: 
    	M = 1.0 
        G = 28.0 
    else: 
    	M = -1.0 
        G = 23.5 
        return M, G

def defA(LA): 
    if LA > 31.0: 
    	A = 31.0 
    elif LA < 18.5: 
    	A = 18.5 
    else: 
    	A = LA 
    return A

The lens position function is complicated :

import math 
def predACD(LA, K, pACD): 
    M, G = defMG(LA) 
    A = defA(LA) 
    p2 = 0.3 * (A - 23.5) 
    p3 = (math.tan(K*(math.pi / 180.0)))**2 
    p4 = 0.1 * M * ((23.5 - A)**2) 
    p5 = math.tan((0.1 * (G - A)**2) * (math.pi / 180.0)) 
    ACD = pACD + p2 + p3 + (p4 * p5) - 0.99166 
    return ACD

Final Hoffer Q function :

def HofferQ_SE(LA, r, pACD, power): 
    K = 337.5/r 
    ACD = predACD(LA, K, pACD) 
    R = (1.336 / (1.336/(1336 / (LA - ACD - 0.05) - power) + (ACD + 0.05) / 1000.0)) - K 
    SEpred = R / (1.0 + 0.012 * R) 
    return round(SEpred, 3)

The Holladay 1 Formula

The Holladay 1 formula (8) uses a keratometric index of 4/3. The lens position (ACD) is inferred from the ARC (with a flooring below 7.0mm) and from the AL (with a ceiling after  25.32mm, approximately).

def setRag(R): 
    if R < 7: 
    	Rag = 7 
    else: 
    	Rag = R 
    return Rag

def setAG(LA): 
    AG = 12.5 * LA / 23.45 
    if AG > 13.5: 
    	AG = 13.5 
    else: 
        AG = AG 
    return AG
    
# the AG has a ceiling when greater than 13.5 : this corresponds to an AL value of 25.32mm

The lens position, ACD, is a function of Rag and AG :

def setACD(Rag, AG): 
    ACD = 0.56 + Rag - (math.sqrt( (Rag**2) -((AG**2) /4) )) 
    return ACD

A retinal thickness value of 0.2mm is added to the AL.

Final Holladay 1 function :

def Holladay_SE(LA, R, SF, power): 
    Rag = setRag(R) 
    AG = setAG(LA) 
    ACD = setACD(Rag, AG) 
    nc = 4/3 
    na = 1.336 
    RT = 0.2
    V = 12 
    ALm = LA + RT 
    num = 1000*na*(na*R - (nc - 1)*ALm) - power*(ALm - ACD - SF)*(na*R - (nc - 1)*(ACD + SF)) denum = na*(V*(na*R-(nc-1)*ALm)+ALm*R)-0.001*power*(ALm-ACD-SF)*(V*(na*R-(nc-1)*(ACD+SF))+(ACD+SF)*R) result = round(num / denum, 3) 
    return result

The Haigis Formula

The Haigis formula (9) is the most simple third generation formula... and also consistently has the best outcomes when using its triple-optimized version. The lens position d is obtained using a multiple regression taking ACD and AL as inputs :

d = a0 + a1 x ACD + a2 x AL

What's your favourite approach ?

References

1. Retzlaff JA, Sanders DR, Kraff MC. Development of the SRK/T intraocular lens implant power calculation formula. J Cataract Refract Surg. 1990 May;16(3):333-40.

2. Retzlaff JA, Sanders DR, Kraff MC. Development of the SRK/T intraocular lens implant power calculation formula: Erratum. J Cataract Refract Surg. 1990;16(4):528.

3. Haigis W. Occurrence of erroneous anterior chamber depth in the SRK/T formula. J Cataract Refract Surg. 1993 May;19(3):442-6.

4. Hoffer, Kenneth J. M.D.^a. The Hoffer Q formula: A comparison of theoretic and regression formulas. Journal of Cataract & Refractive Surgery: November 1993 - Volume 19 - Issue 6 - p 700-712

5. Hoffer, Kenneth J. MD. Reply: Errata in printed Hoffer Q formula. Journal of Cataract & Refractive Surgery: January 2007 - Volume 33 - Issue 1 - p 2-3
doi: 10.1016/j.jcrs.2006.08.056

6. Zuberbuhler B, Morrell AJ. Errata in printed Hoffer Q formula. J Cataract Refract Surg. 2007 Jan;33(1):2; author reply 2-3.

7. Hoffer, K. Errors in self-programming the Hoffer Q formula. Eye21, 429 (2007).

8. Holladay JT, Musgrove KH, Prager TC, Lewis JW, Chandler TY, Ruiz RS. A three-part system for refining intraocular lens power calculations. J Cataract Refract Surg. 1988;14(1):17–24.

9. Haigis W, Lege B, Miller N, Schneider B. Comparison of immersion ultrasound biometry and partial coherence interferometry for intraocular lens calculation according to Haigis. Graefes Arch Clin Exp Ophthalmol. 2000;238(9): 765–773.

Descemet membrane endothelial keratoplasty (DMEK) was introduced in 2006 by Melles et al (1). This procedure revolutionized the management of endothelial pathologies by allowing a near perfect anatomical replacement of the diseased endothelium.

In most of the cases, the diseased (pre-DMEK) posterior corneal surface is (fortunately !) not taken into account in IOL formula calculations. As this posterior surface is restored back to its physiological shape by DMEK surgery, precise IOL calculation in triple procedure (i.e. prediction of the adequate IOL power for a post-DMEK eye using measurements made on a pre-DMEK eye) should be possible without any surprise.

However, a so-called "hyperopic shift" is observed both in standalone DMEK and in DMEK triple procedure. Why ? What is the difference between those phenomena ?

Hyperopic shift in DMEK standalone procedure

The refractive shift observed in DMEK single procedure is logical and easy to understand. The pathological, flattened posterior corneal surface is restored to its physiological value by the surgery. The posterior corneal radius decreases, thus decreasing the corneal power*. The eye is more hyperopic after the surgery (2-4).

*An increase in anterior corneal radius decreases the corneal power ; an increase in posterior corneal radius increases the corneal power.

Does this phenomenon have an impact in IOL calculation? Theoretically, no : let's see why.

Restoring the posterior corneal surface to its physiological value does not impact IOL calculation

As explained in 2011 by Ham et al. (5), biometric measurements do not usually take into account the posterior corneal radius. The corneal power is extrapolated from the anterior corneal radius, and (it was initially thought that) no modification of the anterior corneal radius happens after DMEK surgery. If the anterior radius is not modified and the posterior radius goes back to its physiological value, a refractive shift (in a single procedure) should be observed, but no IOL calculation error (in DMEK triple procedure) should occur.

Note : Of course this is not true for ray-tracing methods or total corneal power calculations using a measured posterior corneal radius, available in the most recent biometers. Those methods should by avoided at all costs in DMEK-triple procedure, because the posterior corneal radius will change after DMEK surgery.

Since 2011, various authors have in fact described a modification of the anterior corneal radius, and steeper-than-normal posterior corneal radii (6-11); IOL calculation error in triple-DMEK has also been well described by different teams (12-15). If the anterior radius is indeed different at the time of the biometry and after DMEK, it is logical to observe an error. Similarly, if the posterior corneal radius is steeper-than-normal after DMEK, the usual relationship between the anterior radius and the posterior radius is no longer valid and standard keratometric indices will be flawed. Both phenomena can explain an IOL calculation error.

As explained in a recent paper by our team, it is then necessary to distinguish two different phenomena (17) :

• DMEK-induced refractive shift (DIRS) : the (usually hyperopic) refractive shift observed in standalone procedure, which is explained by the difference between the pre-DMEK corneal power and the post-DMEK corneal power. It is a pure modification of corneal power.
• DMEK-induced IOL calculation error (DICE) : the IOL calculation error happening because of anterior corneal radius modifications before and after DMEK, and non-physiological post-DMEK posterior radii. It is the difference between the corneal power estimated by IOL formulas using pre-DMEK measurements and the real post-DMEK corneal power. IOL formulas are flawed because the anterior radius changes (or is incorrectly measured pre-DMEK), or because the anterior/posterior relationship is broken, or both.

Surprisingly, both phenomena are usually referred to as "hyperopic shift" in the literature. They should be differentiated !

NB : it could also be hypothesized that the refractive index of the cornea is also non-physiological after DMEK. This phenomenon is very difficult to isolate in clinical practice, but could also partly explain both DIRS and DICE.

Relative impact of anterior and posterior corneal radii variations on corneal power

Anterior and posterior corneal radii variations both influence the corneal power. But what is the relative importance of both phenomena ?

It should be remembered that the difference between the refractive index of the air (n_air = 1) and of the cornea (n_cor = 1.376) is much greater than the difference between the refractive index of the cornea and of the aqueous (n_aq = 1.336) : 0.376 and 0.04, respectively.

For a theoretical cornea (ARC = 7.5mm, PRC = 6.5mm, CCT = 0.520mm), a variation of 0.1mm in ARC leads to a difference in corneal power of 0.68D, while a the same variation of PRC modifies it by 0.1D. This is almost a sevenfold difference!

Is it possible to predict the variation in anterior corneal radius and/or the post-DMEK anterior/posterior ratio ?

DIRS can't be prevented : the corneal power will always be modified by DMEK surgery. By contrast, DICE could theoretically be avoided (by correcting the IOL calculation) if its underlying mechanisms were clearly understood.

Flatter and more oblate posterior corneal surfaces, as well as a higher posterior to anterior corneal curvature radii ratio have been cited as DIRS or DICE risk factors (8,15,16).

In a recent study (17), we did not find any strong predictor for DIRS or DICE. However, we found, like Schoenberg et al. (14), a lower variation of the ARC measured before and after DMEK when using a Scheimpflug camera, compared to the measurement obtained with the IOLMaster. Could the "variation" in ARC be partly explained by an ARC measurement error made by our biometers, which could be lowered by using the ARC measured by Scheimpflug camera in our IOL formulas ?

Conclusion

• DIRS is the DMEK-induced variation in corneal power, observed in DMEK single procedure, which can't be avoided. Any anterior or posterior corneal radius modification induces a DIRS. It is not preventable.
• DICE is the IOL calculation error induced by modifications/measurement errors of the ARC, and/or non-physiological post-DMEK posterior corneal radii. Any anterior corneal radius modification induces a DICE, but, unlike DIRS, posterior corneal radius modifications are involved in DIRS only when this radius is non-physiological after DMEK. It is theoretically preventable.
• It could be wise to aim for a more myopic target when the posterior corneal surface is very flat and oblate. The ARC value measured using the Pentacam device should be preferred to the ARC value obtained using a biometer. However, no strong DICE predictor has been found to date.

References :

1. Melles GR. Posterior lamellar keratoplasty: DLEK to DSEK to DMEK. Cornea. 2006 Sep;25(8):879-81.
2. Dunker SL, Veldman MHJ, Winkens B, van den Biggelaar FJHM, Nuijts RMMA, Kruit PJ, Dickman MM; Dutch Cornea Consortium. Real-World Outcomes of DMEK: A Prospective Dutch registry study. Am J Ophthalmol. 2021 Feb;222:218-225.
3. Price MO, Giebel AW, Fairchild KM, Price FW Jr. Descemet's membrane endothelial keratoplasty: prospective multicenter study of visual and refractive outcomes and endothelial survival. Ophthalmology. 2009
4. Agha B, Ahmad N, Dawson DG, Kohnen T, Schmack I. Refractive outcome and tomographic changes after Descemet membrane endothelial keratoplasty in pseudophakic eyes with Fuchs' endothelial dystrophy. Int Ophthalmol. 2021 Aug;41(8):2897-2904.
5. Ham L, Dapena I, Moutsouris K, Balachandran C, Frank LE, van Dijk K, Melles GR. Refractive change and stability after Descemet membrane endothelial keratoplasty. Effect of corneal dehydration-induced hyperopic shift on intraocular lens power calculation. J Cataract Refract Surg. 2011 Aug;37(8):1455-64.
6. Alnawaiseh M, Rosentreter A, Eter N, Zumhagen L. Changes in Corneal Refractive Power for Patients With Fuchs Endothelial Dystrophy After DMEK. Cornea. 2016 Aug;35(8):1073-7.
7. Arnalich-Montiel F, Mingo-Botín D, Diaz-Montealegre A. Keratometric, Pachymetric, and Surface Elevation Characterization of Corneas With Fuchs Endothelial Corneal Dystrophy Treated With DMEK. Cornea. 2019;38:535-541.
8. Cheung AY, Chachare DY, Eslani M, et al. Tomographic changes in eyes with hyperopic shift after triple Descemet membrane endothelial keratoplasty. J Cataract Refract Surg. 2018;44:738-744.
9. Parker J, Dirisamer M, Naveiras M, et al. Outcomes of Descemet membrane endothelial keratoplasty in phakic eyes. J Cataract Refract Surg. 2012;38:871-877.
10. van Dijk K, Ham L, Tse WHW, et al. Near complete visual recovery and refractive stability in modern corneal transplantation: Descemet membrane endothelial keratoplasty (DMEK). Cont Lens Anterior Eye. 2013;36:13-21.
11. van Dijk K, Rodriguez-Calvo-de-Mora M, van Esch H, et al. Two-Year Refractive Outcomes After Descemet Membrane Endothelial Keratoplasty. Cornea. 2016;35:1548-1555.
12. Augustin VA, Weller JM, Kruse FE, Tourtas T. Refractive Outcomes After Descemet Membrane Endothelial Keratoplasty + Cataract/Intraocular Lens Triple Procedure: A Fellow Eye Comparison. Cornea. 2021 Jul 1;40(7):883-887
13. Bae SS, Ching G, Holland S, McCarthy M, Ritenour R, Iovieno A, Yeung SN. Refractive Outcomes of Descemet Membrane Endothelial Keratoplasty Combined With Cataract Surgery in Fuchs Endothelial Dystrophy. J Refract Surg. 2020 Oct 1;36(10):661-666.
14. Schoenberg ED, Price FW Jr, Miller J, et al. Refractive outcomes of Descemet membrane endothelial keratoplasty triple procedures (combined with cataract surgery). J Cataract Refract Surg. 2015;41:1182-1189.
15. Fritz M, Grewing V, Böhringer D, et al. Avoiding Hyperopic Surprises After Descemet Membrane Endothelial Keratoplasty in Fuchs Dystrophy Eyes by Assessing Corneal Shape. Am J Ophthalmol. 2019;197:1-6.
16. Diener R, Eter N, Alnawaiseh M. Using the posterior to anterior corneal curvature radii ratio to minimize the risk of a postoperative hyperopic shift after Descemet membrane endothelial keratoplasty. Graefes Arch Clin Exp Ophthalmol. January 2020.
17. Debellemanière G, Ghazal W, Dubois M, et al. Descemet Membrane Endothelial Keratoplasty–Induced Refractive Shift and Descemet Membrane Endothelial Keratoplasty–Induced Intraocular Lens Calculation Error. Cornea 2022.

The SRK/T formula

The SRK/T formula (1,2) has long been one of the most popular IOL calculation methods : it is still widely used and its optimized constant is often used to tune other formulas.

What is an optimization ?

Optimizing a formula involves shifting its constant up or down, to obtain a mean prediction error equal to zero.

SRK/T Optimization process

The following code allows you to obtain the optimized A constant for a given dataset.

The OptimizeSRKT() function takes various variables as inputs : dataframe is the pd.DataFrame() object containing the data; col_AL , col_R, col_power, col_SE are the names of the related dataframe columns (string);  aconst_start (float) should be the closest value you can guess for the adjusted A constant. The SRKTES() function calculates the SRK/T SE prediction for a given eye / implanted IOL power.

The function will calculate the predicted SRK/T spherical equivalent, calculate the prediction error for each eye, then its mean for the whole dataset ; by adding the mean error to the A constant (it's a trick !), we'll quickly find the A constant leading to a prediction error equal to zero, which is the adjusted A constant.

def OptimizeSRKT(dataframe, col_AL, col_R, col_power, col_SE, aconst_start):
    dataframe['aconst'] = aconst_start
    dataframe['SRKTES'] = dataframe[[col_AL, col_R, 'aconst', col_power]].apply(lambda x : SRKTES(*x), axis = 1)
    dataframe['error'] = dataframe[col_SE] - dataframe['SRKTES']
    mean_error = dataframe.error.mean()
    while mean_error > 0.00001:
        dataframe['aconst'] += mean_error
        dataframe['SRKTES'] = dataframe[[col_AL, col_R, 'aconst', col_power]].apply(lambda x : SRKTES(*x), axis = 1)
        dataframe['error'] = dataframe[col_SE] - df['SRKTES']
        mean_error = dataframe.error.mean()
        print('Mean error : ', mean_error)
    print('Optimized SRK/T A constant : ', dataframe.aconst.unique()[0])

# Example : 

OptimizeSRKT(df, 'AL', 'R', 'Power', 'ES_postop', 118.0)

# Output : 
# Mean error :  0.0773036659614707
# Mean error :  0.007425076192446311
# Mean error :  0.0007240370609196819
# Mean error :  7.070440730831753e-05
# Mean error :  6.90546869455154e-06
# Optimized SRK/T A constant :  119.08180447676536

References

1- Retzlaff JA, Sanders DR, Kraff MC. Development of the SRK/T intraocular lens implant power calculation formula. J Cataract Refract Surg. 1990 May;16(3):333-40.

2- Retzlaff JA, Sanders DR, Kraff MC. Development of the SRK/T intraocular lens implant power calculation formula: Erratum. J Cataract Refract Surg. 1990;16(4):528.

Regular Eyes

This page allows the user to perform a calculation for 'standard eyes', i.e. eyes which have not undergone refractive surgery, have no corneal scar, and for which information about the first operated eye is not available.

The "keratometric index" field allows selection of the index used by the user's biometer. In most cases, it is 1.3375 ; however, some biometers use a different value. The PEARL methodology is based on thick lens equations and does not use the K value delivered by the biometer in its equations, but rather the anterior corneal radius of curvature measurement. It is then fundamental to select the right keratometric index value, because it is used by the calculator to determine this anterior corneal radius of curvature.

The "Biometer" field is used to apply slight changes to the AL measurement. If "Argos" or "US (immersion)" are selected, the approximation of the Sum-of-Segments AL utilised in the PEARL formula is not used. If US (applanation) is selected, a correction factor of 0.15 mm (1-4) is added to the AL measurement to compensate for the underestimation due to inadvertent compression.

The "IOL Model" field allows the calculator to determine which correction factor should be applied to modify the AL value used in the Theoretical Internal Lens Position (TILP) prediction algorithm. It also allows to perform a calculation for a meniscus IOL (e.g. Alcon MA60). In this case, the A constant can't be modified, which is normal : the geometrical particularities of this meniscus lens is integrated into the formula and customized for each lens power along the -5 to +5 range.

You may notice that the "LT", "CCT" and "WTW" fields are optional, this is to allow for calculation even with biometers which do not perform those measurements. However, it is strongly recommended to fill them in if they are available, especially the LT and CCT.

Complex Eyes

The "Complex Eyes" platform allows the user to perform a calculation for eyes which have undergone previous corneal refractive surgery, have corneal scarring, or an Implantable Collamer Lens (ICL) in-situ.

If the "Corneal Refractive Surgery" field is activated, it is mandatory to determine which LVC procedure (myopic or hyperopic) was performed, as the corneal power adjustment will not be the same. Selecting this option also automatically removes the ARC and CCT from the lens position predictors.

If available, the "Pre-LVC anterior corneal radius" or the "Corrected ametropia" fields will allow to respectively obtain or approximate the pre-LVC anterior corneal radius, which will then be used to predict the posterior corneal radius more accurately.

If the "Radial Keratotomy" option is activated, a different method is used to predict the corneal power. ARC and CCT are also removed from the lens position predictors in this scenario. This option can be combined with the Corneal Refractive Surgery fields in order to perform a calculation for eyes with a history of RK and subsequent PRK.

The "Scarred cornea" option allows removal of the anterior corneal radius from the lens position predictors. It is wise to use it in those cases, to avoid adding a lens position prediction error to the corneal power prediction error which will probably occur.

The "ICL" option is used to apply a small correction to the AL measurement, due to the AL measurement error induced by those lenses, as described in the literature (5,6).

Second Eyes

In this section, it is possible for the user to fill in the information allowing to back-calculate the lens position of the first operated eye, which will then be used as a predictor to enhance the lens position prediction of the second eye.

The options here are the same as the options available for the 'Complex Eyes' section.

Note that the Second Eye function is not available for eyes with a discordant corneal surgery history, neither for MA60 IOLs.

References :

1. Rose LT, Moshegov CN. Comparison of the Zeiss IOLMaster and applanation A-scan ultrasound: biometry for intraocular lens calculation. Clin Exp Ophthalmol. 2003 Apr;31(2):121-4.

2. Bjeloš Rončević M, Bušić M, Cima I, Kuzmanović Elabjer B, Bosnar D, Miletić D. Comparison of optical low-coherence reflectometry and applanation ultrasound biometry on intraocular lens power calculation. Graefes Arch Clin Exp Ophthalmol. 2011 Jan;249(1):69-75.

3. Rajan MS, Keilhorn I, Bell JA. Partial coherence laser interferometry vs conventional ultrasound biometry in intraocular lens power calculations. Eye (Lond). 2002 Sep;16(5):552-6.

4. Pereira A, Popovic M, Lloyd JC, El-Defrawy S, Schlenker MB. Preoperative measurements for cataract surgery: a comparison of ultrasound and optical biometric devices. Int Ophthalmol. 2021 Apr;41(4):1521-1530.

5. Chen X, Zhang D, Liu Z, Liu Y, Cai H, Wu Q, Zhang Y. Effect of Implantable Collamer Lens on Anterior Segment Measurement and Intraocular Lens Power Calculation Based on IOLMaster 700 and Sirius. J Ophthalmol. 2021 Dec

6. Pitault G, Leboeuf C, Leroux les Jardins S, Auclin F, Chong-Sit D, Baudouin C. Biométrie optique des yeux avec implants phaques [Optical biometry of eyes corrected by phakic intraocular lenses]. J Fr Ophtalmol. 2005 Dec;28(10):1052-7.