Original Article Open Access

Theoretical Relationship Between the Anterior-Posterior Corneal Curvature Ratio, Keratometric Index, and Estimated Total Corneal Power

Correspondence: Damien Gatinel, MD, PhD, Rothschild Foundation Hospital, Anterior Segment and Refractive Surgery Deptartment, 25 rue Manin, Paris 75019, France. Email:

E-mail Address: [email protected]

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Guillaume Debellemanière, MD

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Alain Saad, MD

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, and

Radhika Rampat, MD

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Journal of Refractive Surgery, 2023;39(4):266–272

Published Online:April 01, 2023https://doi.org/10.3928/1081597X-20230131-02Cited by:5

Abstract

Purpose:

To predict the relationships between the keratometric index value that would match the total Gaussian corneal power and its related variables: anterior and posterior radii of curvature of the cornea, anterior-posterior corneal radius ratio (APR), and central corneal thickness.

Methods:

The relationship between the APR and the keratometric index was approximated by calculating the analytical expression for the theoretical value of the keratometric index, which would make the keratometric power of the cornea equal to the total paraxial Gaussian power of the cornea.

Results:

The study of the impact of variations in the radius of anterior and posterior curvature and central corneal thickness showed that the difference between exact and approximated best-matching theoretical keratometric index was less than 0.001 for all of the performed simulations. This translated to a variation in the total corneal power estimation of less than ±0.128 diopters. After refractive surgery, the estimated optimal keratometric index value is a function of the preoperative anterior keratometry, the preoperative APR, and the delivered correction. The larger the magnitude of myopic corrections, the greater the increase in postoperative APR value.

Conclusions:

It is possible to estimate the most compatible value of the keratometric index that allows simulated keratometric power to equal the total Gaussian corneal power. The obtained equations enable the evaluation of the impact of corneal variables such as the APR on the ideal keratometric index value. The use of 1.3375 for the keratometric index results in an overestimation of the total corneal power in most clinical situations.

[J Refract Surg. 2023;39(4):266–272.]

Introduction

Conventional keratometry is mostly used for corneal power measurements and intraocular lens (IOL) power calculation. It relies on converting the anterior corneal curvature into an estimate of the total corneal power using a standard keratometric index value. The most commonly used value for the keratometric index of refraction is 1.3375. Standard simulated keratometry assumes that the anterior-posterior corneal radius ratio (APR) remains constant among patients. Although this ratio varies between the eyes, it is also altered after laser corneal surgery. Recent advances in diagnostic devices in ophthalmology make it possible to obtain total corneal power by measuring the anterior and posterior corneal surfaces. Comparisons have been made in normal individuals and suggested that conventional keratometry was significantly higher than total keratometry computed using Gaussian optics or ray-tracing through the anterior and posterior corneal surfaces.1–3

The theoretical relationship between conventional keratometry and total keratometry computed from Gaussian paraxial optics has not been fully investigated. Reference is often made to a relationship between the optimal value of the keratometric index and the ratio between the anterior and posterior corneal curvature. However, to the best of our knowledge, there is no explicit equation connecting these parameters. In this study, we aimed to determine the equations that would enable us to predict the relationships between the keratometric index value and the variables used to compute the total corneal power: anterior and posterior radii of curvature of the cornea, APR, and central corneal thickness. By carrying out this investigation, it is possible to establish the theoretical value of the keratometric index to make simulated keratometry equal to total keratometry. Our study does not aim to replace the value of the keratometric index in a formula or a keratometry measuring instrument, but to judge the relevance of the commonly used values. This facilitates study of the relevance of choosing a keratometric index value to estimate the total power of the cornea in the context of an instrumental measurement and power calculation using biometry data. Although the APR varies between the eyes, it is also altered after laser corneal surgery. The analysis was also extended to eyes that had undergone laser-based corneal refractive surgery.

Materials and Methods

Relationship Between the APR and the Keratometric Index

The keratometric power of the cornea D_k is computed using the keratometric index n_k and the radius of the anterior corneal curvature R_a as: ((1))

The total paraxial Gaussian power of the cornea is computed with the following formula: ((2)) where R_a is the radius of curvature of the anterior cornea, R_p the radius of curvature of the posterior cornea, n_s the index of refraction of the stroma, na the index of refraction of the aqueous, and d_c the corneal thickness.

Let X be the ratio between the anterior and posterior radii of curvature of the cornea: ((3))

Substituting R_p with R_a/X in Equation 2 gives: ((4))

Equation 4 can be rearranged as: ((5))

Equation 5 can be simplified to: ((6))

By analogy with Equation 1, we get the analytical expression for the theoretical value of the keratometric index that would make D_k = D_c ((7))

This equation enables the “ideal” value of the keratometric index to be computed, to obtain an estimated corneal power value of a given cornea with Equation 1, which is equal to the total Gaussian power obtained from Equation 2.

Since: n_s R_a >> (n^s – 1) d_c, we obtain the following approximation: ((8))

This equation enables the computation of an approximate value of the optimal keratometric index, which only depends on the ratio between the anterior and posterior corneal curvatures.

Reciprocally, the value of the ratio between the anterior and posterior corneal curvatures (APR) that corresponds to a given keratometric index n_k is given by: ((9))

The theoretical difference between the most compatible keratometric power D_k and approximated total Gaussian power D_ka obtained from Equation 1 using n_k and n_ka, respectively, can be expressed as: ((10))

Theoretical Impact of Corneal Laser Refractive Surgery on the Keratometric Index

Laser corneal surgery to correct myopia and hyperopia alters the power of the anterior corneal surface. The relationship between the refractive error at the corneal plane (D_r) and the preoperative (R_a1) and postoperative (R_a2) anterior corneal radius of curvature is given by: ((11))

Solving Equation 10 for R_a2, we obtain: ((12))

Let us define the postoperative APR as X_post. It is given by: ((13))

Substituting R_a2 with the right term of Equation 13: ((14)) which can be rearranged as follows: ((15)) which is equivalent to: ((16))

Hence, using Equation 8, we get the approximated “ideal” value of the keratometric index that can be used to compute the total Gaussian corneal power after laser refractive correction: ((17))

The right term of this equation is the same as for Equation 8 for D_r = 0.

Results

Comparison Between Exact and Approximated Theoretical Keratometric Index Value N_KA

For all numerical calculations, the value of the stromal refractive index n_s equals 1.376, and that of the aqueous humor n_a equals 1.336.

The theoretical best matching and approximated keratometric index values obtained by Equation 7 (n_k) versus Equation 8 (n_ka) and the corresponding corneal powers (D_c vs Dk) were compared for various theoretical values of anterior and posterior corneal curvature radius and corneal thickness.

Table A (available in the online version of this article) demonstrates the study of the impact of variations in the R_a between 7 and 8.5 mm in steps of 0.10 mm. The value of the R_p is set at 6.8 mm.

**Table A Impact of Anterior Radius of Curvature on the Exact and Approximated Ideal Keratometry Index Values and Estimated Total Corneal Powers**
R_a	X	n_k	n_ka	n_ka – n_k	D_k = D_c	D_ka	D_ka – D_k
7.00	1.0294	1.3357	1.3348	−0.0009	47.955	47.832	−0.123
7.10	1.0441	1.3351	1.3342	−0.0009	47.197	47.075	−0.121
7.20	1.0588	1.3345	1.3336	−0.0009	46.459	46.340	−0.119
7.30	1.0735	1.3339	1.3331	−0.0009	45.742	45.624	−0.118
7.40	1.0882	1.3333	1.3325	−0.0009	45.045	44.928	−0.116
7.50	1.1029	1.3327	1.3319	−0.0009	44.366	44.251	−0.115
7.60	1.1176	1.3322	1.3313	−0.0009	43.704	43.591	−0.113
7.70	1.1324	1.3316	1.3307	−0.0009	43.060	42.949	−0.112
7.80	1.1471	1.3310	1.3301	−0.0009	42.433	42.323	−0.110
7.90	1.1618	1.3304	1.3295	−0.0009	41.821	41.713	−0.109
8.00	1.1765	1.3298	1.3289	−0.0009	41.225	41.118	−0.107
8.10	1.1912	1.3292	1.3284	−0.0009	40.644	40.537	−0.106
8.20	1.2059	1.3286	1.3278	−0.0009	40.076	39.971	−0.105
8.30	1.2206	1.3280	1.3272	−0.0009	39.522	39.419	−0.104
8.40	1.2353	1.3274	1.3266	−0.0009	38.982	38.880	−0.102
8.50	1.2500	1.3269	1.3260	−0.0009	38.454	38.353	−0.101

D_c = corneal thickness; D_k = keratometric power of the cornea; n_k = keratometric index; n_ka = approximate values of the keratometric index; R_a = radius of the anterior corneal curvature; X = ratio between the anterior and posterior radii of corneal curvature

The APR varies between 1.029 (R_a = 7 mm) and 1.250 (R_a = 8.5 mm).

The values of the most suitable keratometric index, which can be used to obtain the total corneal power (Equation 7), varies between 1.3340 (R_a = 7.00 mm) and 1.3251 (R_a = 8.50 mm). The approximate values of the keratometric index (n_ka) computed from the APR using Equation 8 ranged from 1.3348 (R_a = 7 mm) to 1.326 (R_a = 8.5 mm). The absolute difference between these two values was less than 0.0009 for all performed simulations.

The absolute difference between the values of the total corneal power calculated using Equation 4 (D_c = D_k) and that obtained using Equation 1, with the computed value of n_ka (D_ka), was less than 0.123 D.

Table B (available in the online version of this article) demonstrates the study of the impact of variations in the posterior radius of curvature between 6.2 and 6.7 mm. The anterior radius of curvature was set at 7.8 mm.

**Table B Impact of Posterior Radius of Curvature on the Exact and Approximated Ideal Keratometry Index Values and Estimated Total Corneal Powers**
R_p	X	n_k	n_ka	n_ka – n_k	D_k = D_c	D_ka	D_ka – D_k
6.20	1.2581	1.3266	1.3257	−0.0009	41.874	42.323	0.121
6.30	1.2381	1.3274	1.3265	−0.0009	41.975	42.323	0.119
6.40	1.2188	1.3282	1.3273	−0.0009	42.072	42.323	0.117
6.50	1.2000	1.3289	1.3280	−0.0009	42.167	42.323	0.115
6.60	1.1818	1.3296	1.3287	−0.0009	42.258	42.323	0.114
6.70	1.1642	1.3303	1.3294	−0.0009	42.347	42.323	0.112
6.80	1.1471	1.3310	1.3301	−0.0009	42.433	42.323	0.110
6.90	1.1304	1.3316	1.3308	−0.0008	42.517	42.323	0.109
7.00	1.1143	1.3323	1.3314	−0.0008	42.598	42.323	0.107
7.10	1.0986	1.3329	1.3321	−0.0008	42.677	42.323	0.106
7.20	1.0833	1.3335	1.3327	−0.0008	42.754	42.323	0.104
7.30	1.0685	1.3341	1.3333	−0.0008	42.828	42.323	0.103
7.40	1.0541	1.3346	1.3338	−0.0008	42.901	42.323	0.101
7.50	1.0400	1.3352	1.3344	−0.0008	42.972	42.323	0.100
7.60	1.0263	1.3357	1.3349	−0.0008	43.041	42.323	0.099
7.70	1.0130	1.3362	1.3355	−0.0008	43.108	42.323	0.097

D_c = corneal thickness; D_k = keratometric power of the cornea; n_k = keratometric index; n_ka = approximate values of the keratometric index; R_p = radius of the posterior corneal curvature; X = ratio between the anterior and posterior radii of corneal curvature

The APR varies between 1.2581 (R_p = 6.2 mm) and 1.0130 (R_p = 7.7 mm).

The ideal values of the keratometric index that would enable computation of D_k such that it equals the total corneal power D_c (Equation 7) varied between 1.3247 (R_p = 6.2 mm) and 1.3347 (R_p = 7.70 mm). The approximate values of n_ka (Equation 8) ranged from 1.3257 (R_a = 6.2 mm) to 1.3355 (R_p = 7.7 mm). The absolute difference between these two values was less than 0.00095.

The absolute difference between the values of the total corneal power calculated using Equation 4 (D_c = D_k) and that obtained using Equation 1 with n_ka (D_ka) was less than 0.121 D.

Table C (available in the online version of this article) shows the impact of variations in central corneal thickness, which was made to vary between 470 and 620 µm (10-µm steps). The value of the anterior radius of curvature was 7.8 mm, and the value of the posterior radius of curvature was 6.8 mm (the corresponding APR is 1.1471).

**Table C Impact of Central Corneal Thickness on the Exact and Approximated Ideal Keratometry Index Values and Estimated Total Corneal Powers**
R_p	X	n_k	n_ka	n_ka – n_k	D_k = D_c	D_ka	D_ka – D_k
0.470	1.1471	1.3309	1.3301	−0.0008	42.420	42.323	−0.097
0.480	1.1471	1.3309	1.3301	−0.0008	42.422	42.323	−0.099
0.490	1.1471	1.3309	1.3301	−0.0008	42.424	42.323	−0.101
0.500	1.1471	1.3309	1.3301	−0.0008	42.426	42.323	−0.103
0.510	1.1471	1.3309	1.3301	−0.0008	42.428	42.323	−0.105
0.520	1.1471	1.3310	1.3301	−0.0008	42.430	42.323	−0.107
0.530	1.1471	1.3310	1.3301	−0.0008	42.432	42.323	−0.109
0.540	1.1471	1.3310	1.3301	−0.0009	42.434	42.323	−0.111
0.550	1.1471	1.3310	1.3301	−0.0009	42.436	42.323	−0.113
0.560	1.1471	1.3310	1.3301	−0.0009	42.438	42.323	−0.115
0.570	1.1471	1.3310	1.3301	−0.0009	42.440	42.323	−0.117
0.580	1.1471	1.3310	1.3301	−0.0009	42.442	42.323	−0.120
0.590	1.1471	1.3311	1.3301	−0.0009	42.444	42.323	−0.122
0.600	1.1471	1.3311	1.3301	−0.0010	42.446	42.323	−0.124
0.610	1.1471	1.3311	1.3301	−0.00010	42.448	42.323	−0.126
0.620	1.1471	1.3311	1.3301	−0.0010	42.451	42.323	−0.128

D_c = corneal thickness; D_k = keratometric power of the cornea; n_k = keratometric index; n_ka = approximate values of the keratometric index; X = ratio between the anterior and posterior radii of corneal curvature

The values of the ideal keratometric index, which can be used to derive the total corneal power (Equation 7) varied between 1.3294 (d_c= 470 µm) and 1.3291 (d^c = 620 µm). The approximate value of the optimal keratometric index (Equation 8) was 1.3301. The absolute difference between these exact and approximated ideal keratometric values was less than 0.001 for the tested pachymetric range.

The absolute difference between the values of the total corneal power calculated using Equation 4 (D_c = D_k) and that obtained using Equation 1 with n_ka (D_ka) was less than 0.128 D for all numerical corneal thickness simulations.

Figure 1 shows the theoretical differences, computed from Equation 10, between corneal powers computed using simulated keratometry with a fixed value for n_k = 1.3375 (APR = 0.962) versus n_ka values corresponding to APR values varying between 1.520 (n_ka =1.3150) and 0.962 (n_ka =1.3375). The value of R_a was made to vary between three intervals, to match the considered APR (R_a = 8.5 mm for 1.5125 ≥ X > 1.3250; R_a = 7.8 mm for 1.3250 ≥ X > 1.1375; R_a = 7.1 mm for 1.1375 ≥ X > 0.9625). As an indication, the green braces and horizontal dotted lines frame the interval corresponding to the mean ±2 standard deviations of APR values reported by Fam and Lim4 in healthy participants and their corresponding ideal keratometric index values.

Theoretical Impact of Corneal Laser Refractive Surgery on the Keratometric Index

Equation 17 demonstrates that after laser corneal refractive surgery, the approximated ideal keratometric index value is a function of both the preoperative anterior keratometry and the preoperative APR, as well as the delivered correction D_r. The greater the magnitude of myopic corrections (D_r < 0), the larger the increase in postoperative APR value.

Table 1 provides a theoretical estimate of the values of the theoretical keratometric index calculated with Equation 18, corresponding to different correction magnitudes (D_r) in corneal refractive surgery.

**Table 1 Theoretical Approximated Values of Keratometry Index Following Laser Corneal Refractive Surgery for Various Anterior and Posterior Corneal Radii Combinations**
D_r	R_a = 7.2 mm, R_p = 6 mm	R_a = 7.8 mm, R_p = 6.4 mm	R_a = 8.5 mm, R_p = 6.9 mm
D_r	n_ka	n_ka	n_ka
−10	1.3166	1.3145	1.3133
−9	1.3180	1.3161	1.3150
−8	1.3193	1.3175	1.3167
−7	1.3206	1.3190	1.3183
−6	1.3218	1.3203	1.3198
−5	1.3229	1.3216	1.3212
−4	1.3240	1.3228	1.3225
−3	1.3251	1.3240	1.3238
−2	1.3261	1.3251	1.3250
−1	1.3271	1.3262	1.3262
0	1.3280	1.3273	1.3273
1	1.3289	1.3282	1.3284
2	1.3298	1.3292	1.3294
3	1.3306	1.3301	1.3304
4	1.3314	1.3310	1.3313
5	1.3322	1.3318	1.3322

D_r = refractive error at the corneal plane; n_ka = approximate values of the keratometric index; R_a = radius of the anterior corneal curvature; R_p = radius of the posterior corneal curvature

For these simulations, different combinations of preoperative anterior and posterior radii of corneal curvature were used: R_a = 7.20 mm/R_p = 6 mm (APR = 1.200), R_a = 7.80 mm/R_p = 6.4 mm (APR = 1.219), and R_a = 8.4 mm/R_p = 6.9 mm (APR = 1.217). The approximate ideal keratometric refractive index values ranged from 1.3133 (−10.00 D photoablative correction, preoperative R_a = 8.4 mm and R_p = 6.9 mm) to 1.3318 (+5.00 D correction, preoperative R_a = 7.8 mm and R_p = 6.4 mm).

Discussion

The keratometric index is an effective index that accounts for the negative power introduced by the posterior corneal surface. In this current study, we have established a theoretical relationship between the expected “ideal” value of the keratometric index that would make the corneal power, obtained from simulated keratometry, equivalent to the total Gaussian corneal power both before and after corneal laser refractive surgery. Equation 8 can provide a clinically relevant approximation of the most compatible keratometric value to minimize the difference between corneal power estimated via simulated keratometry and Gaussian total corneal power, highlighting the major influence of the ratio of anterior to posterior corneal curvature. The maximum difference between the total Gaussian corneal power and the power obtained via simulated keratometry, using the approximated ideal keratometric indices, was less than 0.128 D, which can be considered clinically insignificant.

Using n_a =1.336 and n_s = 1.376, Equations 8 and 17 can be rewritten as: ((18)) ((19))

The higher the value of X (APR), the lower the n_ka value.

Various methods have been used to evaluate the ratio of the anterior and posterior corneal radius in different studies. Using slit scanning topography, Fam and Lim4 calculated the mean ratio between the anterior and posterior corneal curvature from actual measurements on one eye of 2,429 participants. They found that it was 1.22 ± 0.03 (95% CI: 1.16 to 1.28). Based on these measurements, they derived a mean keratometric index of 1.3273 ± 0.0013 (95% CI: 1.3248 to 1.3298). Using our Equation 8 and an APR of 1.22, we obtain a quasi-identical value for the keratometric index (n_ka = 1.3272).

According to the data reported by Fam et al,4 the choice of an index value close to 1.3375 induces an overestimation of the total corneal power and corresponds to an APR ratio less than 1 (posterior radius of curvature larger than the anterior radius of curvature). The APR increases after myopic corneal laser surgery because of the negative sign of D_r, which makes the denominator inferior to the numerator (Equation 16). This implies that the greater the correction of myopia, the more the value of the most suitable theoretical keratometric index decreases. This accentuates the difference between the keratometric power and the theoretical total corneal power calculated, by taking into account the value of the posterior corneal curvature.

Previously, some investigators have aimed to assess the impact of corneal laser surgery on the keratometric index. They found the keratometric index to be a function of the surgically induced correction.5–7 Equation 17 allows us to establish the theoretically predicted impact of the surgical refractive correction delivered at the anterior corneal plane, on the most compatible keratometric index value. The numerator of Equation 17 shows that the preoperative front corneal curvature also influences the postoperative change in the APR. For the same correction D_r, the flatter the preoperative anterior cornea, the larger the increase in the postoperative APR.

Jin et al8 reported a preoperative mean ratio of 1.225 ± 0.0281 and a keratometric index of 1.3277 ± 0.0010 in 102 Chinese eyes. After myopic laser corneal refractive surgery, the APR increased to 1.3705 ± 0.0634 and the derived keratometric index was 1.3217 ± 0.0026. Using these reported APR values in Equation 8, we predict preoperative and postoperative keratometric index values of 1.3270 and 1.3212, respectively.

In converting the corneal radius to keratometric power, it is customary to use the keratometric index of refraction n_k = 1.3375 instead of the actual index of refraction of the cornea. For n_ka = 1.3375, the corresponding APR computed from Equation 9 is 0.9625, which corresponds to a non-physiological situation because the anterior radius of curvature is smaller than the posterior radius of curvature for any APR less than 1. Based on our simulations, this situation could correspond to the effect of hyperopic laser correction on a steep cornea. The theoretical value of the keratometric index calculated for a correction of +5.00 D is 1.3318 (Table 4, preoperative R_a = 7.8 mm), which is always slightly less than the most frequently used value (1.3375). As shown by previous authors,4,9 our optical analysis shows that the use of 1.3375 is not adequate to convert radii of curvature into absolute dioptric power of the cornea and leads to an overestimation of the corneal power measured by simulated keratometry.2,3,10

Figure 1 displays the theoretical differences that could be observed between conventional simulated keratometry with n_k = 1.3375 (APR = 0.962) and keratometry computed with n_ka values corresponding to APR values varying between 1.520 (n_ka = 1.3150) and 0.962 (n_ka = 1.3375). The difference in keratometric power can reach 2.60 D for an APR of 1.3155, a ratio corresponding to postoperative high myopia laser correction. In the interval corresponding to the values reported in the general population by Fam and Lim,4 the theoretical power difference varies between 1.00 and 1.50 D. The difference gradually reduces for lower APR, such as after hyperopic laser corneal surgery.

Our simulations are not primarily intended to be used for the estimation of corneal power in certain clinical applications (eg, calculation of the power of an IOL), but to quantify the potential difference between the estimated corneal power with the keratometric index and the total corneal power and appreciate the quantitative influence of the corneal variables involved. The differences in corneal power estimation methods influence IOL power calculation results. Using ray-tracing to compute total corneal power, Savini et al2 found that simulated keratometry provided higher corneal power than total corneal power. This difference was not constant and depended on the APR. However, using total corneal power did not improve the results of the IOL power calculation formulas, because they were developed and optimized using keratometric values such as simulated keratometry. The value of the keratometric index varies according to the implant power calculation formulas. Although the Hoffer Q formula uses 1.3375 for the keratometric index, the Haigis formula uses 1.3315, the SRK/T formula uses 1.333, and the Holladay 1 formula uses 4/3. The lens constants used to zeroize the average prediction error for a particular IOL also vary according to these formulas. In a recent study,11 we have shown that the consequences of variations in the lens constant mainly concern eyes receiving high-power IOLs. Hence, depending on the ocular biometric characteristics, the compensation of a systematic corneal power overestimation by a constant increment of the effective lens position may induce a non-systematic modification of the predicted IOL power. This non-linearity could increase the standard deviation of the postoperative refraction prediction error.

Kim et al12 evaluated the accuracy of IOL power calculation using adjusted corneal power according to the ratio of anterior and posterior radii of corneal curvature. Adjusted corneal power of patients with cataract was calculated using a fictitious refractive index obtained from the corneal curvature radii ratio of controls and adjusted anterior and predicted posterior corneal curvature radii from conventional keratometry using the ratio of anterior and posterior radii of corneal curvature. Without a compact analytical formula, the authors had to perform iterative computations of the anterior radius of corneal curvature using the total corneal power and the APR. In their reference population, the average APR was 0.808 (corresponding to an APR of 1.238), and the corresponding fictitious refractive index was 1.3275. Equation 7 yields the same value as the authors (1.3275), and using Equation 8 yields a fictitious refractive index value of 1.3265. IOL power calculation using the Haigis and SRK/T formulas and adjusted corneal power according to the ratio of anterior and posterior radii of corneal curvature provided more accurate refractive outcomes than calculation using conventional keratometry.

It is currently possible to measure anterior and posterior curvatures using topographers that rely on Scheimpflug or optical coherence tomography technology. Therefore, it seems preferable to estimate the total corneal power according to the values of anterior and posterior radii of curvature, the corneal thickness, and the physical refractive indices of the media concerned, especially when refining or developing new IOL power calculation formulas.

When it is possible to obtain posterior corneal curvature measurements, total corneal power can be determined using either the Gaussian optics thick lens formula or ray-tracing. Our goal was to establish analytic formulas to explore the links between simulated keratometric power and total Gaussian corneal power. Therefore, we did not use the total corneal power calculation method by ray-tracing, which does not provide explicit formulas. The Gaussian formula has been found to overestimate total corneal power; hence this should not change the interpretation of our results.1

We have developed equations that allow calculation of the ideal keratometric index value, which in turn enables simulated keratometric power to equal the total Gaussian corneal power. These equations make it possible to directly evaluate the impact of corneal variables such as the APR on the optimal keratometric index value. These calculations could aid analysis of the origin of errors in IOL power calculation formulas.

AUTHOR CONTRIBUTIONS

Study concept and design (DG) data collection (DG, AS, GD); analysis and interpretation of data (DG, GD, AS, RR); writing the manuscript (DG); critical revision of the manuscript (DG, GD, AS RR)

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This is an Open Access article distributed under the terms of the Creative Commons Attribution 4.0 International ( https://creativecommons.org/licenses/by/4.0). This license allows users to copy and distribute, to remix, transform, and build upon the article, for any purpose, even commercially, provided the author is attributed and is not represented as endorsing the use made of the work.

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Correspondence: Damien Gatinel, MD, PhD, Rothschild Foundation Hospital, Anterior Segment and Refractive Surgery Deptartment, 25 rue Manin, Paris 75019, France. Email: gatinel@gmail.com

From Rothschild Foundation Hospital, Anterior Segment and Refractive Surgery Deptartment, Paris, France.

Disclosure: The authors have no financial or proprietary interest in the materials presented herein.

Received10/25/22
Accepted1/27/23
Published online4/01/23

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Theoretical Relationship Between the Anterior-Posterior Corneal Curvature Ratio, Keratometric Index, and Estimated Total Corneal Power