Abstract
Introduction: The purpose of this study was to compare the accuracy of seven formulas for intraocular lens power calculation in patients with microspherophakia (MSP). Methods: A retrospective case series included 44 eyes from 28 patients with MSP. The mean prediction error (PE) was calculated, and the accuracy was determined by formula performance index (FPI), median absolute error (MedAE), and percentage of eyes with a PE within ±0.25 diopters (D), ±0.50 D, ±0.75 D, and ±1.00 D. Depending on whether the patients had Marfan syndrome (MFS), MSP patients 36 were sub-divided into MFS and non-MFS group. Results: In the non-MFS subgroup, the performance of formulas ranked by FPI from highest to lowest was BUII, Emmetropia Verifying Optical (EVO), Kane, Haigis, Sanders-Retzlaff-Kraff/Theoretical (SRK/T), Holladay 1, and Hoffer Q. In the MFS subgroup, Kane achieved the best accuracy regarding the lowest MedAE and the largest percentage of PE in the range of ±0.50 D. Similar results were obtained in eyes with shallow anterior chamber depth (ACD). In the regular ACD subgroup, the EVO provided the highest prediction accuracy and SRK/T took the second place. In the deep ACD subgroup, Holladay 1 performed superiorly presenting the lowest standard deviation values, mean absolute error and MedAE. Conclusions: Overall, new generation formulas showed a better trend of refractive outcomes in MSP patients. The Holladay 1 formula was suggested for eyes with deep ACD, while Haigis was not recommended.
Introduction
Microspherophakia (MSP) is a rare congenital eye disorder characterized by the abnormal spherical shape of the crystalline lens with an increased anteroposterior diameter and a reduced equatorial diameter due to the developmentally hypoplastic and weak zonules [1]. It typically presents with visibility of the lenticular equator on mydriasis, defective accommodation, and varying degrees of myopia [2]. MSP exists as an isolated condition or an ocular manifestation of hereditary systemic diseases such as Marfan syndrome (MFS) [3], homocystinuria [4], Weill-Marchesani syndrome [5], and so on. Recently, with an improved understanding of the clinical characteristics of MSP in combination with genetic testing, the overall identification of the disease drastically increased. The gradual progressive laxity of the zonular fibers is conducive to lens subluxation or dislocation. This may lead to glaucoma attributed to the pupillary block, which is the leading cause of vision impairment and irreversible blindness in MSP patients. Therefore, early surgical intervention removing the abnormal lens is recommended to improve the prognosis of this condition.
Various operations are available for managing MSP, including lensectomy and anterior vitrectomy followed by scleral-fixated intraocular lens (IOL) implantation, which are more susceptible to postoperative complications such as retinal detachment and suture rupture [6]. With the introduction of lens capsule stabilizing devices, modified capsular tension ring (MCTR) has been recognized as providing better stability for the lens capsule with zonular dialysis and improving visual rehabilitation [7]. It is suggested that phacoemulsification combined with transscleral-fixated MCTR and in-the-bag intraocular lens (MCTR-IOL) implantation is an effective management for MSP patients with an increased success rate [8]. However, accurate measurements of ocular parameters in MSP eyes have always been difficult, as significant refractive errors are often seen in MSP patients. Meanwhile, an earlier onset of the disease was found in most MSP patients beginning in adolescence or early adulthood, who have higher requirements for postoperative vision. Therefore, it is crucial to improve the accuracy of IOL calculation and prevent MSP patients from ametropia after surgery with the demand for precision therapy.
The hallmarks of ocular biometrics in MSP patients include shallower anterior chamber depth (ACD), steeper corneal curvature and thicker lens thickness (LT) [9]. The inaccuracy of IOL power calculations in MSP patients is attributed primarily to incorrect calculation of the effective lens position (ELP) due to the decreased ACD as a result of the forward movement of the spherical lens [10]. Alternatively, the extensive relaxation of the zonular fibers covering 360-degrees may also lead to posterior dislocation of the lens, resulting in iris concavity and deepening of ACD.
Previously, traditional IOL calculation formulas were widely used in eyes with ectopia lentis, including Sanders-Retzlaff-Kraff/Theoretical (SRK/T) [11], Holladay 1 [12] and Hoffer Q [13] and Haigis [14] formulas. Nowadays, several new generation formulas have been introduced to improve the accuracy of IOL power predictions. Barrett Universal II (BUII) is based on a theoretical model, in which the LT and white-to-white distance are recommended as optional variables. Integrating artificial intelligence into the calculation, Kane formula uses three variables with LT and central corneal thickness to make its prediction [15]. Emmetropia Verifying Optical (EVO) formula is an advanced thick lens formula based on the theory of emmetropization [16]. The version 2.0 has improved prediction in long and short eyes, taking into account axial length (AL) and corneal curvature (K) with ACD, LT, and central corneal thickness as optional dimensions. In addition, PEARL-DGS, Hill-RBF, K6, and Castrop formulae are available online and are recently reported in various studies. However, considering the small cohort size due to the rarity of this disease, we decide to analyze only three of the most commonly utilized new generation formulas (BUII, Kane, and EVO). Recently, numerous studies on the new generation IOL power calculation formulas have demonstrated that BUII, EVO, and Kane produced good performance in routine cataract surgery [17]. However, in eyes suffering from MSP, the accuracy of these IOL calculation formulas currently in use remain unknown. The purpose of this study was to compare the accuracy of seven formulas, including SRK/T, Holladay 1, Hoffer Q, Haigis, BUII, Kane, and EVO in predicting the refractive outcome for phacoemulsification combined with transscleral-fixated MCTR-IOL implantation in MSP patients.
Materials and Methods
Patient Eligibility
This retrospective observational study comprised MSP patients who underwent phacoemulsification combined with transscleral-fixated MCTR and in-the-bag IOL (MCTR-IOL) implantation. Surgeries were performed at the Eye and Ear, Nose, and Throat Hospital of Fudan University between January 2018 and December 2021. This study protocol was reviewed and approved by the Human Research Ethics Committee of Eye and ENT Hospital of Fudan University, approval number 2020126-1. This study adhered to the tenets of the Declaration of Helsinki and served as an extension of our randomized controlled trial, registered with the China Clinical Trial Registry (identifier: ChiCTR2000039132). All patients were informed about the study in detail and written informed consent has been obtained from all adult participants and from the parents/legal guardians/next of kin of all underage participants.
Selection Criteria
Participant selection criteria are outlined in Figure 1. MSP patients who underwent phacoemulsification combined with transscleral-fixated MCTR-IOL implantation were eligible for inclusion. The diagnostic criteria for MSP were as follows: (1) binocular involvement; (2) lenticular myopia; (3) visibility of lens equatorial edge in the mydriatic state under slit lamp or operating microscope; (4) sparse and lax lens zonular fibers in 360° detected by ultrasound biomicroscopy; (5) dislocation of lens seen in supine position.
Taking into account the differences in ocular characteristics of MSP patients with and without MFS, we have categorized the MSP patients into two subgroups. MSP patients that met the Ghent-2 criteria were classified in the MFS subgroup, while those who did not meet the Ghent-2 criteria were put into the non-MFS subgroup.
The exclusion criteria were as follows: (1) a history of ocular trauma or other ophthalmic surgery, such as congenital cataract, retinal detachment, epiretinal membrane, refractive surgery, or anti-glaucoma surgery; (2) potential intraoperative complications, including posterior capsule rupture and radial tears in capsulorhexis; (3) failure to cooperate with optometric measurements and/or the postoperative data were missing.
Examinations
All enrolled patients underwent a comprehensive preoperative ophthalmologic examination, including slit-lamp biomicroscopy, fundoscopy, optical coherence tomography, and B-scan ultrasonography. Ocular biometric parameters including AL, K, ACD (measured from epithelium to lens), and LT were performed with a partial coherence interferometer (IOL Master 700, Carl Zeiss Meditec AG, Jena, Germany). The manifest refraction after surgery was performed postoperatively at one and 3-month follow-up visits.
Surgical Technique
All surgeries were performed under general anesthesia by an experienced surgeon (Dr. Y.J.) with a superior corneal clear incision of 2.6 mm [18]. After the injection of the ophthalmic viscosurgical device into the anterior chamber, a continuous curvilinear capsulorhexis with a diameter of 4.0–5.0 mm was made. Four capsular retractors (CapsuleCare, Med Devices Lifesciences, India) were used to suspend and stabilize the capsular bag. The surgeon performed the stop and chop technique to deal with nuclei over grade three in adult subjects, or irrigation/aspiration under a low vacuum with a reduced bottle height of 60 cm by phacoemulsifier to remove the lens material in children. The MCTR (Morcher GmbH, Germany) was then sutured to the sclera 2 mm posterior to the corneal limbus with 9-0 polypropylene (MANI Inc. Japan) using a modified knot-free z-suture technique. After removal of the capsular hooks, a foldable IOL was implanted into the capsular bag. Finally, the corneal incision was closed with 10-0 nylon sutures, and the conjunctiva flap was subsequently closed using 8-0 nylon sutures. Postoperatively, dexamethasone/tobramycin ophthalmic ointment was topically applied to the conjunctival sac of the operated eyes.
IOL Power Calculation Methods
Taking into account the IOL Master biometric data, the IOL power was calculated using the different formulas under consideration.
- 1.
The SRK/T, Holladay 1, Hoffer Q, and Haigis formulas were calculated on an Excel spreadsheet (Office 2019, Microsoft Corp.) according to their originally published reports and errata.
- 2.
Barrett Universal II formula (BUII, version 1.05, http://calc.apacrs.org/barrett_universal2105/), Emmetropia Verifying Optical formula (EVO, version 2.0, https://www.evoiolcalculator.com), Kane formula (https://www.iolformula.com) were calculated via their respective websites.
In all cases, one of the following IOL models was implanted in this study: TECNIS ZCB00 (Johnson & Johnson, New Jersey, USA), AcrySof SN60WF and SA60AT (Alcon Laboratories Inc., TX, USA). Considering the similar characteristics among these IOLs, the risk of potential bias introduced by the inclusion of eye implanted with different IOLs have been decreased. For all methods, we used the optimized A-constant of the SRK/T, Holladay 1, Hoffer Q, and Haigis formulas from the User Group for Laser Interference Biometry (ULIB) website (www.ocusoft.de/ulib/c1.htm, accessed on November 4, 2022). For BUII, Kane, and EVO, the recommended A-constants were obtained via their respective websites. According to Wang et al. [19], IOL constants are not optimized in atypical eyes including short eyes, eyes post-laser vision correction or eyes where IOLs are sutured to the sclera. Thus, we did not zero out the refractive prediction error (PE) separately in this study. The constants used in calculations and the features of IOL are illustrated in online supplementary Table S1 (for all online suppl. material, see https://doi.org/10.1159/000545050).
Evaluation of the Accuracy in Predicted Refraction
The manifest refraction after surgery was obtained at 3 months. The IOL PEs were defined as the difference of the actual postoperative refractive spherical equivalent minus the formula-predicted postoperative spherical equivalent using the actual power of the implanted IOL. A negative value indicated a refractive myopic shift resulted from the lower IOL power predicted by each formula, whereas a positive value indicated a refractive hyperopic shift. The absolute PE (AE), the mean absolute error (MAE) and median absolute error (MedAE) for each formula were calculated. The percentage of eyes within ±0.25 diopter (D), ±0.50 D, ±0.75 D, ±1.00 D of the predicted refraction were evaluated.
- 1.
The standard deviation (SD) of the PE.
- 2.
The MedAE.
- 3.
The slope (m) of the correlation between the PE and the AL.
- 4.
The inverse value of the percentage of eyes with a PE within 0.50 D.
It was recommended by the IOL Power Club that the higher the FPI, the more accurate the formula [20].
Statistical Analyses
Statistical analyses were performed using SPSS statistical software for Windows (version 22, IBM Corp.). Normality of the data distribution was tested by the Kolmogorov-Smirnov test. The continuous data that satisfied the normal distribution were shown as the mean ± SD. Otherwise, the data were shown as median with interquartile range. Group comparisons between continuous variables were performed using the Student’s t test for parametric variables or Mann-Whitney U test for nonparametric variables. Generalized estimated equation model was used for adjustment of correlation between 2 eyes of a participant. Friedman’s test was employed to compare arithmetic PE, MAE, and MedAE. The Cochran’s Q test was used to evaluate the percentage of ±0.25 D, ±0.50 D, ±0.75 D, and ±1.00 D range of PE between formulas. Post hoc pairwise comparisons with Bonferroni correction were performed for multiple comparisons. Differences were considered statistically significant if p values <0.05.
Results
Demographic and Ocular Biometry Characteristics of Participants
A total of 44 eyes from 28 patients eligible for the selection criteria were included. The demographic characteristics and ocular biometrics are summarized in Table 1. The mean age of the investigated subjects was 19.07 years ± 16.53 (SD) ranged between 4 and 59 years. The mean AL was 24.98 ± 2.57 mm, with 19 (43.18%) eyes greater than 25 mm. The mean corneal power was 42.09 ± 2.41 D, the mean ACD was 2.83 ± 0.74 mm, and the mean LT was 4.64 ± 0.51 mm. The mean power of the implanted IOL was 22.23 ± 6.45 D. In total, 27 eyes of 18 patients and 17 eyes of 10 patients were identified in the non-MFS subgroup and the MFS subgroup, respectively. There were significant differences in the ACD (p = 0.03), average K (p < 0.001), and corneal astigmatism (p = 0.01) between the two subgroups. MSP patients in the non-MFS subgroup had shallower ACD, steeper corneal power (average K, K1, K2) and higher corneal astigmatism compared with the MFS subgroup (all p < 0.05).
Demographics and ocular biometry information of microspherophakia participants in the non-MFS subgroup and the MFS subgroup
. | Overall . | Non-MFS subgroup . | MFS subgroup . | p value . | ||||
---|---|---|---|---|---|---|---|---|
count . | % of total . | count . | % of total . | count . | % of total . | |||
Subjects | 28 | 18 | 10 | |||||
Eyes | 27 | 17 | 0.569a | |||||
Right | 21 | 47.73% | 12 | 44.44% | 9 | 52.94% | ||
Left | 23 | 52.27% | 15 | 55.56% | 8 | 47.06% | ||
Gender | 0.583a | |||||||
Male | 12 | 42.86% | 7 | 38.89% | 5 | 50.00% | ||
Female | 16 | 57.14% | 11 | 61.11% | 5 | 50.00% |
. | Overall . | Non-MFS subgroup . | MFS subgroup . | p value . | ||||
---|---|---|---|---|---|---|---|---|
count . | % of total . | count . | % of total . | count . | % of total . | |||
Subjects | 28 | 18 | 10 | |||||
Eyes | 27 | 17 | 0.569a | |||||
Right | 21 | 47.73% | 12 | 44.44% | 9 | 52.94% | ||
Left | 23 | 52.27% | 15 | 55.56% | 8 | 47.06% | ||
Gender | 0.583a | |||||||
Male | 12 | 42.86% | 7 | 38.89% | 5 | 50.00% | ||
Female | 16 | 57.14% | 11 | 61.11% | 5 | 50.00% |
. | mean±SD . | median (min, max) . | mean±SD . | median (min, max) . | mean±SD . | median (min, max) . | p value . | |
---|---|---|---|---|---|---|---|---|
Age, years | 19.07±16.53 | 7.50 (4, 59) | 22.67±18.24 | 20.50 (5, 59) | 12.60±10.92 | 6.50 (4, 29) | 0.15c | |
IOL power, D | 22.00±6.45 | 21.50 (10, 32) | 20.50±6.60 | 20.50 (10, 31) | 24.38±5.58 | 26.50 (14, 32) | 0.05b | 0.098d |
ACD, mm | 2.83±0.74 | 2.81(1.05, 4.80) | 2.69±0.87 | 2.48 (1.05, 4.80) | 3.10±0.28 | 3.12 (2.78, 3.54) | 0.03b,* | 0.01d,* |
LT, mm | 4.64±0.51 | 4.74 (3.48, 5.83) | 4.71±0.49 | 4.79 (3.90, 5.83) | 4.53±0.53 | 4.62 (3.48, 5.11) | 0.33b | 0.402d |
AL, mm | 24.98±2.57 | 24.32 (21.21, 30.37) | 25.16±2.81 | 24.36(21.21, 30.37) | 24.69±2.17 | 24.15 (21.72, 28.74) | 0.74c | 0.621d |
Average keratometry, D | 42.09±2.41 | 42.24 (37.36, 48.67) | 43.40±1.84 | 42.80 (40.81, 48.67) | 40.01±1.62 | 39.86 (37.36, 42.95) | <0.001b, * | <0.001d,* |
Keratometry K1, D | 41.25±2.60 | 41.61 (35.75, 48.49) | 42.72±1.95 | 42.30 (39.89, 48.49) | 38.92±1.61 | 39.03 (35.75, 41.57) | <0.001b, * | <0.001d,* |
Keratometry K2, D | 42.99±2.29 | 43.06 (38.58.48.84) | 44.13±1.78 | 43.61 (41.72, 48.84) | 41.17±1.81 | 40.91 (38.58, 44.44) | <0.001b,* | <0.001d,* |
Corneal astigmatism, D | 1.57±0.93 | 1.57 (0.14, 4.16) | 1.41±0.71 | 1.55 (0.14, 2.87) | 2.25±1.03 | 1.88 (1.00, 4.16) | 0.01b,* | 0.012d |
. | mean±SD . | median (min, max) . | mean±SD . | median (min, max) . | mean±SD . | median (min, max) . | p value . | |
---|---|---|---|---|---|---|---|---|
Age, years | 19.07±16.53 | 7.50 (4, 59) | 22.67±18.24 | 20.50 (5, 59) | 12.60±10.92 | 6.50 (4, 29) | 0.15c | |
IOL power, D | 22.00±6.45 | 21.50 (10, 32) | 20.50±6.60 | 20.50 (10, 31) | 24.38±5.58 | 26.50 (14, 32) | 0.05b | 0.098d |
ACD, mm | 2.83±0.74 | 2.81(1.05, 4.80) | 2.69±0.87 | 2.48 (1.05, 4.80) | 3.10±0.28 | 3.12 (2.78, 3.54) | 0.03b,* | 0.01d,* |
LT, mm | 4.64±0.51 | 4.74 (3.48, 5.83) | 4.71±0.49 | 4.79 (3.90, 5.83) | 4.53±0.53 | 4.62 (3.48, 5.11) | 0.33b | 0.402d |
AL, mm | 24.98±2.57 | 24.32 (21.21, 30.37) | 25.16±2.81 | 24.36(21.21, 30.37) | 24.69±2.17 | 24.15 (21.72, 28.74) | 0.74c | 0.621d |
Average keratometry, D | 42.09±2.41 | 42.24 (37.36, 48.67) | 43.40±1.84 | 42.80 (40.81, 48.67) | 40.01±1.62 | 39.86 (37.36, 42.95) | <0.001b, * | <0.001d,* |
Keratometry K1, D | 41.25±2.60 | 41.61 (35.75, 48.49) | 42.72±1.95 | 42.30 (39.89, 48.49) | 38.92±1.61 | 39.03 (35.75, 41.57) | <0.001b, * | <0.001d,* |
Keratometry K2, D | 42.99±2.29 | 43.06 (38.58.48.84) | 44.13±1.78 | 43.61 (41.72, 48.84) | 41.17±1.81 | 40.91 (38.58, 44.44) | <0.001b,* | <0.001d,* |
Corneal astigmatism, D | 1.57±0.93 | 1.57 (0.14, 4.16) | 1.41±0.71 | 1.55 (0.14, 2.87) | 2.25±1.03 | 1.88 (1.00, 4.16) | 0.01b,* | 0.012d |
MSP, microspherophakia; MFS, Marfan syndrome; D, diopters; SD, standard deviation; IOL, intraocular lens; ACD, anterior chamber depth; as measured from corneal epithelium to lens, LT, lens thickness; AL, axial length; K, keratometry.
aChi-square test, a0 Fisher’s exact tests, bIndependent samples t test, cMann-Whitney U, dGeneralized estimated equation model with adjustment of correlation between 2 eyes within same person.
*Statistically significant (p < 0.05).
Prediction Accuracy of IOL Formulas in Non-MFS and MFS Subgroups
The refractive outcomes calculated for each formula in the two subgroups are illustrated in Table 2 and Figure 2. In the non-MFS subgroup, all formulas displayed negative PE except EVO, indicating a myopic refractive surprise. However, the Friedman test failed to identify a significant difference in PE among formulas (p = 0.084). In the MFS subgroup, significant differences in PE were detected between 7 formulas (p < 0.001). Post hoc comparison with Bonferroni correction showed a significant difference of SRK/T (0.35 D) formula compared with Hoffer Q (−0.44 D) and Kane (−0.21 D) formulas (Bonferroni method adjusted p < 0.001 and p < 0.05, respectively). Notably, the PE of Haigis (−0.66 D) formula was significantly more myopic than SRK/T (0.35 D), EVO (0.16 D), BUII (−0.02 D) (all adjusted p < 0.05), and Holladay 1 (0.08 D) (adjusted p < 0.001).
Performance of IOL calculation formula in the non-MFS subgroup and the MFS subgroup
Formula . | FPI . | PE . | Absolute PE . | |||||
---|---|---|---|---|---|---|---|---|
mean . | SD . | range . | mean . | SD . | median . | range . | ||
Non-MFS subgroup (N = 27) | ||||||||
BUII | 0.2033 | −0.0350 | 1.1994 | (−2.70, 2.00) | 0.8928 | 0.7825 | 0.7350 | (0.03, 2.70) |
Kane | 0.1955 | −0.2770 | 1.1324 | (−2.73, 1.38) | 0.8574 | 0.7723 | 0.7950 | (0.02, 2.73) |
EVO | 0.1768 | 0.0309 | 1.1483 | (−2.48, 1.80) | 0.9328 | 0.6451 | 0.8850 | (0.07, 2.48) |
Haigis | 0.1693 | −0.0739 | 1.2580 | (−3.04, 1.94) | 0.9946 | 0.7489 | 0.8750 | (0.01, 3.04) |
SRK/T | 0.1377 | −0.1735 | 1.3355 | (−3.67, 2.13) | 0.9987 | 0.8826 | 0.7150 | (0.04, 3.67) |
Holladay 1 | 0.1236 | −0.0124 | 1.3872 | (−3.20, 2.19) | 1.0809 | 0.8433 | 0.9850 | (0.05, 3.20) |
Hoffer Q | 0.1212 | −0.1428 | 1.3499 | (−3.07, 2.14) | 1.0961 | 0.7719 | 0.9250 | (0.02, 3.07) |
MFS subgroup (N = 17) | ||||||||
Kane | 0.3416 | −0.2128 | 0.8159 | (−2.07, 1.12) | 0.6025 | 0.5704 | 0.3050 | (0.05, 2.07) |
BUII | 0.3243 | −0.0201 | 0.8504 | (−1.82, 1.58) | 0.6104 | 0.5724 | 0.3950 | (0.05, 1.82) |
Hoffer Q | 0.3144 | −0.4390 | 0.6532 | (−2.05, 0.55) | 0.5922 | 0.5087 | 0.4600 | (0.03, 2.05) |
Holladay 1 | 0.2945 | 0.0793 | 0.6978 | (−1.81, 1.09) | 0.5234 | 0.4500 | 0.5250 | (0.01, 1.81) |
SRKT | 0.2867 | 0.3510 | 0.7431 | (−1.53, 1.52) | 0.6575 | 0.4730 | 0.5100 | (0.02, 1.53) |
Haigis | 0.2376 | −0.6575 | 0.6862 | (−2.08, 0.35) | 0.7632 | 0.5568 | 0.5800 | (0.19, 2.08) |
EVO | 0.2219 | 0.1587 | 0.9245 | (−1.79, 1.97) | 0.6963 | 0.6052 | 0.5100 | (0.02, 1.97) |
Formula . | FPI . | PE . | Absolute PE . | |||||
---|---|---|---|---|---|---|---|---|
mean . | SD . | range . | mean . | SD . | median . | range . | ||
Non-MFS subgroup (N = 27) | ||||||||
BUII | 0.2033 | −0.0350 | 1.1994 | (−2.70, 2.00) | 0.8928 | 0.7825 | 0.7350 | (0.03, 2.70) |
Kane | 0.1955 | −0.2770 | 1.1324 | (−2.73, 1.38) | 0.8574 | 0.7723 | 0.7950 | (0.02, 2.73) |
EVO | 0.1768 | 0.0309 | 1.1483 | (−2.48, 1.80) | 0.9328 | 0.6451 | 0.8850 | (0.07, 2.48) |
Haigis | 0.1693 | −0.0739 | 1.2580 | (−3.04, 1.94) | 0.9946 | 0.7489 | 0.8750 | (0.01, 3.04) |
SRK/T | 0.1377 | −0.1735 | 1.3355 | (−3.67, 2.13) | 0.9987 | 0.8826 | 0.7150 | (0.04, 3.67) |
Holladay 1 | 0.1236 | −0.0124 | 1.3872 | (−3.20, 2.19) | 1.0809 | 0.8433 | 0.9850 | (0.05, 3.20) |
Hoffer Q | 0.1212 | −0.1428 | 1.3499 | (−3.07, 2.14) | 1.0961 | 0.7719 | 0.9250 | (0.02, 3.07) |
MFS subgroup (N = 17) | ||||||||
Kane | 0.3416 | −0.2128 | 0.8159 | (−2.07, 1.12) | 0.6025 | 0.5704 | 0.3050 | (0.05, 2.07) |
BUII | 0.3243 | −0.0201 | 0.8504 | (−1.82, 1.58) | 0.6104 | 0.5724 | 0.3950 | (0.05, 1.82) |
Hoffer Q | 0.3144 | −0.4390 | 0.6532 | (−2.05, 0.55) | 0.5922 | 0.5087 | 0.4600 | (0.03, 2.05) |
Holladay 1 | 0.2945 | 0.0793 | 0.6978 | (−1.81, 1.09) | 0.5234 | 0.4500 | 0.5250 | (0.01, 1.81) |
SRKT | 0.2867 | 0.3510 | 0.7431 | (−1.53, 1.52) | 0.6575 | 0.4730 | 0.5100 | (0.02, 1.53) |
Haigis | 0.2376 | −0.6575 | 0.6862 | (−2.08, 0.35) | 0.7632 | 0.5568 | 0.5800 | (0.19, 2.08) |
EVO | 0.2219 | 0.1587 | 0.9245 | (−1.79, 1.97) | 0.6963 | 0.6052 | 0.5100 | (0.02, 1.97) |
MSP, microspherophakia; MFS, Marfan syndrome; FPI, formula performance index; SD, standard deviation; IOL, intraocular lens; BUII, Barrett Universal II; EVO, Emmetropia Verifying Optical.
General performance of IOL calculation formulas in the non-MFS subgroup and the MFS subgroup. a The PE and MAE of seven formulas in the two subgroups. b, c The violin plot of the absolute PE (in diopters) ranked in ascending order of the MedAE of each formula in the non-MFS subgroup (b) and the MFS subgroup (c). The medians are shown in red lines, and the interquartiles are presented as blue lines. d Comparisons of predictive capabilities of seven formulas in the MFS subgroup. p values indicated by related-samples Friedman’s Two-way analysis of variance with Bonferroni correction. The red lines indicated p < 0.001; the blue lines indicated p < 0.05 while the gray dashed lines indicated p > 0.05. MFS, Marfan syndrome; PE, prediction error; MAE, mean absolute error; MedAE, median absolute error; BUII, Barrett Universal II formula; EVO, Emmetropia Verifying Optical formula.
General performance of IOL calculation formulas in the non-MFS subgroup and the MFS subgroup. a The PE and MAE of seven formulas in the two subgroups. b, c The violin plot of the absolute PE (in diopters) ranked in ascending order of the MedAE of each formula in the non-MFS subgroup (b) and the MFS subgroup (c). The medians are shown in red lines, and the interquartiles are presented as blue lines. d Comparisons of predictive capabilities of seven formulas in the MFS subgroup. p values indicated by related-samples Friedman’s Two-way analysis of variance with Bonferroni correction. The red lines indicated p < 0.001; the blue lines indicated p < 0.05 while the gray dashed lines indicated p > 0.05. MFS, Marfan syndrome; PE, prediction error; MAE, mean absolute error; MedAE, median absolute error; BUII, Barrett Universal II formula; EVO, Emmetropia Verifying Optical formula.
The distribution of the MedAE by IOL formulas in the order from the lowest to the highest in the two subgroups are shown in Figure 2. In the non-MFS subgroup, the best MedAE were obtained with the SRK/T (0.72 D), BUII (0.74 D), and Kane (0.80 D). In the MFS subgroup, the Kane formula yielded the lowest MedAE (0.31 D), followed by BUII (0.40 D) and Hoffer Q (0.46 D). However, the Friedman test revealed no statistically significant differences in PE among 7 formulas in both groups, which was most likely related to the limited sample size with the possibility of a lack of adequate power to detect statistical differences.
Figure 3 displayed the proportion of eyes within a given diopter range of PE in the two subgroups, respectively. In the non-MFS subgroup, the Kane formula exhibited the highest percentage of PE within ±0.25 D (28.00%), ±1.00 D (72.00%), and the BUII within ±0.50 D (40.74%). With respect to MSP patients in the MFS subgroup, BUII exhibited the highest percentage of PE within ±0.25 D (47.06%) and Kane had the highest percentage of cases within ±0.50 D (53.33%). The lowest percentages within ±0.25 D, ±0.50 D were achieved by Haigis (6.67% and 40.00%, respectively). Holladay 1 and Hoffer Q formulas had the highest percentage within ±1.00 D at 88.24%. However, there were no significant differences among formulas in the ±0.25 D, ±0.50 D, ±0.75 D, and ±1.00 D range of PE using Cochran’s Q test in two subgroups.
Stacked histogram showing the percentage of eyes within a given diopter range of PE in the non-MFS subgroup (a) and the MFS subgroup (b). The formulas were arranged in descending order of the percentage of eyes within ±0.50 D. MFS, Marfan syndrome; PE, prediction error; BUII, Barrett Universal II formula; EVO, Emmetropia Verifying Optical formula.
Stacked histogram showing the percentage of eyes within a given diopter range of PE in the non-MFS subgroup (a) and the MFS subgroup (b). The formulas were arranged in descending order of the percentage of eyes within ±0.50 D. MFS, Marfan syndrome; PE, prediction error; BUII, Barrett Universal II formula; EVO, Emmetropia Verifying Optical formula.
As shown in Table 2, BUII formula displayed the highest IOL FPI values, followed by Kane and EVO in the non-MFS subgroup. In the MFS subgroup, the highest FPI was achieved by Kane, BUII and Hoffer Q formulas.
Subgroup Analysis according to ACD
To investigate the accuracy of IOL formulas in relation to preoperative ACD in MSP patients, we divided the patients into three subgroups of shallow ACD (≤3.00 mm, n = 27), regular ACD (3.01–3.49 mm, n = 8), and deep ACD (≥3.50 mm, n = 7). Table 3 showed the refractive outcomes for the three ACD subgroups of seven formulas ranked by FPI. For the ACD of 3.00 mm or less subgroup, there were the significant differences in PE (p < 0.001) between 7 formulas. Meanwhile, statistically significant differences in the ±0.25 D range of PE (p = 0.031) were identified between 7 formulas and Kane performed better than Haigis (adjusted p = 0.021). In the ACD of 3.01–3.49 mm subgroup, we found significant differences in PE (p < 0.001), while no significant differences in the percentages of eyes within different diopter ranges were detected between formulas (p > 0.05). The post hoc comparison with Bonferroni correction are shown in Figure 4a and b. In the ACD of 3.50 mm or more group, the Holladay 1 displayed the lowest MAE and MedAE, and the highest percentage of cases within ±0.25 D, ±0.50 D, ±0.75 D, and ±1.00 D. However, there were no statistically significant differences among formulas in all variables. As shown in Figure 4c, the Kane had the lowest mean absolute PE for eyes with the shallow ACD. In the regular ACD subgroup, the EVO generated the lowest mean absolute PE. In eyes with deep ACD subgroup, the Hoffer Q had the lowest mean absolute PE and Haigis had the greatest. In addition, the variation in PE produced by each formula for ACD is presented with smoothed line graphs in Figure 4d.
Comparison of formulas according to the preoperative anterior chamber depth in MSP eyes
Formulas . | FPI . | PE . | Absolute PE . | Percentage of eyes within diopter range indicated . | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
mean . | SD . | range . | mean . | SD . | median . | range . | ±0.25 . | ±0.50 . | ±0.75 . | ±1.00 . | ||
ACD ≤3.00 (N = 27) | ||||||||||||
Kane | 0.2355 | −0.0397 | 0.9203 | (−2.73, 1.12) | 0.6587 | 0.6298 | 0.5400 | (0.02, 2.73) | 40.00% | 48.00% | 60.00% | 80.00% |
BUII | 0.2253 | 0.2107 | 0.9940 | (−2.37, 2.00) | 0.7673 | 0.6502 | 0.5900 | (0.03, 2.37) | 25.93% | 48.15% | 55.56% | 70.37% |
EVO | 0.2142 | 0.3718 | 0.9356 | (−1.90, 1.97) | 0.8288 | 0.5527 | 0.7850 | (0.07, 1.97) | 14.81% | 40.74% | 48.15% | 62.96% |
Haigis | 0.2075 | −0.0608 | 0.9470 | (−2.17, 1.93) | 0.7369 | 0.5803 | 0.5000 | (0.01, 2.17) | 7.41% | 51.85% | 70.37% | 70.37% |
SRK/T | 0.1844 | 0.1262 | 1.1053 | (−3.67, 1.52) | 0.8121 | 0.7439 | 0.6700 | (0.04, 3.67) | 18.52% | 37.04% | 59.26% | 74.07% |
Hoffer Q | 0.1441 | −0.1690 | 1.0585 | (−2.68, 1.45) | 0.8377 | 0.6491 | 0.5900 | (0.02, 2.68) | 11.11% | 33.33% | 55.56% | 74.07% |
Holladay 1 | 0.1427 | 0.0641 | 1.1049 | (−3.20, 1.64) | 0.8351 | 0.7069 | 0.6850 | (0.01, 3.20) | 22.22% | 33.33% | 55.56% | 66.67% |
3.00 < ACD < 3.50 (N = 8) | ||||||||||||
EVO | 0.2108 | −0.0738 | 1.1794 | (−1.79, 1.79) | 0.8913 | 0.6995 | 0.7750 | (0.21, 1.79) | 12.50% | 50.00% | 50.00% | 50.00% |
SRK/T | 0.1833 | 0.2963 | 1.1884 | (−1.53, 2.13) | 0.8838 | 0.7874 | 0.7250 | (0.02, 2.13) | 37.50% | 37.50% | 50.00% | 62.50% |
BUII | 0.1787 | −0.2838 | 1.1277 | (−1.82, 1.60) | 0.8738 | 0.7009 | 0.8900 | (0.06, 1.82) | 37.50% | 37.50% | 37.50% | 50.00% |
Kane | 0.1654 | −0.3225 | 1.1404 | (−2.07, 1.38) | 0.9250 | 0.6644 | 0.9950 | (0.11, 2.07) | 12.50% | 37.50% | 37.50% | 50.00% |
Haigis | 0.1183 | −0.4425 | 1.2667 | (−2.08, 1.28) | 1.1525 | 0.5571 | 1.0600 | (0.42, 2.08) | 12.50% | 25.00% | 25.00% | 37.50% |
Holladay 1 | 0.1165 | 0.2425 | 1.3322 | (−1.81, 2.19) | 1.0275 | 0.7972 | 0.9350 | (0.11, 2.19) | 25.00% | 25.00% | 50.00% | 50.00% |
Hoffer Q | 0.0785 | −0.1838 | 1.3325 | (−2.05, 1.76) | 1.1263 | 0.6037 | 1.0250 | (0.17, 2.05) | 25.00% | 37.50% | 50.00% | 75.00% |
ACD ≥3.50 (N = 7) | ||||||||||||
Holladay 1 | 0.2184 | 0.1064 | 0.7680 | (−0.99, 1.38) | 0.5779 | 0.4620 | 0.4350 | (0.07, 1.38) | 28.57% | 57.14% | 71.43% | 85.71% |
SRK/T | 0.1628 | −0.2093 | 0.9250 | (−1.36, 0.92) | 0.7821 | 0.4394 | 0.6750 | (0.27, 1.36) | 0.00% | 28.57% | 57.14% | 71.43% |
Kane | 0.1400 | −0.3293 | 0.9652 | (−1.80, 1.35) | 0.7307 | 0.6597 | 0.6450 | (0.05, 1.80) | 28.57% | 42.86% | 57.14% | 71.43% |
Hoffer Q | 0.1292 | −0.0607 | 1.1106 | (−1.27, 2.14) | 0.7979 | 0.7037 | 0.4550 | (0.19, 2.14) | 28.57% | 42.86% | 57.14% | 71.43% |
BUII | 0.1128 | −0.0979 | 1.0410 | (−1.61, 1.67) | 0.7679 | 0.6380 | 0.5800 | (0.10, 1.67) | 28.57% | 28.57% | 71.43% | 71.43% |
EVO | 0.0840 | −0.3150 | 0.9910 | (−1.82, 1.18) | 0.8221 | 0.5561 | 0.7250 | (0.06, 1.82) | 14.29% | 14.29% | 57.14% | 71.43% |
Haigis | 0.0741 | −0.3479 | 1.1962 | (−1.70, 1.94) | 1.0250 | 0.5885 | 0.8750 | (0.44, 1.94) | 0.00% | 14.29% | 42.86% | 57.14% |
Formulas . | FPI . | PE . | Absolute PE . | Percentage of eyes within diopter range indicated . | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
mean . | SD . | range . | mean . | SD . | median . | range . | ±0.25 . | ±0.50 . | ±0.75 . | ±1.00 . | ||
ACD ≤3.00 (N = 27) | ||||||||||||
Kane | 0.2355 | −0.0397 | 0.9203 | (−2.73, 1.12) | 0.6587 | 0.6298 | 0.5400 | (0.02, 2.73) | 40.00% | 48.00% | 60.00% | 80.00% |
BUII | 0.2253 | 0.2107 | 0.9940 | (−2.37, 2.00) | 0.7673 | 0.6502 | 0.5900 | (0.03, 2.37) | 25.93% | 48.15% | 55.56% | 70.37% |
EVO | 0.2142 | 0.3718 | 0.9356 | (−1.90, 1.97) | 0.8288 | 0.5527 | 0.7850 | (0.07, 1.97) | 14.81% | 40.74% | 48.15% | 62.96% |
Haigis | 0.2075 | −0.0608 | 0.9470 | (−2.17, 1.93) | 0.7369 | 0.5803 | 0.5000 | (0.01, 2.17) | 7.41% | 51.85% | 70.37% | 70.37% |
SRK/T | 0.1844 | 0.1262 | 1.1053 | (−3.67, 1.52) | 0.8121 | 0.7439 | 0.6700 | (0.04, 3.67) | 18.52% | 37.04% | 59.26% | 74.07% |
Hoffer Q | 0.1441 | −0.1690 | 1.0585 | (−2.68, 1.45) | 0.8377 | 0.6491 | 0.5900 | (0.02, 2.68) | 11.11% | 33.33% | 55.56% | 74.07% |
Holladay 1 | 0.1427 | 0.0641 | 1.1049 | (−3.20, 1.64) | 0.8351 | 0.7069 | 0.6850 | (0.01, 3.20) | 22.22% | 33.33% | 55.56% | 66.67% |
3.00 < ACD < 3.50 (N = 8) | ||||||||||||
EVO | 0.2108 | −0.0738 | 1.1794 | (−1.79, 1.79) | 0.8913 | 0.6995 | 0.7750 | (0.21, 1.79) | 12.50% | 50.00% | 50.00% | 50.00% |
SRK/T | 0.1833 | 0.2963 | 1.1884 | (−1.53, 2.13) | 0.8838 | 0.7874 | 0.7250 | (0.02, 2.13) | 37.50% | 37.50% | 50.00% | 62.50% |
BUII | 0.1787 | −0.2838 | 1.1277 | (−1.82, 1.60) | 0.8738 | 0.7009 | 0.8900 | (0.06, 1.82) | 37.50% | 37.50% | 37.50% | 50.00% |
Kane | 0.1654 | −0.3225 | 1.1404 | (−2.07, 1.38) | 0.9250 | 0.6644 | 0.9950 | (0.11, 2.07) | 12.50% | 37.50% | 37.50% | 50.00% |
Haigis | 0.1183 | −0.4425 | 1.2667 | (−2.08, 1.28) | 1.1525 | 0.5571 | 1.0600 | (0.42, 2.08) | 12.50% | 25.00% | 25.00% | 37.50% |
Holladay 1 | 0.1165 | 0.2425 | 1.3322 | (−1.81, 2.19) | 1.0275 | 0.7972 | 0.9350 | (0.11, 2.19) | 25.00% | 25.00% | 50.00% | 50.00% |
Hoffer Q | 0.0785 | −0.1838 | 1.3325 | (−2.05, 1.76) | 1.1263 | 0.6037 | 1.0250 | (0.17, 2.05) | 25.00% | 37.50% | 50.00% | 75.00% |
ACD ≥3.50 (N = 7) | ||||||||||||
Holladay 1 | 0.2184 | 0.1064 | 0.7680 | (−0.99, 1.38) | 0.5779 | 0.4620 | 0.4350 | (0.07, 1.38) | 28.57% | 57.14% | 71.43% | 85.71% |
SRK/T | 0.1628 | −0.2093 | 0.9250 | (−1.36, 0.92) | 0.7821 | 0.4394 | 0.6750 | (0.27, 1.36) | 0.00% | 28.57% | 57.14% | 71.43% |
Kane | 0.1400 | −0.3293 | 0.9652 | (−1.80, 1.35) | 0.7307 | 0.6597 | 0.6450 | (0.05, 1.80) | 28.57% | 42.86% | 57.14% | 71.43% |
Hoffer Q | 0.1292 | −0.0607 | 1.1106 | (−1.27, 2.14) | 0.7979 | 0.7037 | 0.4550 | (0.19, 2.14) | 28.57% | 42.86% | 57.14% | 71.43% |
BUII | 0.1128 | −0.0979 | 1.0410 | (−1.61, 1.67) | 0.7679 | 0.6380 | 0.5800 | (0.10, 1.67) | 28.57% | 28.57% | 71.43% | 71.43% |
EVO | 0.0840 | −0.3150 | 0.9910 | (−1.82, 1.18) | 0.8221 | 0.5561 | 0.7250 | (0.06, 1.82) | 14.29% | 14.29% | 57.14% | 71.43% |
Haigis | 0.0741 | −0.3479 | 1.1962 | (−1.70, 1.94) | 1.0250 | 0.5885 | 0.8750 | (0.44, 1.94) | 0.00% | 14.29% | 42.86% | 57.14% |
MSP, microspherophakia; ACD, anterior chamber depth; FPI, formula performance index; SD, standard deviation; BUII, Barrett Universal II; EVO, Emmetropia Verifying Optical.
Comparisons of predictive capabilities of seven formulas in the (a) shallow ACD (≤3.00 mm) and (b) regular ACD (3.01–3.49 mm). p values indicated by related-samples Friedman’s two-way analysis of variance with Bonferroni correction. The red lines indicated p < 0.001; the blue lines indicated p < 0.05 while the gray dotted lines indicated p > 0.050. c Mean PE (in diopters) of each formula, distributed by ACD subgroups, listed by alphabetic order. d Smoothed line graph of PE (in diopters) of the 7 formulas versus ACD. ACD, anterior chamber depth; D, diopters; BUII, Barrett Universal II formula; EVO, Emmetropia Verifying Optical formula.
Comparisons of predictive capabilities of seven formulas in the (a) shallow ACD (≤3.00 mm) and (b) regular ACD (3.01–3.49 mm). p values indicated by related-samples Friedman’s two-way analysis of variance with Bonferroni correction. The red lines indicated p < 0.001; the blue lines indicated p < 0.05 while the gray dotted lines indicated p > 0.050. c Mean PE (in diopters) of each formula, distributed by ACD subgroups, listed by alphabetic order. d Smoothed line graph of PE (in diopters) of the 7 formulas versus ACD. ACD, anterior chamber depth; D, diopters; BUII, Barrett Universal II formula; EVO, Emmetropia Verifying Optical formula.
Discussion
The calculation of IOL power in CEL patients is challenging due to the inaccurate measurement of ocular parameters including corneal power, ACD and AL. As suggested previously by Zhang et al. [21], Haigis formula had the best predictive capability for young patients with MFS who had undergone MCTR-IOL implantation. In CEL patients with scleral-fixated IOL implantation, SRK/T and EVO formulas showed the best performance [22]. Considering the different biometric parameters of MSP patients from other patients with CEL, it is clinically important to investigate the IOL power calculation methods in order to calculate the IOL power accurately when managing surgery in these cases. To the best of our knowledge, the current study is the first to evaluate the accuracy of new generation and traditional IOL formulas for MSP patients who underwent phacoemulsification combined with transscleral-fixated MCTR-IOL implantation.
In the non-MFS subgroup, the SD of the PE, in order of lowest to highest, was the Kane (1.13), EVO (1.15), BUII (1.20), Haigis (1.26), SRK/T (1.34), Hoffer Q (1.35), and Holladay 1 (1.39). BUII produced the lowest MAE, and the highest percentage of eyes within ±0.50 D range of PE. Of the seven formulas evaluated in this study, the highest percentage of PE within ±0.25 D and ±1.00 D was obtained by Kane. Considering the FPI, the most accurate prediction might be achieved by BUII (0.20), closely followed by Kane (0.20) and EVO (0.18). In the MFS subgroup, the lowest MedAE and the highest percentage of eyes within ±0.50 D range of PE were achieved by Kane, followed by the BUII. The BUII formula had the highest percentage of eyes within PE of ±0.25 D, and Hoffer Q, Holladay 1 within PE of ±1.00 D. Based on the FPI values from highest to lowest, Kane performed superiorly, and BUII took the second place. These findings suggested that good results in MSP patients could be achieved using artificial intelligence-based formulas (Kane), and the other new generation formulas (BUII and EVO). These findings were in agreement with the conclusions of Stopyra et al. [23] demonstrating that BUII among vergence formulas and Kane among artificial intelligence-based formulas are currently most often reported as the most precise in routine cataract surgery.
According to the comparison on the preoperative biometric parameters between the two subgroups, there were significant shallower ACD, steeper corneal curvature and lower corneal astigmatism in MSP patients without MFS compared with MSP patients with MFS. Similar conclusions were also reported by the existing case reports that isolated MSP patients were characterized by relatively shorter AL, shallower ACD, steeper corneal curvature and thicker LT compared to CEL patients with MFS [24]. This possibly led to the differences in the accuracy of prediction by different IOL formulas between two subgroups. Preoperative ACD, as one of the significant predictors of ELP has a great effect on the accuracy of the IOL power calculation in MSP patients [25]. In eyes with shallow anterior chamber resulted from the lens-related factors which can be eliminated after crystalline lens removal, the postoperative ACD deepened due to the backward shift of the iris and the relief of potential pupillary block, achieving virtually the same as ordinary eyes [26]. Therefore, as preoperative ACD decreased, the ELP predicted by the formulas reduced, resulting in the tendency of hyperopic surprise postoperatively [27]. Similar results were found in the present study (Fig. 4d) that the median PE was positive using all formulas except Hoffer Q in eyes with shallow ACD less than 3.00 mm. A subgroup analysis of eyes in the category of ACD was further performed to investigate the accuracy of IOL formulas in MSP eyes with different ACD. In eyes with shallow ACD ≤3.00 mm, Kane had the lowest SD values, MAE and MedAE, and the highest percentage of eyes within ± 0.25 D and ± 1.00 D. The highest FPI was achieved by Kane, followed by BUII and EVO, suggesting that the new generation formulas provided good performance in MSP patients with shallow ACD. This result was consistent with that previously reported by Diogo et al. [28] and Gökce et al. [25] who found that new generation formulas including Kane, EVO, and BUII tended to have better and more stable performances than traditional formulas in eyes with shallow ACD.
In the subgroup of regular ACD, the EVO provided the highest prediction accuracy concerning the highest FPI and the percentage of cases within the ±0.50 D range of PE (0.21, 50.00%), and SRK/T took the second place (0.18, 37.50%). In addition, BUII had the lowest SD values (1.13 D), MAE (0.87 D), and the highest percentage of PE within ±0.25 D (37.50%). Regarding the deep ACD subgroup, Holladay 1 performed superiorly presenting the lowest SD values (0.77 D), MAE (0.58 D), MedAE (0.44 D), and the highest percentage of eyes within ±0.50 D (57.14%). The Haigis formula displayed the lowest percentages of eyes within different diopter ranges of PE and the highest SD values (1.20 D) and MAE (1.03 D), indicating that the Haigis was less accurate than other formulas in predicting the IOL power in MSP patients with deep ACD. In addition, PEs of the Haigis and EVO seem to be more affected by variation in preoperative ACD compared to the third-generation formulas of Hoffer Q, Holladay 1, and SRK/T and fourth-generation formulas of BUII, similarly to the results of Lian et al. [22] in eyes with CEL. Overall, the BUII and Kane appeared to have the less bias than the other formulas as measured by PE with variations in anterior chamber depth. Notably, these results were contrary to the conclusion of Yang et al. [29] who reported that Haigis was more preferable than the other traditional formulas in eyes with ACD ≥3.50 mm and Melles et al. [30] who suggested that the Haigis formula showed little deviation in PE with varying anterior chamber depth. This may be because the deepening of ACD was caused by the posterior dislocation of the lens owing to the extensive relaxation of the zonular fibers, which could be corrected after surgery in MSP patients. Therefore, the formulas that consider preoperative ACD into the prediction of ELP may be more inaccurate in MSP patients with deep ACD.
In addition to ACD, ELP errors across surgical procedure for MSP patients stem from the IOL position (tilt and decentration) as well as the sutured location. IOL decentration is the potential complication that can affect the accuracy of IOL power calculations and refractive outcomes [31, 32]. Sandhu et al. [33] reported that 7 eyes (17%) required secondary surgery due to decentration of the MCTR-capsular bag-IOL complex in eyes with subluxated lenses, highlighting the challenges of IOL positioning in this patient population. In contrast, Chen et al. found no instances of decentration requiring additional surgical intervention in patients with ectopia lentis who underwent the MCTR procedure [34]. Similarly, none of the MSP cases in our study exhibited intervention-required IOL decentration. However, it should be noted that our study did not specifically measure IOL decentration, and future research should consider assessing this aspect more comprehensively. Additionally, the effects resulting from sutures and endocapsular support devices, such as MCTRs, introduce additional challenges in predicting the ELP, primarily due to inherent weakness of capsular support [21]. To minimize the uncertainty in ELP caused by the variable suture site, an experienced surgeon in our study applied a precise suturing technique, positioning the sutures 2 mm posterior to the limbus. Moreover, in the MCTR groups, the position of IOL is constrained by the remaining zonules, capsule, and vitreous body, which makes the ELP less sensitive to variations in suture location. Although transscleral fixation of the IOL has been adapted for MSP patients in most cases, this technique has shown a wider distribution of ELP and greater ELP errors compared to in-the-bag IOL implantation [35]. Van Os et al. [36] introduced a novel approach, the bag-in-the-lens implantation technique, for pediatric patients with ectopia lentis. This technique improves IOL centration and provides a stable lens position, offering an effective alternative for managing IOL implantation in these challenging cases. The bag-in-the-lens technique helps preserve the natural ELP, which may improve refractive outcomes and reduce the need for secondary interventions. Nevertheless, further studies are required to refine and improve ELP prediction in MSP patients.
There were some limitations in this study. First, as to be expected in the context of rare diseases, we included both eyes with MSP owing to the small number of MSP patients in the whole population. However, to address the interdependence between paired eyes within individuals, a regression analysis employing generalized estimating equations was executed. Second, the difference between formulas was not statistically significant, making it difficult to make inferences about IOL power formula accuracy for MSP eyes based on this study. Therefore, we have introduced FPI when comparing the accuracy between formulas to make the results more reliable in this study. Additionally, corneal incision was closed with 10-0 nylon sutures, which could induce a remarkable astigmatism and affect IOL power calculation accuracy.
Conclusions
In conclusion, BUII performed superiorly in terms of FPI values, followed by EVO and Kane in MSP patients without MFS, and similar results were obtained in eyes with an ACD that is less than 3.00 mm. In MSP patients with MFS, Kane achieved the best accuracy regarding the lowest MedAE and the largest percentage of PE in the range of ±0.50 D among seven formulas, and BUII provided comparable outcomes. Our results suggested that new generation formulas (BUII, Kane, and EVO) were recommended in MSP patients compared to traditional formulas (SRK/T, Holladay 1, Hoffer Q, and Haigis). The EVO were the most accurate formulas in eyes with regular ACD. When dealing with MSP eyes with ACD more than 3.50 mm, Hollday 1 performed the best, SRK/T, and Kane achieved satisfying performance, while Haigis was not recommended.
Statement of Ethics
This study protocol was reviewed and approved by the Human Research Ethics Committee of Eye and ENT Hospital of Fudan University, Approval No. 2020126-1. This study adhered to the tenets of the Declaration of Helsinki and served as an extension of our randomized controlled trial, registered with the China Clinical Trial Registry (identifier: ChiCTR2000039132). All patients were informed about the study in detail and written informed consent has been obtained from all adult participants and from the parents/legal guardians/next of kin of all underage participants.
Conflict of Interest Statement
The authors have no conflicts of interest to declare.
Funding Sources
This study was funded by the Shanghai Science and Technology Commission (Scientific Innovation Project, Grant No. 22Y11910400) and the National Natural Science Foundation of China (Grant No. 82271068).
Author Contributions
Yang Sun and Tianhui Chen contributed equally to this work. Yang Sun: formal analysis; writing – original draft; and validation. Tianhui Chen: methodology; formal analysis; and writing – review and editing. Zexu Chen: software and formal analysis. Wannan Jia: data curation and investigation. Zhennan Zhao: conceptualization; investigation; and writing – review and editing. Yongxiang Jiang: conceptualization; supervision; project administration; and funding acquisition.
Additional Information
Yang Sun and Tianhui Chen contributed equally as co-first authors.
Data Availability Statement
The datasets generated or analyzed during the current study are included in this article. Further inquiries can be directed to the corresponding author (Yongxiang Jiang, [email protected]).