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Abstract

Intraocular lens power calculation methods are categorized as thin lens and thick lens (paraxial and full aperture, respectively). The Olsen formula is a paraxial thick-lens method. Effective lens position, the distance between the theoretical planes of the cornea and the IOL, is used by the thin-lens method; measurable pseudophakic ACD is used by the thick-lens method. The reasons that ELP and ACD prediction algorithms can be used interchangeably (with optimization) are based on the following facts. First, both thin-lens and paraxial thick-lens methods are based on Gaussian optics; therefore, a paraxial thick lens can be simplified as a thin lens approximation. The theoretical position (ELP) and the actual position (ACD) of the IOL can be converted to each other.1 Second, ELP can be back-calculated (ELPback) using postoperative refraction, vertex distance, axial length, corneal power, and power of the implanted IOL. As the measuring errors of these parameters cannot be avoided, the error of ELPback is unavoidable. Using ELPback as the benchmark to perform formula optimization and develop IOL position prediction algorithms cannot avoid introducing errors; fewer errors are introduced using measurable pseudophakic ACD. Therefore, deriving ELP algorithms using measurable ACD is advocated. This approach, which has been proven reliable, is applied by modern thin-lens formulas.2–4 In our study, lens thickness was obtained using ultrasound A-scan. Previous publications have shown that ACD values measured by different devices are in relatively high correlation,5,6 indicating that with calibration or formula optimization these devices can be used interchangeably. We agree that regression algorithms for the prediction of IOL position function best if the clinical setup is a copy of the setup from which they were derived; however, if there are relatively high correlations among the results measured by different instruments, the algorithms will work best after optimization. Corneal radius measured by Scheimpflug imaging (Pentacam) and the IOLMaster were compared for our cases. The correlation between the 2 instruments in our study was lower than that in our large-sample research (n = 52, r2 = 0.85, P<.001 and n = 250, r2 = 0.97, P<.001). Using corneal power measured by the IOLMaster, MAEs were 0.45 diopter (D) ± 0.57 (SD) (Hoffer Q), 0.41 ± 0.35 D (Haigis), 0.41 ± 0.58 D (Norrby), and 0.41 ± 0.36 D (Olsen), indicating that higher MAEs were induced by the Pentacam in corneal radius measurements. The reason might be related to poor tear film and poor fixation because of old age and poor preoperative visual acuity. Nevertheless, our purpose was not to compare the algorithms and the accuracies of different instruments, but to address the relationship between thin-lens and thick-lens methods and to compare thin-lens and thick-lens methods using the matched devices and algorithms. We agree that incorrect prediction of IOL position is the major source of error in IOL power calculation, which was emphasized in our publication.