Calculation of the total corneal astigmatism using the virtual cross cylinder method on the secondary principal plane of the cornea.

This study aimed to establish a virtual cross cylinder method to calculate the total corneal astigmatism by combining the anterior and posterior corneal astigmatism on the secondary principal plane of the cornea based on Gaussian optics. The meridian with the least refractive power, namely, the flattest meridian of the virtual cross cylinder of a ± 0.5 × C diopter, is set as the reference meridian, and the power (F) at an angle of φ between an arbitrary meridian and the reference meridian is defined as F(φ) = - 0.5 × C × cos2φ. The magnitude and axis of the total corneal astigmatism were calculated by applying trigonometric functions and the atan2 function based on the combination of the virtual cross cylinders of the anterior corneal astigmatism and the posterior corneal astigmatism. To verify the performance of the virtual cross cylinder method, a verification experiment with two Jackson cross cylinders and a lensmeter was performed, and the measured and calculated values were compared. The limit of the natural domain of the arctangent function is circumvented by using the atan2 function. The magnitude and axis of the total corneal astigmatism are determined through generalized mathematical expressions. The verification experiment results showed good agreement between the measured and calculated values. Compared to the vector analysis method, the virtual cross cylinder method is mathematically sound and straightforward. A novel technique for calculating total corneal astigmatism, the virtual cross cylinder method, was developed and verified.

Modification of the Barrett Universal II formula by the combination of the actual total corneal power and virtual axial length.

PURPOSE: This study aims to investigate whether a combination of the total corneal power (TCP) and virtual axial length (AL) based on Gaussian optics makes the refractive prediction accuracy of the Barrett Universal II (BUII) formula better than the conventional anterior keratometry (K) and axial length. METHODS: The TCP and the virtual AL were calculated in two ways: the corneal index strategy and the TK index strategy. The former uses the corneal refractive index n1 as a variable, and the latter uses the TK index nx as a variable. In a dataset of 225 eyes, the calculated TCP and the virtual AL were input into the BUII formula along with the anterior chamber depth, lens thickness, and white-to-white measured with the IOLMaster 700, and the refractive prediction accuracy was evaluated by the mean numerical prediction error (MNE), standard deviation (SD), mean absolute prediction error (MAE), median absolute prediction error (MedAE), percentages of eyes with prediction error (PE) within ± 0.50 diopter, and IOL formula performance index (FPI). The refractive prediction outcomes also underwent subgroup analyses and were compared with those of the anterior keratometry-based BUII-K of the IOLMaster 700. RESULTS: In the corneal index strategy, the FPI had the highest value at approximately n1 = 1.346. In the TK index strategy, the FPI had the highest value at approximately nx = 1.3858. There was no tendency for the refractive prediction outcomes of the BUII-n1 = 1.346 and the BUII-nx = 1.3858 to be inferior to those of the BUII-K, particularly in the medium range of subgroups. CONCLUSION: The combination of the actual TCP and the virtual AL based on Gaussian optics may lead to a better refractive prediction accuracy of the BUII formula than that of BUII-K.

Lower refractive prediction accuracy of total keratometry using intraocular lens formulas loaded onto a swept-source optical biometer.

PURPOSE: To compare refractive outcomes calculated using intraocular lens (IOL) power calculation formulas loaded onto the IOLMaster 700 with the employment of anterior keratometry (K) and total keratometry (TK). METHODS: A total of 225 eyes of 225 patients underwent uneventful cataract surgery and implantation of a single model of nontoric monofocal IOL by a single surgeon. All eyes underwent preoperative ocular biometric measurements with the IOLMaster 700. Refractive outcomes, including the mean numerical prediction error (MNE); standard deviation (SD); adjusted mean absolute prediction error (MAE); adjusted median absolute prediction error (MedAE); percentages of eyes with adjusted prediction error (PE) within ± 0.25, ± 0.50, ± 0.75, and ± 1.00 diopter; and IOL Formula Performance Index (FPI), were compared between the K-based formula and the TK-based formula of Barrett Universal II (BUII), Haigis, SRK/T, Holladay 2, and Hoffer Q. Axial length (short, medium, and long) subgroup analyses and anterior and posterior keratometry (flat, medium, and steep) subgroup analyses were conducted. RESULTS: The K-based formula performed better than the TK-based formula in the accuracy of refractive prediction of each IOL calculation formula: BUII-K (FPI 0.690), BUII-TK (0.677), Haigis-K (0.617), Haigis-TK (0.584), SRK/T-K (0.608), SRK/T-TK (0.595), Holladay 2-K (0.419), Holladay 2-TK (0.406), Hoffer Q-K (0.364), and Hoffer Q-TK (0.356). The subgroup analyses of refractive prediction outcomes showed that TK influenced the refractive outcomes in eyes with relatively normal ranges of axial length and anterior keratometry. CONCLUSIONS: Using TK instead of K leads to lower refractive prediction accuracy of the IOL power calculation formulas loaded on the IOLMaster 700.

The role of calcium in mucin packaging within goblet cells.

Recent reports hypothesize that calcium plays an important role in providing cationic shielding to keep negatively charged mucins condensed and tightly packed within mucus granules of goblet cells. Vitamin D controls mineral ion homeostasis and intestinal calcium absorption, which is mediated by the nuclear vitamin D receptor (VDR). Hypocalcemia is observed in mice in which the VDR has been ablated. The purpose of this study was to test the hypothesis that normal levels of calcium are required for the physiological packaging of mucins, by comparing the morphology and mucin extractability of conjunctival goblet cells of VDR-ablated to wild-type control mice. Whole eyes from C57/129/sv hybrid wild-type, VDR-ablated, and VDR-ablated mice fed a diet high in calcium to normalize serum ionized calcium levels were fixed in situ and processed for light and transmission electron microscopy (TEM). Mucin extractability from sections of mouse eyes was assessed by lectin-blot, using helix pomatia agglutinin (HPA), and mucin content within goblet cells was assessed by immunohistochemistry, using an antibody specific to the goblet cell mucin Muc5AC. Altered mucin packaging in the goblet cells of VDR-ablated mice as compared to control mice was observed by both light and electron microscopy. In the VDR-ablated mice, the mucin packets varied in size and staining. In contrast, in the controls, the secretory granules appeared regular and uniform. By TEM, mucin packets in the VDR-ablated mice showed dispersed fibrillar and less electron-dense material compared to the homogeneous and more electron-dense packets in wild type. The appearance of mucin packets in the VDR-ablated mice with restored calcium levels was comparable to those of the wild-type control mice. HPA binding to mucin extracted from sections of VDR mouse eyes was reduced when compared to that from wild type. By immunohistochemistry, there was markedly less binding of the antibody to the mucin Muc5AC to goblet cells of VDR-ablated mice compared to controls.VDR-ablated mice presented altered conjunctival mucin packaging. There were lower levels of extractable and immunohistochemically localizable mucin in VDR-ablated mouse conjunctivas than in the wild-type controls. Restoration of ionized calcium levels in the VDR-ablated mice prevented altered mucin packaging, supporting the hypothesis that calcium is required for the physiological packaging of mucins in goblet cells.

Specific transduction of the leading edge cells of migrating epithelia demonstrates that they are replaced during healing.

As wounds in stratified epithelia close, the numbers of cells at the leading edge of migration decreases. It is not known whether cells at the leading edge are continually replaced or whether some retain their position at the leading edge over time. Replication-deficient adenovirus carrying the green fluorescent protein gene was applied to corneal epithelial wounds in mice and it was found that they primarily infect the leading edge cells of healing epithelium. Eighteen hr after viral transduction, green fluorescent protein expressing cells were located in the apical layer at varying distances behind the leading edge. These data indicate that leading edge cells are replaced during healing of stratified epithelia.