Assessment and statistics of surgically induced astigmatism

Refractive Astigmatism Outcomes of Femtosecond Laser-Assisted Arcuate Keratotomies Combined with Femtosecond Laser-Assisted Cataract Surgery: Two-Year Results

PURPOSE

To evaluate the effectiveness and stability of refractive astigmatism reduction after penetrating femtosecond laser-assisted arcuate keratotomy performed at the time of femtosecond laser-assisted cataract surgery.

METHODS

Non-randomized retrospective data analysis of all patients that underwent femtosecond laser-assisted cataract surgery with femtosecond laser-assisted arcuate keratotomy over a 4-year period with a non-toric monofocal intraocular lens (2017-2021) at a tertiary care academic center. Postoperative visual acuity, manifest refraction, and predicted residual refractive error were also recorded at 1 month, 3-6 months, 12-18 months, and 2 years postoperatively. Preoperative keratometric astigmatism was compared to postoperative refractive astigmatism using vector calculations and the ASCRS double-angle plot tool.

RESULTS

This study comprised 266 eyes (179 patients) that met inclusion criteria. The mean preoperative keratometric astigmatism magnitude was 0.99 ± 0.53 D. At 1 month, 3-6 months, 12-18 months, and 2 years postoperatively, the mean refractive cylinder was 0.49 ± 0.45 D, 0.49 ± 0.45 D, 0.55 ± 0.54 D, and 0.52 ± 0.46 D, respectively. Horizontal against-the-rule astigmatism showed a higher tendency toward undercorrection than vertical with-the-rule astigmatism, which had a slightly higher tendency toward overcorrection. With-the-rule astigmatism had smaller difference vectors between target-induced astigmatism and surgically induced astigmatism.

CONCLUSIONS

Femtosecond laser-assisted arcuate keratotomy performed at the time of femtosecond laser-assisted cataract surgery was an effective option for correcting low-to-moderate corneal astigmatism for up to 2 years.

Meridional analysis for calculation of the toric power of phakic IOLs

PURPOSE

To present a reproducible method to calculate the toricity needed at the intraocular lens (IOL) plane with toric phakic IOLs (ICL, Staar Surgical) and compare its results with those obtained with the online calculator provided by the manufacturer.

DESIGN

Retrospective case series.

SETTING

Private practice, Buenos Aires, Argentina.

METHODS

The formula originally described by Holladay to calculate the IOL power in phakic eyes was used to calculate the required spherical power along the less refractive meridian and along the more refractive meridian. Meridional analysis was applied to calculate the required toricity at the IOL plane and the surgically induced corneal astigmatism was incorporated into the calculations. The refractive cylinder predicted by this method and by the online calculator of the manufacturer were compared to the postoperative refractive cylinder by means of vector analysis. The possible changes in the ratio of toricity in patients with different amounts of astigmatism and anterior chamber depth are assessed in a theoretical section.

RESULTS

In 35 eyes, the measured mean postoperative refractive cylinder was 0.09 D @ 99°, the mean predicted postoperative refractive astigmatism was 0.04 D @ 102° according to the manufacturer's online calculator and 0.09 D @100° according to our method. With both methods, 91.43% of eyes had an absolute cylinder prediction error within ±0.50 diopters.

CONCLUSIONS

The method described in this article to calculate the toricity of phakic IOLs has a refractive accuracy similar to that of the original calculator developed by the manufacturer.

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.

Characteristics of surgically induced astigmatism after standardized microincisional cataract surgery with a superior limbal incision

PURPOSE

To determine (1) if measurements of surgically induced astigmatism (SIA) as measured by keratometry (K) and total keratometry (TK) differ (2) if SIA affects the magnitude and/or meridian of keratometric astigmatism (3) if SIA evolves over time.

SETTING

Tertiary care center.

DESIGN

Retrospective data analysis.

METHODS

A swept-source optical coherence tomography biometry dataset (IOLMaster700) consisting of 498 eyes (327 patients) from a tertiary care center was analyzed. For all eyes preoperative and postoperative biometric measurements at 1-month, 3-month, and 6-months postoperative visits were considered for vector analysis of SIA K and SIA TK .

RESULTS

Centroids in right and left eyes were 0.26 diopters (D) @5 degrees/0.31 D @1 degree for SIA K and 0.27 D @4 degrees/0.34 D @1 degree for SIA TK . Centroids for difference vectors K-TK in right and left eyes were 0.02 D @ 176 degrees/0.03 D @6 degrees. The mean SIA magnitudes in right and left eyes were 0.48 ± 0.41 D and 0.50 ± 0.37 D for SIA K and 0.53 ± 0.42 D and 0.54 ± 0.40 D for SIA TK . In eyes with ATR astigmatism, an increase in postoperative astigmatism magnitude was more common than a decrease. More than 30% of eyes showed changes in the meridian of more than 15 degrees.

CONCLUSIONS

Overall, we observed differences in K- and TK-derived SIA, and changes in SIA magnitude over time. For postsurgical interventions, postoperative astigmatism meridian values should be measured to base treatments. Astigmatism magnitude showed a tendency to decrease for steep-meridian incisions and to increase in flat-meridian incisions.

Repeatability of new optical biometer and agreement with 2 validated optical biometers, all based on SS-OCT

PURPOSE

To evaluate the repeatability of the measurements provided by a new optical biometer (EyeStar 900) based on swept-source optical coherence tomography (SS-OCT) and their agreement with the measurements given by 2 validated biometers based on the same technology, the IOLMaster 700 and Argos.

SETTING

IRCCS G.B. Bietti Foundation, Rome, Italy.

DESIGN

Prospective evaluation of diagnostic test.

METHODS

In a series of unoperated eyes, 3 consecutive scans were acquired with the EyeStar 900, and 1 with the IOLMaster 700 and the Argos. The following biometry parameters were analyzed: axial length (AL), keratometry (K), corneal astigmatism, central corneal thickness, corneal diameter (CD), anterior chamber depth (ACD), lens thickness (LT), and lens tilting. Repeatability was assessed using test-retest variability, the coefficient of variation (CoV), and the intraclass correlation coefficient (ICC); agreement was based on the 95% limits of agreement.

RESULTS

56 eyes of 56 patients were analyzed. High repeatability was achieved for all measured parameters, as the CoV was <1% in most cases and ICC was >0.95 for all parameters. Good to high agreement was found among the measurements of the 3 optical biometers, although some statistically significant differences were detected between the EyeStar 900 and Argos (mean K, ACD, LT, and CD were higher with the Argos). The Argos measured a shorter AL in eyes >25 mm.

CONCLUSIONS

The new generation SS-OCT EyeStar 900 optical biometer produces highly repeatable measurements that are in good agreement with those provided by 2 previously validated instruments.

Evaluation of Ocular Residual Astigmatism in Eyes with Myopia and Myopic Astigmatism and Its Interaction with Other Forms of Astigmatism

Purpose

To evaluate the prevalence, magnitude, and direction of ocular residual astigmatism (ORA) in eyes with myopia and myopic astigmatism, and its interaction with refractive, anterior corneal, posterior corneal, and true net power astigmatism.

Patients and Methods

Refractive surgery candidates with myopia and myopic astigmatism were studied. Refractive astigmatism (RA) was measured using the Nidek® AR-310A autorefractometer. Anterior corneal astigmatism (ACA), posterior corneal astigmatism (PCA), and true net power astigmatism (TNP) were measured using the Wavelight® Oculyzer II. Astigmatism was converted from polar to vector notation. ORA was calculated by vector subtraction of ACA from RA vertexed to corneal plane. Compensation factor (CF) was calculated as the ratio of ORA that compensates ACA for both J0 and J45.

Results

154 eyes of 88 patients (mean age 31.7±7.1 years) were included. With-the-rule (WTR) astigmatism was the most common for both RA (55.6%) and ACA (74%), while against-the-rule (ATR) was the most common for PCA (87.7%) and ORA (74.0%). The axes of RA and ACA were within 10° of each other in 46.8% of the eyes, and within 30° of each other in 76.0%. The mean difference in value between the axis of RA and ACA was 25.6°. 71.4% of eyes in the study had an ORA ≥ 0.5D, 44.1% had ORA ≥ 0.75D and 26% had ORA ≥ 1D. There was a statistically significant difference between ACA and each of RA and TNP. Using TNP to calculate ORA instead of ACA reduced its magnitude. RA is positively correlated to ACA and more strongly to TNP. The most common pattern of compensation between ORA and ACA was under-compensation for J0 (49%) and same-axis-augmentation for J45 (35%).

Conclusion

ORA, PCA, and the interaction between ORA and ACA can affect results during refractive planning.

Astigmatism analysis and reporting of surgically induced astigmatism and prediction error

PURPOSE

To provide a method for determining the vector that, when added to the preoperative astigmatism, results in no prediction error (PE) and to specify statistical methods for evaluating astigmatism and determining the 95% confidence convex polygon.

SETTING

Baylor College of Medicine, Houston, Texas, and University of Southern California, Los Angeles, California.

DESIGN

Retrospective consecutive case series.

METHODS

An analysis of 3 clinical trials involving toric intraocular lenses was performed. 3 formulas were evaluated (generic vergence formula with zero surgically induced astigmatism, the Barrett toric formula, and the Holladay toric formula). Scalar and vector analyses were performed on each dataset with each formula and the results compared. Since the PE was not a Gaussian distribution, a 95% convex polygon was used to determine the spread of the data.

RESULTS

The mean values for the vector absolute astigmatism PEs were not different for the 3 formulas and 3 datasets. The Barrett and Holladay toric calculators were statistically superior to the zero formula for 3 intervals (0.75, 1.0, and 1.25) in the high astigmatism dataset.

CONCLUSIONS

Residual astigmatism and vector absolute astigmatism PE mean values and SDs are useful but require extremely large datasets to demonstrate a statistical difference, whereas examining percentages in 0.25 diopters (D) steps from 0.25 to 2.0 D reveals differences with far fewer cases using the McNemar test for a P value. Double-angle plots are especially useful to visualize astigmatic vector PEs, and a 95% confidence convex polygon should be used when distributions are not Gaussian.

Precision of the Nidek Tonoref II autokeratometer: how many repeated measurements are required?

PURPOSE

To determine the minimal number of repeated measurements required for precise Nidek Tonoref II autokeratometry.

METHODS

This prospective, non-intervention study was performed at the Department of Ophthalmology, Randers, Denmark. We used the Nidek Tonoref II autokeratometer to perform 10 successive measurements on 100 right eyes of cooperative individuals. Each keratometry was converted to the spherical equivalent power (SE), while the net astigmatism was converted to polar values along zero (KP(0)) and 45 degrees (KP(45)). All units were in dioptres (D). The precision was calculated as the mean absolute difference between paired measurements, using one or the average of two, three, four or five autokeratometries. Statistical assessment was performed with Dunn's test for repeated measurements with a Bonferroni correction.

RESULTS

The precision of SE, KP(0) and KP(45) increased statistically significantly from one to three measurements, with no significant improvement for autokeratometries based on four or five measurements. There was no significant precision difference between one and two measurements.

CONCLUSION

A single keratometry is inadequate, but the vector average of three measurements is sufficient for precise autokeratometry with the Tonoref II device. The consistent use of three keratometries with this device may increase the precision of spherical and toric IOL calculation.

Rethinking the optimal methods for vector analysis of astigmatism

PURPOSE

To evaluate the accuracy and usefulness of certain methods of analyzing astigmatic vectors.

SETTING

Cullen Eye Institute, Baylor College of Medicine, Houston, Texas.

DESIGN

Case samples.

METHODS

Using 2 sample cases for analysis of corneal surgically induced astigmatism and an actual toric intraocular lens (IOL) case, univariate analyses from the ASSORT program were compared to double-angle plots of preoperative and postoperative astigmatism and prediction errors.

RESULTS

Certain univariate figures for analyzing the 2 sample cases were misleading. For the toric IOL case, some of the key outcome vectors were inaccurate.

CONCLUSIONS

ASSORT's univariate analysis of astigmatic vectors can be unpredictably erroneous and misleading. Recommended vector analyses should include double-angle plots with centroids and confidence ellipses of preoperative and postoperative astigmatism and the prediction errors, along with means and standard deviations of these vector magnitudes.

Surgically induced astigmatism made easy: calculating the surgically induced change in sphere and cylinder for corneal incisional, corneal laser, and intraocular lens-based surgery

Net cylinder and spherocylinder formats characterize individual keratometries and prescriptions but must be converted to dioptric vectors to allow for calculations and statistical analyses. Næser's polar value system was specifically developed for the analysis of the surgically induced refractive change along the surgical meridian. This study provides a short description together with a practical manual and a computer program for the use of this dioptric vector method. Measurement techniques, vector equations, statistical methods, and terminology are reviewed. The analysis is identical for corneal and refractive measurements and for corneal incisional, corneal laser, and intraocular lens-based surgery. The choice of appropriate surgical reference meridians for standard surgical procedures is demonstrated. The Excel file may be used by the reader for future studies.

Influence of posterior corneal astigmatism on the outcomes of toric intraocular lens implantation in eyes with oblique astigmatism

PURPOSE

To assess whether the outcomes of toric intraocular lens (IOL) implantation in eyes with oblique astigmatism can be improved by direct measurements of posterior corneal astigmatism using anterior segment optical coherence tomography (AS-OCT) instead of by using anterior corneal measurements alone.

STUDY DESIGN

Retrospective case series.

METHODS

Two toric IOL power calculation methods were compared: anterior corneal astigmatism was used in the keratometry group, whilst total corneal astigmatism determined by ray tracing through the measured anterior and posterior corneal surfaces was used in the AS-OCT group. In a total of 279 eyes of 232 patients, subgroup analysis was conducted for with-the-rule (WTR) (85 eyes in the keratometry group and 34 eyes in the AS-OCT group), against-the-rule (ATR) (73/29 eyes), and oblique (26/32 eyes) astigmatism.

RESULTS

In the WTR and ATR astigmatism groups, the uncorrected distance visual acuity (UDVA) was significantly better in the AS-OCT group than in the keratometry group (P = 0.012 and P < 0.001, Mann-Whitney test), and the residual astigmatism was significantly smaller in the AS-OCT group than in the keratometry group (P = 0.037 and P < 0.001). In eyes with oblique astigmatism, the UDVA (P = 0.299) and residual astigmatism (P = 0.373) of the keratometry and AS-OCT groups did not differ.

CONCLUSION

Incorporation of posterior corneal astigmatism measured with AS-OCT can significantly improve the outcomes of toric IOL implantation in eyes with WTR and ATR astigmatism, but not in eyes with oblique astigmatism.

Repeatability of total Keratometry and standard Keratometry by the IOLMaster 700 and comparison to total corneal astigmatism by Scheimpflug imaging

OBJECTIVES

We aimed (1) to assess the repeatability of Total Keratometry (TK) and standard keratometry (K) measurements, as provided by the IOLMaster 700 (Carl Zeiss Meditec), and (2) to compare the corneal astigmatism measured by TK to the total corneal astigmatism (TCA) measured by a Scheimpflug camera (Pentacam AXL, Oculus).

METHODS

Two groups of patients were prospectively enrolled: Group A included previously unoperated eyes undergoing cataract surgery, and Group B eyes with previous myopic corneal excimer laser surgery. TK and K were measured three times by the same examiner. Repeatability was assessed based on the within-subject standard deviation (Sw), test-retest variability, coefficient of variation and intraclass correlation coefficient (ICC). In Group A, TCA was measured once and compared to TK astigmatism. Vector analysis was performed according to Næser.

RESULTS

In Group A (69 eyes) the mean K and TK were, respectively, 43.14 ± 1.37 D and 43.18 ± 1.37 D. In Group B (51 eyes) the mean K and TK were, respectively, 40.14 ± 2.20 D and 39.71 ± 2.35 D. The repeatability of the average K and TK was high (Sw < 0.10D). All measurements revealed an ICC > 0.9. For most measurements the variance of K and TK did not show any statistically significant difference either within groups or between groups. Vectors KP(45) were significantly different between TK astigmatism and TCA.

CONCLUSIONS

TK measurements offer high repeatability in unoperated and post-excimer laser surgery eyes. TK astigmatism and TCA measurements could not be considered interchangeable.

Polar value analysis of astigmatic change and rotational stability after implantation of V4c toric implantable collamer lens

Background

To evaluate the clinical results and rotational stability of V4c toric implantable collamer lens (TICL, STAAR Surgical Company, Monrovia, CA, USA) in patients with moderate to high myopic astigmatism. Retrospective, interventional case series was performed at Shenzhen Eye Hospital, Shenzhen, Guangdong, China.

Methods

This study enrolled 43 patients (72 eyes) who received TICL implantation to correct myopia and myopic astigmatism. The patients underwent visual and refractive examinations before and 1 month after surgery. Astigmatic changes were estimated using polar value analysis. The difference between the achieved axis and the intended axis at the last follow-up was taken as the rotation of the V4c TICL.

Results

At 1 month postoperatively, the mean safety and efficacy indices were 1.17 and 1.13, respectively. A significant reduction of 8.92±2.58 D was observed in the spherical equivalent refraction (SER), which decreased from −9.29±2.41 D preoperatively to −0.37±0.55 D postoperatively. The astigmatic error of treatment in cylinder format was calculated to 0.50±0.41 @ 15.08° relative to the preoperative stronger meridian at 1 month, postoperatively. At 1 month postoperatively, the mean absolute rotation was 8.30±10.00 degrees (median =5.46 degrees; range, 0.00–58.88 degrees).

Conclusions

TICL could achieve good astigmatic outcomes for correcting moderate to high myopic astigmatism. After TICL implantation, corneal astigmatism remained unchanged. To optimize postoperative astigmatic outcomes in TICL, polar value analysis can be used to build a nomogram.

A Comparison of the Accuracy of 6 Modern Toric Intraocular Lens Formulas

PURPOSE

To compare the accuracy of the Abulafia-Koch, the Barrett, the EVO 2.0, the new Holladay 2 with total surgical-induced astigmatism, the Kane, and the Næser-Savini toric intraocular lens (IOL) power formulas using a large database of toric IOL refractive outcomes.

DESIGN

Retrospective consecutive case series.

PARTICIPANTS

Eight hundred twenty-three eyes of 823 patients who had a toric IOL inserted during surgery.

METHODS

One eligible eye from patients having uncomplicated cataract surgery with insertion of an Alcon SN6AT(2-9) IOL (Alcon Laboratories, Inc, Fort Worth, TX) from 1 surgeon were included in the study. Both preoperative and postoperative biometry were measured using either the IOLMaster 500 or 700 (Carl Zeiss Meditec AG, Jena, Germany). Using vector calculation, the predicted postoperative refractive astigmatism was calculated for each formula. This was compared with the actual postoperative refractive astigmatism to give the prediction error.

MAIN OUTCOME MEASURES

Mean absolute prediction error, standard deviation of the prediction error, and percentage of eyes with a prediction error within ±0.50 diopter (D).

RESULTS

The Kane formula showed the highest proportion of eyes with a prediction error within ±0.50 D with 65.6%, followed by the Barrett formula (59.9%), Abulafia-Koch formula (59.5%), EVO 2.0 formula (58.9%), Næser-Savini formula (56.7%), and Holladay 2 formula (53.9%). The Kane formula showed a statistically significantly lower mean absolute prediction error (P < 0.001) and a significantly lower variance of the prediction error (P < 0.01) compared with all other formulas. No statistically significant difference existed among the mean absolute prediction errors for the Abulafia-Koch, Barrett, and EVO 2.0 toric formulas.

CONCLUSIONS

Use of the Kane toric formula significantly improved the prediction of postoperative astigmatic outcome compared with the other formulas studied.

[Refractive shift after glaucoma surgery]

Filtering glaucoma surgery can affect certain biometric features of the eye: it can change the axial length and anterior chamber depth, while redistribution of mechanical tensions in the fibrous tunic can alter the shape of the cornea. Among these changes that affect refraction, reshaping of corneal curvature is the principle one. Contrary to the expectations, and in contrast to changes associated with cataract surgery, glaucoma surgery led to decrease in vertical corneal radius (steepening) and development of the with-the-rule astigmatism. A number of studies helped reveal the features of corneal astigmatism that appears after glaucoma surgery: its power, duration, possibility of horizontal meridian flattening, influence of topical cytostatic drugs and drainage devices, etc. Potential reasons of astigmatism development were suggested: conjunctival incisions and sutures in the limbal area, quantity and strength of flap sutures, intraocular pressure level, shift of fistula edges, tissue contraction after cauterization, etc. The key role in pathogenesis of the refractive shift due to change of corneal curvature may belong to particularities of wound healing in the cornea and sclera: healing in sclera is similar to one of connective tissue - its ultrastructure undergoes aging process followed by change of rigidity. At the same time, the main reason for the development of corneal astigmatism after glaucoma surgery remains unclear.

Rotational stability and refractive outcomes of a single-piece aspheric toric intraocular lens with 4 fenestrated haptics

PURPOSE

To assess the outcomes of implantation of a single-piece toric intraocular lens (IOL) with 4 fenestrated haptics.

SETTING

IRCCS Fondazione Bietti, Rome, Italy.

DESIGN

Prospective case series.

METHODS

All patients who had implantation of the Mini Toric Ready IOL were consecutively enrolled. Intraoperatively, the IOL was aligned using an automated system. Follow-up visits were performed at 1 day, 1 week, and 1, 3, and 6 months. At each visit, retroillumination pictures were taken to assess IOL orientation; visual acuity and refraction were also measured.

RESULTS

The final analysis comprised 63 eyes (63 patients). From the first to the last follow-up, the mean arithmetic rotation was -0.2 degrees ± 3.5 (SD) (range -13 to +10 degrees) and the mean absolute rotation was 1.6 ± 3.1 degrees. Intraocular lens rotation from the first to the last examination was within 5 degrees in 92.1% of eyes and on consecutive visits, within 5 degrees in 98.4% or more of eyes. By 6 months, 10 IOLs (15.9%) had rotated clockwise and 10 counterclockwise. Linear regression did not show a statistically significant relationship between rotational stability and the axis of placement with any preoperative parameter (eg, axial length). The mean magnitude of preexisting corneal astigmatism was 1.9 ± 0.7 diopters (D) (range 0.76 to 3.72 D). At the last follow-up, the mean magnitude of refractive astigmatism was 0.5 ± 0.4 D (range 0.0 to 1.5 D); the difference was statistically significant (P < .05).

CONCLUSION

The toric IOL showed good rotational stability and is an option for correcting corneal astigmatism at the time of cataract surgery.

Age-related changes in with-the-rule and oblique corneal astigmatism

PURPOSE

To describe the age-related changes in with-the-rule (WTR) and oblique keratometric astigmatism (KA), posterior corneal astigmatism (PCA) and total corneal astigmatism (TCA).

METHODS

We used a Pentacam HR (high-resolution) rotating Scheimpflug camera to determine the KA, PCA and TCA in the right eyes of 710 patients, aged from 20 to 88 years. The age-related changes along the vertical, horizontal and oblique meridians were analyzed with Naeser's polar value method in a cross-sectional study.

RESULTS

In the whole group, all meridional astigmatic powers and polar values were stable in the age groups from 20 to 49 years, followed by a 1.0 dioptre (D) against-the-rule (ATR) change in KA and TCA, and a 0.12 D reduction in against-the-rule PCA. A nasal rotation of the steep meridian in KA and TCA was noted in the 70-88 years old. The PCA averaged approximately 0.25 D ATR in all age groups. Females displayed the same early astigmatic stability as in the whole group, while male eyes demonstrated a linear decay from 1.5 D WTR at 20 years to 0.5 D ATR astigmatism for the oldest patients.

CONCLUSION

Corneal astigmatism is stable until the age of 50 years; thereafter both keratometric and total corneal astigmatism show a 0.25 D ATR change per 10 years. The average 0.25 D ATR PCA compensates the predominant keratometric WTR astigmatism in the younger patients and increases the TCA in the elderly with keratometric ATR astigmatism. The gender-based differences in age-related astigmatism require further studies.

Surgically induced astigmatism following trabeculectomy

PURPOSE

Surgically induced astigmatism (SIA) has attracted much interest in recent times because changes in corneal astigmatism can lead to decreased uncorrected visual acuity and patient discomfort. This study aimed to evaluate SIA and to identify factors correlated therewith after trabeculectomy.

METHODS

We retrospectively reviewed medical charts of patients who were treated with trabeculectomy at 120° meridian (superotemporal area on right eye and superonasal area on left eye) by the same surgeon. Preoperative keratometric data were compared with data collected from 2 months to 12 months postoperatively. SIA was evaluated using Naeser's polar value analysis.

RESULTS

Using Naeser's method, ΔKP(120) was calculated as 0.7 ± 0.7 (0.82@104°), which indicates a with-the-rule change. After surgery, the combined mean polar values changed significantly (Hotelling T² = 22.47; p < 0.001). Multivariate analysis of variance indicated that postoperative intraocular pressure and location of surgery were independent factors that were significantly associated with SIA (p = 0.002 and 0.03, respectively).

CONCLUSIONS

Trabeculectomy at the 120° meridian was not astigmatically neutral. In addition, the SIA after trabeculectomy appears to be greater in eyes with low postoperative intraocular pressure and a superonasal surgical wound rather than a superotemporal wound.

Estimating Total Corneal Astigmatism From Anterior Corneal Data

PURPOSE

To determine keratometric astigmatism (KA), posterior corneal astigmatism (PCA), and total corneal astigmatism (TCA) in 951 normal eyes, to establish a model for estimating TCA from anterior corneal data, and to test this method in a new group of eyes with toric intraocular lenses (TIOLs).

METHODS

We used a Pentacam HR (high-resolution) Scheimpflug camera to determine KA, PCA, and TCA in 951 normal eyes. A model to estimate TCA from anterior corneal data was evaluated by the difference (=error) between the measured TCA and the estimated value. The model was tested in 40 eyes with TIOLs.

RESULTS

KA, TCA, and PCA averaged 1.06 (±0.85) D, 1.05 (±0.83) D, and 0.33 (±0.17) D. The error of the model to estimate TCA averaged zero with an SD of ±0.21 D. Application of this model and of direct Pentacam TCA measurements in TIOL calculation gave similar results, namely a slight reduction of overcorrection in with-the-rule astigmatism, but an eradication of undercorrection in against-the-rule astigmatism.

CONCLUSIONS

It was possible to estimate TCA accurately from anterior corneal data with a new formula. However, application of both this model on keratometric data and of direct Pentacam measurements in a group of 40 eyes with TIOLs did not completely eradicate the refractive error in TIOL calculation. More studies comparing Pentacam TCA and refractive astigmatism are required.

[Comparison of two optical biometric devices for intraocular lens calculation]

BACKGROUND

Modern cataract surgery not only consists of a minimally invasive lens extraction but also of the implantation of a suitable intraocular lens.

OBJECTIVE

The aim of this prospective trial was a comparison of the predicted refractive error of two optical biometers, the IOLMaster 500 and LenStar LS 900 for intraocular lens power calculation in cataract surgery.

MATERIAL AND METHODS

This was a prospective, analytical, comparative, non-masked study. A total of 86 eyes of 86 patients were examined and measured with both instruments before and after uneventful cataract surgery. Primary outcome measures were the differences of the predicted refractive error of both instruments. The predicted refractive error was calculated with different formulas. The results were compared to each other, to the desired target refraction as well as to the postoperative spherical equivalent.

RESULTS

The mean differences in predicted refractive error of both instruments varied between 0.9 ± 0.19 (standard deviation) diopters (D) and 0.18 ± 0.30 D depending on the chosen formula. The IOLMaster 500 predicted less difference to the desired target refraction as well as to the spherical equivalent than the LenStar LS 900 with nearly all formulas.

CONCLUSION

Both devices generated reproducible exact data with only a small deviation from the desired target refraction and from the postoperative spherical equivalent. There were statistically significant differences based on the chosen a‑constants as well as the utilized measurement methods of both instruments.

Polar Value Analysis of Low to Moderate Astigmatism with Wavefront-Guided Sub-Bowman Keratomileusis

Purpose

To evaluate the astigmatic outcomes of wavefront-guided sub-Bowman keratomileusis (WFG-SBK) for low to moderate myopic astigmatism.

Methods

This study enrolled 100 right eyes from 100 patients who underwent WFG-SBK for the correction of myopia and astigmatism. The polar value method was performed with anterior and posterior corneal astigmatism measured with Scheimpflug camera combined with Placido corneal topography (Sirius, CSO) and refractive astigmatism preoperatively and 1 month, 3 months, and 6 months postoperatively.

Results

Similar results for surgically induced astigmatism (SIA) and error of the procedure in both anterior corneal astigmatism (ACA) and total ocular astigmatism (TOA). There was a minor undercorrection of the cylinder in both ACA and TOA. Posterior corneal astigmatism (PCA) showed no significant change.

Conclusions

Wavefront-guided SBK could provide good astigmatic outcomes for the correction of low to moderate myopic astigmatism. The surgical effects were largely attributed to the astigmatic correction of the anterior corneal surface. Posterior corneal astigmatism remained unchanged even after WFG-SBK for myopic astigmatism. Polar value analysis can be used to guide adjustments to the treatment cylinder alongside a nomogram designed to optimize postoperative astigmatic outcomes in myopic WFG-SBK.

Calculations of actual corneal astigmatism using total corneal refractive power before and after myopic keratorefractive surgery

Purpose

To calculate actual corneal astigmatism using the total corneal refractive astigmatism for the 4-mm apex zone of the Pentacam (TCRP4astig) and keratometric astigmatism (Kastig) before and after photorefractive keratectomy or laser in situ keratomileusis

Methods

Uncomplicated 56 eyes after more than 6 months from the surgery were recruited by chart review. Various corneal astigmatisms were measured using the Pentacam and autokeratometer before and after surgery. Three eyes were excluded and 53 eyes of 38 subjects with with-the-rule astigmatism (WTR) were finally included. The astigmatisms were investigated using polar value analysis. When TCRP4astig was set as an actual astigmatism, the efficacy of arithmetic or coefficient adjustment of Kastig was evaluated using bivariate analysis.

Results

The difference between the simulated keratometer astigmatism of the Pentacam (SimKastig) and Kastig was strongly correlated with the difference between TCRP4astig and Kastig. TCRP4astig was different from Kastig in magnitude rather than meridian before and after surgery; the preoperative difference was due to the posterior cornea only; however, the postoperative difference was observed in both anterior and posterior parts. For arithmetic adjustment, 0.28 D and 0.27 D were subtracted from the preoperative and postoperative magnitudes of Kastig, respectively. For coefficient adjustment, the preoperative and postoperative magnitudes of Kastig were multiplied by 0.80 and 0.66, respectively. By arithmetic or coefficient adjustment, the difference between TCRP4astig and adjusted Kastig would be less than 0.75 D in magnitude for 95% of cases.

Conclusions

Kastig was successfully adjusted to TCPR4astig before and after myopic keratorefractive surgery in cases of WTR. For use of TCRP4astig directly, SimKastig and Kastig should be matched.

Torsional and flattening effect on corneal astigmatism after cataract surgery: a retrospective analysis

Background

To evaluate the torsional and flattening effect of steep meridian incisions and influence of posterior corneal astigmatism (PCA) on total corneal astigmatism (TCA) after cataract surgery.

Methods

One hundred thirty-two eyes underwent cataract surgery with steep meridian 2.2 mm microcoaxial and 2.85 mm conventional clear corneal incisions. Eyes were divided into with-the-rule (WTR) astigmatism and against-the-rule (ATR) astigmatism groups depending on the steeper meridian and measured with autokeratorefractor and Pentacam® before surgery, at 1 day, 1 week, 1 and 2 months postoperatively. Polar vector analysis was used to evaluate torsional effect of steep meridian incisions.

Results

A decrease in astigmatic polar value (AKP) (+0) was observed in both keratometric and total astigmatism (TA) after 1 and 2 months, although the decrease was only statistically significant in TA (p < 0.05). The AKP(+45) was more significant in the conventional group than the microcoaxial group at 2 months postoperatively (p < 0.05, respectively). There was a significant correlation between corneal thickness of the superior quadrant and PCA in the WTR group (p = 0.028). In eyes with anterior corneal astigmatism smaller than 0.55D of WTR astigmatism and PCA greater than 0.35D of WTR astigmatism showed greater shifting of steep axis and also increment of refractive cylinder powers.

Conclusions

In eyes with superior corneal thickness greater than 714.5 μm and PCA greater than 0.35D of WTR astigmatism, steep meridian incision may cause a significant torsional effect and off-steep meridian change, contributing to an increment of postoperative residual manifest astigmatism after cataract surgery.

Polar Value Analysis of Corneal Astigmatism in Intrastromal Corneal Ring Segment Implantation

Purpose. To evaluate surgically induced astigmatism (SIA) and the average corneal power change in symmetric intrastromal corneal ring segment (ICRS) implantation. Methods. The study included 34 eyes of 34 keratoconus patients who underwent symmetric Intacs SK ICRS implantation. The corneal pocket incision meridian was the preoperative steep meridian. Corneal power data were obtained before and 3 months after Intacs SK ICRS implantation using scanning-slit topography. Polar value analysis was used to evaluate the SIA. Hotelling's trace test was used to compare intraindividual changes. Results. Three months postoperatively, the combined mean polar value for SIA changed significantly (Hotelling's T² = 0.375; P = 0.006). The SIA was 1.54 D at 99° and the average corneal power decreased significantly by 3.8 D. Conclusion. Intacs SK ICRS placement decreased the average corneal power and corneal astigmatism compared to the preoperative corneal power and astigmatism when the corneal pocket incision was made at the preoperative steep meridian.

Vector analysis of low to moderate astigmatism with small incision lenticule extraction (SMILE): results of a 1-year follow-up

BACKGROUND

To evaluate the refractive outcomes for the correction of low to moderate astigmatism up to 1 year following small incision lenticule extraction (SMILE) surgery.

METHODS

This retrospective study enrolled 98 eyes from 98 patients who underwent SMILE surgery for the correction of myopia and astigmatism. Only right eyes were included in this study to avoid the bias of orientation errors. The vector method was used to analyze the outcomes of astigmatism at 1 month, 6 months and 12 months after the procedure, including the double-angle plots, correction index (CI), index of success (IOS), angle of error (AofE) and magnitude of error (MofE). The effectiveness, safety, stability and predictability were also investigated during the 12-month follow-up.

RESULTS

The preoperative cylinder ranged from -2.75 D to -0.25 D (average of -0.90±0.68 D), and the mean postoperative cylinder values were -0.24±0.29 D, -0.24±0.29 D, and -0.20±0.27 D at 1 month, 6 months, and 12 months, respectively. The mean astigmatism in vector form was -0.14 D×27.19° at 1 month, -0.13 D×27.29° at 6 months, and -0.10 D×28.63° at 12 months after surgery. The CI was 1.00±0.32 and IOS was 0.29±0.44 at the 12-month follow-up. Significant negative correlations were found between the CI and absolute target induced astigmatism (TIA) value, and positive correlations were found between the IOS and absolute AofE value (P<0.05). The MofE was limited within ±1.00 D at the 12-month follow-up. Fifty-six eyes (57.1%) gained one line in corrected distance visual acuity (CDVA) and five eyes (5.1%) gained two lines. There were no significant differences observed in the refractive outcomes among time points.

CONCLUSIONS

SMILE surgery was effective and safe in correcting low to moderate astigmatism, and stable refractive outcomes were observed at the long-term follow-up. The undercorrection of astigmatism could possibly be influenced by attempted astigmatism correction preoperatively, the axis rotation during the surgery or wound healing postoperatively. This study suggested that nomograms should be adjusted in correcting astigmatism with SMILE surgery.

Pseudophakic monovision: optimal distribution of refractions

PURPOSE

To determine the optimal distribution of refractions in monofocal, pseudophakic monovision.

METHODS

A previously reported mathematical method for describing defocus for a single eye (Acta Ophthalmol, 89, 2011, 111) is expanded to the binocular situation. The binocular distribution of refractions yielding the least defocus over the most extended fixation intervals is identified by mathematical optimization. The results are tested in a group of 22 pseudophakic patients.

RESULTS

For the fixation interval 0.25-6.0 m, the optimal refractions are pure spheres of -0.27D for the distance eye and -1.15D for near eye. The mathematically derived defocus structure is confirmed in the clinical series.

CONCLUSIONS

The reported mathematical method enables identification of the optimal distribution of refractions over any fixation interval. Monovision with refractions of approximately -0.25 and -1.25D may lead to spectacle independence for distance and intermediate vision. Binocular problems--such as monovision suppression, reduced stereoacuity and binocular inhibition--are likely to be minimal with the suggested anisometropia of 1.0D. This moderate monovision is fully reversible with spectacle correction, as the induced aniseikonia is minimal and it therefore represents a safe alternative to multifocal intraocular lenses (IOLs).

Combining refractive and topographic data in corneal refractive surgery for astigmatism: a new method based on polar value analysis and mathematical optimization

PURPOSE

To provide a theoretical approach for combining refractive and topographic data in the planning of corneal laser refractive surgery for astigmatism.

METHODS

Refractive and topographic data for astigmatism were transformed to the corneal plane. Net astigmatisms were converted to polar values. An optimization process was performed with the use of differential calculus.

RESULTS

With this method, the magnitude of the corneal astigmatism is reduced or unaltered, while its orientation is maintained. The method identifies the reduction in corneal astigmatism, which will yield the largest reduction in refractive astigmatic magnitude.

CONCLUSIONS

The advantage of the optimization method described in this article is a consistent reduction in corneal astigmatism towards sphericity. No new corneal astigmatism is carved on the cornea, and probably less tissue is ablated. The optimization method may also be used to combine refractive and topographic data for higher order aberrations with sinusoidal components. However, compared to the traditional purely refractive driven treatment, more refractive astigmatism will remain in the eye in most cases. A controlled clinical trial is necessary for comparing these two treatment modalities.

Comparison of patient outcomes after implantation of Visian toric implantable collamer lens and iris-fixated toric phakic intraocular lens

PURPOSE

We compared visual and refractive outcomes after implantation of Visian toric implantable collamer lenses (toric ICLs) and iris-fixated toric pIOLs (toric Artisans).

PATIENTS AND METHODS

A comparative retrospective analysis was performed. Toric ICLs were implanted into 30 eyes of 18 patients, and toric Artisans into 31 eyes of 22 recipients. We measured the logarithms of the minimum angle of resolution of uncorrected visual acuity (logMAR UCVA), logMAR of best spectacle-corrected corrected VA (logMAR BSCVA), MR, SE, and astigmatism (by the power vector method) before surgery and 1, 3, and 6 months thereafter. Differences between patients receiving each type of lens were compared by using a mixed model of repeated measures.

RESULTS

Visual improvements were evident after operation in both groups. By comparing the attempted to the achieved SE values, we were able to confirm that correction of refractive error was similar in both groups. However, the logMAR UCVA was significantly higher in the toric ICL group at all postoperative time points. Although manifest cylinder power and astigmatism (calculated by using the power vector method) gradually decreased in the toric ICL group, cylinder power 1 month postoperatively increased from -2.62 to -2.75 D; astigmatism was also increased at this time in the toric Artisan group.

CONCLUSION

The two tested toric pIOLs were similar in terms of the ability to correct refractive error, as assessed 3 months postoperatively. However toric ICLs corrected astigmatism more rapidly and safely. Notably, the large difference in astigmatism level between the two groups 1 month postoperatively indicates that toric ICLs are more effective when used to correct astigmatism.

Optimal refraction with monofocal intraocular lenses: no beneficial effect of astigmatism

PURPOSE

This study aimed to determine the optimal spherocylindrical refraction in the monofocal, pseudophakic eye using power vectors in dioptric space.

METHODS

For parallel incident light the defocus of a spherocylinder may be described in dioptric space as: Defocus equivalent for distance fixation = D((SEP,M,x=∞)) = √SEP(2)+(1/2M)(2), where SEP = spherical equivalent power in dioptres (D) and M = astigmatic magnitude in D. In the pseudophakic eye the defocus for any fixation distance x is: Defocus equivalent for the fixation distance x = D((SEP,M,x)) = √(SEP-1/x)(2)+ (1/2M)(2). The cumulative defocus over a fixation interval is the integral of D((SEP,M,x)) . A minimal value for cumulative defocus will indicate a maximal unaided visual acuity (VA) over the chosen fixation interval. We calculated the summated defocus for various spherocylinders for fixation distances ranging from 0.5 m to 6.0 m.

RESULTS

Minimal cumulative defocus was present for pure spheres of -0.25 D to -0.5 D. No beneficial effect of the presence of astigmatism was detected.

CONCLUSIONS

In monofocal pseudophakia the highest possible VAs over the most extended fixation ranges may be achieved with slight myopic refractions without astigmatic components.