Fourier series harmonic analysis of corneal topography following suture removal after penetrating keratoplasty

Regular and irregular astigmatism of bullous keratopathy using Fourier harmonic analysis with anterior segment optical coherence tomography

Bullous keratopathy (BK) is known to present with corneal edema and Descemet's folds, which can cause corneal astigmatism. However, no report quantitatively evaluated BK astigmatism by separating it into regular and irregular astigmatism. This study investigated the regular and irregular astigmatism of the anterior and posterior corneal surface with Fourier harmonic analysis and anterior segment optical coherence tomography. Preoperative data from 43 eyes of 41 BK patients who received corneal endothelial transplantation were compared with the data from 43 eyes of 43 subjects without corneal disease. Anterior and posterior cylinder power, central corneal thickness (CCT) and thinnest corneal thickness were significantly greater in BK. With Fourier harmonic analysis, BK eyes were found to have significantly larger anterior and posterior regular astigmatism, asymmetry component and higher-order irregularity. Asymmetry component and higher-order irregularity that accounted for the posterior irregular astigmatism increased as CCT increased in BK. Higher-order irregularity in the posterior cornea also positively correlated with worsening best corrected visual acuity. Subgroup analysis found significant correlations between CCT and posterior higher-order irregularity for intraocular surgery and laser iridotomy, but not Fuchs endothelial corneal dystrophy. This study has significance in that it revealed the characteristics of the corneal posterior irregular astigmatism of BK.

The Association between Fourier Parameters and Clinical Parameters in Myopic Children Undergoing Orthokeratology

Purpose: To explore how Fourier parameters are associated with axial length growth (ALG) and clinical parameters in children who underwent orthokeratology.Materials and Methods: A total of 267 children received orthokeratology. Baseline cycloplegic autorefraction was performed. Axial length was measured at baseline and one year after the lens dispatch, and the difference was defined as ALG. Corneal topography was performed at the same two visits. Central treatment zone (CTZ) was identified from the difference between the two tangential maps, and its center distance to corneal center was defined as decentration. A relative refractive corneal power (RCRP) map was derived by subtracting the center value from every point on the one-year axial map. It was decomposed into 3 Fourier components: a mean (F0), a single-cycle sinewave (F1), and a double-cycle sinewave (F2). Linear regressions were used to reveal the association between ALG and these parameters.Results: At baseline, the age was 10.18 ± 1.48 year, spherical equivalent (SE) was - 3.10 ± 1.15D, astigmatism was 1.17 ± 0.58D, and axial length was 24.69 ± 0.81 mm. The mean ALG was 0.181 ± 0.22 mm. In multiple regression, ALG was negatively associated with F1 (p < .001), not F0 and F2. Amplitude-wise, F0 and F1 were correlated with decentration (p < .01) and SE (p < .01), and F2 was associated with astigmatism (p < .001). Direction-wise, F1 was correlated with decentration (p < .001) and F2 was associated with astigmatism (p < .001).Conclusions: Among Fourier parameters, F0 and F1 were negatively associated with ALG in myopic children undergoing orthokeratology. Their associations to SE and CTZ decentration may partially explain the effect on ALG retardation.

Comparison of refractive outcomes in three corneal transplantation techniques for keratoconus

BACKGROUND

Deep anterior lamellar keratoplasty (DALK) has a much lower incidence of immunologic reactions than penetrating keratoplasty (PK) for patients with keratoconus. However, it is unclear whether DALK is better on refractive outcomes than PK, due to its high postoperative myopia.

METHODS

We retrospectively studied the clinical records of keratoconus patients who underwent PK, DALK, or predescemetic DALK (pre-DALK, DALK with residual stroma) between June 2004 and September 2008. The main outcome measures included refractive sphere, manifest cylinder, corneal power, keratometric astigmatism, and best-corrected visual acuity (BCVA) at the latest visit and the methods of visual correction. Postoperative manifest refractions and topography data were compared at postoperative 3, 5, 7, and 9 years among the three groups. Additionally, the final BCVA and the methods of vision correction were compared.

RESULTS

A total of 172 subjects (172 eyes) screened out of 207 keratoconus patients underwent PK (79 eyes), DALK (68 eyes), or pre-DALK (25 eyes). Postoperative myopic refractive sphere increased in all groups, but the most obvious increase was noted in the pre-DALK group. At the 9-year follow-up, both the pre-DALK group (-6.5 ± 1.7 D) and DALK group (-6.1 ± 1.8 D) had higher myopic refractive sphere than the PK group (-5.0 ± 1.5 D, p < 0.05). Postoperative myopic manifest astigmatism progressively increased in 5 years, but there were no differences among the groups. The progressive increases in postoperative corneal power were recorded in all groups, with the highest one in the pre-DALK group and the lowest in the PK group. At the 9-year follow-up, both the pre-DALK (49.8 ± 2.7 D) and DALK (48.8 ± 2.1 D) groups had higher corneal power than the PK group (47.3 ± 2.0 D); meanwhile, the corneal power was higher in the pre-DALK group than the DALK group (p < 0.05). No differences were noted with respect to keratometric astigmatism among the groups. Mean LogMAR BCVA was 0.12 ± 0.12 in the DALK group, 0.17 ± 0.10 in the pre-DALK group, and 0.1 ± 0.11 in the PK group (p = 0.325) at 9 years after surgery. Moreover, the methods of achieving BCVA seem to be similar among the treatment groups.

CONCLUSIONS

Although DALK has a slightly higher degree of myopic refraction than PK, DALK and PK have comparable visual acuity outcomes and similar methods of vision correction. DALK is recommended for the treatment of keratoconus.

Contact lenses and special back surface design after penetrating keratoplasty to improve contact lens fit and visual outcome

AIMS

To describe the fitting of patients with high or irregular astigmatism following penetrating keratoplasty with contact lenses and to answer the question whether or not contact lenses with special back surface design can improve visual acuity in complex cases after penetrating keratoplasty.

METHODS

28 eyes were included. They were fitted with contact lenses with a special back surface that was designed for optical rehabilitation after penetrating keratoplasty. Four different types of these lenses (tricurve, keratoconus, reverse, oblong) were used selectively depending on abnormal eccentricity determined by videokeratoscope. The patients were followed up for an average period of 15.5 months. Lens tolerance and corrected visual acuity were evaluated and compared with that corrected with spectacles.

RESULTS

The visual acuity was significantly improved in nearly all eyes with an average increase of 3.6 lines (maximal nine lines) accompanied by good contact lens tolerance and satisfactory contact lens fit. No noticeable complications were observed.

CONCLUSION

Contact lenses with special back surface design can improve visual results and lens tolerance, and minimise problems in contact lens fitting. This is in favour of contact lenses as an alternative to surgical procedures for correction of high or irregular astigmatism after penetrating keratoplasty. This procedure is recommended especially in cases of patients who decline further operative interventions.

Long-term changes in corneal surface configuration after penetrating keratoplasty

PURPOSE

To examine the long-term longitudinal changes in corneal surface configuration as determined by Fourier series harmonic analysis of videokeratography data and of visual acuity and refraction after penetrating keratoplasty (PK).

DESIGN

Interventional case series.

METHODS

One hundred thirty eyes of 130 consecutive patients who were scheduled for PK using 16 interrupted 10-0 nylon sutures were recruited. Spherical equivalent power, regular astigmatism component, irregular astigmatism (asymmetry and higher-order irregularity) component of the central cornea as determined by Fourier analysis of videokeragraphic data, spectacle-corrected visual acuity, and spherical equivalent were examined at 1 week, and at 1, 3, 6, 9, 12, 18, and 24 months after PK.

RESULTS

Spherical equivalent power increased considerably for up to 1 month after PK, but thereafter showed no further appreciable change up to the final follow-up at 24 months. The regular astigmatism component decreased markedly for up to 6 months after PK, while the total irregular astigmatism (sum of the asymmetry and higher-order irregularity) component decreased considerably up to approximately 3 months, and then these showed no further relevant change for up to 24 months. Spectacle-corrected visual acuity also improved markedly until approximately 3 months after PK, after which it was virtually stable. Furthermore, important correlations were found between regular and irregular astigmatism and the spectacle-corrected visual acuity.

CONCLUSIONS

Corneal surface configuration after PK appears to be stable by approximately 6 months after PK, concurrent with postkeratoplasty stabilization of visual acuity.

Corneal irregular astigmatism after hyperopic laser in situ keratomileusis

PURPOSE

To evaluate the changes in irregular astigmatism after hyperopic laser in situ keratomileusis (LASIK).

METHODS

In a prospective case series, 15 eyes of 12 patients who had hyperopic LASIK were evaluated. Corneal topography was obtained before and after hyperopic LASIK. Corneal irregular astigmatism (asymmetry and higher-order irregularity) was calculated using Fourier harmonic analysis of the topography data.

RESULTS

Hyperopic LASIK significantly increased the asymmetry component at 3 (P = 0.0085) and 6 months (P = 0.0307) postoperatively. The mean higher-order irregularity was not significantly changed at any postoperative time-point (P = 0.222). The achieved change in the spherical equivalent was significantly correlated with the post/preoperative ratio of asymmetry (R = 0.695, P = 0.0030).

CONCLUSION

Hyperopic LASIK significantly increases the asymmetry component of the cornea, which is correlated with the achieved change in the spherical equivalent.

Visual acuity measurements using Fourier series harmonic analysis of videokeratography data in eyes after penetrating keratoplasty

PURPOSE

Fourier harmonic analysis can decompose videokeratography data into spherical power, regular astigmatism, and irregular astigmatism (asymmetry and higher-order irregularity). The aim of this study was to evaluate whether determination of cylinder power by Fourier analysis facilitates measurements of visual acuity and refraction in eyes after penetrating keratoplasty.

DESIGN

Cross-sectional study.

PARTICIPANTS

Sixty-six eyes of 56 subjects who had undergone penetrating keratoplasty.

METHODS

Spectacle-corrected visual acuity was measured in 2 ways: by the conventional and the Fourier methods. In the conventional method, the refraction was determined subjectively by reference to the measurement results of the autokeratometer and autorefractometer. In the Fourier method, the magnitude and axis of regular astigmatism were calculated by Fourier analysis of the videokeratography data, and spherical lenses were adjusted until best spectacle-corrected visual acuity was attained.

MAIN OUTCOME MEASURES

Logarithm of the minimum angle of resolution (logMAR) visual acuity and refraction used for correction.

RESULTS

The spectacle-corrected visual acuity obtained with the Fourier method (logMAR, 0.23+/-0.32; Snellen equivalent, 20/34) was significantly better than that attained with the conventional method (logMAR, 0.31+/-0.29; Snellen equivalent, 20/41; P<0.001, paired t test). The cylinder power used for spectacle-corrected visual acuity measurements was significantly lower with the Fourier method (-2.41+/-1.26 diopters [D]) than with the conventional method (-3.53+/-1.64 D; P<0.001). The spherical equivalent at the final refraction was not different between groups (P = 0.207).

CONCLUSIONS

Fourier analysis of videokeratography data significantly facilitates determination of refraction and measurement of best spectacle-corrected visual acuity in eyes with corneal irregular astigmatism, such as eyes that have undergone penetrating keratoplasty.

Quantitative Assessment of Videokeratography Data Using Fourier Series Harmonic Analysis

PURPOSE

To describe a method of mathematically decomposing videokeratography data using Fourier series harmonic analysis and present examples of its clinical application.

METHODS

Videokeratography data were decomposed by Fourier analysis into spherical component, regular astigmatism, asymmetry (decentration or skewness), and higher-order irregular astigmatism. These 4 Fourier components were analyzed in both normal and pathologic eyes. Color-coded maps were generated to present the 4 Fourier components.

RESULTS

Color-coded mapping of the results of Fourier analysis of videokeratography data facilitated visual and instant interpretation of complex corneal topographic information. By using Fourier components, time course of changes in corneal topography following penetrating keratoplasty and influence of suture removal were quantitatively evaluated. The Fourier analysis method was successfully applied to determine the most appropriate correction lenses in eyes after penetrating keratoplasty.

CONCLUSIONS

Fourier analysis of videokeratography data allows mathematical separation of regular and irregular astigmatism and is useful in the quantitative assessment of corneal optics in eyes with both pathologic and postsurgical conditions.

Surgical technique for control of postkeratoplasty myopia, astigmatism, and anisometropia

PURPOSE

We previously demonstrated that selective suture removal reduces keratoplasty astigmatism; however, a myopic shift was induced with the increasing number of interrupted sutures removed. This study is an attempt to determine the effects of a modified surgical technique on postkeratoplasty myopia, astigmatism, and anisometropia.

DESIGN

A cohort study compared with historical controls.

METHOD

Optical penetrating keratoplasties were performed on 92 eyes of 84 patients. The study group consisted of 92 consecutive penetrating keratoplasties performed using 12 interrupted 10-0 nylon sutures and a tight 12-bite continuous suture and an average K reading of 46.00 diopters for eyes undergoing combined and intraocular lens exchange procedures. All patients had refraction, keratometry, and videokeratoscopy postoperatively starting at 6 weeks and at the completion of selective suture removal.

RESULTS

Before suture removal, the average spherical equivalent was -0.160 +/- 3.59 diopters; it was -1.58 +/- 3.66 diopters at the completion of suture removal at 1 year and -1.44 +/- 3.72 at the last follow-up visit, averaging 20.7 months. Final refractive, keratometric, and videokeratoscopy astigmatism was 2.81 +/- 1.82, 4.19 +/- 2.94, and 3.58 +/- 2.03 diopters, respectively. Anisometropia, using the spherical equivalent of the operated and fellow eyes, was 2.49 +/- 2.25 diopters at completion of the study. A best-corrected visual acuity of 20/50 or better was achieved in 59% of patients.

CONCLUSIONS

Low myopic spherical equivalent and anisometropia were achieved using a K reading of 46 diopters for calculation of intraocular lens power. The use of tighter continuous sutures and selective removal of fewer interrupted sutures only served to increase final astigmatism, with no significant effect on the final spherical equivalent.