Popperian falsification of methods of assessing surgically induced astigmatism.

To test several methods of assessing surgically induced astigmatism (SIA). Department of Ophthalmology, Arhus University Hospital, Arhus, Denmark. Assessment methods can be divided into 3 groups. Group 1 includes methods that consider only astigmatic magnitude and disregard astigmatic direction, such as the algebraic and simple subtraction methods. Group 2 can be termed "astigmatic magnitude not considering axis" and includes several almost identical techniques known as the methods of Naylor, Jaffe, Kaye, Holladay, and Olsen. Group 3 includes Naeser polar value analysis and the methods later described by Alpins and Holladay. The methods were tested in situations in which the expected result was known. When this result was not produced, the specific assessment method was considered falsified in a classical Popperian manner. The simple falsification experiments revealed that the methods in Groups 1 and 2 are erroneous. Mathematical analysis disclosed that the methods in Group 3 are similar, although derived from different concepts. The algebraic, simple subtraction, astigmatic magnitude not considering axis, and vector decomposition methods for assessment of SIA are erroneous and should not be used. The Naeser, Alpins, and Holladay methods are identical and in agreement with current research in optometry.

Polar value analysis of refractive data.

PURPOSE: To demonstrate the use of polar value analysis of surgically induced astigmatism (SIA). SETTING: Department of Ophthalmology, Arhus University Hospital, Arhus, Denmark. METHODS: Univariate polar value analysis of SIA was demonstrated for a single patient and for aggregate data. Bivariate polar value analysis was performed for aggregate data. RESULTS: The meridional polar value AKP expresses the surgically induced flattening, while the oblique polar value AKP(+45) indicates the torque. This pair of polar values characterizes a regular astigmatism completely. In bivariate polar value analysis, the average SIA is the combined mean for AKP and AKP(+45), while the spread is a confidence area delineated by an ellipse. CONCLUSIONS: Univariate and bivariate polar value analyses, together with the surgically induced change in spherical equivalent power, yield an exact description of surgically induced change following refractive procedures.

Multivariate analysis of refractive data: mathematics and statistics of spherocylinders.

PURPOSE: To develop methods for multivariate statistical analysis of spherocylinders and to use these methods to compare autorefraction and manifest subjective refraction in 50 healthy eyes. SETTING: Department of Ophthalmology, Arhus University Hospital, Arhus, Denmark. METHODS: A method was developed to transform a spherocylinder to a suitable format as a spherical equivalent power (SEP) and 2 polar values, separated by an arch of 45 degrees, a so-called power-vector format. The accuracy of autorefraction was defined as the difference between autorefraction and manifest refraction, using the described power vector. These entities were subjected to multivariate analysis using the Hotelling T2 test. A method of graphic analysis was developed, using matrix algebra and computation of eigenvectors and eigenvalues. RESULTS: For individual data, the variation was considerably larger for the SEP than for the astigmatism. For aggregate data, univariate, bivariate, and trivariate statistical analysis did not demonstrate significant average differences between the 2 refraction methods. No refractive components and no combinations of refractive components displayed significant mean differences. CONCLUSIONS: The study confirmed our clinical experience that the astigmatism derived from autorefraction is nearly identical to manifest refraction, while the sphere needs some adjustment. In groups of healthy eyes, autorefraction can be used as a substitute for manifest refraction. Statistical analysis of spherocylinders, including evaluation of refractive procedures, can be performed in an exact manner with multivariate statistics.

Precision of autokeratometry expressed as confidence ellipses in Euclidian 2-space.

A number of studies have examined the repeatability or precision of keratometers. All studies have found exceptionally high precision in keratometry of the spherically equivalent proportion, while the joint variation in astigmatic direction and magnitude barely has been explored. The purpose of this study was to examine the simultaneous variation in astigmatic direction and magnitude between two single autokeratometries, using a Nidek ARK 2000-S autokeratorefractometer. A single autokeratometry was performed on two occasions on 50 right eyes of patients with cataracts. The precision was defined as the paired difference between these two measurements. Each net astigmatism was transformed to polar values, and uni- and bivariate polar value analysis was performed. Precision of autokeratometry, expressed as a mean difference and a 95% confidence area, was calculated as a confidence ellipse in Euclidian 2-space. The accompanying net astigmatisms with confidence perimeters were derived by point-for-point transformation from polar values. Clinical variability may overwhelmingly be attributed to patient-related factors and only to a small degree to autokeratometry itself. Clinicians should know the precision of their keratometers, both for daily use and in the planning and dimensioning of scientific studies. Our results indicate that a minimum number of 25 eyes in each group is necessary in order to detect a difference of 0.25 diopters in surgically induced astigmatism between two surgical techniques. Precision of keratometry can only be determined from polar values or similar entities and never by the use of net astigmatisms.

Persistent corneal oedema following ICCE. Influence of IOL type.

PURPOSE: To examine the frequency of persistent corneal oedema following intracapsular cataract extraction (ICCE). To examine whether the type of intraocular lens has any influence on persistent corneal oedema following ICCE. METHODS: A retrospective study of 1041 consecutive ICCE operations followed for at least eight years. The cumulative incidence of persistent corneal oedema was calculated for the whole group and compared to the incidence in subgroups defined by type of intraocular lens. RESULTS: The cumulative incidence of persistent corneal oedema following ICCE was 2.3% for the whole group. The highest incidence (10.3%) was found in the group of patients, who received a 3-M style 77 anterior chamber lens while the lowest incidence (1.0%) were found among patients receiving a Choyce anterior chamber lens. Compared to this, the patients who received no intraocular lens showed a frequency of persistent corneal oedema of 1.4%. Among the patients who developed persistent corneal oedema the number of re-operations was higher (27.3%) compared to the patients who did not develop persistent corneal oedema (4.4%). The frequency of preoperative dystrophy was the same whether or not the patients developed persistent corneal oedema. There were no difference in gender, age or other pre-operative data between the two groups. CONCLUSION: After ICCE 2.3% developed persistent corneal oedema. There was a significant difference between the frequencies of persistent corneal oedema depending on the type of intraocular lens from 1.0% in eyes receiving a Choyce anterior chamber lens to 10.3% in eyes receiving a semi-flexible 3-M style 77 anterior chamber lens.

Mortality and causes of mortality among cataract-extracted patients. A 10-year follow-up.

PURPOSE: The purpose of this study was to compare the mortality among patients undergoing intracapsular cataract extraction to the mortality in a gender-and age-identical Danish reference population, and to compare the patients' primary causes of death to those in the general population. MATERIALS AND METHODS: We reviewed medical records of patients undergoing ICCE from January 1st 1984 to December 31st 1986 at the Department of Ophthalmology, Aalborg Hospital, Denmark. Information on the deaths of these patients was obtained from the Danish National Population Register. Information on mortality in Denmark was obtained from published statistics. RESULTS: We found an increased mortality among the patients with cataract with an SMR (standard mortality rate) of 1.12 (95% confidence interval 1.02-1.23). The slightly increased mortality was observed for both men and women and for all examined causes of death. CONCLUSION: The slightly increased mortality among patients with cataract may indicate a general deterioration of health for these patients.

Bivariate analysis of surgically induced regular astigmatism. Mathematical analysis and graphical display.

OBJECTIVE: The purpose of the study was to develop methods for simultaneous description of astigmatic direction and magnitude on aggregate data, with special reference to refractive surgery. DESIGN: Mathematical analysis of astigmatisms employing bivariate statistical methods. RESULTS: The mean of several astigmatisms is a new astigmatism of specific direction and magnitude, while the confidence region is an area, which may be determined exactly. CONCLUSIONS: Astigmatisms may conveniently be symbolized as an astigmatic direction and magnitude, but are actually composed of refractive powers in the form of polar values. We are operating with two different entities, a net astigmatism and a power vector in the form of polar values. There is an unequivocal point-to-point correlation between these entities. Mathematical conversions can only be performed with polar values, but never by using net astigmatisms. All net astigmatisms must be converted to their appropriate refractive powers and the relevant calculations performed with these entities. The final result, such as an average of several astigmatisms, variances or confidence areas, may be point-to-point reconverted to and symbolized by a net astigmatism. These principles allow for exact description and comparison of surgical methods, but may be employed to describe and analyze any other population of astigmatisms, such as subjective cylinders and spectacle corrections.

Retinal detachment following intracapsular cataract extraction. A 10-year follow-up study.

PURPOSE: To examine the incidence of and risk factors for retinal detachment during a 10-year follow-up on intracapsular cataract extraction (ICCE). METHODS: Retrospective analysis of medical records of 1041 eyes operated on with ICCE in the years 1984-86. A complete follow-up was achieved, and actuarial methods were used in the risk assessment. The risk time averaged 82 months. RESULTS: Twenty-two (2.1%) eyes developed retinal detachment; half of the cases occurred during the first postoperative year, but new cases emerged throughout the period. The cumulative incidence of RD amounted to 2.8%; 95% confidence interval: 1.5-4.2%. Multivariate Cox regression analysis identified younger age at surgery (relative risk for each 10-year increase in age=0.6; 95% confidence interval: 0.39-0.95) and male gender (relative risk=2.5; 95% confidence interval 1.04-6.04) as significant risk factors for RD. Eleven eyes, 50% of eyes with RD and 1% of the total number of eyes, lost useful vision in spite of retinal surgery. CONCLUSION: Even though the risk for both RD and an unfavourable result following retinal surgery may be smaller using contemporary surgical techniques, the present study indicates a substantial morbidity following cataract surgery, when a sufficiently long observation period is considered.

Intraocular lens power formula based on vergence calculation and lens design.

PURPOSE: To present a new method of intraocular lens (IOL) power calculation that takes into account the power-dependent variation in lens design. SETTING: Department of Ophthalmology, Aalborg, Denmark. METHODS: Information on exact IOL design is derived from the manufacturers' cutting cards. These data were built into an IOL calculation formula based on exact ray tracing and vergence calculation. All algorithms are demonstrated. RESULTS: The method is optically correct as all refractive surfaces are characterized with respect to both position and refractive power. In simulation models, the Naeser and the Holladay formulas performed similarly, while the SRK/T formula predicted higher postoperative refractions for low-power IOLs. CONCLUSION: It is possible to incorporate the exact IOL design into an IOL power calculation formula. Theoretically, the Naeser formula should increase the accuracy of IOL power calculation; however, this has yet to be proved from empirical data. The formula provides an advantage in analysis of postoperative pseudophakia for experimental/scientific purposes because all intraocular distances and powers may be measured or calculated.

Correlation between polar values and vector analysis.

PURPOSE: To evaluate the possible correlation between polar value and vector analysis assessment of surgically induced astigmatism. SETTING: Department of Ophthalmology, Aalborg Sygehus Syd, Denmark. METHODS: The correlation between polar values and vector analysis was evaluated by simple mathematical and optical methods using accepted principles of trigonometry and first-order optics. RESULTS: Vector analysis and polar values report different aspects of surgically induced astigmatism. Vector analysis describes the total astigmatic change, characterized by both astigmatic magnitude and direction, while the polar value method produces a single, reduced figure that reports flattening or steepening in preselected directions, usually the plane of the surgical meridian. There is a simple Pythagorean correlation between vector analysis and two polar values separated by an arch of 45 degrees. CONCLUSION: The polar value calculated in the surgical meridian indicates the power or the efficacy of the surgical procedure. The polar value calculated in a plane inclined 45 degrees to the surgical meridian indicates the degree of cylinder rotation induced by surgery. These two polar values can be used to obtain other relevant data such as magnitude, direction, and sphere of an induced cylinder. Consistent use of these methods will enable surgeons to control and in many cases reduce preoperative astigmatism.

Experience with a broth culture technique for diagnosis of bacterial keratitis.

PURPOSE: To determine if a broth culture technique is a practical means for bacteriological investigation of keratitis. MATERIAL AND METHODS: Twenty-seven eyes of 27 patients with a clinical diagnosis of bacterial keratitis were included in a prospective and non-comparative study at a Danish referral hospital. A corneal scrape was inoculated directly into broth medium which was transferred to the diagnostic laboratory for incubation and subculture. RESULTS: Culture was negative in 4 patients, and 19 of the remaining 23 patients had a pure growth of either Pseudomonas aeruginosa (n = 8), Staphylococcus aureus (n = 2), Streptococcus pneumoniae (n = 2), Haemophilus influenzae biotype III (n = 1), Moraxella species (n = 1), Corynebacterium species (n = 1), or coagulase-negative staphylococci (n = 4). In 4 patients there was a mixed gram-positive growth. There was no association between microbiological findings and previous topical antibiotic therapy. Contamination and lack of quantitative assessment of growth proved not to be a problem. CONCLUSIONS: By broth culture technique we identified a definite pathogen (P. aeruginosa, S. aureus or S. pneumoniae) in 44% of patients (95% binomial confidence limits: 25-65%). The technique may replace the standard technique of direct plate culture under circumstances where it is difficult to keep a supply of fresh media or transport inoculated plates.

Indications for cataract surgery in a Danish county 1980 and 1990.

From 1980 to 1990 the number of cataract extractions in our department increased from 268 to 827, i.e. 209% within the same referral area. A review was made to see if the indications for cataract extraction had changed in that period. The increase in frequency of cataract extractions was statistically significant in all age groups except males aged 60-69. The increase was most noticeable in the older age groups. Preoperative visual activities were moderately higher in 1990 compared with 1980. The frequency of second eye surgery did not change in the period. Females had in 1980 as in 1990 a higher frequency of cataract extractions than males in all age groups > 60 years.

Intraocular pressure seven years after extracapsular cataract extraction and sulcus implantation of a posterior chamber intraocular lens.

Seven years after extracapsular cataract extraction (ECCE) and sulcus implantation of a posterior chamber intraocular lens, we measured the intraocular pressure (IOP) in 28 eyes of 28 patients. The results were compared with the preoperative IOP and with the postoperative IOP at four months and 2 1/2 years. The mean IOP value seven years after surgery was 1.3 mm Hg lower than the preoperative mean value. No significant difference was found among the values at four months, 2 1/2 years, and seven years. One patient experienced a marked rise in IOP between 2 1/2 years and seven years and was excluded from the calculations. However, we could not tell whether it was a consequence of the cataract surgery. In this study, we found that IOP stabilized at a postoperative level that was significantly lower than the preoperative value and has remained there for seven years.

Refraction and anterior chamber depth before and after neodymium: YAG laser treatment for posterior capsule opacification in pseudophakic eyes: a prospective study.

Anterior chamber depth and refraction were evaluated in 52 pseudophakic eyes before and about one month after neodymium: YAG laser capsulotomy for posterior capsule opacification. External anterior chamber depth averaged 4.06 mm before and 4.07 mm after laser treatment, a statistically insignificant change. Mean spherical equivalent refraction before laser treatment, estimated from the prescription of spectacles, was 0.30 diopters (D). Mean subjective refraction after laser treatment was 0.24 D. The difference was not significant. Mean capsulotomy opening diameter increased from 3.44 mm +/- 0.61 mm (+/- SD) immediately after the laser treatment to 3.67 mm +/- 0.61 mm one month later. The increase was statistically significant. Intraocular lens position and spherical equivalent refraction did not change after the YAG laser capsulotomy, despite a significant increase in area of the capsulotomy opening.

Retinal detachment following intracapsular and extracapsular cataract extraction.

In 1984, our ophthalmology department switched from intracapsular cataract extraction (ICCE) to extracapsular cataract extraction (ECCE). We reviewed the postoperative incidence of retinal detachment (RD) in two consecutive series: (1) 604 eyes operated on by ICCE from 1982 to 1983 and (2) 1726 eyes operated on by ECCE from 1985 to 1986. Follow-up averaged 39 months in both groups. The RD incidence was 1.30% after ICCE and 0.41% after ECCE, a statistically significant difference. In both groups, the risk of RD was high for patients less than 70 years of age at the time of surgery but minimal for patients older than 70 years. The proportion of younger patients was significantly higher in the ICCE group (29.5%) than in the ECCE group (23.2%). When the data were stratified by age and the difference in age composition adjusted for statistically, the difference between the two groups in the incidence of postoperative RD was less pronounced. We conclude that although not significant at the 5% level after adjusting for age distribution, our results suggest a decreased risk of RD with ECCE.