Squaring the refractive power matrix, the equivalent of squaring the sphero-cylinder?
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Biomedical subjects
Publications and source records attributed to H Saunders.
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Changes in the axis of astigmatism have been followed up in the same individuals over several decades. Only a proportion of subjects with direct astigmatism in their youth change to inverse astigmatism by way of oblique astigmatism.
This study enquires into the manner in which the axis of astigmatism changes in the course of individual refractive histories. Specifically, two related problems are addressed: (1) how is the change from direct to inverse astigmatism mediated, and (2) what is the range of relative proportions of each of four variables (spherical ametropia, direct, inverse and oblique astigmatism) that occur in a sample population so that it can be considered randomly sampled and well distributed? Solutions to both problems are obtained by calculation of the probabilities with which transitions between such variables occur. A moderately sized longitudinal sample is used to demonstrate the new method. One of the conclusions is that the biological strategy for the mutation of the astigmatic axis is multi-faceted and that there is unlikely to be a single cause which can explain the process by which inverse astigmatism is achieved.
Following on from a cross-sectional analysis of refraction data (Saunders, 1981), the present paper attempts the evaluation of serial recordings of a new sample of refractive corrections using longitudinal methods. This study compares the results of the cross-sectional and longitudinal methods, investigates whether or not the latter supports the conclusions of the former, examines to what accuracy this is achieved and, where the results differ, seeks a reason for this. It is demonstrated that in spite of such differences the two methods coincide in their conclusions.
A sample population of myopes with an initial correction of 2 DS or more is extracted from the longitudinal sample of ametropes reported by Saunders (1986). The myopes are partitioned by means of cluster analysis and, as a result, three distinct groups of myopes are identified. The time/regression equations which best describe the groups are stated. It is concluded that meaningful long-term prognosis of medium and high myopes is unlikely and that reasonable prediction of short-term trends requires at least two consecutive refraction data to determine the group allocation of a myope.
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A new regression equation for the change in the axis of astigmatism with age, as deduced from cross-sectional studies, is presented. Possible artefacts arising from the methods used to obtain mean prescriptions are discussed; it is shown that these may result in over-estimation of the occurrence of oblique cylinders in middle-age and that a previously demonstrated gradual change of orientation of the axis of astigmatism may have no basis in reality. The need for further longitudinal studies is emphasized.
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Sphero-cylinders are shown to be representable by formal vectors. An algebra applicable to sphero-cylinders is stated and mathematically consistent operations are defined. Examples of practical applications of some operations are given.
Parametric statistical analysis requires a rule by which the variates are quantitatively ranked. In this study an isomorphic transformation of sphero-cylinders is developed and two alternative ranking hierarchies for the sphero-cylinder are proposed.
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The validity and efficacy of the prognosis equation published by Saunders (1984b) is tested against previously reported longitudinal data. In a fair and random sample and over a short interval, nearly 60% of the sample was found to have a prediction error of less than 0.25 DS and, in 92%, the error involved was less than 0.5 DS. Long-term prediction was found to have a less favourable outcome but 50% were correct within an error of 0.5 DS and 90% were found to have a prediction error of less than 1 DS. The largest prediction errors occur in the medium to high myopes whose myopia progresses rapidly.
The question is posed as to why the modulus of the astigmatic vector appears to be randomly distributed with age. This paper investigates astigmatic population distributions. On the assumption of statistical independence, the expected probabilities are determined and compared with the observed values. Measures of central location are examined so as to determine skew distributions. A correlation is sought between the spherical and the astigmatic components of refractive corrections. It is concluded that the modulus is age-dependent but that the variations that occur across the age groups are smaller than can be measured by clinical routines.
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An investigation is made into the correlation between anterior chamber volume and intra-ocular pressure. It is suggested that patients can be screened for possible ocular hypertension by measuring their corneal radii and the depth of their anterior chamber. A nomogram shows which combinations of the parameters may lead to ocular hypertension and thus indicates which patients need to be investigated at greater length.
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