Principal Meridians Research Articles

Refractive error and ocular biometry in Jordanian adults

The aim of this study was to establish the prevalence of refractive errors in Jordanian adults of working age, and to study the ocular biometric correlates of refractive error in this population. Refractive error and ocular biometry were measured in 1093 Jordanian adult subjects aged 17-40 years to determine the prevalence of refractive error, and explore structural correlations of ametropia. Refractive error was measured using a Grand-Seiko GR-3100K closed-view infrared autorefractor. Ocular component measurements were made using A-scan ultrasonography and autokeratometry. The prevalence of myopia [spherical equivalent refraction (SER) less than -0.50 DS] and hyperopia (SER greater than +0.50 DS) was 53.71 and 5.67% respectively; 40.62% of the sample was emmetropic (refraction between +0.50 D and -0.50 D inclusive in both principal meridians). The distribution of SER was found to show marked leptokurtosis, exhibiting a peak between plano and 1 D of myopia. Corneal radius, anterior chamber depth, crystalline lens thickness, vitreous chamber depth and axial length (AL) parameters were normally distributed in the population studied. AL to corneal curvature ratio was not normally distributed, and showed marked leptokurtosis. Linear regression analysis showed that AL correlated most closely with spherical equivalent refractive error. This study has established a database of refractive error prevalence and ocular biometric correlates of ametropia in a Middle Eastern population of working age.

Comparison of Keratometric and Topographic Cylinder and Axis Measurements on Normal Corneas with Low Astigmatism

To evaluate agreement in measurements of astigmatic axis power and location between keratometry and computer assisted videokeratography (corneal topography) on normal corneas with less than 1.50 D of idiopathic astigmatism. Keratometric readings with the 10 SL/O Zeiss ophthalmometer and corneal topographic maps with the TMS-1 were obtained by two independent examiners on 32 normal corneas. Measurement agreement between the two instruments was evaluated in regard to steep and flat meridian power and location, and in astigmatism magnitude (D). The limits of agreement (d-2 SD to d+2 SD) between the two instruments were found to be broad for clinical purposes in measuring the steep meridian power (-0.16 to -1.20 D), flat meridian power (0.43 to -1.25 D), and astigmatism (0.60 to -1.12 D). A constant bias of the TMS-1 towards the 10 SL/O Zeiss ophthalmometer was found, in measuring steeper both principal meridians and higher amount of astigmatism. Mean location difference was 19 degrees (+/-190) for the steep meridian and 17 degrees (+/-20 degrees) for the flat meridian. Despite the differences seen in measurements between the 10 SL/O ophthalmometer and the TMS-1, these differences may be clinically small enough for the methods to be used interchangeably in measuring only the magnitude of astigmatism on normal corneas. However, the disagreement in astigmatism axes is too great to be ignored.

Very High Frequency Ultrasound Biometry of the Anterior and Posterior Chamber Diameter

To measure the largest diameter of the anterior chamber (AC) and posterior chamber (PC) dimension and its orientation and determine the relationship with the principal keratometric meridians. Twenty-eight eyes of 14 subjects were scanned with high frequency (50 MHz) ultrasound in sequential meridional scan planes at 30 degrees increments. Observer identified angle and ciliary sulcus recess boundaries in each patient scan set were fit with an elliptical model to obtain the ellipse semi-major axis corresponding to the largest diameter and its meridional orientation. Anterior and posterior chamber diameters from raw data and model fit were compared using linear statistics. Circular statistics were used to compare the orientation of the largest diameter for raw ultrasound measurements, model estimations of largest diameter, and autorefractor determined keratometric axes. The mean model diameters were anterior chamber OD 12.07 mm (0.32 SD); anterior chamber OS 12.06 mm (0.36 SD); posterior chamber OD 12.35 mm (0.42 SD); posterior chamber OS 12.33 mm (0.43 SD). The general trend for orientation of the meridian of largest diameter was in the horizontal meridian. In over 35% of eyes the difference between AC or PC meridian and the flat keratometric axis was greater than 20 degrees. Accurate and reproducible anterior segment biometry depends on visualization of structures and minimization of eye and head movement error. The range and standard deviation of the diameter and orientation measures suggests anatomic variation is sufficient to require biometry for proper sizing and placement of intraocular devices that use angle or sulcus fixation.

Effects of optically imposed astigmatism on emmetropization in infant monkeys.

Although astigmatism is prevalent during early infancy, the influence of astigmatism on early refractive development is unclear. This study was undertaken to determine the effects of astigmatism on emmetropization in monkeys. Infant rhesus monkeys (n = 39) were exposed to optically simulated astigmatism in one or both eyes from approximately 1 to 4 months of age. With-the-rule, against-the-rule, and oblique astigmatisms were optically simulated by appropriately orienting the principal meridians of the spherocylindrical treatment lenses (+1.50 -3.00 D x 90 degrees, 180 degrees, 45 degrees, or 135 degrees; i.e., +1.50 and -1.50 D powers in the two principal meridians). Refractive development was assessed every 2 to 3 weeks by cycloplegic retinoscopy, keratometry and corneal videotopography, and A-scan ultrasonography. Data from 19 control monkeys, including 3 animals that were reared with binocular plano lenses, were used for comparison purposes. Most of the cylinder-lens-reared monkeys, regardless of the orientation of the imposed astigmatism, showed clear signs of either hyperopic or myopic growth compared with control monkeys. The distributions of refractive error and vitreous chamber depth both showed bimodal patterns that differed from normal by amounts equivalent to the optical powers of the principal meridians of the treatment lenses. More frequently, refractive development was biased toward the eye's least-hyperopic focal plane. The refractive changes were mainly axial. After lens removal, the lens-reared monkeys recovered and as a group exhibited refractive errors and axial dimensions similar to those in control monkeys. In the presence of significant amounts of astigmatism, emmetropization is directed toward one of the two focal planes associated with the astigmatic principal meridians and not the circle of least confusion. These results suggest that the mechanisms responsible for emmetropization are insensitive to stimulus orientation and the global form of the retinal image. It appears that emmetropization seeks out the image plane that contains the maximum effective contrast integrated across spatial frequency and stimulus orientation.

Influence of akupoints of principal meridians on a skeletal musculation of the person

The author asserts, that each point of Principal meridian renders differential influence on a skeletal musculation. Particularly on each muscle renders direct influence four points, though there are also exceptions. Whereas the quantity of muscles size constant, occurs an opportunity to prognosticate opening new points. The creation of the completed system of active points of a body will enable to lead Qi in any site of a skeletal musculation of the person, and system will allow to describe interrelation between akupoints and skeletal muscles. And though the belonging of points to a concrete meridian is defined by their direct influence on an internal body usually appropriate to the name of a meridian. Nevertheless, this difficult process of identification is easier for beginning from interrelation akupoints and skeletal muscles. The detailed description of influence of each concrete point on sites of skeletal muscles, internal bodies, veins, arteries will frame an opportunity to consider very exact influence of each point on all organism as a whole. On an example of the Lung meridian will are considered general principles of interaction between akupoints and skeletal musculation. Muscularly––tendon meridians described in the ancient medical treatises to the given work have no any attitude.

Refractive error and ethnicity in children.

To report the baseline prevalence of refractive error in the study population. A multicenter, longitudinal, observational study of refractive error and ocular development in children from 4 ethnic groups. The study population included 2523 children (534 African American, 491 Asian, 463 Hispanic, and 1035 white) in grades 1 to 8 (age, 5-17 years). Myopia was defined as -0.75 diopters (D) or more and hyperopia as +1.25 D or more in each principal meridian, and astigmatism was defined as at least a 1.00-D difference between the 2 principal meridians (cycloplegic autorefraction). Overall, 9.2% of the children were myopic, 12.8% were hyperopic, and 28.4% were astigmatic. There were significant differences in the refractive error prevalences as a function of ethnicity (chi2, P<.001), even after controlling for age and sex (polychotomous logistic regression, P<.001). For myopia, Asians had the highest prevalence (18.5%), followed by Hispanics (13.2%). Whites had the lowest prevalence of myopia (4.4%), which was not significantly different from African Americans (6.6%). For hyperopia, whites had the highest prevalence (19.3%), followed by Hispanics (12.7%). Asians had the lowest prevalence of hyperopia (6.3%) and were not significantly different from African Americans (6.4%). For astigmatism, Asians and Hispanics had the highest prevalences (33.6% and 36.9%, respectively) and did not differ from each other (P =.17). African Americans had the lowest prevalence of astigmatism (20.0%), followed by whites (26.4%). There were significant differences in the prevalence of refractive errors among ethnic groups, even after controlling for age and sex (P<.001).

The asphericity, curvature and tilt of the human cornea measured using a videokeratoscope.

The EyeSys videokeratoscope (VK) measurements of the principal corneal meridians of 98 subjects already analysed by Douthwaite et al. [Ophthal. Physiol. Opt. (1999)19:467-474] were re-analysed in order to revise the assessment of asphericity, to derive information on corneal tilt and to assess the degree to which the corneal section approximates to that of a conic section. The range of normality for the revised p-value (asphericity) was from 0.57 to 0.97 for the near horizontal and from 0.56 to 1.08 in the near vertical principal meridians. The approximate corneal tilt angles ranged from -3.95 to +8.13 degrees in the horizontal and from -8.99 to +9.33 degrees in the vertical meridian. A tilted conicoidal surface will display a linear relationship (r = 1) when a scatterplot is drawn of the perpendicular distance squared vs radius squared, after first averaging the two semimeridian results for each VK ring. Analysing the results from the human cornea in the same way allows an assessment of the degree to which the corneal section approximates to that of the conic section.

Oculomotor consequences of feeble image size inequality at near reading distance.

Reading and working with a computer screen are activities of everyday life that take place at near vision. This study examines whether at such a near distance, normal subjects are capable of modifying the natural conjugacy of their saccades when exposed to a feeble image size inequality of 2%; similar inequality exists for persons who wear spectacles of slightly different power for the two eyes. Subjects were seated at 40 cm in front of a screen where a random dot pattern was projected. They were asked to make saccades of 7.5 degrees and 15 degrees along the horizontal and vertical principal meridians and horizontal saccades between secondary and tertiary positions in the upper and lower field. Five subjects performed the experiment with a 2% overall reduction lens inserted over their dominant eye; three subjects participated in a second experiment with an overall magnification lens of 2% also inserted in front of the dominant eye. The results showed a persistent decrease or increase in the size of the saccade of the dominant eye that was subject dependent for horizontal saccades, but consistent over subjects for vertical saccades. Persistent disconjugacy, at least for vertical saccades, is interpreted as evidence of learning.

Determining the power of a thin toric intraocular lens in an astigmatic eye.

Astigmatism poses a number of special difficulties when attempting to achieve a desirable refractive outcome during cataract surgery and intraocular lens implantation. One of the most pertinent difficulties is that traditional Gaussian theoretical formulas are simply unable to handle general astigmatic optical systems, that is, systems in which the principal meridians of the refracting interfaces do not lie in two mutually orthogonal planes. This means that the traditional approach falls short when the cornea is treated as bitoric or when other toric optical devices are already present in the eye. In this paper, the modified step-along procedure is utilized in a demonstration of the derivation of the traditional Gaussian theoretical formulas for the determination of intraocular lens power in a stigmatic eye. Matrices are then used to derive a general formula for the determination of the power of a thin toric intraocular lens in an astigmatic eye. This formula is then modified to allow the user to determine the power of the secondary intraocular lens required to compensate for any residual refraction in a phakic or pseudophakic astigmatic eye. The formulas hold under all conditions, including the case when the cornea is treated as thick and bitoric and when other toric optical devices are already present in the eye. Worked examples are provided.

The stenopaeic slit: an analytical expression to quantify its optical effects in front of an astigmatic eye.

The stenopaeic slit is a trial case accessory used in subjective refraction, especially when high astigmatism is present. In spite of its simplicity, the effect of the slit when it is not oriented along one of the principal meridians of the examined eye is difficult to predict, even in terms of classical geometrical optics. In this paper, the optical principles of the slit are considered with full details in the theoretical framework of the dioptric power space. An analytical expression to obtain the residual refractive error when a stenopaeic slit is placed in front of an astigmatic eye at any orientation is deduced. In the light of these results, some aspects of the clinical procedure are discussed.

The stenopaeic slit: an analytical expression to quantify its optical effects in front of an astigmatic eye

The stenopaeic slit is a trial case accessory used in subjective refraction, especially when high astigmatism is present. In spite of its simplicity, the effect of the slit when it is not oriented along one of the principal meridians of the examined eye is difficult to predict, even in terms of classical geometrical optics. In this paper, the optical principles of the slit are considered with full details in the theoretical framework of the dioptric power space. An analytical expression to obtain the residual refractive error when a stenopaeic slit is placed in front of an astigmatic eye at any orientation is deduced. In the light of these results, some aspects of the clinical procedure are discussed.

Interconverting the matrix and principal meridional representations of dioptric power in general including powers with nonorthogonal and complex principal meridians.

The principal meridians of the powers of thick astigmatic systems, like the eye, are not necessarily at right angles. The consequence is a class of phenomena included in the category commonly described as irregular astigmatism. The conventional principal meridional representation of power, however, is unsuited to quantitative analysis. This paper presents equations for converting from the principal meridional form of power to a representation, the dioptric power matrix, which is amenable to quantitative analysis. It generalizes an earlier paper which treated only powers of a conventional form in which the principal meridians are always at right angles. It copes in particular with what are known as asymmetric powers. A routine is also presented for converting in the reverse direction, from the power matrix to the principal meridional form of power. The principal meridional form of power turns out not always to be unique, there being distinct powers (they are asymmetric) with the same principal powers and meridians. Thus, in general, the dioptric power matrix is a satisfactory representation of power while the principal meridional representation is not.

Interconverting the matrix and principal meridional representations of dioptric power in general including powers with nonorthogonal and complex principal meridians

The principal meridians of the powers of thick astigmatic systems, like the eye, are not necessarily at right angles. The consequence is a class of phenomena included in the category commonly described as irregular astigmatism. The conventional principal meridional representation of power, however, is unsuited to quantitative analysis. This paper presents equations for converting from the principal meridional form of power to a representation, the dioptric power matrix, which is amenable to quantitative analysis. It generalizes an earlier paper which treated only powers of a conventional form in which the principal meridians are always at right angles. It copes in particular with what are known as asymmetric powers. A routine is also presented for converting in the reverse direction, from the power matrix to the principal meridional form of power. The principal meridional form of power turns out not always to be unique, there being distinct powers (they are asymmetric) with the same principal powers and meridians. Thus, in general, the dioptric power matrix is a satisfactory representation of power while the principal meridional representation is not.

Rigid gas permeable contact lens and corneal topography

We investigated the effect of high Dk daily wear rigid gas permeable contact lenses on corneal topography. Eight young myopic subjects wore hard contact lenses for 21 days. Corneal topography was monitored using the EyeSys system. It was measured every day during the next 21 days after the fitting. We recorded the corneal radius of curvature at 16 peripheral points approximately 1, 2, 3 and 4mm along the four principal meridians (nasal, superior, inferior and temporal). Our study showed that daily wear RGP Forum 210 does not produce significant alterations of the corneal curvature as a function of time.

Disconjugate oculomotor learning caused by feeble image-size inequality: differences between secondary and tertiary positions

In order to examine the minimum value of image-size inequality capable of inducing lasting disconjugacy of the amplitude of saccades, six normal emmetropic subjects were exposed for 16 min to 2% image size inequality. Subjects were seated at 1 m in front of a screen where a random-dot pattern was projected and made saccades of 7.5 and 15 deg along the horizontal and vertical principal meridians and to tertiary positions in the upper and lower field. During the training period, compensatory disconjugacy of the amplitude of the saccades occurred for the principal horizontal and vertical meridians; such increased disconjugacy persisted after training, suggesting learning. In contrast, for horizontal saccades to or from tertiary positions made in the upper and lower field, no consistent changes in the disconjugacy occurred, either during training or after the training condition. In an additional experiment, three subjects read sequences of words with the 2% magnifier in front of their dominant eye: in such a task, horizontal saccades to or from tertiary positions at the upper or lower field showed appropriate and lasting disconjugacy for two of the three subjects. We conclude that even a 2% image size inequality stimulates oculomotor learning, leading to persistent disconjugacy of saccades. The small disparity created by the image-size inequality is thus compensated by the oculomotor system rather than tolerated by the sensory system (e.g. by enlarging the Panum's area).

Interconverting the matrix and principal‐meridional representations of dioptric power and reduced vergence

Converting the traditional representation of power as sphere, cylinder and axis to the dioptric power matrix F is usually performed by means of Long's equations and the reverse process by means of Keating's equations. It is sometimes useful to be able to convert directly between the matrix and power expressed in terms of principal powers F1 and F2 along corresponding principal meridians at angles a1 and a2. The equations for interconverting F and the principal-meridional representation expressed as F1(a1)F2 are presented here. Equivalent equations allow direct interconversion of the reduced vergence matrix L and the principal-meridional representation of vergence L1(a1)L2. Vergence becomes infinite at line and point focuses. Similarly effective power and back- and front-vertex power are infinite for some systems. Nevertheless it is possible unambiguously to represent infinite vergence and vertex power in principal-meridional form. However, information is usually lost in these infinite cases when the principal-meridional representation is converted to the matrix representation, and the former is not recoverable from the latter. As a consequence the matrix representation is usually unsatisfactory for vergences and vertex powers that are infinite. On the other hand, the principal-meridional representation of vergence and power is always satisfactory. If one adopts the position that effective powers and vertex powers are really vergences rather than powers then one concludes that the matrix provides a satisfactory representation for powers of thin systems in general but not for vergences. Implied by a vergence at a point is an interval of Sturm. The equations for characterizing the interval from the reduced vergence are presented.

Interconverting the matrix and principal-meridional representations of dioptric power and reduced vergence

Converting the traditional representation of power as sphere, cylinder and axis to the dioptric power matrix F is usually performed by means of Long's equations and the reverse process by means of Keating's equations. It is sometimes useful to be able to convert directly between the matrix and power expressed in terms of principal powers F1 and F2 along corresponding principal meridians at angles a1 and a2. The equations for interconverting F and the principal-meridional representation expressed as F1{a1}F2 are presented here. Equivalent equations allow direct interconversion of the reduced vergence matrix L and the principal-meridional representation of vergence L1{a1}L2. Vergence becomes infinite at line and point focuses. Similarly effective power and back- and front-vertex power are infinite for some systems. Nevertheless it is possible unambiguously to represent infinite vergence and vertex power in principal-meridional form. However, information is usually lost in these infinite cases when the principal-meridional representation is converted to the matrix representation, and the former is not recoverable from the latter. As a consequence the matrix representation is usually unsatisfactory for vergences and vertex powers that are infinite. On the other hand, the principal-meridional representation of vergence and power is always satisfactory. If one adopts the position that effective powers and vertex powers are really vergences rather than powers then one concludes that the matrix provides a satisfactory representation for powers of thin systems in general but not for vergences. Implied by a vergence at a point is an interval of Sturm. The equations for characterizing the interval from the reduced vergence are presented.

Profilometry of toroidal surfaces with an improved Ronchi test

An implementation of the well-known Ronchi test technique, which allows for the profilometric measurement of nonrotationally symmetrical surfaces, is presented and applied to the measurement of toroidal surfaces. Both the experimental setup and the data-processing procedures are described, and parameters such as the radius of curvature of the sample surface, the orientation of its principal meridians, and the position of its vertex are measured by means of the values of the local normal to the surface obtained at a set of sampling points. Integration of these local normal values allows for the reconstruction of the three-dimensional profile of the toroidal surface considered with micrometric accuracy, and submicrometric surface details may be calculated by use of surface-fitting procedures. The density of sampling points on the surface may be tailored to fit test requirements, within certain limits that depend on selection of experimental setup.

Corneal shape of Hong Kong‐Chinese⋆

SummaryCorneal asphericity (the p‐value, p) and apical corneal radius (r0) were calculated for 63 Hong Kong‐Chinese (39 male and 24 female), using the Topographic Modeling System (TMS‐1). The values of p and r0 in, and between, the two principal meridians were compared, and the effects of refractive error and gender were also investigated. The mean±SD r0 and p along the flattest meridian of the right eye were 7.82±0.26 mm and 0.78±0.12 respectively. The mean±SD r0 and p along the steepest meridian of the right eye were 7.64±0.26 mm and 0.83±0.15 respectively. Meridional variations were found in r0 and in p. There was no correlation between p and r0 along the two principal meridians. p was not significantly correlated to the refractive error but r0 was. Our results agree with previous findings that while males have longer r0 than females, their p are not significantly different.

Corneal shape of Hong Kong-Chinese

Corneal asphericity (the p-value, p) and apical corneal radius (r0) were calculated for 63 Hong Kong-Chinese (39 male and 24 female), using the Topographic Modeling System (TMS-1). The values of p and r0 in, and between, the two principal meridians were compared, and the effects of refractive error and gender were also investigated. The mean±SD r0 and p along the flattest meridian of the right eye were 7.82±0.26 mm and 0.78±0.12 respectively. The mean±SD r0 and p along the steepest meridian of the right eye were 7.64±0.26 mm and 0.83±0.15 respectively. Meridional variations were found in r0 and in p. There was no correlation between p and r0 along the two principal meridians. p was not significantly correlated to the refractive error but r0 was. Our results agree with previous findings that while males have longer r0 than females, their p are not significantly different.