A Psychophysical Investigation of Ocular Expansion in Human Eyes

Abstract

purpose. To investigate spatial anisotropies in the peripheral visual field of axially myopic eyes, in an attempt to distinguish between models of isotropic and anisotropic ocular stretching.

methods. Stimuli consisted of two high-contrast Gaussian patches presented in one of four orientations (90°, 180°, 45°, or 135°). For each orientation, perceived separation was established relative to that for all other orientations. The experiment was conducted with central fixation and at 15° in the nasal and inferior visual fields. Eleven myopes and nine emmetropes participated in the study. Biometric data were collected from all subjects.

results. For foveal fixation, the magnitude of the spatial anisotropy (∼5%) was consistent with the well-documented horizontal-vertical illusion (HVI), and unrelated to axial length. In the nasal visual field, much larger misperceptions were found (∼19%), the magnitude of which increased significantly with increasing axial length. Inferiorly, a reversal of the traditional HVI is found in most subjects (∼7%), with a tendency for a larger reversed illusion with increasing axial length. Differences between nasal and inferior misperceptions were significantly correlated with axial length.

conclusions. Isotropic stretching, such as globe expansion, should preserve the aspect ratios of receptive fields, predicting a separation misperception which is independent of axial length. In contrast, the magnitude of the misperception is significantly correlated with axial length, supporting anisotropic stretching models of myopic growth.

Human myopia is primarily the result of elongation of the posterior chamber, ^{1 2 3 4} with changes in corneal curvature and lens power playing a limited role. ³ Clinically, it is well known that ocular elongation in myopic eyes results in retinal stretching. However, the impact of this stretching process on visual performance has produced conflicting results. A number of studies have reported reductions in visual acuity and contrast sensitivity with increasing degrees of myopia in both spectacle ^{5 6} and contact lens wearers, ⁷ whereas others have shown no significant differences in contrast sensitivity with increasing myopia. ^{8 9 10} The influence of retinal stretching on visual performance in myopic eyes depends critically on the nature of eye growth. This could take several possible forms. For example, it could result from an overall expansion of the globe or from more localized growth at the equator or posterior pole. ⁷ Results in previous human studies investigating the shape of myopic eyes have suggested that a general expansion of the vitreous chamber is the main feature of myopic eye growth. ¹ In contrast, findings in other studies have suggested that growth occurs primarily in an anisotropic manner, localized to the posterior pole. ^{4 11 12 13} Indeed, most pathologic fundal changes in high myopia occur in the central area of the posterior pole. ^{14 15} Understanding the nature of ocular expansion has important implications for foveal and peripheral visual performance, both of which are dependent on the structural properties of retinal units. 

McGraw and Whitaker ¹⁶ suggested that the radial/tangential anisotropies of visual space, observed in the visual field of normal observers, were related to the known physiological properties of retinal ganglion cells. ^{17 18 19} Specifically, aspect ratios of ganglion cell receptive fields were consistent with the direction, or orientation, of greatest spatial misperception. This view is supported by Westheimer, ²⁰ who suggested that relative orientation discrimination thresholds, measured in different regions of the visual field, were a consequence of the structural properties of visual sensory organization. If myopic ocular expansion is isotropic (e.g., the type of global expansion seen when a round balloon is blown up), aspect ratios of ganglion cell receptive fields would be maintained resulting in a similar pattern of misperceptions to that found in emmetropic observers. However, if stretching is anisotropic (e.g., the type of expansion seen when a sausage shape balloon is inflated), changes in the aspect ratios of ganglion cell receptive fields occur, resulting in an altered pattern of spatial misperceptions. Furthermore, in this case, the magnitude of spatial misperceptions should be related to the degree of anisotropic stretching. In this study, we measured the pattern of spatial misperceptions at different visual field locations, in normal and myopic eyes, in an attempt to elucidate the nature of ocular stretching mechanisms in human axial myopia. 

Methods

Subjects

Twenty visually normal observers participated in the study (nine emmetropes, mean refraction, −0.06 ± 0.40 DS; range, +0.50 to −0.75 DS; and 11 myopes, mean refraction, −7.15 ± 1.60 DS; range, −5.00 to −9.75 DS). Ophthalmoscopic examination was performed on each subject and revealed no pathologic fundal changes. All subjects had a corrected visual acuity level of 0 logarithm of the minimum angle of resolution (logMAR) or better, no anisometropia (differences <1.00 DS), and <1.00 DC of astigmatism in the eye examined. Full subjective refraction was undertaken before the experiment and correction by ultrathin soft contact lenses was performed where necessary. This is particularly important in the myopic group, in which ophthalmic lens correction introduces various amounts of spectacle minification. Informed consent was obtained from all subjects, and the tenets of the Declaration of Helsinki were observed throughout. 

Stimuli

Stimuli consisted of two high-contrast, luminance-defined Gaussian patches presented in one of four orientations (vertical [90°], horizontal [180°], oblique right [45°], and oblique left [135°]). The mathematical description of the Gaussian patches is given by:  

\[L_{\mathrm{mean}}{+}A\ \mathrm{exp}({-}(x^{2}{+}y^{2})/2{\sigma}^{2}),\]

where L _mean is the mean luminance of the background, A is the amplitude, and σ is the SD of the Gaussian envelope. The vertical and horizontal distances from the peak of the Gaussian envelope are denoted by x and y. Stimuli were generated using the macro capabilities of the public domain software NIH image 1.62 PPC and presented on a 17-in. color monitor (CTX Technology Corp., City of Industry, CA), at a mean luminance of 22 cd/m² and a frame rate of 75 Hz. The nonlinear luminance response of the display was linearized, by using the inverse function of the luminance response, as measured with a photometer (CS-100; Minolta; Osaka, Japan; host computer, Power Macintosh 7200/90; Apple Computer, Cupertino, CA). 

Procedures

On a single 200-ms presentation, any one of seven predetermined separations and four patch orientations was displayed. After each presentation, the subject was required to indicate whether the separation between the patches was perceived to be larger or smaller than the mean of all the previous presentations. ^{21 22 23} The results of the first 20 trials were discarded to allow the subjects to construct their own internal metric with which to compare each trial, after which 40 trials were presented at each combination of separation and orientation. Tasks of this type, in which a single standard is maintained across a dimension such as separation, can be performed with relative ease. ^{18 19} The resultant psychometric functions for each orientation were fitted with a logistic function of the form  

\[y{=}\frac{100}{1{+}e^{{-}{[}(x{-}{\mu})/{\theta}{]}}},\]

where μ is the offset corresponding to the 50% level on the psychometric function (point of subjective equality, PSE), and θ is an estimate of threshold (half the interval between the 27% and 73% levels on the psychometric function, approximately). 

For foveal presentations stimuli were centered on fixation, whereas extrafoveal presentations were made 15° from fixation. Inferior and nasal visual field locations were selected for extrafoveal observations, to avoid potential problems with the physiological blind spot. Since extrafoveal observations were within the central 15° of the visual field, no additional peripheral refractive correction was necessary. ²⁴ Moreover, judgments of spatial localization demonstrate a marked resistance to optical degradation. ²⁵ The baseline separation of the Gaussian blobs was maintained at 10°. All observations were monocular, and subjects undertook several practice sessions before data collection. Experimental trials were performed in a dimly lit room to avoid monitor reflections. In addition, biometric data were collected from all subjects by using an ultrasonograph (Echo Scan US-800; Nidek, Gamagori, Japan). Axial length measurements were taken while the corrected fellow eye fixated a central target situated at 3 m. 

Analysis

Figure 1represents an example of one subject’s foveal data set, showing the percentage of times each stimulus separation was rated as smaller than the mean. As actual separation increased, the percentage of smaller responses predictably decreased. The important point, however, is that horizontal presentations generated a consistently higher percentage of smaller responses than did vertical presentations. This would be expected based on the traditional horizontal-vertical illusion (HVI), because vertical distances are perceived as being larger. Individual psychometric functions were fitted to the data sets at each of the four stimulus orientations, and, from this, the separation required to be perceived as equal to the mean (separation producing 50% smaller responses) was calculated. 

The four separation estimates obtained from the type of data plot shown in Figure 1were then plotted against orientation (Fig. 2) . The data were then fitted with an elliptical function using a method of least squares. ¹⁶ The textbook description of an ellipse in polar coordinates is given by  

\[{[}(a^{2}\mathrm{cos}^{2}{\theta}){+}(b^{2}\mathrm{sin}^{2}{\theta}){]},\]

where a is the magnitude of the major axis of the ellipse, b is the minor axis, and θ is the orientation of the major axis of the ellipse. From this curve fit, we calculated the separation required to be perceived as equal to the mean along both the horizontal (0°) and the vertical (90°) meridians. The dashed lines in Figure 2demonstrate the extrapolated y-values corresponding to the horizontal and vertical orientations. One might argue that we could have simply used the 0° and 90° estimates obtained from the psychometric functions in Figure 1and, in the majority of cases, this would have produced very similar results. However, our ellipse-fitting procedure is more inclusive, in that it allows the oblique data to contribute to the final estimates. 

We then calculated the magnitude of the HVI by expressing the difference between the horizontal (S ₀) and vertical (S ₉₀) separation estimates from Figure 2as a percentage of the mean separation  

\[{[}2(S_{0}{-}S_{90})/(S_{0}{+}S_{90}){]}\ {\cdot}\ 100.\]

 

Thus, the traditional HVI is represented by positive values, whereas the reverse (vertical separations larger than horizontal to be perceived equal) is represented by negative values. 

Results

Perhaps unsurprisingly, a significant correlation (factorial ANOVA, F_1,18 = 55.72, P < 0.01) was found between axial length and refractive error, a finding consistent with previous reports. ^{2 6} For foveal viewing conditions, the magnitude of the illusion was consistent with the well-documented HVI, ²⁶ and vertical space was consistently perceived as being larger than a physically equivalent horizontal separation. Values of HVI were consistent between subjects at a baseline separation of 10° (mean, 5.08% ± 0.73%). The magnitude of the spatial misperception, under foveal viewing conditions, did not change with either axial length (factorial ANOVA, F_1,18 = 0.05, P = 0.83; Fig. 3 ) or refractive error (factorial ANOVA, F_1,18 = 0.52, P = 0.48). 

In the nasal visual field much larger misperceptions were found than at the fovea (mean, 18.63% ± 0.93%). However, the pattern of misperception was similar, with vertical separations perceptually expanded relative to their horizontal counterparts. In the inferior visual field, the illusion was reversed, and horizontal space was expanded relative to vertical space (mean, 6.88% ± 1.37%). 

The magnitude of the spatial misperceptions increased significantly with increasing axial length in the nasal field (factorial ANOVA, F_1,18 = 14.91, P < 0.01; see Fig. 4 ). In the inferior visual field, the magnitude of the orientational misperception decreased with axial length measurement, but the decrease did not reach statistical significance (factorial ANOVA, F_1,18 = 3.91, P = 0.06; Fig. 5 ). 

Previous investigations of spatial anisotropies across the visual field have concluded that the horizontal vertical anisotropy, so readily demonstrated at the fovea, takes on a radial/tangential arrangement in the periphery. ¹⁶ Indeed, threshold data on a number of spatial tasks support this finding. ^{25 27 28 29 30} However, in the peripheral visual field, the misperception, although predominantly radial/tangential, still shows some bias toward vertical orientations. Therefore, the overall perceptual output probably reflects a combination of a radial/tangential anisotropy, and a residual horizontal/vertical anisotropy. ¹⁶ This would account for the differences in magnitude of the effect between horizontal (nasal) and vertical (inferior) visual field locations, but would not account for the increasing spatial misperception that occurs as axial length increases. In the nasal visual field, the two forms of misperception summate to produce a larger misperception, while inferiorly the radial/tangential effect is offset by the horizontal/vertical effect, thus restricting the magnitude of the overall misperception at this field location. 

The residual horizontal/vertical effect can be negated by directly comparing the difference in magnitude of the misperceptions at both nasal and inferior visual field locations, in the same subject. Differences in the magnitude between nasal and inferior misperceptions are plotted as a function of axial length in Figure 6 . This figure clearly demonstrates that the radial/tangential anisotropy, when expressed as a difference between the two field locations, increased significantly with axial length (factorial ANOVA, F_1,18 = 11.51, P < 0.01). 

Discussion

The results of the present study show that misperceptions of spatial distance, such as those measured in spatial interval judgments occur during both foveal and peripheral viewing in emmetropic and myopic subjects. At the fovea, the magnitude and direction of the spatial misperceptions are similar between myopic and emmetropic groups and are consistent with previous findings: Vertical targets are consistently perceived as greater than their horizontal counterparts. Extrafoveally, much larger misrepresentations of visual space are perceived. Furthermore, the traditional HVI undergoes a transformation, with separations in a meridional (tangential) direction consistently perceived as being greater than separations in a radial direction. 

Perhaps more important, significant differences are found between refractive groups for peripheral viewing. Specifically, the magnitude of the spatial misperceptions is greater for the myopic group, and it is related to changes in axial length. This finding has important implications for understanding the nature of ocular growth mechanisms that occur in myopic eyes. The fact that spatial misperceptions increase with the degree of axial myopia suggests that ocular expansion has a dramatic and specific impact on retinal architecture, and this influence is reflected in our perceptual measures. 

To explain the spatial misperceptions that occur in the visual field of normal individuals, McGraw and Whitaker ¹⁶ proposed a model that qualitatively predicted the type of misperceptions we report herein. The basis of this model was the underlying shape of ganglion cell receptive fields. Animal studies examining the spatial layout of ganglion cell receptive fields have shown that the areas of visual space to which they respond is elliptical rather than circular, with the major axis of the ellipse oriented toward fixation. ³⁰ McGraw and Whitaker ¹⁶ made the assumption that this early retinotopic representation of visual space is maintained at higher levels of visual analysis and is present at the level at which judgments of spatial separation are made. Indeed, there is evidence to support this notion. For example, Bauer and Dow ³¹ show that areas of the primate visual cortex that represent perifoveal visual space, display a greater number of neurons with radially oriented receptive fields. Therefore, the precortical distortions that have been reported at the level of ganglion cells units, seem to be present also at the level of the striate cortex. 

In view of the present findings, we propose an adaptation to this model to account for the effects of retinal stretching that occur during myopic eye growth. In Figure 7a , schematic neural units corresponding to the neural representation of elongated receptive fields in an emmetropic eye are represented by overlapping ellipses. The model figure has bar stimuli overlying the schematic receptive field profiles. The size of each bar stimulus is identical. However, if perceived distance is related to the number of neural units spanned by the two patches, then spatial separation will be related to the orientation of the stimulus relative to fixation. This also has consequences for other measures of visual performance, such as spatial resolution, ²⁷ because it directly predicts that resolution is higher for radially oriented stimuli. 

The increased magnitude of the spatial misperceptions in the myopic group may be explained by the retinal stretching process during myopic eye growth, which causes preferential stretching in a radial as opposed to tangential direction (Fig. 7b) . The results of the present study are inconsistent with isotropic stretching models, since the relationship between radial and tangential receptive field dimensions would remain unchanged, predicting a similar pattern of misperception in emmetropic and myopic groups. 

Although not commenting directly on the mechanism of ocular expansion, the overall shape of myopic eyes provides a valuable insight into the changes that may have occurred during the development of myopia. Most of the data suggest that myopic eyes are prolate in shape ^{4 11 13 32} (i.e., ocular shape is created by rotating an ellipse around its major axis such that the axial length exceeds equatorial diameter), indicating selective expansion at certain regions of the globe. The results of the present study are consistent with these data, in that little or no difference is found between refractive groups at the fovea, but marked differences exist at peripheral locations (15°). Van Alphen ³³ examined the influence of internal pressure on eye shape by inflating intact choroids denuded of sclera. He found that ocular expansion was greater in the anteroposterior direction in comparison to the equatorial direction. This suggests that overall global shape may be determined by the relative resistance to stretching demonstrated by different regions of the choroid. However, it should be noted that expanding a globe in the absence of its scleral coat, is sufficiently far removed from the conditions under which myopic expansion normally occurs. 

Both external and internal mechanisms have been proposed to explain the prolate growth pattern associated with myopia. For example, external forces, such as those supplied by the extraocular muscles, exert greater pressure at equatorial regions of the globe, ³⁴ preferentially restricting growth in this area. More recently, crystalline lens thinning, which is thought to be responsible for maintaining the isotropic expansion associated with emmetropic eyes, has been shown to occur to a lesser extent in myopic eyes. Mutti et al. ⁴ hypothesize that the failure of the crystalline lens to thin in myopic eyes restricts growth equatorially, resulting in a prolate ocular shape in these eyes. 

A question of particular interest is why we see such marked differences between refractive groups, in the magnitude of spatial misperceptions at peripheral locations, but not at the fovea. Visual performance for nearly all spatial tasks, including spatial interval judgments, is greatest at the fovea and declines precipitously with increasing retinal eccentricity. Therefore, in many respects, the fact that ocular stretching is restricted to particular regions of the globe, may be beneficial to central myopic visual capacity. In animal models of myopia, ocular growth serves to match the eye’s refractive power to the axial length of the globe. If the visual system limits this growth to certain peripheral regions of the globe, it may be possible to achieve this goal without compromising central visual performance to any great extent. Indeed, the differences in foveal visual performance between myopic and emmetropic eyes are surprisingly small. ⁷ Furthermore, the small differences that do exist may have an optical rather than neural basis. What is clear, though, is that greater changes to the representation of visual space occur in the periphery. Evidence supporting this type of localized peripheral expansion has recently been reported in humans (Watson TA, et al. IOVS 2002;43:ARVO E-Abstract 2005), and is also consistent with measures of cone topography in the primate retina. ³⁵  

 PVM is supported by a Career Development Fellowship from the Wellcome Trust.

 Submitted for publication February 9, 2004; revised June 30, 2004; accepted August 10, 2004.

 Disclosure: F.A. Vera-Diaz, None; P.V. McGraw, None; N.C. Strang, None; D. Whitaker, None

 The publication costs of this article were defrayed in part by page charge payment. This article must therefore be marked “advertisement” in accordance with 18 U.S.C. §1734 solely to indicate this fact.

 

Figure 1.

 

Psychometric functions showing the percentage of presentations on which a stimulus was judged to be smaller than the mean of the ensemble. Actual separation is shown on the abscissa. Data sets for four orientations are shown −0° (circles), 45° (squares), 90° (triangles), and 135° (crosses). Horizontal dashed line: represents the 50% level. For each of the four psychometric functions, extrapolation from here to the abscissa defines the actual separation, which was perceived as being equal to the mean.

Figure 2.

 

The four separation estimates obtained from Figure 1plotted against orientation. The curve represents a best-fitting ellipse. Dashed lines represent an extrapolation from 0° and 90° on the abscissa across to the ordinate. This allows us to define horizontal (S ₀) and vertical (S ₉₀) separations that are perceived as equivalent. From these, the HVI can be calculated.

Figure 3.

 

The size of the misperception under foveal viewing conditions is plotted as a function of axial length in all subjects. The magnitude of the foveal misperception is relatively constant among subjects and is invariant of the subject’s axial length.

Figure 4.

 

Relation between axial length and the size of the misperception in all subjects in the nasal visual field.

Figure 5.

 

Relation between axial length and the size of the misperception in all subjects in the inferior visual field.

Figure 6.

 

The difference between the illusion in the nasal and inferior visual fields in all subjects.

Figure 7.

 

Predicted models of ocular anisotropies of emmetropic and myopic eyes based on McGraw and Whitaker. ¹⁶ The emmetropic model (a) shows that the array oriented along the horizontal has a cross pattern, stimulating neural units in both the horizontal and vertical directions. Because of the radial elongation of the neural units, the vertical bar covers a greater number of units than does the horizontal bar. The opposite occurs in the vertical direction. In myopic eyes (b) the number of units covered by the horizontal bar is smaller than in emmetropic eyes at the same eccentricity. The presumed perceptual consequence of this pattern of stimulation is that vertical space appears expanded relative to horizontal, and this effect is greater in larger myopic eyes.