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To determine the effect of human in vivo accommodation on the stability of the crystalline lens.
Using a dual Purkinje image (DPI) eyetracker, the phase–time difference and amplitudes of Purkinje images I (PI) and IV (P1V) were measured in 37 normal emmetropic subjects (34 women and 3 men; mean age 19.8, range 18–22 years) when they changed focus from 70 to 15 cm and simultaneously rotated their heads horizontally from side to side or made horizontal saccades between two targets 6.8° apart.
When the subjects changed focus from 70 to 15 cm and rotated their heads or made eye saccades, the phase–time difference between PI and PIV decreased. During saccades, the amplitude of both PI and PIV overshoots significantly increased with focus at 15 cm; however, their ratio (PIV overshoot amplitude/PI overshoot amplitude) significantly declined.
The lens is stable during accommodation. The implications of these findings on the mechanism of accommodation are discussed.
Although the changes in surface curvatures of the human crystalline lens during accommodation have been well documented and there is agreement on the central curvature changes, the stability of the lens during accommodation remains controversial. Ascertaining whether or not the lens is stable when it changes shape to accommodate is of fundamental importance for understanding the mechanism of accommodation. Instability of the lens when it is in the accommodated state suggests that the zonule is relaxed. By tracking Purkinje images I (P1, reflection from the anterior corneal surface) and IV (PIV, reflection from the posterior surface of the crystalline lens), a measure of the relative movement of the lens compared with the eye within which it is contained can be obtained for different levels of accommodative effort. Several studies have evaluated these parameters. Two of these demonstrated that the lens remains stable during accommodation,1,2 whereas others concluded the opposite.3,4,5 The latter studies made their conclusions from observed differences in the amplitudes of the PIV overshoots as accommodation increased during saccades. One of these studies simultaneously used a dual Purkinje image (DPI) eye tracker and a scleral search coil to monitor the eye movement.3
The overshoots were observed only with PIV but not with the scleral search coil. From these observations, the authors concluded that the PIV overshoots were specifically associated with intraocular movements of the lens. Understanding the factors that contribute to the PIV overshoots is critical when using them to draw conclusions. A more appropriate comparison, from which conclusions about lens stability could be drawn, would be that made between PI and PIV images.
If increasing zonular relaxation is associated with accommodation, the PIV overshoot would be expected to have a phase–time difference when compared with that of PI. Moreover, this phase–time difference would be anticipated to increase with further accommodative effort. This study evaluates, in young subjects, the effect of changing accommodation on the amplitudes and phase–time differences of the PI and PIV overshoots that are associated with controlled movements of the eye.
A commercially available, calibrated and validated5,6 DPI eyetracker with 400 Hz bandwidth, a sample rate of 3906 Hz and a resolution >1 min of arc (Generation 6.5, Fourward Technologies, Buena Vista, Virginia, USA) was used to monitor the position of PI and PIV of the right eyes of 37 emmetropic normal subjects (34 women, 3 men; mean age 19.8 years, range 18–22 years). In addition to monitoring the horizontal movements of PIV with respect to PI in the transverse plane (x–y plane), the DPI automatically controlled the anterior and posterior movements of Purkinje image I (z‐direction)—that is, the distance between the cornea and the DPI.
The left eye of each subject was patched. An eye chart was attached to a Prince rule that was suspended from the headrest of the DPI. A beam splitter (transparent to the visible spectrum and reflective to the 930 nm illumination source of the DPI) was placed between the DPI and the right eye of each subject. The subjects kept their heads in the headrest of the DPI during all measurements. PI and PIV were monitored while the subjects focused on a 20/80 Early Treatment Diabetic Retinopathy Study backlit near letter (fig 11).). When the letter was either at 70 cm or at 15 cm, the subjects were instructed to simultaneously rotate their heads horizontally from side to side, for approximately 3° on each side of the midline at 5 cycles/s. This was repeated three times at each focal distance. The actual total amplitude and number of cycles/s of the subject's horizontal head rotations were determined from P1. Differences in the amplitude and rate of the measured head rotations were statistically analysed with the t test. The mean (SD) of the difference in the time of oscillations between the maximum horizontal positions of PI and PIV of at least 15 cycles of each subject were measured.
In addition, without moving their heads, the subjects made horizontal saccadic eye movements between two 20/80 Early Treatment Diabetic Retinopathy Study backlit near letters spaced 6.8° apart when the letters were at 70 cm and at 15 cm from the cornea. For each subject and at each focal distance, the amplitudes of the forward overshoots of PI and PIV, their ratios and the phase–time differences between them were measured. For these measurements, the mean (SDs) were obtained from three saccades. All measurements were made subjectively from the computer tracings of the positions of the Purkinje images without knowledge of the subject's point of focus. One‐way analysis of variance (SPSS V.13.0) was used to statistically analyse all the data.
This study adhered to the tenets of the Declaration of Helsinki, was compliant with the Healthcare Insurance Portability and Accountability Act, and was approved by the Institutional Review Board of Southern Methodist University, Dallas, Texas, USA. Written informed consent was obtained from the subjects only after the nature and possible consequences of the study were fully explained.
Although the mean amplitude and rate of the subjects' horizontal head rotations were different when focusing at 70 cm (3.8° (3.5°), 2.8 (0.72) cycles/s) and at 15 cm (2.8° (2.9°), 3.31 (0.96) cycles/s), with (p values <0.01), there was no difference in the angular momentum of their head rotations at the two focal distances, (p value=0.11).
During head rotations and saccadic eye movements, PIV moved synchronously with respect to PI during accommodation ((figsfigs 2, 33).). The mean phase–time difference between PI and PIV significantly decreased when the subjects changed focus from 70 to 15 cm (table 11).). The decrease in phase–time when focusing at 15 cm occurred irrespective of whether the subjects oscillated their heads from side to side, with a velocity of approximately 50°/s and accelerations of approximately 20000°/s2, or whether they made horizontal eye saccades with forward overshoots of 350°/s (table 11).
There was no evidence of overshoots of PI and PIV during head oscillations. On the other hand, there was evidence of both PI and PIV overshoots in all eye saccades (fig 33).). When the subjects changed focus from 70 to 15 cm, the mean amplitudes of the overshoots of both PI and PIV significantly increased; however, the mean ratio of the amplitudes of the overshoots, PIV/PI, significantly decreased (table 22).
The synchrony with which PIV follows PI during head rotations implies that the lens is stable (fig 22).). If the lens were unstable, there should be a significant lag in the directional change of PIV with respect to PI. These findings are consistent with the observations of Sokolowska and Thorn1 and of Kirschkamp et al.2 Sokolowska and Thorn objectively measured the positions of PI and PIV, accommodative amplitude and pupillary size simultaneously during accommodation.1 They found that, for an accommodative distance of 25 cm, the lens was stable and that the tilt of the lens in the horizontal aspect was significantly decreased, whereas there was little change in vertical tilt. The conclusion reached from these observations was that there was good alignment of the lens with the pupillary axis and that this was unaltered during accommodation.1
Using a scleral search coil and a Generation 5.5 DPI eye tracker simultaneously, each of which had a bandwidth and sampling rates approximately half of the Generation 6.5 DPI used in the present study, Deubel and Bridgeman3 observed PIV overshoots. When their subjects focused at 22 cm during a 6.1° saccade, the mean PIV overshoot was 1.3°. This is consistent with the present findings of a mean 1.9° PIV overshoot when subjects focused at 17 cm during a 6.8° saccade.
Deubel and Bridgeman3 attributed the PIV overshoots to instability of the lens as the amplitude of the PIV overshoots increased with accommodation, PIV overshoots were not present in the standard model eye and eye overshoots were not observed with the scleral search coil. Based on von Helmholtz's8 hypothesis of accommodation, they assumed that during accommodation all the zonules relaxed, which permitted the lens to oscillate more in response to a saccade, causing the amplitude of the PIV overshoots to increase.
The scleral search coil is attached to the limbus, and the movement of the coil in a magnetic field identifies the position of the eye. The DPI is an optical device and depends on the reflections of the light from the surfaces of the cornea and posterior surface of the lens—that is catoptric images of the light source. As the axis of rotation of the eye is not at its centre, PIV will be reflected from different parts of the posterior lens surface as the eye rotates. The posterior lens surface is flatter in its periphery than at its centre. For a specific angular rotation of a surface, the catoptric image formed by a flat surface will move faster and with greater amplitude than when formed by a concave surface. Therefore, if PIV is reflected from the peripheral posterior surface of the lens, it will move faster and with greater amplitude than if it is reflected from the posterior pole. During a saccade, the eye minimally overshoots the target, as demonstrated by the approximate 0.1° overshoot of PI (table 22).). During these small eye overshoots, PIV is momentarily formed from a flatter area of the peripheral posterior lens surface. This results in the appearance of the PIV overshoots. The reason that both PI and PIV increased during near fixation was that the eye overshot more at near because of the synergistic reflex of vergence and accommodation.9,10 During accommodation, the extraocular muscles are under greater tension. This would explain the increased amplitude of the overshoots during near saccades.9,10
If the PIV overshoots were due to lens instability, then they should be present with head oscillations. Although the angular velocity of the head rotations was slower than the overshoots, the acceleration of the eye was very similar over the time that the eye changed direction. The major difference between the two experimental paradigms was that relative central fixation was maintained during head rotations and that the eye overshot the target during the saccades.
PIV overshoots are a consequence of the eye overshooting the target during a saccade and are not due to crystalline lens instability. The crystalline lens seems to be stable during accommodation. However, photography11 and ultrasound biomicroscopy (UBM)12 have documented that the anterior and posterior zonules relax to the point of curling during human in vivo accommodation. In view of these observations and that the lens is denser than the aqueous and the vitreous humor, lens stability must be maintained by other zonules that are not readily detectable because of their small size, such as the equatorial zonules.13,14 The equatorial zonules have been observed in vivo with UBM.14 Unfortunately, in Ludwig et al's12 UBM study of zonular function during human in vivo accommodation, the equatorial zonules were specifically excluded because, as described in their methodology, only zonules that were at least 1 mm long were analysed.12
If all the zonules relax during accommodation, then gravity should affect the amplitude of accommodation. In 1962, the astronaut John Glenn did not observe a change in his near vision during his first space flight.15 Glenn was in the supine position during take‐off, and was subjected to eight times the Earth's gravitational force (8 Gs). Researchers expected his vision to blur during take‐off. They believed that all components of the zonule relax during accommodation, which would render the lens unstable. Since the lens is denser than the vitreous, it was expected that it would significantly shift in the posterior direction and may even dislocate during take‐off because of the increased oscillations and the poor support provided by the slackened zonules. Glenn remembered a small eye chart taped to his Mercury console and the instruction to “do an emergency re‐entry” if his vision blurred.15 Glenn's observation that the lens is stable and not affected by gravity, has been confirmed by measuring the accommodative amplitudes of astronauts on earth and in the microgravity environment of the space shuttle,16 and by measuring the maximum accommodative amplitude of young subjects in the supine and prone positions.17 These observations and the present study indicate that gravity and accommodation do not affect lens stability, and, coupled with the following observations, strongly suggest that the generally accepted Helmholtz' hypothesis of accommodation8 may be questionable:
In summary, the crystalline lens is stable during accommodation. During a saccade the eye minimally overshoots a target, and this is greater for near than for distance vision, as demonstrated by the presence of PI overshoots. PIV overshoots are due to the momentary formation of these images from the periphery of the posterior lens surface. The stability of the lens during accommodation is opposite to the predictions of the hypothesis of Helmholtz.
We thank Elise N Schachar, Francesca Allegra and Anne Lowery for arranging for the outstanding participation of the members of Chi Omega Sorority of Southern Methodist University, Dallas, Texas, USA.
DPI - dual Purkinje image
PI - Purkinje image I
PIV - Purkinje image IV
UBM - ultrasound biomicroscopy
Competing interests: RAS has a financial interest in the surgical reversal of presbyopia and WWW has a financial interest in eyetracking.