Longitudinal changes in objective accommodative response, pupil size and spherical aberration: A case study

Previous transverse and a handful of longitudinal studies have shown that the slope of the static accommodation response/stimulus curve declines as complete presbyopia is approached. Changes in pupillary miosis and ocular spherical aberration (SA) are also evident. This study further investigated longitudinal changes in the relationships between the monocular static accommodative response, pupil diameter and SA of a single adult.


INTRODUC TION
The subjective amplitude of accommodation is a measure of the maximal focusing range of the eye.As is well known, it shows a progressive decline with age, 1,2 such that most people in their forties begin to experience difficulties in performing near vision tasks (presbyopia). 3ubjective amplitudes tend to exceed the corresponding objectively measured amplitude, due mostly to the inclusion of ocular depth-of-focus (DOF). 4,5This latter effect is most pronounced beyond 45-50 years of age, when age-associated pupillary miosis increases the DOF. 6,7he few longitudinal studies of objective accommodative response, involving only three subjects, suggest that for an individual presbyope, objective amplitudes fall almost linearly with age to reach zero at about the age of 50-55 years. 2,8,9Since a notable intersubject variability has been observed in transverse studies, 10 further longitudinal investigations are desirable.

O R I G I N A L A R T I C L E
Longitudinal changes in objective accommodative response, pupil size and spherical aberration: A case study Sotiris Plainis 1,2 | Sophia Panagopoulou 1 | W. Neil Charman 3 While the amplitude of accommodation is of obvious clinical importance, it gives only partial information on the overall static characteristics of the accommodation system. 4,8These are more fully illustrated by accommodation response/stimulus curves, which involve measurements of accommodation performance over its full dioptric range rather than just at the near and far points.Such curves typically show steady-state errors in focus.2][13][14] Not surprisingly, the changes in the amplitude of accommodation with age are accompanied by changes in the extent and form of the static response/stimulus curve. 8,10Both longitudinal 8 and transverse 7,10 studies have shown that the slope of the quasi-linear portion of the accommodation response/stimulus curve reduces only slowly with age up to about 40 years and then declines rapidly as complete presbyopia is approached.Such behaviour appears to result from the ageing accommodation system adapting its characteristics to make optimal use of the available objective amplitude of accommodation and the ocular DOF.Age-related pupillary miosis 6,15 and changing amounts of ocular spherical aberration (SA) may also play a role. 11,16,17This study investigated the longitudinal changes in the relationships between these optical parameters for a single subject.

METHODS
The subject's static accommodative responses were measured over a period of 17 years, from the pre-presbyopic age of 33 years until his objective amplitude of accommodation approached zero at the age of 50 years.A constant experimental technique was used.The associated longitudinal changes in pupil size and SA with accommodation were also recorded, in an attempt to obtain better insight into their contribution to the ocular DOF and the static accommodative response.Written informed consent was obtained for identifiable health information used in this case report.The experiment followed the tenets of the Declaration of Helsinki and conformed to a protocol approved by the University research board.
The participant (the author SP) was a myope who experienced minimal changes in his refractive error during the period of the investigation (see Table 1).Performance was evaluated only for his dominant left eye (LE).Visual acuity was better than 0.0 logMAR (6/6) at all ages, with normal binocular vision, heterophorias, the near point of convergence and no ocular pathology.

Wavefront sensing, accommodation response and data analysis
The ocular wavefront error was measured using a wavefront sensor based on the Shack-Hartmann principle (COAS, AMO Wavefront Sciences, amo-inc.com), with a purpose-built Badal optometer mounted on top of the sensor, as described previously in detail. 11Accommodation was stimulated by a target viewed through a beam splitter, allowing for continuous recordings of the wavefront aberration of the tested eye.The Badal system provided a wide, continuous range of calibrated target vergences between +0.84 and −8.05 D, without changing the apparent size of the target, thus creating a blur only stimulus for accommodation.The target was a high-contrast (>80%) single letter E, printed on a white paper and illuminated by an incandescent lamp.The low, photopic background luminance was 5 cd/m 2 .The letter angular subtense was 1.75° (6/126), with limb widths subtending 21′ arc.
Recordings were performed using the best distance spectacle correction, with the participant's head being positioned on a chin rest.The dominant (left) eye was tested, with the right eye being occluded.All measurements were performed with natural pupils without

Key points
• The objective amplitude of accommodation declines linearly with age as complete presbyopia is approached, while the slope of the response/ stimulus curve also falls.• There is a decrease in static accommodation responses with age at almost all target vergences, with the changes being greatest for the higher vergences.• For this subject, the rate of change in pupil diameter with accommodation stimulus was approximately the same at all ages, with pupil constriction occurring even when no active accommodation took place.administering a mydriatic or cycloplegic drug, while room lights were dimmed to maintain large pupil diameters.Wavefront aberration data were recorded initially for a positive target vergence of +0.84 D, that is, the target was placed behind the subject's objective far point.The latter was assumed to coincide with the calibrated vergence of 0.00 D accommodative demand.Note that this assumes the refractive procedure placed the subjective far point at 4 m (vergence −0.25 D) and that due to the ocular distal DOF (which has about this value for larger pupils; see Atchison 18 ), the corresponding objective far point lay close to infinity (zero vergence).In subsequent trials, the target was brought progressively closer to the subject to increase the stimulus vergence up to −8.05 D in about 1.00 D steps.For younger ages, this range was extended slightly to ensure that the full objective amplitude of the subject had been explored.Fifty consecutive measurements were taken at a frequency of 7.7 Hz for each stimulus level, so that each measurement sequence had a duration of 6.5 s.Prior to each set of measurements, the participant was asked to blink, to concentrate on the target and to maintain the best possible focus on the target at all times.Each trial was followed by a 1-min rest interval.A complete recording session lasted about 30 min.The accommodation stimulus value was corrected for spectacle lens effectivity using the following equation 11 : where A is the accommodation stimulus, L is the target vergence, a is the vertex distance (13 mm) and K is the refractive power of the spectacle lens.The corrected accommodation stimulus range was −0.83 to 7.63 D. Data extracted from the COAS consisted of a set of Zernike expansion coefficients (up to fourth order) corrected for chromatic aberration (from 840 to 550 nm) for the natural pupil diameter.Coefficients were also scaled to a constant 3.5 mm pupil diameter.The accommodative response for each recording M was evaluated from the second-order paraxial focus [c 0 2 ] and the fourth-order SA [c 0 4 ] Zernike coefficients for the full natural pupil (see Equation 2).This approximates the equivalent spherical defocus. 19,20ere M is in dioptres (D), the coefficients are measured in μm and the pupil radius, r, in mm.

Response/stimulus curves and objective amplitudes
Figure 1a presents accommodation response/stimulus plots for the full range of stimuli (−0.83 to 7.63 D) at different ages.Lags and leads in the accommodation response are evident, with an obvious fall in the range of response as the participant's age increased.Note that the accommodation response ('lead') for the optically distant stimulus (of ~0.15 D accommodation demand) increased gradually with age, from around 0.18 D at the age of 33.2 years to about 0.70 D at 50.3 years of age.In addition, the slope of the quasilinear portion of each response versus stimulus curve, calculated from the linear region of data at each age, reduces with age, from about 0.85 at 35 years to 0.1 at 50 years (see Figure 1b).It is, however, important to recognise that this relationship only applies over the age and stimulus ranges studied.At ages <35 or >50 years, the slopes would be expected to stabilise at almost constant values of around 0.9 (nearly accurate accommodation across the stimulus range) and zero (no active accommodation), respectively.
(1)   Objective amplitudes of accommodation over the age range studied show a linear decline with age of approximately 0.3 D/year (see Figure S1). Figure 2 presents the data from Figure 1a in a different way.In Figure 2a, the accommodation response to different stimuli is plotted as a function of the participant's age, with least-squares regression lines being fitted to the data for each age.While there is some decrease in response with age at almost all target vergences, the changes were greatest for the higher vergences (i.e., the optically closest targets).This is not surprising, since near targets are the first to appear blurred as accommodative ability declines.Over the age span of 35-50 years, the response at each stimulus value changed approximately linearly with age.In turn, the slope of the linear fit to each set of accommodation response/age data had a near-linear dependence on the stimulus level (Figure 2b).Again, however, this was only valid over the limited age range of the study.

Pupil diameters
The natural pupil diameters corresponding to the accommodation responses as a function (a) of the accommodation stimulus and (b) of the accommodation response in Figure 3.Some irregularity in the data is to be expected  since, at any time, any individual's pupil diameter is susceptible to a wide range of transient physiological and psychological factors. 21It can be seen (Figure 3a) that the absolute pupil diameter for the same accommodation stimulus decreased with age.However, at all ages, the rate of change in pupil diameter with accommodation stimulus was approximately the same (see Figure S2).Thus, even under the monocular conditions of the study and with no proximity cues from the Badal target presentation system, pupil constriction always occurred for near stimuli, even in the older eye. 22,23Figure 3b emphasises that in older eyes, pupil change can occur in the absence of an accommodation response change, as indicated by the vertical portions of the curves.

Spherical aberration
In principle, the value of the fourth-order SA coefficient (c 0 4 ) for natural pupils may change with accommodation as a result of response-related changes in either the form and refractive index distribution of the crystalline lens or in the pupil diameter. 11,14When evaluating the coefficients for a fixed 3.5-mm pupil diameter, any changes in SA must be due to changes in the lens.As the accommodation responses are small in the older eye, then the corresponding changes in SA for the 3.5-mm pupil, with both variations the accommodative stimulus response, would also be expected to be small.In contrast, relatively large lenticular changes would be expected in the actively accommodating eye, resulting in significant changes in SA.Figures 4a,b show results with the 3.5-mm pupil.
Although the data are rather noisy since the amounts of SA are low, for older eyes, c 0 4 generally remains in the positive band of 0.00 to +0.02 μm.In contrast, younger eyes show a tendency for c 0 4 changing from positive to negative at stimulus levels around 4D (response levels around 3D).These results change when SA values appropriate to the full natural pupils are considered (Figures 4c,d).As would F I G U R E 4 Changes in spherical aberration (SA) coefficient (c 0 4 ) as a function of (a) accommodation stimulus and (b) accommodation response with a 3.5 mm pupil.Figure 4c,d show similar plots for a full natural pupil.The values of SA cover a greater range with the natural pupils, which all exceed 3.5 mm, and the older eyes show greater variation, due mainly to the accommodative miosis.be expected, the ranges of natural pupil SA are higher at all ages than those for the smaller 3.5-mm pupil, and the ranges are largest in the younger eye.SA for the older eyes almost always remains positive.

Spherical Aberration coefficient (µm)
To emphasise the differences between SA values with natural and 3.5-mm pupils, Figure 5a shows SA versus accommodation data for all stimuli at all ages.As expected, for a 3.5-mm pupil, SA values were lower; thus, the slope is flatter compared with that for full pupils.For both pupil diameters, SA becomes less positive or more negative as the accommodative response level increases.Figure 5b plots SA as a function of pupil diameter at all target vergences.

DISCUSSION
In general, the results of the present longitudinal study of an individual's static accommodation response/stimulus relationship support a few similar earlier longitudinal studies.They are also compatible with the more numerous cross-sectional investigations.In particular, it was found that after about 35 years of age, the slope of the linear portion of the accommodation response/stimulus curve diminishes with age, reaching zero around 50 years of age, as also found in several transverse studies. 7,9,10,15pparently, rather than following the predictions of the simple Donders-Duane-Fincham or Helmholtz-Hess-Gullstrand models, 24 the accommodation system adapts its characteristics as it ages to make the most effective use of the available range of crystalline lens change, pupil diameter variations and ocular DOF to ensure that the retinal image is of satisfactory (rather than perfect) image quality over as large a range of stimulus vergence as possible.Figure 1b, illustrating the longitudinal changes in the slope of the subject's curve with age, includes a smooth curve prediction derived by Kalsi et al. 10 from their cross-sectional study data combined with estimates of the changes in DOF with age.The simple model predicts the current longitudinal results quite well.
The objective amplitude of accommodation declined linearly over the age period studied.Figure 6 compares the present individual amplitude/age results with those reported by other authors. 2,8The individual results differ somewhat due to the use of different stimulus and measurement conditions (Table 2) and subjects.Studies using a Badal target system might be expected to yield lower accommodation responses since only blur cues are available, whereas, for example, binocular rather than monocular observation might enhance it due to the additional convergence cue. 25 However, in all studies, the subjects were ) as a function of accommodative response at all ages and accommodative stimuli for full (natural) (filled circles) and 3.5 mm pupils (open circles).The solid lines correspond to least-squares linear regression fits.(b) Plots of SA coefficient as a function of pupil diameter for all accommodative stimuli at different ages.experienced observers who had strong voluntary control over their accommodation.For example, Hofstetter 2 remarked 'Both subjects (HWH, MJA) were experienced observers in accommodation experiments and could, at will, accommodate in full without employing any auxiliary motivating device'.Thus, it seems likely that the variations arise mostly from inter-subject differences in the rate of ageing of the accommodation system rather than from the different experimental conditions.
An important clinical question to raise is why, if there is no active accommodation after around 50-53 years of age, do clinically prescribed near additions continue to increase in power in later years?Following earlier suggestions, 26,27 MacMillan et al. 28 showed that this is primarily due to the preference of older spectacle wearers to use reduced working distances to compensate for the loss of visual acuity that occurs later in life.
The reduction in the subject's pupil diameter with age when viewing distant targets (age-related pupillary miosis) is consistent with several previous investigations. 29,30More interesting is the pupil reduction observed with accommodative demand (near miosis), which continues up to 50 years of age when true accommodation has declined to near zero, suggesting the existence of a reserve of ciliary effort.This contrasts with the suggestion of Stakenburg 31 that, even with young subjects, blur-driven accommodation may not be sufficient to drive a pupillary near response.This view was supported by the early dynamic accommodation experiments of Schaeffel et al., 22 Phillips et al., 32 and, at least in part, by the static accommodation investigation of Radhakrishnan and Charman, 15 who, in a group of 48 normal subjects spanning an age range of 17-56 years, found that accommodative miosis was absent in many individuals, particularly after 40 years of age.Although it is possible that in the present study the blur input was supplemented by cues provided by, for example, small misalignments of the Badal system, it seems more likely that pupil constriction in the older eye was linked with ciliary muscle contraction due to voluntary inputs from the experienced subject. 23It is well known that human subjects can learn to accommodate voluntarily in the absence of a true accommodation stimulus. 33,34Moreover, the ciliary muscle remains active after the ability to change the power of the eye has been lost. 35,36Such voluntary activity in a 50-year-old may drive pupillary constriction in the absence of a true accommodation response.
Pupil constriction at near has the advantage of decreasing out-of-focus retinal image blur 5 and improving visual acuity in the presence of a lag of accommodation. 37eductions in the pupil diameter also reduce blur due to the monochromatic aberrations of the eye, particularly SA. 11 Binocular viewing may also result in higher convergence demand and further pupil miosis, with a corresponding increase in the DOF. 38he present case, the subject's positive primary SA coefficient c 0 for an optically distant stimulus and natural pupils appeared to reduce with age.trend was obvious when SA values were calculated for a fixed Note: The x-intercept is the age at which accommodation is no longer active.
3.5 mm pupil (Figure 4; see also Figure S3).However, neither of these trends was statistically significant.Under both pupil conditions, as the accommodation stimulus and response increased, SA became less positive or more negative, a result that is in accordance with the cross-sectional study of López-Gil et al., 17 but not with the modelling of Zapata-Díaz. 39The decrease in c 0 4 with age, accompanied by pupillary miosis, may have also affected the lead of accommodation for the optically distant stimulus, which became more myopic, a condition also observed in previous studies. 11

CONCLUSIONS
The present longitudinal results for a single subject confirm the trends found in the few similar earlier longitudinal studies as well as those inferred from transverse investigations.Individual objective amplitudes of accommodation decline linearly with age as complete presbyopia is approached (i.e., no active accommodation occurs) and the slope of the response/stimulus curve also falls.It is hypothesised that for many, but not all, individuals, the retinal image blur associated with the larger lags of accommodation found at higher stimulus levels is reduced by pupillary constriction and the resultant lower levels of SA.

CO N F L I C T O F I N T E R E S T S TAT E M E N T
The authors declare no competing interests.

10 Accommodation
Accommodation response versus stimulus plots at different ages.The error bars are ±1 SD.The dotted line plots the ideal 1:1 relationship.(b) Plot of the slopes of the regression line fitted to the quasi-linear portion of each response/stimulus curves as a function of age.The smooth curve is from a simple model based on cross-sectional data by Kalsi et al.
Plots of accommodative response data at all stimulus vergences (0.15-7.63 as a function of the age of the participant.(b) Plot the slopes of the response versus age data, as found in (a), as a function of accommodation stimulus.The solid lines correspond to least-squares linear regression fits.Error bars are ±1 SD.

F I G U R E 3
Plots of natural pupil diameter as a function of accommodative stimulus (a, left) and accommodative response (b, right) at different ages.

F I G U R E 6
The least-squares regression line fits the objective amplitude of accommodation data as a function of age for individual subjects (SP, WNC, HWH and MJA) in three longitudinal studies (present investigation; Hofstetter 2 ; Ramsdale and Charman8 ).

T A B L E 1 Distance refractive error and near addition of
Outline details of conditions and regression line results for the age dependence of the response/stimulus curve as found in longitudinal studies.
T A B L E 2