1. Introduction

The human eye can focus both near and far targets by changing its crystalline lens geometry, a capability that is known as accommodation. The response to a near stimulus includes increased accommodation, convergence, and pupillary constriction [1]. Binocular vision, chromatic aberration, and other cues, such as stimulus size have been shown to contribute to accommodation [2], although accommodation can occur in their absence, triggered by blur cues [3].

Myopia’s aetiology is likely multifactorial, but there are still knowledge gaps on why people become myopic. Myopia development has often been linked to continuous near work requiring high levels of accommodation [4]. Several epidemiologic studies have revealed a link between the volume of near work and the development of myopia [5–7] and suggested that the larger amount of accommodative effort needed during near activity is a factor in the development of myopia. More specifically, a large body of work refers to the hyperopic blur produced by the lag of accommodation (i.e the eye not accommodating completely to shift the image plane to the retina) to close targets, which results in the image lying behind the retina, as the trigger or contributor to eye elongation. This is also consistent with studies on experimental models of myopia in many animal species, that show robust responses in eye elongation to hyperopic defocus imposed with negative lenses [8]. Several studies have reported larger lags of accommodation in myopes compared with emmetropes [9–13], although it is debated whether this is a cause or a consequence of myopic changes [14,15]. Differences in accommodative lag have even been related to the higher amounts of high order aberrations, since myopes have, on average, larger high order aberrations (HOAs) [16–19]. The potential link between myopia development, reduced accommodation, optical aberrations, and hyperopic defocus (particularly in the peripheral retina) has motivated various non-pharmacological alternatives for myopia control. Among those options, bifocal and progressive additional spectacle lenses [20–23], orthokeratology [24,25] and soft multifocal contact lenses (MCLs) have shown different levels of success in controlling the progression [20,21].

Bifocal and multifocal contact lenses (CLs), commercialized primarily for presbyopia correction and with some designs emerging for myopia control, are generally based on the principle of simultaneous vision. Simultaneous vision is the general denomination of multifocal corrections that are deployed at the pupil (or near) the pupil plane, in contrast to alternating vision corrections where the patient looks through different part of a spectacle lens for far or near. The superposition of a sharp and blur images (in the case of a pure bifocal correction) results in a decrease in contrast and a degradation of the MTF. Smooth refractive profiles do not result in two distinct foci, but actually in an broader through focus curves.[22,23]. The most accepted hypothesis for the principle of operation for bifocal and multifocal contact lenses in myopia control is their effect on the peripheral retina. Spectacle lenses have been proved to introduce hyperopic defocus in the periphery, supposedly further triggering elongation [26]. Conversely, bifocal lenses with a center distance and near add in the peripheral region of the lens would impose a relative myopic defocus in the peripheral retina, an expected inhibitor of myopia progression. Under this theory, lenses with a zone to correct the central refractive error and a relative plus in the periphery can send a stop signal to an eye that is becoming more myopic [27,28]. Nevertheless, the ability of multifocal contact lenses to remove hyperopic defocus, and introduce myopic defocus, in young eyes depends critically upon the accommodative behavior of the individual eye when fitted with these lenses. Specifically, when talking about both peripheral and central defocus, if the eye relaxes its accommodation to use the near add for near vision tasks, the anticipated myopic defocus may not occur, therefore leaving the eye exposed to the hyperopic blur of the out of focus distant peak [29] and potentially favoring eye elongation.

Given the interplay of pupil diameter, ocular optics, accommodation, and lens design, it is likely that the contact lens design plays a major role in determining the accommodative dynamics in the young myopic subjects fitted with multifocal lens designs. Some prior literature has studied the effect of inducing negative or positive spherical aberration on accommodative lag and myopia control, either using contact lenses, orthokeratology, or a deformable mirror in an adaptive optics system [19,24,25], offering in general conflicting conclusions such as positive spherical aberration decreasing the accommodative lag and negative spherical aberration increasing the accommodative lag.

Adaptive Optics (AO) visual simulators appear to be an ideal experimental platform to test potential differences of the accommodative response across multifocal lens designs. First, AO allows non-invasive simulation of lens designs without having to put the contact lens on eye. Also, since the lens designs are digitally programmed, they are not restricted to those commercially or physically available [30,31]. We have recently presented the accuracy of the representation of commercial center-near multifocal contact lenses (low, medium, and high near add) in the Spatial Light Modulator (SLM) of a custom-developed AO Visual Simulator. Through focus Visual Acuity through the real lens and the simulated lens differed by less than 0.03 logMAR on average, in a -3D to +1D range [32]. Clinically, AO visual simulators can therefore be used to test vision in patients with multiple MCLs designs prior to lens fitting. AO visual simulation enables investigation of interactions between the eye’s optics and a given lens design, as well as assessing differences across lens designs eventually allowing to select the lens that optimizes perceived visual quality and visual performance [23,33]. Also, a key component of the AO system, a Hartmann-Shack (HS) wavefront sensor, can also be used to quantify the accommodation response, through measurements of low and high order aberration, estimates of the retinal image quality, and calculations of the focus shift of the best image quality from the retina [34,35]. Generally, a HS wavefront sensor is not well suited to measure aberrations in presence of segmented or diffractive optics. While this challenge is difficult to overcome in studies that involve contact lenses fitted on eye, it is possible to bypass the SLM that projects the multifocal phase map on the eye’s pupil, as this sits in a conjugate pupil plane [36,37]. The HS wavefront sensor therefore allows estimating the response of the eye (crystalline lens) alone upon an accommodative stimulus. The optical quality and accommodative lag of the eye with the multifocal contact lens can be estimated by computationally adding the eye’s wavefront aberration and the contact lens phase map.

In this work, we programmed six different multifocal contact lens designs: purely bifocal segmented Center Near and Center Far [30,37]; medium and high add center near commercial multifocal designs [30,32], as well as positive and negative spherical aberration. With those lenses projected onto the eye, we measured the changes in eye’s spherical aberration and the accommodative response through each of those designs. We developed new protocols for by-passing the SLM contribution to measure changes associated to the eye alone, and for quantification of the accommodative lag. We found that the accuracy of accommodation in young eyes through the multifocal patterns was highly dependent on the lens design, as well as, to a lesser extent, of individual differences in eye’s aberrations and pupillary dynamics.

2. Methods

The accommodative response (to blur-only cues) was evaluated on six young myopes through six different multifocal patterns, and a control monofocal pattern. The patterns were simulated as phase maps in the Spatial Light Modulator (center near and center distance designs) and in the Deformable Mirror (positive and negative spherical aberrations) in a custom-developed AO Visual Simulator. The change in spherical aberration and focus shift from best retinal image quality were evaluated as a function of accommodative demand.

2.1 Subjects

A total of 6 subjects participated in the study, with age ranging from 23 to 29 years (average, 28 ± 1.5 years) and spherical errors ranging from -1.75 to -3.25 D (-2.41 ± 0.3D), and astigmatism below 0.25D. The subjects were normal beyond their ametropia. The study protocols met the tenets of the Declaration of Helsinki and had been approved by the CSIC Institutional Review Boards. All the participants were informed about the study and experimental procedures and signed informed consent waivers prior to any study procedures.

2.2 Adaptive optics visual simulator

The experiment was performed using a custom-developed AO system at the Visual Optics and Biophotonics Lab (Institute of Optics, Spanish National Research Council, Madrid, Spain), described in detail in previous publications [38,39]. In this study, the MCLs were mapped on a SLM (center near and center distance designs); Spherical Aberration was induced on a DM (positive and negative spherical aberration)

The current configuration of the polychromatic adaptive optics system consists of 8 channels described in previous publications [31,23,39]. Essentially, the illumination was provided by the supercontinuum laser source and acoustic-optic tunable filters (FYLA, Fianium Ltd, United Kingdom) were used to select the desired wavelength. In this study, visible wavelength of 555 nm was chosen to illuminate the visual stimuli and an infrared wavelength of 827 nm for the light beacon in aberration measurements. A Hartmann-Shack (HS) wavefront sensor (32 × 32 microlenses; HASO 32 OEM, Imagine eyes, France), a 52-actuator Deformable Mirror (DM, MIRAO by Imagine Eyes, France) and a reflective phase-only Spatial Light Modulator (SLM, LCoS-SLM, 1920 × 1080 pixels, by Holoeye, Germany) were conjugate to the subject’s pupil and used to measure (HS) or induce (SLM, DM) aberrations. A beam splitter allowed the subjects to visualize a stimulus projected on a Digital Micro-mirror Device (DMD) that was conjugate with the retina. The pupil was monitored to ensure alignment of the subject’s eye with the optical axis of the system throughout the experiment. A Badal optometer was used to correct the subject’s refractive error and to induce defocus.

All optoelectronic elements of the system were automatically controlled and synchronized using custom-built software. The routines made use of the manufacturers Software Development Kit for Hartmann-Shack centroid detection and wave aberration polynomial fitting. Subjects were aligned and stabilized using a dental impression and were aligned using the x-y-z stage using the line of sight as reference. For this study, the pupil size was the natural pupil of the subjects, and not controlled in the system using artificial pupils.

2.3 Multifocal contact lenses

The experiment was performed for 7 conditions: NoLens (NL) (the subjects viewed the target under their natural aberrations through a flat SLM); Center Distance (CD), Center Near (CN), MediumAdd Center Near (MA), High Add Center Near (HA); Positive Spherical Aberration (PSA) and Negative Spherical Aberration (NSA). The MA (+1.75D near add) and HA (+2.50D near add) tested in this study represent commercially available 1-Day Acuvue Moist Multifocal (Johnson and Johnson Vision Care, Jacksonville, FL). The specifications of these lenses are described in previous studies [30,32] The CN, and CD lenses were pure segmented bifocal design lenses with a 4-mm pupil central zone (distance in CD and near in CN). This 4-mm design was selected such that the central zone had a similar diameter to that of the commercial lenses, but instead of a smooth blending zone, to have a segmented, abrupt transition from near to far. The induced PSA and NSA was ±1µm over a 6-mm pupil.

2.4 SLM and DM phase map generation

Figure 1 shows the phase map of the four bifocal/multifocal designs used in this study mapped on the SLM and the two pure 4^th order spherical aberration designs mapped on the DM. MATLAB routines were used to numerically simulate the designs, which were later programmed in the reflective phase-only LCoS-SLM following the same protocols as from previous studies [31]. In order to map the maximum phase difference on the SLM, a 2π wrapping process was applied to the phase pattern generation process [40]. The patterns were generated as a grey-scale image over a 6-mm pupil. The SLM was calibrated for a wavelength of 555 nm. Measurements of the induced PSA and NSA in the HS using an artificial eye showed deviations of less than 0.01% from the attempted 1µm induction. The magnitude of the induced aberrations changed across the experiment due to pupillary miosis when accommodating.

 

Fig. 1. Phase maps of the MCLs simulated in the SLM: MediumAdd (+1.75 D near add), HighAdd (+2.50 D near add), Center Distance (+2.50 D near add), Center Near (+2.50 D near add), right gray scale panels, and 1 µm positive and negative SA, left color panels, were induced on the DM. Maps are represented for a pupil diameter of 6 mm.

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2.5 Experimental procedure in subjects

Measurements in subjects were performed monocularly on the dominant eye (determined with the Miles test) with the natural aberrations of the subject uncorrected, in a darkened room, while fixating at Maltese-Cross (1 deg field) projected on the DMD, illuminated by green light (555 nm, 20 cd/m²). The non-measured eye was covered with a patch throughout the experiment. The residual aberrations of the system were corrected in all cases using an AO closed-loop correction. Subjects were aligned to the system using the line of sight as reference (i.e. pupil the was imaged with the pupil monitoring channel and the pupil center aligned to the optical axis of the instrument as the patient was fixating foveally. Objective refraction was measured immediately before the experiment using a commercial autorefractometer (Zeiss/Humphrey), and this was used as an initial setting for defocus correction in the system. Following centration of the pupil, the subject was asked to adjust the Badal system position to achieve the best focus for far vision, starting with positive defocus values relative to the subject’s expected spherical error correction to avoid the subject accommodating while searching the best focus. The focus setting was repeated multiple times and the average of at least 5 repetitions was defined as the zero-defocus setting. The same procedure was used to find the focus for each simulated pattern, which was selected independently for each of the seven experimental conditions. Ocular aberrations were measured for each condition and for accommodative demands from 0 to 6D, in 1-D steps, introduced using the motorized Badal optometer. Each measurement was repeated at 5-6 times, which took around 40-50 seconds. The pupil diameter was extracted from the HS images. Subjects were familiarized with the setup and procedure by performing some preliminary experimental sequences. All the conditions were measured consecutively in the same session, with the session starting with the NL condition followed by randomized conditions with the multifocal patterns.

2.6 Data analysis

2.6.1 SLM residuals

Figure 2(A) shows the schematic of the AO system that was used in the experiment. Ocular aberrations were measured in infrared light (880 nm), while the subject viewed the accommodative stimulus in green light (555 nm). Since the SLM was calibrated for green wavelength and the aberrations of the eye were measured in IR, to compensate differences in the wavefront induced for the two wavelengths, a baseline measurement was made to remove the residuals of the SLM. The wave aberrations were measured in IR (880 nm) for the different phase maps simulated in the SLM for 555 nm, using a diffraction-limited artificial eye. This was considered the residual baseline which was removed from the real time measurements on eye. The residual measurements were made for a 6 mm pupil diameter and the residual wavefront was cropped according to the subject’s pupil size in each case. This procedure allowed to obtain the wave aberration for the eye alone, eliminating any artifact from the SLM. Figure 2(B) illustrates this process with a real wavefront map captured in a real eye (S4) with the MA design in the SLM. In a second step (Fig. 2(C)), the corresponding phase maps were computationally added to the measured eye alone wave aberration, considering the pupil size of the subjects for each accommodation demand as shown in Fig. 2(C) for 0 and 6D.

 

Fig. 2. Left panel (A) Schematic of the AO system used in this experiment; Right upper panels (B): Illustration of the removal of SLM residuals on S4 with the HA pattern (1) Wave aberration measured in IR light (eye + SLM with MA pattern) (2) SLM residual of MA measured with artificial eye in IR light (3) Wave aberration of the eye alone after removing the SLM residual. Right lower panels (C): Illustration of adding the simulated CL computationally to the eye, shown as example of subject S4 with HA phase map. Pupil diameter was 4.36 mm for 0D and 3.24 mm for 6D.

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2.6.2 From aberrations to accommodative response

Wave aberrations were fitted to seventh-order Zernike polynomials (with nomenclature following the Optica -formerly Optical Society- standard [19]) using a least-mean square procedure. The pupil diameter at each accommodative demand was obtained as average of individual measurements, whereas each Zernike coefficient was the average of 5-repeated measurements. Wave aberration maps (and 4^th order spherical aberration Zernike coefficients) were calculated for the eye alone (i.e., after subtraction of the SLM residuals, as shown in Fig. 2, for the SLM-based conditions, and after direct subtraction of the induced spherical aberration for the DM-based conditions), and for the eye + phase map.

Point Spread Functions (PSF) were calculated from the eye + phase map aberration maps, as the magnitude square of the Fourier transform of the pupil function, where the amplitude pupil function was the normative Stiles-Crawford function [41,42]. The piston and prismatic terms (the first three Zernike terms) were omitted in the analysis, and the Zernike defocus was set such that retinal image quality was maximized at 0 D. The MTF was estimated from the calculated PSFs. Retinal image quality was estimated using two different metrics: (1) Volume under the MTF in the 3-5 c/deg range (thought to be key for accommodation [3,43] and (2) Visual Strehl, defined as the volume enclosed between the MTF and the inverse of the neural CSF [40]. For each accommodative demand a through-focus image quality curve was calculated, including the corresponding defocus term (relative to the Zernike coefficient that maximizes the curve for 0 D demand) in the PSF calculations. The accommodative lag for each accommodative demand was calculated from the defocus shift in the peak of the TF curve from 0 D (assuming best focus for relaxed accommodation).

2.6.6 Statistical analysis

Statistical analysis was performed with SPSS software Statistics 24.0 (IBM, United States) to test differences between conditions. The normality assumption was checked using the Shapiro-Wilk’s test. Specific non-parametric tests were used for different comparisons: (1) For comparing across conditions: Related-Samples Friedman’s analysis of variance by ranks and paired tests (2) For comparing across subjects and across accommodation demands Independent-Samples Kruskal-Wallis and paired tests.

3. Results

3.1 Changes in pupil size with accommodation

Figure 3 shows the pupil size change with accommodation from 0-6 D for different conditions for each subject. The color code represented in shades of brown are the lenses inducing positive spherical aberration (CD and PSA) and in shades of green the lenses inducing negative spherical aberration (CN, HA, MA, NSA).

 

Fig. 3. Left panels: Pupil diameter changes with accommodation for all subjects plotted against accommodation demands from 0 to 6D. Right panel: Average slope (across subjects) for each condition. Red lines/bars represent NL; light brown represent CD; dark brown represent PSA; light green represent CN; bright green represent MA; olive green represent HA; darkest green represent NSA.

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There was a systematic decrease in the pupil diameter with accommodative stimulus for all conditions with an average slope of change from 0D to 6D across conditions of -0.17 mm/D. Even at 0 D, the pupil diameter varies across conditions in majority of the subjects. On average, the standard deviation in pupil diameter across all 7 conditions was 0.21 mm, while the repeated measurement variability in pupil diameter was 0.041 mm. On average across subjects, two conditions showed clearly less response in pupil constriction with accommodative demand (HA and NSA, -0.11 mm/D) and one condition showed higher slope (PSA, -0.2 mm/D), but the maximum slope was found for the NoLens condition (-0.23 mm/D). The rate of change in pupil diameter differed across conditions and subjects significantly (p = 0.003, Related-Samples Friedman’s analysis of variance across conditions and p = 0.000, Independent-Samples Kruskal-Wallis tests across subjects).

3.2 Spherical aberration of the eye at a uniform pupil diameter

Figure 4 shows the spherical aberration of the eye alone (relative to value at 0 D) cropped to the smallest of pupil across conditions in each subject plotted against the tested accommodative demands. The pupil diameter is indicated in the lower right corner in each panel. Data from different subjects are plotted in a different scale to accommodate larger variations associated to a larger pupil diameter. Error bars of five repetitions of the wavefronts are shown at each point.

 

Fig. 4. Left panels: Relative change in 4^th order spherical aberration of the eye alone for a fixed pupil diameter (shown in the lower left corner of each panel, representing the minimum diameter in the series, to which data have been cropped), for all conditions and subjects. Right panels: Average slope (across subjects) for each condition (spherical aberration/D). Red lines/bars represent NL; light brown represent CD; dark brown represent PSA; light green represent CN; bright green represent MA; olive green represent HA; darkest green represent NSA. Error bars stand for standard deviations across 5 repeated measurements.

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Spherical aberration shifted to negative values with accommodative demand, in all subjects except for subject S3 (who happens to be one the subject with the largest pupil diameters). Figure 5 (right panel) shows the average slopes (spherical aberration/D of accommodative demand) for fixed pupil diameters. The conditions that produced a larger shift of spherical aberration towards more negative values were the center distance type (CD, PSA) while for CN, HA, MA and NSA the change in spherical aberration was closer to zero.

 

Fig. 5. Left panels: Spherical aberration of eye + phase maps for all subjects as a function of accommodative demands (D) for natural pupil diameters. The numbers in the left and right bottom of each panel indicate the pupil diameter (averaged across conditions, for 0 and 6D), for each condition and all subjects. Right panels: Average slope (across subjects) for each condition (spherical aberration/D). Red lines/bars represent NL; light brown represent CD; dark brown represent PSA; light green represent CN; bright green represent MA; olive green represent HA; darkest green represent NSA. Error bars stand for standard deviations across 5 repeated measurements.

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The spherical aberration change across demands for each condition was statistically significantly different for NL alone (p = 0.042, Independent-Samples Kruskal-Wallis tests) while for the other conditions the change was not statistically significant (p > 0.05, Independent-Samples Kruskal-Wallis tests). Among subjects the largest change was found for PSA in most of the subjects (error bars shown). The slope for 0-2D was flattest for CN in almost all subjects, indicating that the eye may use the add up to about 2D.

3.3 Combined eye and CL wave aberration, for natural pupils

Figure 5 shows the spherical aberration of the eye + phase maps with natural pupil of each subject across conditions plotted against the tested accommodative demands. As expected, with the lenses inducing positive spherical aberration (CD, PSA in shades of brown) the resulting wavefront has positive spherical aberration, while with the lenses inducing negative spherical aberration to the eye (CN, MA, HA, PSA in shades of green) the resulting wavefront spherical aberration is negative in all subjects. Also, the results show a convergence of spherical aberration towards zero with increasing accommodative demand, triggered mainly by the pupil constriction. The superimposed numbers in the bottom left and right corners represent pupil diameter at 0 and 6 D accommodative demand, averaged across conditions The change in spherical aberration across demands was not statistically significant for NL, CN, HA, MA (p > 0.05, Independent-Samples Kruskal-Wallis tests), while for CD, PSA, NSA the change was significantly different across demands (p = 0.010/0.004/0.003) respectively.

3.4 Volume under the MTF

Figure 6 shows the volume under the through focus (TF) MTF between spatial frequencies 3 to 5 cycles per degree for subject S4 for an example for each accommodative demand and condition). The further the peak appears to the left, the higher the accommodative lag (or signal in the hyperopic defocus). Across subjects (and illustrated in Fig. 7 in S1. While we illustrated the TF performance in terms of volume under MTF in a 3-5 c/deg range, the relative shapes of the curves and peak positions were nearly identical to the Visual Strehl TF. On average across subjects, the difference between defocus shifts obtained from volume under MTF (3-5 c/deg) and visual strehl differed by < 0.02D. Volume under MTF was chosen instead of Visual Strehl for illustration purposes, as the change in pupil diameter artificially increased the peak performance (due to normalization in the definition of the Visual Strehl) for the higher accommodative demands.

 

Fig. 6. Through-focus Volume under the MTF (3-5 c/deg) curves for subject S1 for each condition and all vergences (0-6 D, indicating by different line styles). The first row shows the NL condition, the second-row center distance conditions (PSA, CD), and the third row the center near conditions (CN, MA, HA, NSA).

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Fig. 7. (A) Accommodative lag (defocus shift in best image quality) for all subjects and conditions. (B) Average Slope of Accommodative lag curves (top: 0-3D accommodative demand; bottom: 3-6 D accommodative demand). Red lines/bars represent NL; light brown represent CD; dark brown represent PSA; light green represent CN; bright green represent MA; olive green represent HA; darkest green represent NSA. Error bars stand for standard deviations across 5 repeated measurements.

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3.5 Shift in best image quality

Figure 7 (A panels) shows the accommodative lag calculated as the vergence needed to maximize the visual strehl, i.e., the shift of peak in the through focus visual strehl curves, for all subjects and conditions. The lag of accommodation was analyzed in terms of slopes of the curves for lower accommodative demands (0-3D) and higher accommodative demands (3-6D), as shown in Fig. 7 (B), as well as in terms of area under the curves Fig. 7 (C). The analysis of the slopes shows that the lag in the 0 to 3D range is larger with CN like conditions and that it is more similar between conditions after 3D. When analyzing all the data from different subjects, the largest lags were consistently obtained for center near (CN), HighAdd (HA) and negative spherical aberration (NSA) conditions (p = 0.005/0.004/0.011, Independent-Samples Kruskal-Wallis tests) and the smallest lag were found for the positive spherical aberration (PSA) and Center Distance (CD) (p = 0.001 & p = 0.003, Independent-Samples Kruskal-Wallis tests). In half of the subjects, the accommodative lag was significantly reduced using a correction (ie. MCLs compared to the natural condition). The highest differences were found for the slopes at 0-3 D accommodative demands (B, top panels). The area under the curve metric (C, lower panel) shows significance proving that PSA and CD had the smallest lag.

4. Discussion

MCLs are one of the most frequently used strategy for management of myopia progression. We studied the accommodation behavior in a small group of young myopic adult eyes with different simulated lens designs. We used a custom developed AO Visual Simulator to (1) simulate various multifocal designs in the active AO elements of the system (SLM and DM); (2) present accommodating visual stimuli (on a DMD) through the simulated optics; (3) induce accommodative demands (using a Badal system) and (4) measure wave aberrations for different accommodative demands, from which the retinal image quality and accommodative lag was calculated. Simulating contact lenses, as opposed to having the subject wearing them on eye had several advantages: (1) we were not restricted to contact lenses that are commercially available; (2) increased patient comfort and shorter experimental sessions, as the patient did not need to put contact lenses in an out; (3) the eye contribution to aberration measurements could be separated from the CL contribution, also preventing potential artifacts arising from measuring segmented lenses in a Hartmann Shack [44]. In previous studies we had demonstrated the equivalency of real and SLM-simulated lenses [32], in terms of through-focus visual acuity [45]. The current study we measure for the first time the accommodative response with the simulated lenses.

Our control condition (NL) can be compared to existing literature on accommodation-related changes in spherical aberration and pupil diameter (as a function of accommodative demand). We found that in our subjects, pupil diameter decreased with accommodation at a rate of -0.19 mm/D (NL), which is in agreement with prior studies (for example, -0.18 mm/D from Plainis et al. [34]. The higher rates reported in other studies (i.e., -0.35 mm/D from Gambra et al. [19] or -0.45 mm/D by Alpern et al. [46]) may arise from referring to rates as a function of accommodative response (and not demand). We did not find a constant trend across subjects and conditions as for the slope of change of pupil diameter with accommodation, although on average the PSA condition showed the higher slope. Surprisingly, we even found variations in the pupil diameter in the same subject across different lens designs for the relaxed accommodation. In fact, these findings are consistent with previous literature reports. Gambra et al. [19] reported changes in pupil diameter and slope of variation when subjects accommodated through different patterns (positive or spherical aberration, corrected aberrations or coma) mapped on a deformable mirror. Tarrant et al. [47] observed large changes in pupil diameter following orthokeratology treatment (which induced positive spherical aberration), even in a non-accommodating condition, although in another study those authors did not find significant differences in pupil variation across single vision and multifocal contact lenses [48]. On the other hand, Charman et al. [49] found that accommodative miosis tended to be greater in subjects with a relatively low lag of accommodation, which according to the author’s reasoning appeared counter-intuitive, as poor accommodators would benefit from a smaller pupil diameter to minimize retinal image blur. Differences in the specific definitions of accommodative miosis and accommodative aside between our work and Charman’s, our data appear to support those findings. For example, S5 with large pupils and low accommodative miosis exhibit the larger accommodative lag, and conversely S1 and S6 with higher accommodative miosis exhibit lower accommodative lags, for the NL conditions. Therefore, our results appear to support Lowenfeld’s [50] point that the pupillary constriction is in fact independent on the accommodative response, and although generally occurring while accommodating, it is not driven by the other actors of the near triad (accommodation and convergence). The average trend in our data that higher pupillary constrictions slopes were found with the PSA condition, and the lowest with the HA and CN, which happen to be the conditions producing lower and higher lags respectively, is consistent with Charman et al. [51] conclusion that subjects that were most successful at using blur information to achieve better responses also show most marked miosis.

Under natural conditions (NL), and in agreement with previous studies, SA in natural conditions shifted to more negative values with accommodation, at a rate of -0.006 µm/D on average for a constant pupil diameter, and -0.09 µm/D for natural pupil diameter, which are slightly lower than previous reports likely due to our smaller pupil diameters. When the SA was expressed in diopters to discount the effect of the pupil diameter (-0.174 D/D), the rate of variation was comparable to other studies some of them analyzing the change as a function of accommodative response and others as a function of accommodative demand (−0.153 D/D in Gambra et al. [19], −0.184 D/D in Cheng et al. [52]., −0.230 D/D in He et al. [53]., and −0.170 D/D in Plainis et al. [34]. The specific experimental configuration using an AO system allowed us to directly assess the changes in SA occurring at the crystalline lens level. By comparing the SA of the eye alone across the different conditions we could assess whether the presence of a multifocal lens pattern produced changes in the physical changes undergone by the crystalline lens, taking the SA as a marker of the accommodative-related changes in lens shape. To make all conditions directly comparable we kept the pupil diameter constant across conditions. Gambra et al. [19] in a previous study using AO performed a comparable analysis and concluded that the lens accommodated quite similarly under natural conditions than through induced positive or negative SA, although there were some consistent trends of the induced SA conditions producing more negative SA in the lens at a constant pupil diameter. Our results show a consistent larger shift of SA towards negative values with induced PSA aberration followed by CD, and the lowest shift for the NSA and CN conditions. Only S5 showed a high crystalline lens response (based on the SA negative changes) for NSA. Among all conditions, HA and MA appeared to produce the least activity in the crystalline lens. These results indicate that the accommodative mechanism (understood as response of the crystalline lens to change its curvature/asphericity) responds differently to different multifocal lens designs, with center distance designs eliciting a larger response, and center near designs inhibiting those changes.

When SA-inducing patterns are added to the aberrations of the eye, the rate of change of SA with accommodation drastically changed (Fig. 5). In total agreement with Gambra et al. [19], induction of positive SA (also CD in our study) produced steeper changes in SA towards negative values with accommodation, and conversely, induction of negative SA (and also CN, HA and MA in our study) made SA shift relatively toward positive values with accommodation, when the combination of the eye’s aberration, phase map representing the lenses, and the changes of the natural pupil were considered. The added SA that we report in combination with eye’s measured SA (Fig. 5) is that induced/measured in the DM for the SA-inducing conditions (PSA, NSA), an accurate estimation (-0.3/-0.25µm) for the HA and MA conditions mapped in the SLM, as we showed in previous work [32], and only an approximation for the segmented bifocal corrections (CN, CD), although the trends are consistent. It should be noted that the majority of studies in the literature characterize the optical aberrations of the eye + contact lens on eye, and therefore intrinsically may suffer from a potential misrepresentation of the aberrations with bifocal/multifocal contact lenses that have sharp transitions between near and far [44]. By decoupling the eye and the contact lens in the HS measurements in our AO system, therefore bypassing the multifocal profile, we circumvented this potential problem. Since for calculations of optical quality we added the measured eye’s aberrations and the phase maps (Fig. 1) we did not run into potential artifacts created by a Zernike representation of the bifocal/multifocal patterns.

Estimation of the accommodative lag is controversial, and recent literature suggests that the traditionally believed leads and lags of accommodation may be in fact an artifact of the definition or measurement [54]. As proposed by Tarrant et al. [48], Plainis et al. [34] and Gambra et al. [19] among others, we have used retinal image quality metric (and not Zernike defocus or paraxial defocus) in our estimates of accommodative lag. In particular, we used MTF-based metrics (volume under the MTF in a spatial frequency range and Visual Strehl) to estimate the defocus that optimizes the TF image quality for each accommodative demand. Both metrics resulted in similar defocus shifts. VS was used to estimate lag, as this metric has been identified as that showing the largest correspondence with visual acuity and used in refractive error calculations [37]. We chose to illustrate the TF optical quality curves using the volume under the MTF metric to avoid normalization by the pupil diameter, which changed across measurements, making the maximum values of the VS non comparable between accommodative demands. The use of retinal image quality metrics is particularly important in the study of the impact of multifocal lenses, as they introduce relatively large amounts of spherical aberration which interact with defocus, the eye’s natural aberrations and pupil diameter. Our results show that the lens design drastically contributes to the defocus shifts, resulting in large differences in the defocus shifts across lenses. Some studies assume no accommodative residuals at around 2D of accommodative demand, and accommodative leads for lower accommodative demands [19], however, in this study we set 0D of residual defocus (best focus) at infinity. In contrast with other studies, we did not consider leads of accommodation in 0 and lower accommodative demands. In our experimental setting, subjects searched for best focus in the Badal system starting from a myopic defocus, and they did so individually for each lens design. While the presence of spherical aberration may shift the best focus from the NL condition, the identified best focus represents the refractive error for far (equivalent contact lens distant power of a multifocal lens). The Badal defocus that corrected refractive error at distance is considered the zero defocus, which previous literature [37] have shown to match the peak of the TF Strehl curves.

In this study we found that CN designs consistently produce the largest accommodative lags, followed by the HA, MA and NSA, while CD, and to a larger extent PSA produce the lowest lag of accommodation. In two subjects (S1, S3), PSA drastically reduces accommodative lag with respect to the NL condition. Results from previous literature are inconclusive regarding the effect of multifocal contact lenses or treatments that induce spherical aberration on accommodative response. Some evidence indicates a reduced accommodative response (increased lag) over a range of vergences with multifocal contact lenses. center-near +1.5 D [55]; center-near and center-distance with transition zones [56]; center-near +2.5 D [57]). However, other studies have shown that children accommodate normally at near with a dual focus lens [27]. In addition, several studies have investigated the effect of orthokeratology (a treatment that flattens the central cornea, therefore inducing positive spherical aberration). They consistently show an increase in accommodative amplitude and a decrease in accommodative lag in children and young adults [58], which is in good agreement with the results of our study. In contrast, a contact lens that incorporated negative spherical aberration (-0.1um, i,e, of a much lower magnitude that of our study) was reported to reduce the lag, but only for a short period [59]. In another study, a multifocal contact lens with positive spherical aberration reduced accommodative response at all distances, although surprisingly especially at far [52]. It is likely that the variability across studies arises primarily from the definition and measurement protocol of accommodative response (as pointed out above), and also from the differences across lens designs. In a recent publication Gifford et al. [60] point out that it is the multifocal lens design and not the addition power that drive the accommodative response. In another study, the presence of large transition zones appeared to be the major driver for accommodation to intermediate distances [56] Theoretical modelling based on interactions between lens design and eye’s optics, predicted the accommodative response with dual-focus lenses of different powers and zone distributions and concluded the need to customize the design and correction to increase accommodation accuracy [61]. Despite inter-study and inter-subject differences in the accommodative response through multifocal lenses, studies investigating their impact on myopia progression generally conclude that there is a correlation with lag and progression, and more importantly, eyes that accurately accommodated with the contact lens had reduced progression, whereas the myopia control failed in patients or with designs that reduced the accommodative response, likely because the subject used the near add for near vision, leaving the retina exposed to hyperopic defocus. Some authors have proposed the use of biofeedback strategies to train subjects to accommodate with existing multifocal contact lenses [62]. Alternatively, one could propose improved lens designs that generally (or even customized to the individual subject) may reduce accommodative lag. Customizable parameters for these lenses could include, but not be limited to, near-far zone distribution, diameter of the central zone, extent of transition zones, segmented vs smooth transitions, incorporation of other high order aberrations beyond spherical aberration. Adaptive Optics makes an ideal tool for conducting studies to investigate visual performance, and more specifically, the accommodating response with different lens designs, as demonstrated in the current study. If, as suggested by multiple studies, the accommodative behavior with these lenses is, to some extent, a marker of prediction of the success of a certain contact lenses to control myopia in a subject, these AO visual simulations could be essential to select the most appropriate treatment for a patient.

Despite the advantages of the visual simulator to simulate multifocal contact lens designs and test accommodation, some aspects of the system may lead to some results bias, likely overcome by the fact that the same patient is tested under identical conditions. To avoid chromatic artefacts associated to the SLM, which is normally only programmed for one wavelength, we used a monochromatic stimulus. Although the role of chromatic defocus to drive the accommodative response may not be as critical as anticipated in some studies [63,64], measurements in polychromatic light would capture performance in the natural world with more fidelity. Also, in our study, the stimuli are presented monocularly and vergence was induced by a Badal system (no change in magnification; no proximity cues), therefore isolating blur cues from other cues to drive accommodation. Binocular measurements (which should involve not only aberration/accommodation measurements but also binocular simulation of the lens designs) [39,65,66] would again provide a more realistic environment integrating all available cues in a natural world. It is likely that the success at interpreting proximity from defocus blur is inherent to the subject, whereas other subjects may rely habitually in binocular or proximity cues to drive their accommodation, making a comparison of performance across lens designs direct. However, we cannot rule out that some lens designs interact more or less with a given accommodative trigger mechanism, as suggested by the differences between binocular and monocular measurements with multifocal contact lenses with large transition zones in a recent study [56].

In summary, the present study shows that positive spherical aberration inducing conditions (CD, PSA) produced lower accommodative lag in comparison with other conditions in all the subjects. Factors such as pupil size, multifocal lens design, native aberrations of the eye, amount of spherical aberration induced should be considered in the management of myopia with MCLs and to gain insights on the mechanism of operation of these lenses. Future studies may include a larger sample of patients, binocular simulations, and a systematic study of lens designs parameters on the accommodative response. Studies in Adaptive Optics visual simulators are an important step prior to manufacturing specific contact lenses and fitting them on eyes, to assess additional effects such as tear film, lens-cornea interactions or fitting parameters, or lens decentration among others).