12 children (8–13 years) and 6 naive adults (age: 20–35 years) were recruited from the clinic database at the School of Optometry and Vision Science, University of Waterloo. Informed consent was obtained from the parents for a child and was obtained directly from the adult subjects. The study followed the tenets of Declaration of Helsinki and received ethical approval from the University of Waterloo office of research ethics review board. Subjects with strabismus, amblyopia, anisometropia >1.00D, astigmatism >1.00D and with best corrected visual acuity of less than 6/6 were excluded. All the subjects with refractive error were habitual contact lens wearers and wore the lens during the study.

Dynamic photorefractor (DPR, PROSILICA CAM (EC750), Allied Vision Technologies, BC, Canada) was a custom built eccentric photorefractor used to measure accommodation and disaccommodation. This system has been described elsewhere.21 The sampling rate of the system was 70Hz, giving an output every 14ms. Accommodation data were then loaded into the dynamic photorefraction system (DPRS) for further analysis.21 DPRS was calibrated and validated on children and adults.22 Individual calibration procedure followed in this study was similar to those described previously.11,23 This was done to address the individual variation in the optical factors such as pupil size, fundus reflectance etc. and ensure accuracy in estimating changes in the accommodation state.

Accommodation was stimulated using a Badal optical system.24 As shown above (Fig. 1), the subject was seated 1m away from the photorefractor. An IR passing mirror (Optical cast IR filter, Edmund Optics, USA) in front of the subject allowed an orthogonal presentation of the step targets along with a continuous measure of accommodation using the photorefractor. Two high contrast targets (T1, T2; black on white vertical lines that were illuminated using white LEDs) were placed at different distances from a +5D Badal lens to create various accommodative and disaccommodative demands without a change in the angular size of the target. While the far target was always at infinity, near one was moved to various distances to create demands ranging from 1-3D, 1D steps. The accommodative demand was instantly switched from one distance to the other using a stimulus control tool box with a button. This switch was connected to the dynamic photorefraction system through an input–output control box allowing a time stamp to be created with the onset of the stimulus. Stimulus order and presentation time was randomized to avoid predictability or learning effects.

Figure 1.

Experimental design to stimulate accommodation and disaccommodation. The subject was seated 1m away from the photorefractor with the left eye occluded. An IR passing mirror (Optical cast IR filter, Edmund Optics, USA) was placed in front of the right eye for an orthogonal presentation of the accommodative targets along with a continuous measure of accommodation using the dynamic photorefractor. High contrast targets (T1, T2) were placed at different distances from the +5D Badal lens to create various accommodative and disaccommodative demands. Step stimuli were presented using a stimulus control tool box with a button that helps in switching the target distance instantly.

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After an initial assessment of the anterior chamber, both eyes of each subject were dilated using 2.5% Mydfrin (Phenylephrine hydrochloride). This was done to optimize the photorefraction measures by providing a larger pupil size (>4mm). The left eye was occluded throughout the experiment to open the loop of the vergence system. Practice trials were given in order to familiarize the subjects with the procedures involved. Single step responses to both accommodation and disaccommodation were presented using a Badal system and recorded using the photorefractor. Multiple trials (ranging from 6 to 12) were conducted for each stimulus level of accommodation and disaccommodation and each trial lasted for 5–10s. The stimulus presentation time was varied from 2 to 5s after the initiation of the trial to avoid prediction. Frequent breaks were given to both children and adults between the trials to avoid fatigue effects on accommodation and disaccommodation.

Final position traces (units of diopters) obtained from the DPRS were used for further dynamic analysis on MATLAB (Mathworks, Inc., MA, USA). Velocity (diopters/s) and acceleration (diopters/s2) profiles were obtained by differentiating the response traces using a 2-point-difference algorithm. Velocity threshold criterion1 was used to identify start and end points of the dynamic accommodative response. An inverse of this criterion was used for disaccommodative responses.

Fourier transformation (FFT) was then applied on the individual unsmoothed position, velocity and acceleration traces obtained from all the subjects. As shown in Fig. 2, FFT was applied only to the dynamic response between the two red dotted lines i.e. between the start and end points of the response. Ideal sampling rates for measuring the accommodative and disaccommodative position, velocity and acceleration traces were estimated using the peak frequency obtained from FFT. Instrument or measurement noise was identified by applying Fast Fourier transform on the measurements with a static model eye. The power spectrum due to noise was removed from the final accommodation frequency data to ensure that the measures were valid (Fig. 3) and only frequencies with a power spectrum larger than this limit were considered to be accommodative origin.

Figure 2.

Typical dynamic accommodative and disaccommodative traces obtained from the subjects for a 3D stimulus. The solid line indicates the mean vlaue and shaded area indicates the standard error in the reponse. The red dotted lines indicate the start and end points of the dynamic traces and FFT was applied only on this area.

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Figure 3.

Fourier analysis of dynamic accommodation and disaccommodation. Unsmoothed time domain traces of position (a), velocity (b) and acceleration (c) obtained were converted into frequency domain using fast Fourier analysis across different accommodative demands, 1D (red line), 2D (green line) and 3D (black dotted line). The connecting lines indicate the mean values and shaded area indicates the standard error.

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Accommodation data were obtained from 12 children (11.16±1.83 years) and 6 adults (26.16±3.37 years). Fig. 3 shows the FFT output (mean and SE) obtained from unsmoothed accommodative and disaccommodative traces (mean and SE) measured across different accommodative demands (1-3D, 1D steps). The typical frequencies present in a dynamic position and velocity trace were limited to frequencies less than 10Hz. For acceleration, frequencies ranging from 15 to 35Hz were present. The ideal sampling rate (Nyquist rate) was calculated using the peak frequency present in the response. As shown in Fig. 3, stimulus direction (accommodation or disaccommodation) and demand (1/2/3D steps) had no influence on the range of frequencies present in a dynamic response. Based on the FFT data, the ideal sampling rate should be 5Hz, 10Hz and at least 70Hz to accurately measure accommodative position, velocity and acceleration respectively.

Three adult subjects (26, 28 and 32 years) were recruited later for the second study where the dynamic main sequence was compared when measured at different sampling rates. Informed consent was obtained separately for this study visit. For main sequence comparison,

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  Accommodation was measured on the 3 subjects using two separate photorefractors, a custom built eccentric DPR (70Hz) and a commercially available PowerRefractor (25Hz) on two separate days. The order was randomized.

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  Accommodation was recorded using the Dynamic photorefractor (DPR). Data were subsequently analyzed at two sampling rates. First, the data were analyzed at its original sampling rate (DPR – 70Hz). It was then down sampled to 30Hz and the dynamic measures were re-analyzed (DPR – 30). This was done to understand the influence of differing analysis algorithms that might occur with the previous analysis.

Dynamic photorefractor (DPR, PROSILICA CAM (EC750), Allied Vision Technologies, BC, Canada): As described in the first section (study 1).

PowerRefractor (PR, Multichannel systems, Reutlingen, Germany) is a commercially available photorefractor that works at a sampling rate of 25Hz, providing an output every 40ms. Numerous studies3,27,28 have used it to measure static and dynamic characteristics accommodation on both children and adults. This was one of the first few photorefractors to successfully calibrate the optical principle of eccentric photorefraction for use in measures of accommodation.

The design used was similar to that described above. Similar procedures (as in study 1) were followed on two separate visits while accommodation data from the three subjects were recorded using the two photorefractors.

Dynamic accommodative and disaccommodative position traces obtained from the DPR were then loaded into MATLAB for further analysis. Velocity (diopters/s) and acceleration (diopters/s2) profiles were obtained by differentiating the response traces using a 2-point-difference algorithm. All the traces were subsequently smoothed using a 100ms window. Velocity threshold criterion was used to identify the start and end of the response. The start of the response was the first point where the velocity exceeded 0.5D/s and continued to do so for the next 100ms. Similarly, end of the response was identified as the point where velocity fell below 90% of peak velocity and continued to do for the next 100ms. The start and the end points obtained using this criterion were later confirmed by visual inspection.1

Accommodative response (D) was defined as the dioptric difference between the start and end points. Highest values on the velocity and acceleration traces were defined as the peak velocity (D/s) and peak acceleration (D/s2) respectively. “First order main sequence” relationship was defined by plotting the accommodative and disaccommodative peak velocities as a function of their respective response amplitudes. Similarly “Second order main sequence” relationship was peak acceleration as a function of the response amplitude. Historically, linear regression was used to identify the main sequence relationship. However, given the variability in the velocity/acceleration and amplitude measures, a bivariate regression analysis such as Deming regression was chosen in the current study. Regression and other statistical analysis were performed using GraphPad Prism (GraphPad Software Inc., USA).

Accommodative traces were obtained on three adults (26, 28 and 32 years). Fig. 4 shows the main sequence characteristics of both accommodation and disaccommodation obtained from the three photorefractor conditions.

Figure 4.

Main sequence data were compared between PR (blue) and DPR 70 (red) and DPR 30 (green). Deming regression was used to fit the MS data of velocity and acceleration for both accommodation (a, b) and disaccommodation (c, d). p value shows the difference between the slope of the regression fits from a zero slope.

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For accommodation (Fig. 4(a) and (b)), Deming regression slopes of velocity and acceleration were significantly different from zero (p<0.01). For accommodative velocity, the MS slopes were similar between the three conditions (DPRS (70Hz): 2.69x+2.05; PR: 2.58x+0.73; DPRS (30Hz): 2.34x+1.06; PR: 2.58x+0.73; Slopes: F2,66=0.120; p=0.88). However, the intercepts were significantly lower (F2,68=4.653; p=0.01) with PR (p=0.01) and DPRS 30 (p=0.02). Similarly, for accommodative acceleration, the MS slopes were similar between the three measurements (PR: 8.40x+4.32; DPRS 70: 12.93x+21.38; DPRS 30: 8.93x+8.31; Slopes: F2,66=0.164; p=0.84) but the intercepts were significantly lower (F2,68=19.79; p<0.0001) with PR (p<0.0001) and DPRS 30 (p<0.0001). For disaccommodative velocity (Fig. 4(c)), the MS slopes of velocity were similar between the three photorefractor conditions (PR: 1.94x+0.09; DPRS 70: 2.38x+0.55; DPRS 30: 1.63x+0.80; Slopes: F2,56=0.686; p=0.50). However, the intercepts were significantly lower (F2,58=4.017; p=0.02) with PR (p=0.04) and DPRS 30 (p=0.04). For disaccommodative acceleration, the MS slopes were similar between the three photorefractor conditions (PR: 3.46x+7.52; DPRS 70: 12.70x+10.72; DPRS 70: 6.82x+4.93; Slopes: F2,56=2.130; p=0.13) but the intercepts were significantly lower (F2,58=24.145; p<0.0001) with PR and DPRS 30 (p<0.0001).