Effects of Lens-Induced Astigmatism at Near and Far Distances

Figures & data

Table 1 Measured Contrast

			Measured Contrast (%)
Far	Photopic	HC	97.8±0.2
		LC	10.4±0.1
	Mesopic	HC	92.0±0.2
		LC	10.6±0.1
Near	Photopic	HC	96.1±0.1
		LC	10.0±0.1
	Mesopic	HC	96.2±0.1
		LC	9.4± 0.1

Notes: Contrast (mean ± standard deviation) measured as described in paragraph 2.3 in the different experimental conditions.

Abbreviations: HC, high contrast; LC, low contrast.

Figure 1 Scheme of the study design showing the conditions under which VA was measured, ie at far and at near distance, in photopic and mesopic conditions, at high contrast and low contrast, and for six different level of power and two different axis orientations of the added cylindrical lens.

Abbreviations: VA, visual acuity; D, diopters; WTR, astigmatism with-the-rule; ATR, astigmatism against-the-rule; HC, high contrast; LC, low contrast.

Table 2 Preliminary Assessment

	Far	Near	p-value
N of enrolled subjects who met the inclusion criteria (of which women)	14 (5)
Age (years)	Mean: 57.0
	Std Dev: 5.1
	Min: 51
	Max: 69
Mean spherical equivalent (MSE) of the two eyes (diopters)	Mean: −2.75
	Std Dev: 2.11
	Min: −6.38
	Max: −0.25
Mean natural astigmatism (cyl value) of the two eyes (diopters)	Mean: −0.72
	Std Dev: 0.42
	Min: −1.50
	Max: −0.25
Addition for near (diopters)		Mean: 2.36
		Std Dev: 0.21
		Min: 2.0
		Max: 2.5
Binocular HC BCVA (logMAR) in photopic condition	Mean: −0.14	Mean: −0.14	0.824
	Std Dev: 0.10	Std Dev: 0.08
	Min: −0.30	Min: −0.25
	Max: 0.04	Max: 0.02
Binocular HC BCVA (logMAR) in mesopic condition	Mean: 0.09	Mean: 0.05	0.123
	Std Dev: 0.09	Std Dev: 0.13
	Min: 0.00	Min: −0.10
	Max: 0.30	Max: 0.32
Binocular LC BCVA (logMAR) in photopic condition	Mean: 0.10	Mean: 0.27	0.001
	Std Dev: 0.10	Std Dev: 0.09
	Min: 0.00	Min: 0.14
	Max: 0.34	Max: 0.46
Binocular LC BCVA (logMAR) in mesopic condition	Mean: 0.55	Mean: 0.62	0.027
	Std Dev: 0.16	Std Dev: 0.08
	Min: 0.36	Min: 0.50
	Max: 0.94	Max: 0.72

Notes: Preliminary visual assessment outcomes and p-values of the paired comparison between far and near distance data (Wilcoxon signed-rank test). Bold characters indicate that the difference is statistically significant within the significance level of 0.05.

Abbreviations: BCVA, best corrected visual acuity; logMAR, logarithm of minimum angle of resolution; HC, high contrast; LC, low contrast.

Figure 2 Visual acuity (logMAR) of one participant measured at far and at near distance, in photopic (full markers) and mesopic (empty markers) conditions, for HC (squares) and LC (diamonds) stimuli at different levels of induced WTR and ATR astigmatism. The continuous lines show the results of the linear regressions of the data.

Abbreviations: D, diopters; logMAR, logarithm of minimum angle of resolution; WTR, with-the-rule; ATR, against-the-rule.

Table 3 VA Degradation vs Myopia Level

	WTR				ATR
	Photopic		Mesopic		Photopic		Mesopic
	HC	LC	HC	LC	HC	LC	HC	LC
Far	0.158 (0.589)	−0.246 (0.396)	0.099 (0.736)	0.224 (0.441)	−0.123 (0.675)	0.101 (0.731)	0.308 (0.284)	−0.062 (0.834)
Near	−0.018 (0.952)	−0.066 (0.823)	0.317 (0.270)	0.029 (0.923)	−0.059 (0.840)	0.400 (0.156)	0.451 (0.106)	−0.261 (0.388)

Notes: Rank correlation coefficients of Spearman (first value in each cell) and p-value (second value in brackets) showing the correlation between the myopia level (mean spherical equivalent (MSE) of the two eyes) and the VA degradation due to the lens-induced astigmatism (slopes of the regression lines as those in Figure 2).

Abbreviations: HC, high contrast; LC, low contrast; WTR, with-the-rule; ATR, against-the-rule.

Figure 3 (a) Mean slopes indicating the visual acuity (A) drop induced by astigmatism (WTR and ATR) at far and at near distance, for HC and LC stimuli, in photopic and mesopic conditions. (b) Mean DoF calculated as one tenth of the reciprocal of the slopes, thus representing the cylindrical power which produces a 0.1 logMAR worsening of the visual acuity. The bars indicate the standard deviations of the data.

Abbreviations: DoF, depth of focus; D, diopters; D⁻¹, diopters⁻¹; WTR, astigmatism with-the-rule; ATR, astigmatism against-the-rule; HC, high contrast; LC, low contrast.

Table 4 Far vs Near Comparison

	WTR				ATR
	Photopic		Mesopic		Photopic		Mesopic
	HC	LC	HC	LC	HC	LC	HC	LC
Far	0.22 (0.06)	0.22 (0.07)	0.18 (0.07)	0.12 (0.06)	0.18 (0.06)	0.20 (0.06)	0.17 (0.04)	0.14 (0.06)
Near	0.15 (0.05)	0.13 (0.04)	0.16 (0.08)	0.11 (0.04)	0.12 (0.05)	0.10 (0.05)	0.16 (0.05)	0.10 (0.04)
P-value Far vs Near	0.0061	0.0001	0.4263	0.2676	0.0017	0.0001	0.2676	0.0266
Δ	0.07	0.09	0.02	0.01	0.06	0.10	0.01	0.04
Δthreshold	0.054	0.049	0.069	0.050	0.052	0.052	0.044	0.049

Notes: Mean slopes in diopters⁻¹ (and standard deviations in diopters⁻¹ units in parentheses) indicating the VA worsening due to lens-induced astigmatism (WTR and ATR), at far and at near distance, for HC and LC stimuli, in photopic and mesopic conditions. The p-values obtained by Wilcoxon test are reported for the paired comparison between the data measured at far and those measured at near in corresponding experimental conditions, together with Δ and Δ_threshold (both in diopters⁻¹). Bold values indicate that the difference is statistically significant within the significance level of 0.05/8 (Bonferroni correction where 8 is the number of comparisons) ie significance is reached only for a p-value lower than 0.0063. Δ, difference between the means of the measured data; Δ_threshold, threshold value for the difference between the means that can be proved statistically with significance at 0.05 based on the number of recruited subjects and the standard deviations of the two groups.

Abbreviations: HC, high contrast; LC, low contrast; WTR, with-the-rule; ATR, against-the-rule.

Table 5 WTR vs ATR Comparison

	FAR				NEAR
	Photopic		Mesopic		Photopic		Mesopic
	HC	LC	HC	LC	HC	LC	HC	LC
WTR	0.22 (0.06)	0.22 (0.07)	0.18 (0.07)	0.12 (0.06)	0.15 (0.05)	0.13 (0.04)	0.16 (0.08)	0.11 (0.04)
ATR	0.18 (0.06)	0.20 (0.06)	0.17 (0.04)	0.14 (0.06)	0.12 (0.05)	0.10 (0.05)	0.16 (0.05)	0.10 (0.04)
P-value WTR vs ATR	0.0785	0.1726	0.6257	0.2412	0.0580	0.0504	0.2958	0.5049
Δ	0.04	0.02	0.01	0.02	0.03	0.03	0.00	0.01
Δthreshold	0.057	0.062	0.054	0.058	0.049	0.044	0.063	0.039

Notes: Mean slopes in diopters⁻¹ (and standard deviations in diopters⁻¹ in parentheses) indicating the va worsening due to lens-induced astigmatism (WTR and ATR) at far and at near distance, at HC and at LC, in photopic and mesopic conditions. The p-values obtained by Wilcoxon test are reported for the paired comparison between the data measured by inducing WTR astigmatism and those measured inducing ATR astigmatism in corresponding experimental conditions, together with Δ and Δ_threshold (in diopters⁻¹). Δ, difference between the means of the measured data; Δ_threshold, threshold value for the difference between the means that can be proved statistically with significance at 0.05 based on the number of recruited subjects and the standard deviations of the two groups.

Abbreviations: HC, high contrast; LC, low contrast; WTR, with-the-rule; ATR, against-the-rule.

Table 6 Photopic vs Mesopic Comparison

	FAR				NEAR
	WTR		ATR		WTR		ATR
	HC	LC	HC	LC	HC	LC	HC	LC
Photopic	0.22 (0.06)	0.22 (0.07)	0.18 (0.06)	0.20 (0.06)	0.15 (0.05)	0.13 (0.04)	0.12 (0.05)	0.10 (0.05)
Mesopic	0.18 (0.07)	0.12 (0.06)	0.17 (0.04)	0.14 (0.06)	0.16 (0.08)	0.11 (0.04)	0.16 (0.05)	0.10 (0.04)
P-value Photopic vs Mesopic	0.1189	0.0006	0.6750	0.0023	0.4420	0.3636	0.0353	0.9687
Δ	0.04	0.10	0.01	0.06	0.01	0.02	0.04	0.00
Δthreshold	0.062	0.062	0.050	0.058	0.063	0.039	0.049	0.044

Notes: Mean slopes in diopters⁻¹ (and standard deviations in diopters⁻¹ in parentheses) indicating the VA worsening due to lens-induced astigmatism (WTR and ATR) at far and at near distance, for HC and LC stimuli, in photopic and mesopic conditions. The p-values obtained by Wilcoxon test are reported for the paired comparison between the data measured in photopic and mesopic conditions in corresponding experimental conditions, together with Δ and Δ_threshold (both in diopters⁻¹). Bold values indicate that the difference is statistically significant within the significance level of 0.05/8 (Bonferroni correction where 8 is the number of comparisons) ie significance is reached only for a p-value lower than 0.0063. Δ: difference between the means of the measured data; Δ_threshold: threshold value for the difference between the means that can be proved statistically with significance at 0.05 based on the number of recruited subjects and the standard deviations of the two groups.

Abbreviations: HC, high contrast; LC, low contrast; WTR, with-the-rule; ATR, against-the-rule.

Table 7 HC vs LC Comparison

	FAR				NEAR
	WTR		ATR		WTR		ATR
	Photopic	Mesopic	Photopic	Mesopic	Photopic	Mesopic	Photopic	Mesopic
HC	0.22 (0.06)	0.18 (0.07)	0.18 (0.06)	0.17 (0.04)	0.15 (0.05)	0.16 (0.08)	0.12 (0.05)	0.16 (0.05)
LC	0.22 (0.07)	0.12 (0.06)	0.20 (0.06)	0.14 (0.06)	0.13 (0.04)	0.11 (0.04)	0.10 (0.05)	0.10 (0.04)
P-value HC vs LC	0.6698	0.0085	0.3910	0.0353	0.1242	0.04187	0.0830	0.0081
Δ	0.00	0.06	0.02	0.03	0.02	0.05	0.02	0.06
Δthreshold	0.062	0.062	0.058	0.050	0.044	0.060	0.049	0.044

Notes: Mean slopes in diopters⁻¹ (and standard deviations in diopters⁻¹ in parentheses) indicating the VA worsening due to lens-induced astigmatism (WTR and ATR) at far and at near, for HC and LC stimuli, in photopic and mesopic conditions. The p-values obtained by Wilcoxon test are reported for the paired comparison between the data acquired at HC and at LC in corresponding experimental conditions, together with Δ and Δ_threshold (both in diopters⁻¹). Δ, difference between the means of the measured data; Δ_threshold, threshold value for the difference between the means that can be proved statistically with significance at 0.05 based on the number of recruited subjects and the standard deviations of the two groups.

Abbreviations: HC, high contrast; LC, low contrast; WTR, with-the-rule; ATR, against-the-rule.