Clinical Tolerance to Experimentally Induced with-the-Rule and Against-the-Rule Astigmatism After Implantation of an Extended Depth-of-Focus Intraocular Lens: A Defocus-Curve Study

Introduction

Cataract surgery has evolved from a rehabilitative procedure into one of the most frequently performed refractive surgeries worldwide. The introduction of presbyopia-correcting intraocular lenses (IOLs), including multifocal, trifocal, and extended depth-of-focus (EDOF) designs, has broadened patient expectations from simple visual restoration to functional spectacle independence across distance, intermediate, and near ranges.^1,2 Despite these advances, residual refractive errors, particularly astigmatism, remain among the most important limiting factors affecting postoperative visual outcomes and patient satisfaction.^3–5

Residual astigmatism of 0.50 to 0.75 diopters (D) has been shown to reduce distance visual acuity (VA), contrast sensitivity, and overall visual quality in eyes implanted with monofocal, EDOF, and multifocal IOLs.^6–8 This effect is especially pronounced in diffractive multifocal and trifocal optics, which exhibit higher sensitivity to optical aberrations.^9,10 In contrast, EDOF IOLs are designed to elongate the depth of focus without generating multiple foci, thereby demonstrating slightly greater tolerance to low levels of astigmatism than bifocal and trifocal lenses.^11,12 However, clinically relevant deterioration in VA has been consistently reported when residual cylinders exceed 1.00 D.^13,14

Astigmatism orientation also plays a crucial role in functional outcomes. With-the-rule (WTR) astigmatism, in which the vertical meridian is steeper, tends to preserve distance vision. In contrast, against-the-rule (ATR) astigmatism, with a steeper horizontal meridian, may provide an extended depth of focus, favoring intermediate and near visual tasks.^15–17 Age-related corneal remodeling, with a gradual shift from WTR to ATR profiles, further emphasizes the importance of axis-specific tolerance when planning refractive targets and surgical strategies.^18,19 Recent clinical studies have confirmed that ATR induction may preserve intermediate vision more effectively, whereas WTR maintains sharper contours for distance.^20–22

Validated experimental protocols have employed induced astigmatism through defocus curves to quantify tolerance thresholds in pseudophakic eyes.^22–24 These methodologies have been applied to various lens platforms, demonstrating reproducibility and clinical applicability for evaluating the functional impact of both the magnitude and axis of residual astigmatism. Within this context, the diffractive echelette-design EDOF IOL has shown favorable intermediate and near performance. Still, data remain limited regarding its tolerance to induced astigmatism across different orientations.

This study adds to previous literature by quantifying axis-specific effects of induced astigmatism on defocus curves and clarifying how these patterns may influence clinical decision-making.

The present study aims to evaluate the clinical tolerance of pseudophakic patients implanted with an EDOF IOL with induced cylindrical defocus of +1.00, +2.00, and +3.00 D, oriented along WTR and ATR axes. By integrating validated methodologies and focusing on axis-specific differences, this study seeks to provide clinically relevant thresholds to guide toric planning, residual refractive targeting, and patient counseling in EDOF cataract surgery.

Methods

Study Design and Ethics

This was a prospective, non-randomized clinical study conducted at the Hospital Oftalmológico de Brasília (HOB), Brazil. The protocol adhered to the Declaration of Helsinki and was approved by the HOB Institutional Review Board (approval code: 42915320.3.0000.5667). Written informed consent was obtained from all participants.

Patients

Nine pseudophakic patients (nine dominant eyes) aged 18 years or older were included. All had undergone uneventful phacoemulsification with implantation of a Tecnis Symfony^® extended depth-of-focus (EDOF) intraocular lens (Johnson & Johnson Vision, Santa Ana, CA, USA) in the dominant eye. Exclusion criteria were: inability to perform standardized visual acuity testing; corrected distance visual acuity (CDVA) worse than 20/25; optic nerve, macular or corneal pathology; media opacities beyond minimal posterior capsule opacification; ocular inflammation; or any prior intraocular surgery other than cataract extraction.

Preoperative corneal astigmatism was not systematically recorded, as the study evaluated optically induced astigmatism rather than relying on preoperative corneal values.

Surgical Procedure

All surgeries were performed by the same experienced surgeon using a standardized technique. A 2.2 mm clear corneal incision was created on the steepest meridian, followed by a ~5.0 mm continuous curvilinear capsulorhexis, hydrodissection, phacoemulsification, cortical cleanup, and in-the-bag implantation of a diffractive echelette-design EDOF IOL using the manufacturer’s injector. No intraoperative complications occurred.

Visual Acuity Testing

Monocular visual performance was assessed under photopic conditions (85 cd/m²) at 4 m with Early Treatment Diabetic Retinopathy Study (ETDRS) charts using the CSV-1000 system (VectorVision, Greenville, OH, USA). Testing included uncorrected distance visual acuity, manifest refraction, and CDVA. Visual acuity values were recorded and converted to logarithm of the minimum angle of resolution (logMAR) for analysis.

Before each defocus and cylinder-induction measurement, the cylindrical axis was carefully aligned and reconfirmed through repeated verification in the trial frame to ensure consistent vertex distance and axis stability throughout all measurements.

Defocus Curves and Cylinder Induction

Defocus curves were obtained by adding spherical trial lenses from −5.00 D to +2.50 D in 0.50-D steps over the patient’s best subjective refraction (cylinder neutralized). Regular myopic astigmatism was then optically induced with positive cylindrical lenses of +1.00 D, +2.00 D, and +3.00 D at canonical axes (0°, 45°, 90°, and 135°). For analytical purposes, 90° was treated as with-the-rule (WTR) and 0°/180° as against-the-rule (ATR); oblique axes (45° and 135°) were recorded and may be reported separately.

Axis convention note: in plus-cylinder notation, WTR corresponds to +cyl at 90° (≡ −cyl at 180° in minus-cyl notation) and ATR corresponds to +cyl at 180° (≡ −cyl at 90°).

Outcomes

The primary outcome was the change in logMAR visual acuity across defocus vergences for each induced cylinder magnitude, relative to the control (no cylinder). Secondary outcomes included the effect of axis orientation (WTR vs ATR) at each vergence and the interaction between cylinder magnitude and axis orientation. For clinical interpretation in figures, the 0.3 logMAR reference line (≈20/40) was annotated but not used as a statistical decision threshold.

Statistical Analysis

Repeated-measures analysis of variance (ANOVA) was used to assess the effects of vergence and cylinder magnitude/axis on logMAR acuity, with Tukey post hoc testing for pairwise comparisons (α=0.05). Demographic homogeneity (sex, age distribution, laterality) was explored with Kruskal–Wallis tests. Analyses were performed with Microsoft^® R Open 3.5.1 and RStudio 1.1.456, and Microsoft^® Excel 2007.

Results

Patient Demographics

Nine eyes from nine patients were analyzed. The mean age was 60.9 ± 5.6 years; three patients (33%) were 50–59 years and six (67%) 60–69 years. Five patients were female (56%) and four male (44%). Six eyes (67%) were left and three (33%) right. Kruskal–Wallis testing confirmed homogeneity for sex (p=0.323) and laterality (p=0.602), while age distribution was significant (p=0.019). Full demographics are shown in Table 1.

Table 1 Patient Demographics and Baseline Characteristics

Visual Acuity with Induced Astigmatism (Magnitude Effect)

Distance visual acuity remained functionally preserved with +1.00 D of induced regular astigmatism, whereas +2.00 D produced clinically meaningful deterioration and +3.00 D caused widespread loss of acuity across most vergences. A qualitative summary by cylinder magnitude is presented in Table 2.

Table 2 Summary of Visual Acuity Outcomes with Induced Regular Astigmatism

Defocus Curves (Overall)

Figure 1 depicts the defocus curves for control (no cylinder) versus +1.00 D, +2.00 D, and +3.00 D across vergences from −5.00 D to +2.50 D. With +1.00 D, the curve remained close to control, with minor decrements near plano and in low hyperopic vergences. With +2.00 D, acuity worsened at multiple vergences along the curve, and with +3.00 D the deterioration was broad, sparing essentially only the most myopic defocus points (very near). The dashed line at 0.3 logMAR marks the 20/40 functional threshold and illustrates the transition from acceptable to impaired distance function as cylinder increases.

Figure 1 Defocus curves under control and induced cylinders (+1.00 D, +2.00 D, +3.00 D). Monocular logMAR visual acuity across vergences from −5.00 D to +2.50 D under photopic conditions; dashed line indicates 0.3 logMAR (20/40).

Axis-Specific Tolerance (WTR = 90° vs ATR = 0°/180°)

Axis orientation significantly modulated functional performance (Figure 2). At +1.00 D, both WTR (90°) and ATR (0°/180°) maintained functional acuity with minimal differences across vergences. At +2.00 D, ATR preserved intermediate and very near performance more effectively (approximately −2.00 D to −3.50 D), whereas WTR tended to preserve sharper distance acuity near plano. At +3.00 D, the same pattern persisted—ATR relatively superior at intermediate/near and WTR relatively superior at distance—although both orientations resulted in clinically meaningful deterioration overall due to the higher cylinder magnitude.

Figure 2 Defocus curves comparing ATR and WTR at +1.00 D (A), +2.00 D (B), and +3.00 D (C). Axis convention (plus-cylinder): WTR = 90°, ATR = 0°/180°. Dashed line indicates 0.3 logMAR (20/40).

Statistical Analysis

Repeated-measures ANOVA showed significant main effects for cylinder magnitude (p<0.01) and vergence (p<0.01), and a significant interaction between axis and vergence near plano and +0.50 D (p<0.05). Tukey post hoc comparisons confirmed that +2.00 D and +3.00 D differed from control across most vergences, while +1.00 D generally did not. These analyses support a practical tolerance envelope of approximately +1.00 D for EDOF IOL recipients; beyond this level, functional penalties become evident and expand across the defocus curve.

Discussion

This study quantified the functional impact of optically induced regular astigmatism after implantation of an extended depth-of-focus (EDOF) intraocular lens by combining defocus curves with explicit axis analysis. Three consistent observations emerged across the dataset. First, distance visual acuity remained largely functional under +1.00 D, whereas +2.00 D produced clinically relevant decrements and +3.00 D caused broad deterioration along the defocus curve. Second, axis orientation modulated performance: with-the-rule (WTR, 90°) tended to preserve distance acuity near plano, while against-the-rule (ATR, 0°/180°) relatively favored intermediate and very near vergences. Third, these axis-dependent differences were present at all cylinder levels but were most evident at +2.00 D, where clinical trade-offs are easiest to appreciate.

The magnitude-dependent pattern aligns with current knowledge about presbyopia-correcting optics. Diffractive multifocal and trifocal lenses are more sensitive to residual ametropia and show decrements in visual performance even with modest cylinders, reflecting the penalty of splitting light into multiple foci.^9,10 In contrast, EDOF designs, which elongate the focal zone rather than create discrete focal points, generally show slightly greater tolerance to low residual cylinders, often up to about 0.50–1.00 D, while values beyond ~1.00 D consistently produce clinically meaningful losses, especially at distance.^11–14 Our finding that +1.00 D was broadly tolerated, whereas +2.00 D and +3.00 D produced progressively larger penalties, is therefore congruent with prior clinical and psychophysical evidence indicating that small cylinders (≈0.50–0.75 D) can already reduce visual quality and that ≥1.00 D frequently crosses a pragmatic threshold of functional impact in eyes with presbyopia-correcting optics.^{6–8,11,12,14}

Axis orientation behaved as predicted by optical theory and empirical work. With a steeper vertical meridian, WTR tends to maintain sharper distance contours. In contrast, ATR shifts the circle of least confusion, effectively extending the depth of focus toward intermediate and near tasks.^15–17 In the present series, the ATR advantage was most evident at vergences that map to common working distances, approximately −1.50 D to −2.50 D (about 66 to 40 cm), which correspond to computer and reading ranges. At the same time, WTR preserved distance around plano, a priority for activities such as driving. These axis-resolved results are clinically relevant in the context of age-related corneal remodeling, which shows a well-documented shift from WTR to ATR with aging; such remodeling can alter how residual astigmatism is perceived postoperatively and should be factored into lens selection and counseling.^18,19 Recent clinical studies further support the idea that ATR may preserve intermediate performance more effectively, whereas WTR tends to maintain distance clarity, a pattern that closely mirrors our defocus curves.^20–22

Methodologically, induced-defocus paradigms provide within-subject, lens-specific characterization of functional performance across vergences and have become a standard framework to benchmark presbyopia-correcting IOLs [23,24.25]. Using a photopic, high-contrast ETDRS protocol reduces ceiling effects and supports reproducibility. In this context, separating cylinder magnitude from axis orientation clarifies which component drives losses at each vergence. The present analysis focuses on WTR (90°) and ATR (0°/180°) because these orientations are the most clinically actionable and best represented in the literature; oblique axes were collected but intentionally not emphasized here to maintain clarity and because their functional profile commonly falls between the WTR and ATR extremes in everyday tasks. Nonetheless, the absence of a dedicated analysis of oblique astigmatism constitutes a limitation, as oblique axes (45° and 135°) may present intermediate behavior that could refine axis-specific interpretation.

The interaction between magnitude and axis has direct practical implications. For patients implanted with EDOF IOLs, residual cylinders around +1.00 D were generally tolerated, while +2.00 D and +3.00 D produced broad functional penalties along the defocus curve. When small residuals are unavoidable, tailoring the axis to visual priorities can be helpful: ATR tends to favor intermediate/near tasks (eg, office work, reading, smartphone use), whereas WTR better supports distance acuity. This does not imply that leaving the cylinder is desirable; rather, it provides a framework for risk-benefit discussions when perfect neutrality is uncertain, and it emphasizes that the magnitude should remain low to avoid global degradation.^{6–8,11–17,20–22} These principles should be integrated with careful preoperative planning and counseling that acknowledge the natural WTR-to-ATR corneal evolution with age and the patient’s visual demands.^18,19 However, patient-reported outcomes (such as visual satisfaction, photic phenomena, and functional complaints) were not collected, which limits the ability to correlate objective findings with subjective experience.

The present findings are also consistent with broader differences among presbyopia-correcting platforms. Compared with diffractive multifocal and trifocal lenses—which can show clear penalties with relatively small cylinders^9,10—EDOF optics typically provide a slightly wider tolerance window at low cylinder levels.^11–14 Even within non-diffractive presbyopia-oriented designs, tolerance is not uniform and depends on the specific optical design; some designs deliver tolerance closer to that of conventional monofocals, while others confer modest but clinically meaningful robustness under ATR at intermediate vergences.^{11,12,23–25} Because real-world performance depends on multiple interacting factors, biometry accuracy, posterior corneal power, surgically induced astigmatism, ocular surface stability, and individual neural adaptation, these lens-specific characteristics should be interpreted within the context of comprehensive surgical planning and postoperative optimization.^{3–8,11–14,18–25} Additionally, as all measurements were performed monocularly, the study does not capture potential binocular summation effects, which in clinical practice often enhance contrast and improve distance performance compared to monocular viewing. Furthermore, only photopic and high-contrast acuity were assessed; mesopic conditions, glare/halo perception, and contrast sensitivity, which are clinically relevant, especially for EDOF lenses, were not evaluated.²⁶

This study has limitations, including a modest sample size and a single-center design, which limit precision for small effect sizes and generalizability. The use of optically induced regular astigmatism provides a controlled model but does not fully replicate postoperative irregular astigmatism or neural adaptation dynamics.

In summary, the study met its objective by defining clinically relevant tolerance limits to induced astigmatism after EDOF implantation and by demonstrating that axis orientation meaningfully modulates functional performance. In practical terms, about +1.00 D represents a reasonable upper bound for tolerance, +2.00 D and +3.00 D produce progressive losses across the defocus curve, WTR better preserves distance, and ATR relatively supports intermediate and near. These findings provide actionable thresholds and axis-aware guidance for toric planning, residual-targeting, and patient counseling in EDOF cataract surgery.