Multifocal Corneal Surgery for Presbyopia





Introduction


Presbyopia can be defined as the point where accommodative function declines to less than 3 to 4 diopters (D), receding the near point beyond arms’ length at reading distance. It is usually manifested in the fourth decade of life. Theories of the mechanism of presbyopia were traditionally categorized as either lenticular or extra-lenticular. The compensation of presbyopia by the induction of a controlled amount of multifocality to the cornea is an attractive technique for presbyopes, especially those having concomitant distance ametropia. Surgical techniques to restore full or partial dynamic accommodation using foldable intraocular lenses (IOLs), ciliary sclerotomy, scleral expansion bands, and femtosecond (FS) laser crystalline lens relaxing incisions are not routinely used and are still under investigation. Inducing optical multifocality requires simpler and less invasive procedures. The results of recent studies suggest that multifocal contact, phakic, and pseudo-phakic IOLs can afford presbyopes a viable alternative to spectacles. Diffractive multifocal (e.g., bifocal and trifocal) intraocular lenses have gained popularity over the last decade, and newer refractive designs have also been introduced.




Theoretical Considerations


The human eye exhibits a certain amount of multifocality. The ability to discern a target over a range of distances without noticeable loss in image quality relates to depth of focus. Many elements determine the value of the depth of focus of an optical system such as the eye. The level of optical aberration that the surgeon can modify to increase the depth of focus in order to compensate for the loss of accommodation and induce a state of “pseudoaccommodation” is an important consideration.


Depth of Focus and Optical Aberrations


Depth of focus determines the distance range for which a target can be seen clearly without a change in focusing power. For an emmetropic no-accommodating eye, the depth of focus relates to the position of the hyperfocal distance, which is the nearest distance that the retina can focus on without significant reduction of the visual performance for a target located at infinity. Thus the age-related reduction in amplitude of accommodation could be ameliorated by increasing the depth of focus of the eye. Atchison and Smith have stated that the depth of focus corresponds to “the range of focusing error that does not result in objectionable deterioration in retinal image quality.” According to these authors, depth of field depends on several factors, including the optical properties of the eye (pupil diameter, accommodation level, monochromatic and chromatic aberrations, diffraction), retinal and visual processing properties (photoreceptor size and ganglion cell density, visual acuity and contrast thresholds, ocular pathway disease), and target properties (luminance, space detail, contrast, color spectral profile).


Due to the combined effects of diffraction and aberrations, the image of focused point light is not a point but a patch of light or point spread function, as discussed in Chapter 5 . When a target such as a point is defocused, its image is an illuminated blur disc ( Fig. 37.1 ). One can assume that depth of field is set by the range over which the blur produced by defocus is smaller than a certain threshold diameter. For example, if the blur disc produced by defocus is less than half the width of the in-focus of the point spread function (PSF, the width at which the light level is equal to half that of the central maximum value), it may be assumed that it has little chance of being detected ( Fig. 37.2 ). At small pupil diameter (e.g., 2 mm), diffraction theory predicts that the width of the PSF is inversely proportional to the square of the pupil diameter. The increase of the width of the PSF results in an increase in the depth of field with the decrease in pupil diameter, the effect of defocus being proportionally less detectable given the larger initial PSF. The results of a study by Campbell show that the depth of field decreases from 1.7 D to 0.3 D between the pupil diameters of 1 mm and 7 mm. Conversely, as pupil diameter increases, the effect of diffraction becomes less important and the influence of aberrations increases. As aberrations increase with the pupil diameter, the diameter of the PSF is expected to increase, thus increasing the threshold of blur due to defocus and subsequently the depth of field. Because natural aberrations of the eye are low or irregular, they do not physiologically contribute to a significant increase in the depth of field for large (above 5–6 mm) pupil diameters. The size and contrast of the target are also positively correlated to the depth of field.




Fig. 37.1


When an optical system (OS) is free of optical aberrations (diffraction limited), the depth of focus is short, due to the rapid increase in the width of the point spread function (PSF) with subsequent loss of visual acuity when the image plane (or object plane) is displaced.



Fig. 37.2


When an optical system (OS) suffers from some amount of optical aberrations (here, positive spherical aberration), the depth of focus is increased owing to the relative maintaining of the width of the point spread function (PSF) with the anterior displacement of the image plane.


The clinical implications of these facts for measurements of refraction and amplitude of accommodation are important. Subjective accommodation measurements may be overestimated owing to the depth of field effect, since it is accentuated by the accommodative pupil constriction and increase in the angular subtense of the target. Modification of the ocular optical properties can be accomplished accordingly to increase the depth of field of presbyopic subjects and restore unaided near visual acuity while maintaining satisfactory unaided distance visual acuity.


What Is Multifocality?


Multifocality reflects the presence of various refractive errors within the area covered by the entrance pupil. An emmetropic eye has refractive power enabling the rays emitted by a source located at infinity to be focused in the retinal plane. Myopic or hyperopic eyes exhibit an excess or a deficit in their refractive power, respectively.


The process of determining the subjective refraction of the eye suggests that a nonemmetropic eye exhibits a single refractive power error that can be corrected by a spherocylindrical lens, for example, 2(−1 × 0 degrees). However, with the eye being an “imperfect” biologic structure, its refractive power is not constant throughout the entrance pupil. Subtle local refractive errors remain after the determination of best refractive correction. Despite the addition of a spherocylindrical lens aimed at making the eye emmetropic, not all rays that are refracted throughout the entrance pupil are focused in the same plane. These residual errors would not exceed ±0.75 D across the pupil in normal emmetropic eyes. Our visual system is built around these imperfections, and this tolerance to some local defocus accounts for the natural depth of field of the human eye. However, it is not sufficient to supply the lack of accommodation power of presbyopic eyes.


Some aberrometers, such as the OPD-Scan III (NIDEK), allow the display of these local variations of refractive errors in a vergence map called the OPD map . This map plots the local variations of the refractive error across the entrance pupil area of the eye of interest, that is, the local excess (myopia) or deficit (hyperopia) in optical power (or vergence; Fig. 37.3 ). Astigmatism corresponds to a meridional variation of the ocular refractive error, usually caused by corneal toricity ( Fig. 37.4 ).




Fig. 37.3


Example of an optical path difference (OPD) map obtained with the topographic aberrometer OPD-Scan III (NIDEK) in an emmetropic eye (uncorrected distance visual acuity, 20/15). The result is a wavefront vergence map that is similar to the refractive power maps in corneal topography but addresses the plot of the local refractive error of the whole ocular optical system (cornea + crystalline lens) within the entrance pupil disc zone. In this example, high-order aberrations are responsible for little fluctuations of the refractive error around zero.



Fig. 37.4


Example of an optical path difference (OPD) map obtained with the topographic aberrometer OPD-Scan III (NIDEK) in a highly astigmatic eye (best corrected distance visual acuity, 20/20). The specific effect of high-order aberrations is difficult to appreciate, as the vergence map is dominated by the astigmatism-induced meridional changes in the refractive error.


Wavefront maps are useful to provide a basis for analyzing and titrating the amount of high-order aberrations but may not intuitively bring clinical relevance. Vergence maps allow the clinician to directly estimate the impact of the low-order and high-order aberrations on the refractive properties of the examined eye. The nonsystemized local variations of the refractive error relate to the presence of high-order aberrations. This clinician-friendly interpretation has a profound impact on the understanding and planning of multifocal corrections.


Spherical aberration is a type of high-order aberration that describes the presence of a concentric gradient of power between the center and the periphery of the pupil. In consequence, the larger the pupil, the larger the amount of measured spherical aberration. In most human eyes looking at infinity, the measured ocular spherical aberration is positive because, regardless of the refractive status, there is a slight increase in refractive power from the center to the edge of the pupil. An emmetropic eye generally exhibits a slight amount of myopic error toward the edges of the pupil ( Fig. 37.5 ).




Fig. 37.5


Removing the effect of the best spherocylindrical error on the display allows one to plot the specific effects of the residual high-order aberrations. There is a moderate gradient of increased myopic error toward the pupil edge, reflecting the presence of a slight amount of positive spherical aberration.


Ocular spherical aberration relates to the difference between the refractive powers of the center and the edge of the functional pupil. The larger this difference, the larger the value of the spherical aberration, regardless of the mathematical function used to quantify this aberration. Zernike polynomials represent a class of mathematical functions that can be used to model the optical aberrations of the human eye. Z40 is the symbol for spherical aberration, which is weighted by a coefficient c40, whose value is expressed in micron units and refers to a specific pupil diameter.


When the refractive power (vergence) is higher at the pupil center than its periphery, spherical aberration is said to be negative (c40 < 0). Conversely, when the refractive power is lower at the pupil center than its periphery, the spherical aberration is said to be positive (c40 > 0). In terms of refractive power, spherical aberration only characterizes the progressive variation of the refractive power from the center to the edge of the pupil independent of the values of these powers themselves.


Multifocality can be induced by increasing the amount of spherical aberration to improve the ability to form retinal images of nearer and farther image targets with reasonable sharpness. The manipulation of spherical aberration may aim at increasing the natural gradient of refractive power from the center to the periphery (i.e., an increase in positive spherical aberration). For combined hyperopic and presbyopic corrections, it is more common to reverse it (i.e., to induce negative spherical aberration). This can be achieved by inducing some myopic defocus at the center of the pupil and reducing some myopic defocus toward the pupil periphery (inducing negative spherical aberration).


Multifocality Versus Monovision


In classic monovision, the dominant eye is corrected to achieve satisfactory uncorrected distance visual acuity, whereas the nondominant eye is made myopic to see well at near without any optical aid.


In such situations, the nondominant eye becomes “fully” myopic, in the sense that the planned correction results in the same myopic refractive error within the pupil area. This consistent negative defocus reduces significantly the uncorrected visual acuity at distance and compromises binocular stereopsis.


When a multifocal correction is planned, although the refraction of the nondominant eye would still be measured myopic (dominated by the paraxial defocus), there is a relative imbalance between the induced myopic error within the paraxial pupil zone and the low myopic to emmetropic paracentral concentric zone.


This reduction of the myopic refractive error toward the edges of the pupil aims at providing the eye with a better uncorrected distance visual acuity. This gradient of defocus from the center to the edge of the pupil is reflected in the induction of negative spherical aberration.


Pseudoaccommodation: The Importance of Corneal Multifocality and Optical Aberrations


Refractive corneal procedures, such as radial keratotomy (RK) and photorefractive keratectomy (PRK), have been known to create corneal multifocality. Multifocal effects of the cornea have also been incriminated for the disparity between residual refractive error and uncorrected visual acuity after refractive surgery. A study in which corneal topography was used showed that corneal multifocality (refractive power gradient within the pupillary area) has a significant positive correlation with the amount of apparent accommodation in pseudophakic eyes. The degree of corneal multifocality was determined on corneal topography by measuring the maximum and minimum corneal refractive powers within the pupillary area. Refractive astigmatism, keratometric astigmatism, pupillary diameter, and age were also analyzed. Multiple regression analysis revealed that corneal multifocality and pupillary diameter had significant positive correlations with apparent accommodation, whereas other explanatory variables showed no relationship with apparent accommodation. Based on the results of this study, corneal multifocality has been demonstrated to play an important role in apparent accommodation (pseudoaccommodation) after cataract surgery.


Oshika et al. further tried to assess the relationship between apparent accommodation in pseudophakic eyes, multifocal corneal effects, and wavefront aberrations of the cornea. Wavefront aberrations of the cornea were calculated by expanding the height data of the corneal topography into Zernike polynomials for individual pupil size. The influence of higher-order aberration on retinal image quality was simulated by computing the PSF and modulation transfer function (MTF) from the aberration function. The coma-like aberration showed a significant positive correlation with the amount of apparent accommodation, but the spherical-like aberration did not. Among the coma-like aberrations, the component representing vertically asymmetric distribution of corneal refractive power with greater refraction located in the lower part of the eye was most relevant to apparent accommodation. Computer simulation of PSF and MTF indicated that a focus shift of 0.5 D led to deterioration of the retinal image significantly more in eyes without higher-order aberrations than in eyes with a moderate amount of coma-like aberrations. The influences on low-contrast visual acuity and contrast sensitivity were not addressed in this study. Patients with multifocal IOLs generally have lower contrast sensitivity and often report ghosting and halos, especially during scotopic conditions. Several reports indicate that such measures would be adversely affected in the setting of a multifocal cornea. Other possible adverse optical effects of a multifocal cornea include monocular diplopia, subjective glare, and halo effects. The influence of scotopic pupil size and optical aberrations on visual symptoms in eyes after conventional laser in situ keratomileusis (LASIK) has been investigated. The analysis showed positive correlation of double vision with total coma and with horizontal coma for the 5-mm and 7-mm pupil sizes, negative correlation between starburst and total coma for the 7-mm pupil size, positive correlation of double vision with horizontal coma, and glare and starburst with spherical aberration and with total aberrations. Scotopic pupil size had a positive association with starburst and a negative association with double vision. Thus multifocality of the cornea may afford clinical advantages, but such multifocality may increase the noise, or static, in the eye’s optical system and potentially decrease some measures of visual performance. The use of adaptive optics has enabled manipulation of the level of ocular higher-order aberrations and enabled investigation of their effects on depth of focus.


Asphericity Modulation


The modulation of corneal asphericity has been proposed by several authors. Increasing negative asphericity (reduction of the local corneal curvature from the apex to the periphery) can successively reduce, cancel, then negate the ocular spherical aberration. In the latter situation, the paraxial area within the pupil has more optical power than its surrounding periphery. In the context of presbyopia compensation with excimer laser surgery, some level of useful multifocality can be achieved by inducing myopic defocus within the paraxial zone and altering the ablation profile to reduce its amount within the paracentral zone. In such a situation, the eye would be best refracted for distance with a negative spectacle correction and hence can be considered as myopic. However, its uncorrected distance acuity would exceed that of an eye in which the whole pupil area (paraxial and paracentral zone) would be equivalently myopic (full myopic correction is intended in pure monovision strategies).


Nuclear cataract can result in a myopic shift, which is unusually predominant within the central pupil zone. This myopic shift results from the increase of the refractive indice of the proteins of the crystalline lens nucleus and is often referred to as indice myopia . In such a situation, an increase in negative spherical aberration is commonly observed and the myopic shift within the paraxial pupil area induces an improvement in uncorrected near visual acuity. However, in contrast with a situation in which the pupil would be affected by a myopic error, the less myopic (or close to emmetropia) paracentral concentric pupil zone provides the eye with improved distance uncorrected visual acuity ( Fig. 37.6 ).




Fig. 37.6


This left eye optical path difference (OPD) map was obtained in 2016 of a 55-year-old patient referred for early nuclear cataract in the left eye (his 2013 OPD examination appears in Fig. 37.1 ). The central increase in the index of refraction of the central part of the crystalline lens resulted in a myopic shift: best corrected visual acuity was 20/20 with a −2.50 D correction. The patient can now read Jaeger 2 (J2) without any optical aid with the left eye, whereas the right eye (deprived from cataract) needs an addition of +2 D to read J2. The ocular spherical aberration coefficient measured in 2016 was negative (c40 = −0.283 µm for a 6-mm zone). In 2013, this same coefficient value was c40 = +0.113 for a 6-mm zone. Because there is a relative reduction of the myopic error toward the pupil edges, uncorrected distance visual acuity is 20/30 with the left eye. In the latter, the paraxial pupil myopic shift incurred by nuclear sclerosis has provided some useful multifocality.




Depth of Focus and Optical Aberrations


Depth of focus determines the distance range for which a target can be seen clearly without a change in focusing power. For an emmetropic no-accommodating eye, the depth of focus relates to the position of the hyperfocal distance, which is the nearest distance that the retina can focus on without significant reduction of the visual performance for a target located at infinity. Thus the age-related reduction in amplitude of accommodation could be ameliorated by increasing the depth of focus of the eye. Atchison and Smith have stated that the depth of focus corresponds to “the range of focusing error that does not result in objectionable deterioration in retinal image quality.” According to these authors, depth of field depends on several factors, including the optical properties of the eye (pupil diameter, accommodation level, monochromatic and chromatic aberrations, diffraction), retinal and visual processing properties (photoreceptor size and ganglion cell density, visual acuity and contrast thresholds, ocular pathway disease), and target properties (luminance, space detail, contrast, color spectral profile).


Due to the combined effects of diffraction and aberrations, the image of focused point light is not a point but a patch of light or point spread function, as discussed in Chapter 5 . When a target such as a point is defocused, its image is an illuminated blur disc ( Fig. 37.1 ). One can assume that depth of field is set by the range over which the blur produced by defocus is smaller than a certain threshold diameter. For example, if the blur disc produced by defocus is less than half the width of the in-focus of the point spread function (PSF, the width at which the light level is equal to half that of the central maximum value), it may be assumed that it has little chance of being detected ( Fig. 37.2 ). At small pupil diameter (e.g., 2 mm), diffraction theory predicts that the width of the PSF is inversely proportional to the square of the pupil diameter. The increase of the width of the PSF results in an increase in the depth of field with the decrease in pupil diameter, the effect of defocus being proportionally less detectable given the larger initial PSF. The results of a study by Campbell show that the depth of field decreases from 1.7 D to 0.3 D between the pupil diameters of 1 mm and 7 mm. Conversely, as pupil diameter increases, the effect of diffraction becomes less important and the influence of aberrations increases. As aberrations increase with the pupil diameter, the diameter of the PSF is expected to increase, thus increasing the threshold of blur due to defocus and subsequently the depth of field. Because natural aberrations of the eye are low or irregular, they do not physiologically contribute to a significant increase in the depth of field for large (above 5–6 mm) pupil diameters. The size and contrast of the target are also positively correlated to the depth of field.




Fig. 37.1


When an optical system (OS) is free of optical aberrations (diffraction limited), the depth of focus is short, due to the rapid increase in the width of the point spread function (PSF) with subsequent loss of visual acuity when the image plane (or object plane) is displaced.



Fig. 37.2


When an optical system (OS) suffers from some amount of optical aberrations (here, positive spherical aberration), the depth of focus is increased owing to the relative maintaining of the width of the point spread function (PSF) with the anterior displacement of the image plane.


The clinical implications of these facts for measurements of refraction and amplitude of accommodation are important. Subjective accommodation measurements may be overestimated owing to the depth of field effect, since it is accentuated by the accommodative pupil constriction and increase in the angular subtense of the target. Modification of the ocular optical properties can be accomplished accordingly to increase the depth of field of presbyopic subjects and restore unaided near visual acuity while maintaining satisfactory unaided distance visual acuity.


What Is Multifocality?


Multifocality reflects the presence of various refractive errors within the area covered by the entrance pupil. An emmetropic eye has refractive power enabling the rays emitted by a source located at infinity to be focused in the retinal plane. Myopic or hyperopic eyes exhibit an excess or a deficit in their refractive power, respectively.


The process of determining the subjective refraction of the eye suggests that a nonemmetropic eye exhibits a single refractive power error that can be corrected by a spherocylindrical lens, for example, 2(−1 × 0 degrees). However, with the eye being an “imperfect” biologic structure, its refractive power is not constant throughout the entrance pupil. Subtle local refractive errors remain after the determination of best refractive correction. Despite the addition of a spherocylindrical lens aimed at making the eye emmetropic, not all rays that are refracted throughout the entrance pupil are focused in the same plane. These residual errors would not exceed ±0.75 D across the pupil in normal emmetropic eyes. Our visual system is built around these imperfections, and this tolerance to some local defocus accounts for the natural depth of field of the human eye. However, it is not sufficient to supply the lack of accommodation power of presbyopic eyes.


Some aberrometers, such as the OPD-Scan III (NIDEK), allow the display of these local variations of refractive errors in a vergence map called the OPD map . This map plots the local variations of the refractive error across the entrance pupil area of the eye of interest, that is, the local excess (myopia) or deficit (hyperopia) in optical power (or vergence; Fig. 37.3 ). Astigmatism corresponds to a meridional variation of the ocular refractive error, usually caused by corneal toricity ( Fig. 37.4 ).




Fig. 37.3


Example of an optical path difference (OPD) map obtained with the topographic aberrometer OPD-Scan III (NIDEK) in an emmetropic eye (uncorrected distance visual acuity, 20/15). The result is a wavefront vergence map that is similar to the refractive power maps in corneal topography but addresses the plot of the local refractive error of the whole ocular optical system (cornea + crystalline lens) within the entrance pupil disc zone. In this example, high-order aberrations are responsible for little fluctuations of the refractive error around zero.



Fig. 37.4


Example of an optical path difference (OPD) map obtained with the topographic aberrometer OPD-Scan III (NIDEK) in a highly astigmatic eye (best corrected distance visual acuity, 20/20). The specific effect of high-order aberrations is difficult to appreciate, as the vergence map is dominated by the astigmatism-induced meridional changes in the refractive error.


Wavefront maps are useful to provide a basis for analyzing and titrating the amount of high-order aberrations but may not intuitively bring clinical relevance. Vergence maps allow the clinician to directly estimate the impact of the low-order and high-order aberrations on the refractive properties of the examined eye. The nonsystemized local variations of the refractive error relate to the presence of high-order aberrations. This clinician-friendly interpretation has a profound impact on the understanding and planning of multifocal corrections.


Spherical aberration is a type of high-order aberration that describes the presence of a concentric gradient of power between the center and the periphery of the pupil. In consequence, the larger the pupil, the larger the amount of measured spherical aberration. In most human eyes looking at infinity, the measured ocular spherical aberration is positive because, regardless of the refractive status, there is a slight increase in refractive power from the center to the edge of the pupil. An emmetropic eye generally exhibits a slight amount of myopic error toward the edges of the pupil ( Fig. 37.5 ).




Fig. 37.5


Removing the effect of the best spherocylindrical error on the display allows one to plot the specific effects of the residual high-order aberrations. There is a moderate gradient of increased myopic error toward the pupil edge, reflecting the presence of a slight amount of positive spherical aberration.


Ocular spherical aberration relates to the difference between the refractive powers of the center and the edge of the functional pupil. The larger this difference, the larger the value of the spherical aberration, regardless of the mathematical function used to quantify this aberration. Zernike polynomials represent a class of mathematical functions that can be used to model the optical aberrations of the human eye. Z40 is the symbol for spherical aberration, which is weighted by a coefficient c40, whose value is expressed in micron units and refers to a specific pupil diameter.


When the refractive power (vergence) is higher at the pupil center than its periphery, spherical aberration is said to be negative (c40 < 0). Conversely, when the refractive power is lower at the pupil center than its periphery, the spherical aberration is said to be positive (c40 > 0). In terms of refractive power, spherical aberration only characterizes the progressive variation of the refractive power from the center to the edge of the pupil independent of the values of these powers themselves.


Multifocality can be induced by increasing the amount of spherical aberration to improve the ability to form retinal images of nearer and farther image targets with reasonable sharpness. The manipulation of spherical aberration may aim at increasing the natural gradient of refractive power from the center to the periphery (i.e., an increase in positive spherical aberration). For combined hyperopic and presbyopic corrections, it is more common to reverse it (i.e., to induce negative spherical aberration). This can be achieved by inducing some myopic defocus at the center of the pupil and reducing some myopic defocus toward the pupil periphery (inducing negative spherical aberration).


Multifocality Versus Monovision


In classic monovision, the dominant eye is corrected to achieve satisfactory uncorrected distance visual acuity, whereas the nondominant eye is made myopic to see well at near without any optical aid.


In such situations, the nondominant eye becomes “fully” myopic, in the sense that the planned correction results in the same myopic refractive error within the pupil area. This consistent negative defocus reduces significantly the uncorrected visual acuity at distance and compromises binocular stereopsis.


When a multifocal correction is planned, although the refraction of the nondominant eye would still be measured myopic (dominated by the paraxial defocus), there is a relative imbalance between the induced myopic error within the paraxial pupil zone and the low myopic to emmetropic paracentral concentric zone.


This reduction of the myopic refractive error toward the edges of the pupil aims at providing the eye with a better uncorrected distance visual acuity. This gradient of defocus from the center to the edge of the pupil is reflected in the induction of negative spherical aberration.




What Is Multifocality?


Multifocality reflects the presence of various refractive errors within the area covered by the entrance pupil. An emmetropic eye has refractive power enabling the rays emitted by a source located at infinity to be focused in the retinal plane. Myopic or hyperopic eyes exhibit an excess or a deficit in their refractive power, respectively.


The process of determining the subjective refraction of the eye suggests that a nonemmetropic eye exhibits a single refractive power error that can be corrected by a spherocylindrical lens, for example, 2(−1 × 0 degrees). However, with the eye being an “imperfect” biologic structure, its refractive power is not constant throughout the entrance pupil. Subtle local refractive errors remain after the determination of best refractive correction. Despite the addition of a spherocylindrical lens aimed at making the eye emmetropic, not all rays that are refracted throughout the entrance pupil are focused in the same plane. These residual errors would not exceed ±0.75 D across the pupil in normal emmetropic eyes. Our visual system is built around these imperfections, and this tolerance to some local defocus accounts for the natural depth of field of the human eye. However, it is not sufficient to supply the lack of accommodation power of presbyopic eyes.


Some aberrometers, such as the OPD-Scan III (NIDEK), allow the display of these local variations of refractive errors in a vergence map called the OPD map . This map plots the local variations of the refractive error across the entrance pupil area of the eye of interest, that is, the local excess (myopia) or deficit (hyperopia) in optical power (or vergence; Fig. 37.3 ). Astigmatism corresponds to a meridional variation of the ocular refractive error, usually caused by corneal toricity ( Fig. 37.4 ).




Fig. 37.3


Example of an optical path difference (OPD) map obtained with the topographic aberrometer OPD-Scan III (NIDEK) in an emmetropic eye (uncorrected distance visual acuity, 20/15). The result is a wavefront vergence map that is similar to the refractive power maps in corneal topography but addresses the plot of the local refractive error of the whole ocular optical system (cornea + crystalline lens) within the entrance pupil disc zone. In this example, high-order aberrations are responsible for little fluctuations of the refractive error around zero.



Fig. 37.4


Example of an optical path difference (OPD) map obtained with the topographic aberrometer OPD-Scan III (NIDEK) in a highly astigmatic eye (best corrected distance visual acuity, 20/20). The specific effect of high-order aberrations is difficult to appreciate, as the vergence map is dominated by the astigmatism-induced meridional changes in the refractive error.


Wavefront maps are useful to provide a basis for analyzing and titrating the amount of high-order aberrations but may not intuitively bring clinical relevance. Vergence maps allow the clinician to directly estimate the impact of the low-order and high-order aberrations on the refractive properties of the examined eye. The nonsystemized local variations of the refractive error relate to the presence of high-order aberrations. This clinician-friendly interpretation has a profound impact on the understanding and planning of multifocal corrections.


Spherical aberration is a type of high-order aberration that describes the presence of a concentric gradient of power between the center and the periphery of the pupil. In consequence, the larger the pupil, the larger the amount of measured spherical aberration. In most human eyes looking at infinity, the measured ocular spherical aberration is positive because, regardless of the refractive status, there is a slight increase in refractive power from the center to the edge of the pupil. An emmetropic eye generally exhibits a slight amount of myopic error toward the edges of the pupil ( Fig. 37.5 ).




Fig. 37.5


Removing the effect of the best spherocylindrical error on the display allows one to plot the specific effects of the residual high-order aberrations. There is a moderate gradient of increased myopic error toward the pupil edge, reflecting the presence of a slight amount of positive spherical aberration.


Ocular spherical aberration relates to the difference between the refractive powers of the center and the edge of the functional pupil. The larger this difference, the larger the value of the spherical aberration, regardless of the mathematical function used to quantify this aberration. Zernike polynomials represent a class of mathematical functions that can be used to model the optical aberrations of the human eye. Z40 is the symbol for spherical aberration, which is weighted by a coefficient c40, whose value is expressed in micron units and refers to a specific pupil diameter.


When the refractive power (vergence) is higher at the pupil center than its periphery, spherical aberration is said to be negative (c40 < 0). Conversely, when the refractive power is lower at the pupil center than its periphery, the spherical aberration is said to be positive (c40 > 0). In terms of refractive power, spherical aberration only characterizes the progressive variation of the refractive power from the center to the edge of the pupil independent of the values of these powers themselves.


Multifocality can be induced by increasing the amount of spherical aberration to improve the ability to form retinal images of nearer and farther image targets with reasonable sharpness. The manipulation of spherical aberration may aim at increasing the natural gradient of refractive power from the center to the periphery (i.e., an increase in positive spherical aberration). For combined hyperopic and presbyopic corrections, it is more common to reverse it (i.e., to induce negative spherical aberration). This can be achieved by inducing some myopic defocus at the center of the pupil and reducing some myopic defocus toward the pupil periphery (inducing negative spherical aberration).




Multifocality Versus Monovision


In classic monovision, the dominant eye is corrected to achieve satisfactory uncorrected distance visual acuity, whereas the nondominant eye is made myopic to see well at near without any optical aid.


In such situations, the nondominant eye becomes “fully” myopic, in the sense that the planned correction results in the same myopic refractive error within the pupil area. This consistent negative defocus reduces significantly the uncorrected visual acuity at distance and compromises binocular stereopsis.


When a multifocal correction is planned, although the refraction of the nondominant eye would still be measured myopic (dominated by the paraxial defocus), there is a relative imbalance between the induced myopic error within the paraxial pupil zone and the low myopic to emmetropic paracentral concentric zone.


This reduction of the myopic refractive error toward the edges of the pupil aims at providing the eye with a better uncorrected distance visual acuity. This gradient of defocus from the center to the edge of the pupil is reflected in the induction of negative spherical aberration.




Pseudoaccommodation: The Importance of Corneal Multifocality and Optical Aberrations


Refractive corneal procedures, such as radial keratotomy (RK) and photorefractive keratectomy (PRK), have been known to create corneal multifocality. Multifocal effects of the cornea have also been incriminated for the disparity between residual refractive error and uncorrected visual acuity after refractive surgery. A study in which corneal topography was used showed that corneal multifocality (refractive power gradient within the pupillary area) has a significant positive correlation with the amount of apparent accommodation in pseudophakic eyes. The degree of corneal multifocality was determined on corneal topography by measuring the maximum and minimum corneal refractive powers within the pupillary area. Refractive astigmatism, keratometric astigmatism, pupillary diameter, and age were also analyzed. Multiple regression analysis revealed that corneal multifocality and pupillary diameter had significant positive correlations with apparent accommodation, whereas other explanatory variables showed no relationship with apparent accommodation. Based on the results of this study, corneal multifocality has been demonstrated to play an important role in apparent accommodation (pseudoaccommodation) after cataract surgery.


Oshika et al. further tried to assess the relationship between apparent accommodation in pseudophakic eyes, multifocal corneal effects, and wavefront aberrations of the cornea. Wavefront aberrations of the cornea were calculated by expanding the height data of the corneal topography into Zernike polynomials for individual pupil size. The influence of higher-order aberration on retinal image quality was simulated by computing the PSF and modulation transfer function (MTF) from the aberration function. The coma-like aberration showed a significant positive correlation with the amount of apparent accommodation, but the spherical-like aberration did not. Among the coma-like aberrations, the component representing vertically asymmetric distribution of corneal refractive power with greater refraction located in the lower part of the eye was most relevant to apparent accommodation. Computer simulation of PSF and MTF indicated that a focus shift of 0.5 D led to deterioration of the retinal image significantly more in eyes without higher-order aberrations than in eyes with a moderate amount of coma-like aberrations. The influences on low-contrast visual acuity and contrast sensitivity were not addressed in this study. Patients with multifocal IOLs generally have lower contrast sensitivity and often report ghosting and halos, especially during scotopic conditions. Several reports indicate that such measures would be adversely affected in the setting of a multifocal cornea. Other possible adverse optical effects of a multifocal cornea include monocular diplopia, subjective glare, and halo effects. The influence of scotopic pupil size and optical aberrations on visual symptoms in eyes after conventional laser in situ keratomileusis (LASIK) has been investigated. The analysis showed positive correlation of double vision with total coma and with horizontal coma for the 5-mm and 7-mm pupil sizes, negative correlation between starburst and total coma for the 7-mm pupil size, positive correlation of double vision with horizontal coma, and glare and starburst with spherical aberration and with total aberrations. Scotopic pupil size had a positive association with starburst and a negative association with double vision. Thus multifocality of the cornea may afford clinical advantages, but such multifocality may increase the noise, or static, in the eye’s optical system and potentially decrease some measures of visual performance. The use of adaptive optics has enabled manipulation of the level of ocular higher-order aberrations and enabled investigation of their effects on depth of focus.


Asphericity Modulation


The modulation of corneal asphericity has been proposed by several authors. Increasing negative asphericity (reduction of the local corneal curvature from the apex to the periphery) can successively reduce, cancel, then negate the ocular spherical aberration. In the latter situation, the paraxial area within the pupil has more optical power than its surrounding periphery. In the context of presbyopia compensation with excimer laser surgery, some level of useful multifocality can be achieved by inducing myopic defocus within the paraxial zone and altering the ablation profile to reduce its amount within the paracentral zone. In such a situation, the eye would be best refracted for distance with a negative spectacle correction and hence can be considered as myopic. However, its uncorrected distance acuity would exceed that of an eye in which the whole pupil area (paraxial and paracentral zone) would be equivalently myopic (full myopic correction is intended in pure monovision strategies).


Nuclear cataract can result in a myopic shift, which is unusually predominant within the central pupil zone. This myopic shift results from the increase of the refractive indice of the proteins of the crystalline lens nucleus and is often referred to as indice myopia . In such a situation, an increase in negative spherical aberration is commonly observed and the myopic shift within the paraxial pupil area induces an improvement in uncorrected near visual acuity. However, in contrast with a situation in which the pupil would be affected by a myopic error, the less myopic (or close to emmetropia) paracentral concentric pupil zone provides the eye with improved distance uncorrected visual acuity ( Fig. 37.6 ).




Fig. 37.6


This left eye optical path difference (OPD) map was obtained in 2016 of a 55-year-old patient referred for early nuclear cataract in the left eye (his 2013 OPD examination appears in Fig. 37.1 ). The central increase in the index of refraction of the central part of the crystalline lens resulted in a myopic shift: best corrected visual acuity was 20/20 with a −2.50 D correction. The patient can now read Jaeger 2 (J2) without any optical aid with the left eye, whereas the right eye (deprived from cataract) needs an addition of +2 D to read J2. The ocular spherical aberration coefficient measured in 2016 was negative (c40 = −0.283 µm for a 6-mm zone). In 2013, this same coefficient value was c40 = +0.113 for a 6-mm zone. Because there is a relative reduction of the myopic error toward the pupil edges, uncorrected distance visual acuity is 20/30 with the left eye. In the latter, the paraxial pupil myopic shift incurred by nuclear sclerosis has provided some useful multifocality.




Asphericity Modulation


The modulation of corneal asphericity has been proposed by several authors. Increasing negative asphericity (reduction of the local corneal curvature from the apex to the periphery) can successively reduce, cancel, then negate the ocular spherical aberration. In the latter situation, the paraxial area within the pupil has more optical power than its surrounding periphery. In the context of presbyopia compensation with excimer laser surgery, some level of useful multifocality can be achieved by inducing myopic defocus within the paraxial zone and altering the ablation profile to reduce its amount within the paracentral zone. In such a situation, the eye would be best refracted for distance with a negative spectacle correction and hence can be considered as myopic. However, its uncorrected distance acuity would exceed that of an eye in which the whole pupil area (paraxial and paracentral zone) would be equivalently myopic (full myopic correction is intended in pure monovision strategies).


Nuclear cataract can result in a myopic shift, which is unusually predominant within the central pupil zone. This myopic shift results from the increase of the refractive indice of the proteins of the crystalline lens nucleus and is often referred to as indice myopia . In such a situation, an increase in negative spherical aberration is commonly observed and the myopic shift within the paraxial pupil area induces an improvement in uncorrected near visual acuity. However, in contrast with a situation in which the pupil would be affected by a myopic error, the less myopic (or close to emmetropia) paracentral concentric pupil zone provides the eye with improved distance uncorrected visual acuity ( Fig. 37.6 ).




Fig. 37.6


This left eye optical path difference (OPD) map was obtained in 2016 of a 55-year-old patient referred for early nuclear cataract in the left eye (his 2013 OPD examination appears in Fig. 37.1 ). The central increase in the index of refraction of the central part of the crystalline lens resulted in a myopic shift: best corrected visual acuity was 20/20 with a −2.50 D correction. The patient can now read Jaeger 2 (J2) without any optical aid with the left eye, whereas the right eye (deprived from cataract) needs an addition of +2 D to read J2. The ocular spherical aberration coefficient measured in 2016 was negative (c40 = −0.283 µm for a 6-mm zone). In 2013, this same coefficient value was c40 = +0.113 for a 6-mm zone. Because there is a relative reduction of the myopic error toward the pupil edges, uncorrected distance visual acuity is 20/30 with the left eye. In the latter, the paraxial pupil myopic shift incurred by nuclear sclerosis has provided some useful multifocality.




Practical Consequences


General Considerations


From a clinical perspective and in an optical system such as the presbyopic eye, an increased depth of focus can be used to enlarge the range of distance at which a target that is first brought into focus appears to be too blurred to be discerned. Surgically increasing the depth of focus of the presbyopic eye can be achieved by introducing a controlled amount of multifocality via the insertion of a multifocal designed lens or reshaping the anterior surface of the cornea with a multifocal profile of ablation.


Literally, multifocality supposes that a portion of the light of emitting sources located at different distances of the eye can be properly focused on the fovea. In the case of presbyopia compensation, two main foci are expected, which would bring into focus to the fovea images located at infinity and at near, respectively. Because the reading distance and the distance required for near tasks are usually between 25 and 50 cm, the maximum additional power required in a nonaccommodating patient is about 3 D. However, for the eye viewing a near object, it is often the case that the amount of accommodation used will be less than might be expected given the viewing distance. The early presbyopic eye will utilize its depth of focus so that just enough accommodation is used to bring the object to the edge of the depth of field. Here, the eye is actually focused slightly farther away than the object; thus the accommodative effort needed is minimized.


When the eye is no longer able to accommodate, multifocal presbyopic compensation relies on the principle of simultaneous vision. Owing to the multiple refractive powers simulatenously present within the entrance pupil of a successfully operated multifocal eye, part of the light rays emitted by a single target source will be in focus at the retinal place, regardless of the location of that source, from reading distance to infinity. As a consequence, the remaining light rays will not be in focus, but if the resulting blur is unnoticed or moderate, the patient will not be experiencing a significant decrease in distance visual quality and will regain the possibility of reading without spectacles. When satisfactory, this whole process corresponds to the state of successful pseudoaccommodation ( Fig. 37.7 ).


Oct 10, 2019 | Posted by in OPHTHALMOLOGY | Comments Off on Multifocal Corneal Surgery for Presbyopia
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