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Presbyopia & hyperopia Correction using corneal asphericity (Q value) and multifocal

Presbyopia can be corrected with multifocal corneal laser surgery in Selected Presbyopic Hypercipo patients using customized multifocal aspheric correction.

We have reported in the November 16 issue of the Journal of Refractive Surgery the clinical results of combined presbyopic hyperopic LASIK Corrections obtained with a uncorneally designed multifocal method liked at reshaping the Asphericity profile (Q value) using the custom Q program mode of the EX500 excimer laser (1).

This page will explain the theoretical basis that underpins the principles used to achieve multifocal presbyopic corneal surgery. These principles can be translated into surgical planning with any laser platform that enables the targeting of a specific postoperative corneal asphericity (Q value) such as the Alcon/Wavelight refractive suite.

Spherical aberration and corneal asphericity Are the main variables at play in the domain of multifocal. These terms will be explained and their respective roles and mutual interplay defined.


What is multifocality?

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

The process of determining the subjective refraction of the eye suggests that has non-emmetropic eye exhibits a single refractive power error which can be corrected by a sphero-cylindrical lens, for example: 2(-1 x 0°). However, with the eye being year "imperfect" biological structure. its refractive power is actually not constant throughout the entrance pupil. Subtle local refractive errors remain even after the determination of best refractive correction. Despite the addition of a sphero-cylindrical lens liked at making the eye emmetropic, not all the 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 replace the lack of accommodation power of presbyopic eyes.

Some aberrometers, such as the OPDscan III (Nidek, Japan), allow the display of these local variations of refractive errors in has vergence map called the "OPD map". This map plots the local variations of the refractive error across the entrance pupil of the eye of the area interest, that is, the local excess (myopia) or deficit (hyperopia) in optical power (gold vergence) (see Figure 1).

OPD amp, vergence emmetropic eye map

Figure 1: Example of year OPD map obtained with the topographic aberrometer OPDscan III (Nidek) in year emmetropic eye (information distance visual acuity is: 20/15). The result is a wavefront map that is similar to the refractive power maps vergence in corneal topography purpose addresses the plot of the local refractive error of the whole ocular optical system (cornea and crystalline lens) within the entrance pupil disc area. In this example, high order aberrations are responsible for little fluctuations of the refractive error around zero.


Astigmatism correspond to a meridional variation of the ocular refractive error, usually caused by corneal toricity (Figure 2).

OPDmap, astigmatism

Figure 2: Example of an OPD map obtained with the topographic aberrometer OPD scan III (Nidek) in an 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 dominateded by the astigmatism-induced meridional changes in the refractive error.

Instead of a wavefront map, which may not intuitively bring clinical relevance, the OPD map enables the clinician to directly estimate the impact of the low and high order aberrations on the refractive properties of the examined eye. The non-systematic local variations of the refractive error relate to the presence ofhigh order aberrations”. This clinician-friendly interpretation has profound impact on understanding and planning of the multifocal corrections.


Spherical aberration is a type of high-order aberration which describes the presence of concentric gradient of power between the center and the periphery of the pupil. Consequently, 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 (Figure 3). Enabling the option "High Order (HO)" On the machine allows one to visualize the sole impact on the local refractive error of these higher order aberrations, which cannot be corrected by spectacles.

index myopia nuclear cataract

Figure 3: 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 moderate gradient of myopic error towards the pupil edge increased, reflecting the presence of a sllght 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 tradeoff this aberration. Laurence Zernike represent a class of mathematical functions which 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 c40whose value is expressed in units and refers to a micronPecific pupil diameter. The Zernike Spherical aberration mode has some distinctive features: it contains some "defocus" (low degree) which is myopic for negative spherical aberration and hypercipo for positive spherical aberration. This characteristic will not be discussed here, and when mentioning Z40 We will refer to the true "higher degree" component (term in R ^ 4, that is in the fourth power of the radial distance to the center of the pupil, which modulates significantly the refraction within the pupil toward the periphery: increased hyperopia/decreased myopia For negative spherical aberration).

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 simply characterizes the gradual 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 (ie year increase in positive spherical aberration). For combined hyperopic and presbyopic corrections, it is more common to reverse it (ie 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 towards the pupil periphery (inducing negative spherical aberration).

In what follows, we will use the terms"Central pupil area power"gold"paraxial power"to refer to the average optical power (ocular vergence, expressed in diopters) within the central disc of 1.5 mm radius centered on the corneal vertex." The"answers power"gold"peripheral pupil area power"correspond to year outer annular concentric area surrounding the central 1.5 mm area, which is delineated by the pupil edge."

This distinction is somewhat arbitrary, as it is not possible with laser corneal surgery to induce two different refractive powers delineated by a sharp transition between these areas. Rather, the smooth character of the corneal profile results in a smooth gradient in curvature, and by consequence, has gradual variation of the refractive power from the corneal center to its periphery. However, this distinction carries some functional relevance. The SPHERO-cylindrical refractive giving the best corrected visual acuity is largely governed by the optical power of the central (paraxial) area of the refracted eye. When best correction is achieved (i.e. maximizing the visual acuity for distance targets), the contrast sensitivity and depth of focus depends on the differences between the respective optical power distribution between the paraxial and cancer areas; the more are the refractive error throughout the pupil area, the lower the depth of focus and the higher the retinal contrast of the picture, and vice versa.

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 and altering the ablation area profile to reduce its amount within the cancer area. In such a situation, the eye would be best refracted for distance with a negative show correction, and hence can be considered as myopic.  However, its information distance acuity would exceed that of year eye where the whole pupil area (paraxial cancer and area) would both be equivalently myopic.

Nuclear cataract can result in a myopic shift, the effect of which is predominant within the paraxial pupil area. This myopic shift results from the increase of the refractive indices of the crystalline lens as nucleus, is often referred as to "index myopia".  In such situations, year increase in negative spherical aberration is commonly observed, and the myopic shift within the paraxial pupil area induces year improvement in the information near visual acuity. However, in contrast with a situation where the whole pupil would be affected by a myopic error, the less myopic (or closer to emmetropia) answers pupil area provides the eye with improved information distance visual acuity (Figure 4).

nuclear cataract opd map multifocality

Figure 4: This left eye 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 was used in the figure 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 read now Jaeger 2 without any optical aid with the left eye, whereas the right eye (without a cataract) needs an addition of + 2d to read J2. The ocular spherical aberration coefficient measured in 2016 was negative (C40 =-0283 microns for a 6 mm zone). In 2013, this same coefficient value was C40 = + 0113 for a 6 mm zone.
Because there is a relative reduction of the myopic error toward the pupil edges, information distance visual acuity is 20/30 with the left eye!
The paraaxial pupil myopic shift incurred by the nuclear sclerosis has provided some "useful multifocal".


How does multifocality differ from monovision?

In classic monovision, the dominant eye is corrected to achieve satisfactory information distance Visual acuity, whereas the non-dominant eye is made myopic to see well at near without any optical aid.

In such situations, non-dominant the eye becomes "fully" myopic in the sense that the planned correction results in the same myopic refractive error within the pupil area. This include negative defocus reduces significantly the information distance visual acuity and compromised binocular stereopsis.

When has Multifocal correction is planned, non-dominant although the refraction of the eye would still be measured myopic (dominated by the paraxial defocus), there is a relative imbalance between the induced myopic error within the pupil area and the "low myopic to emmetropic" paraxial answers area.

This reduction of the myopic refractive error toward the pupil edge aims at providing the eye with better information 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.


Why is spherical aberration useful for presbyopic correction multifocal?

Spherical aberration corresponds to a variation of the ocular and can be manipulated to increase the power ocular depth of field.  However, some requirements must be fulfilled to make spherical aberration has "useful aberration" in the context of presbyopia compensation.

There is year obvious benefit to inducing myopic defocus error at the pupil Center to make the fovea conjugate with targets located at a reading distance. In such situations, the paraxial pupil area corresponds to the area near, Whilst the refractive power within the cancer area (mid and extreme periphery of the pupil) can be reduced towards emmetropia. Placing the "near Gold reading area" (inducing a myopic refraction) at the central area of the pupil enables one to take advantage of the near constriction effect of the pupil, which occurs when the eye attempts to accommodate and gauzes at a near target. The reduced vergence (progressive reduction of the myopic error) at the cancer area allows one to achieve a better information distance visual acuity than if the whole pupil area was myopic.

In aberrometric language, this relative increase in refractive power at the center of the pupil with respect to its periphery (or the relative decrease of refractive power at the pupil periphery) translates into year increase in negative spherical aberration (see Figure 4). It is important to keep in mind that, in this context,. negative spherical aberration must be accompanied by selective central pupil myopia to provide the operated eye with efficient multifocality.

To better understand this constraint, consider a presbyopic eye where the pupil portion would be emmetropic central, and for which consist of amounts of negative spherical aberration would be found using aberrometry measurement. This eye would only be able to attain satisfactory information distance visual acuity and may suffer from halos night due to the hyperopia present within the peripheral area pupil relative. Satisfactory information near vision would not be possible due to the accommodation power being insufficient in a presbyopic eye, no. rays emitted by near source would be focused at the flat retinal.


How is it possible to modify the ocular spherical aberration with laser corneal ablation?

Ocular spherical aberration results from the balance between anterior corneal spherical aberration, and internal (corneal posterior surface and crystalline lens) spherical aberration. Ocular spherical aberration is usually mildly positive and governed by the anterior corneal spherical aberration. Anterior corneal spherical aberration depends on the difference between the central and peripheral corneal curvature.

A curved surface whose power gradually decreases or increases from its center to its periphery is said to be aspheric. The corneal profile of the human eye has negative asphericity; its curvature decreases from the apex toward the periphery. Level mathematical variable, named "Q", can the tradeoff of asphericity of the corneal contour model did year ellipse (Figure 5). Negative Q-value characterizes a prolate asphericity (the curvature decreases toward the periphery), whereas a positive Q-value characterizes year oblate asphericity (the curvature increases toward the periphery).

Asphericity depiction

Figure 5: The of the cornea can be calculated by approximating the corneal asphericity profile of interest by a best - fit ellipse. The Q value is computed from the ratio of the respective lengths of the major axis of the ellipse. On the left: some theoretical profiles having the same paraxial curvature purpose different asphericities are shown.

The local refractive power of the cornea depends on its local radius of curvature.  For the same ray impact, the lesser the curvature, the lesser the local refractive power. In most normal eyes, the reduction of the corneal curvature toward the periphery is not well pronounced to reduce the effect of the increase in the angle of incidence of peripheral rays with the corneal surface. Despite local curvature reduction toward the periphery (prolate profile, lesser keratometry towards the corneal periphery), the corneal power at the periphery of the cornea is still more pronounced than at its center; This explains why the physiological spherical aberration of the cornea is slightly positive (Figure 6ab). To cancel spherical aberration, the corneal asphericity should be, on average, more negative than what is found in most human corneas. Such a surface, derived from spherical aberration, is referred to as oval. To reverse the corneal positive spherical aberration to a negative value, the corneal asphericity must take a more negative value.  Hence, to create a multifocal corneal profile, the laser correction must increase the negative asphericity of the cornea.


Asphericity and spherical aberration

Figure 6: In This example, the paraaxial powers of both corneas are identical and have the same refractive index (n), but the profiles have different asphericities. Spherical aberration depends on the value of the change in asphericity of the corneal profile. On the left, the cornea is slightly prolate (Q =-0.2) and flattens toward the periphery. This flattening is not sufficient to cancel spherical aberration, which remains slightly positive. On the right, the cornea is highly prolate (Q =-0.8). The important flattening reduces sufficiently the angle of incidence of peripheral rays to revert the sign of spherical aberration, which becomes negative.

We have now described the two conditions which are necessary to provide a presbyopic eye with useful corneal multifocality:

(1) to induce has central (paraxial) myopic refraction, and

(2) to reduce the refractive power value toward the pupil peripherywith a concentric outer near emmetropic area aimed at improving information distance vision. Reduction of the refractive power toward the pupil periphery can be achieved by increasing the value of the negative corneal asphericity (increasing prolateness). In such year eye, some amount of negative spherical aberration is expected.

Figure 6b: The combined correction of presbyopia and hyperopia can be schematically what the change of curvature to paraxial as value (shorter radius) which induces a myopic refraction post (ex:-2.50 D). Curvarture can be adjusted by selecting a specific target asphericity answers. Asphericity this change aims at reducing cancer the curvature, the refractive power of the cancer area is close to emmetropia.

Figure 6 B: The combined correction of presbyopia and hyperopia can be schematically depicted as the change of paraaxial curvature to a value (shorter radius) which induces a postoperative myopic refraction (ex:-2.50 D). Paracentral curvature can be appropriated by selecting a specific target asphericity. This asphericity Change aims to reduce the paracentral curvature, so that the refractive power of the paracentral zone is close to Emmetropia.


What is the optimal value of the negative spherical aberration to provide the outer pupil near-emmetropic power area?

Several clinical observations, which include presbyopic patients rendered show independent after hyperopic LASIK surgery, but presenting with nuclear cataract (see Figure 4), point towards value of negative spherical aberration which can be rounded to c40 = - 0.3 microns for a 6 mm pupil. As the value of the ocular spherical aberration is usually close to c40 = + 0.1 microns for a 6 mm pupil, the beneficial changes in spherical aberration (Δ c40) should be equal to Δ c40 = - 0.4 microns for a 6 mm pupil. This change must be achieved through the alteration of the corneal contour and some increase in negative asphericity (ΔQ).


What value for changes in corneal asphericity)Δ(Q) can induce a change in spherical aberration of Δc40= - 0.4 microns we have 6 mm optical zone?

This issue can be addressed through theoretical modelling which was addressed in 2014 in a publication in the Journal of Refractive Surgery (2). The theoretical pre-and postoperative corneal profiles were modelled as ellipses, each having a specific apical radius of curvature (R1, R2) and asphericity (Q1, q2, with ΔQ = Q2-Q1). The change in refraction (D) was directly influenced by the change in apical curvature (R1 to R2) while the changes in the corneal asphericity (Q1 to Q2) governs the change in spherical aberration (Δc40). The spherical aberration is also partly affected by the change in the apical curvature of the cornea; Increasing the corneal curvature (i. e steepening the cornea) without changing the asphericity of the corneal profile would result in an increase in the positive spherical aberration.

However, as shown in the following graph, the theoretical influence of the refractive correction does not have much effect on the change in corneal asphericity (ΔQ necessary to induce the shift towards negative spherical aberration. To achieve a change of Δc40= - 0.4 microns there are 6 mm optical zone, an increase in prolateness of ΔQ = 0.6 in the corneal asphericity should be targeted, regardless of the positive spherical correction program in laser, and of the value of the original corneal asphericity (Q1) (Figure 7).

theoretical modelling for asphericty and spherical aberration influences

Figure 7: To induce a reduction of spherical aberration of Δc40 = – 0.4, the change theoretically required in corneal asphericity is close To Q ~-0.6. This change is not significantly affected by the amount of positive sphere correction (D). The X axis represents the amount of sphere correction (from myopic corrections to Hypercipo corrections). The Y axis corresponds to the value of the theoretical change in asphericity. The higher the intended change in spherical aberration, the large the required change in corneal asphericity, which must always be planned toward increased prolateness in the case of positive (HYPERCIPO) correction.


In conclusion:

To induce efficient in multifocality has presbyopic hyperopic eye, the following steps are required on the non-dominant eye:

  • Choose the custom-Q mode did the treatment program
  • Target emmetropia we the dominant eye, with no. intended changes in corneal asphericity
  • Target a post refraction of - 2.50 D (ie if the initial distance correction is + 2.25D, enter + 4.75D for the sphere correction) there are 6 mm optical zone in the non-dominant eye
  • Increase prolateness by targeting a value post Q2 such as Q2 = Q1 - 0.6. For example, if Q1 = - 0.25, the target asphericity is Q2 =-0.85


Clinical example:

Clinical example is shown in the following figures: (Figure 8 a - d):


hyperopia and presbyopia

Figure 8: Example of preoperative refractive errors and Q-values for a presbyopic patient hyperopic.


Figure 8B: The nomogram for the non-dominant eye is derived from the principles explained on this page for the non-dominant eye. Induction of very prolate cornea results in a rapid reduction of the amount of induced negative defocus. The latter provides the non-dominant eye with improved information near vision, while the peripheral demyopisation reflected in the amount of negative spherical aberration reduces the number of lost lines for distance vision.

Figure 8B: The nomogram for the non-dominant eye is derived from the principles explained on this page for the non-dominant eye. Induction of very prolate cornea results in a rapid reduction of the amount of induced negative defocus. The latter provides the non-dominant eye with improved information near vision, while the peripheral demyopisation reflected in the amount of negative spherical aberration reduces the number of lost lines for distance vision.



Figure 8: Schematic representation of the expected post result

Figure 8: Schematic representation of the expected post result



Figure 8 d: Representation of the ablation profiles for the dominant vs non-dominant eye. Targeting more prolate cornea causes the reduction of the peripheral depth of ablation.

Figure 8 d: Representation of the ablation profiles for the dominant vs non-dominant eye. Targeting more prolate cornea causes the reduction of the peripheral depth of ablation.



Figure 8: comparison between preoperative and post the aberrometric and Topographic data. Notice the "myopic island" on the post OPD map of the no domiant eye (left)

Figure 8e: Topographic and aberrometric comparison between the preoperative and postoperative data. Notice the "Myopic Island" on the postoperative OPD map of the non-dominant eye (left)


The figure 9 shows some screenshots obtained while programming the hyperopic-presbyopic correction using the described nomogram.

Figure 9: screen captures of the Wavenet / EX500 excimer laser program software (custom Q)

Figure 9: Screen captures of the Wavenet / EX500 excimer laser program software (custom Q)


The results will be improved by the laser correction centering refractive we now close to the corneal vertex, using technologies like Iris recognition. and cyclotorsion compensation. In this context, the integration of pupillometry information, along with the profile of ablation and LASIK flap design within the same software program unit (Wavenet TM) represents a useful feature. In our practice, all the operated patients benefit from preoperative pupillometry and iris mapping in order to center the photoablation at 75% of the distance between the center and the pupil corneal apex. The minimum diameter of the flap cut performed with the FS200 femtosecond laser was 9.5 mm.

The changes in asphericity, which is the mechanism by which negative spherical aberration can be increased, results in a progressive reduction of the induced myopia from the paraxial area to the cancer area. Typically, information visual acuity of J2 and 20/30 can be obtained after the wound healing phase, and provides the patient with show independence for distance and near vision. The clinical results of this multifocal strategy have been reported recently in the Journal of Refractive Surgery (1) (Figure 10).


Figure 10: Results extracted from a recent publication in the Journal of Refractive Surgery (1) reporting on the clinical results obtained when applying the presented nomogram for the LASIK correction of hyperopic candidates presbyopic. The attained binocular information visual acuity at near and far distances seem sufficient to provide operated patients with full show independence for most of their daily and professional tasks.

Figure 10: Results extracted from a recent publication in the Journal of Refractive Surgery (1) reporting on the clinical results obtained when applying the presented nomogram for the LASIK correction of presbyopic Hypercipo candidates. The attained binocular uncorrected visual acuity at near and far distances seem sufficient to provide operated patients with full spectacle independence for most of their daily and professional tasks.


The understanding of the interplay of key variables that serve as a basis of multifocal corneal laser Photoablation allows the design of a non-empirical approach for the combined treatment of hyperopia and presbyopia. This strategy is based on a theoretical approach, which translates into are and encouraging clinical results.










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