Intraocular Lens Calculations After Keratorefractive Surgery





Introduction


As part of the normal aging process, patients who are undergoing keratorefractive procedures may ultimately develop cataracts and may need cataract extraction with intraocular lens (IOL) implantation. The increasing volume of cataract surgical procedures after corneal refractive surgery is associated with similar expectations of perfect vision without correction after cataract surgery. Early results, however, have shown a hyperopic shift after cataract surgery in eyes that underwent corneal refractive surgery. IOL lens power calculation depends on the axial length (AL), anterior chamber depth (ACD), and keratometry reading (K-reading). With few exceptions, the AL and ACD are not changed following refractive surgery. Keratometry, on the other hand, may show significant changes. The current methods for measuring keratometry include manual keratometer, automated keratometry and corneal topography. These methods underestimate corneal flattening after myopic radial keratotomy (RK), photorefractive keratectomy (PRK), and laser in situ keratomileusis (LASIK) with an overestimation of the K-reading. Such reading may lead to falsely low IOL power calculation with subsequent hyperopia following cataract surgery.




Source of Error in K-Reading Following Corneal Refractive Surgery


Current instruments measure with accuracy the anterior corneal radius of curvature (R a ) by measuring the reflected images of the projected mires; the posterior corneal radius of curvature is not assessed but is compensated for by the use of a modified (effective) index of refraction ( Fig. 27.1 ). For example, the Zeiss ophthalmometer uses an effective index of refraction of 1.3315, whereas EyeSys corneal topography uses an effective index of refraction of 1.3375. The keratometric diopters are derived from the anterior radius of curvature using an effective refractive index (n) in the paraxial formula :


<SPAN role=presentation tabIndex=0 id=MathJax-Element-1-Frame class=MathJax style="POSITION: relative" data-mathml='keratometric diopters(D)=(n−1)/Ra(m).’>keratometric diopters(?)=(?−1)/??(?).keratometric diopters(D)=(n−1)/Ra(m).
keratometric diopters(D)=(n−1)/Ra(m).
keratometric diopters(D)=(n−1)/Ra(m).
keratometric diopters(D)=(n−1)/Ra(m).
Because there is a constant ratio between the anterior and posterior surface curvatures in the central optical zone of normal corneas, the use of these indices in the current instruments to compensate for the posterior corneal power is acceptable. However, corneal refractive surgery changes the architecture of the central cornea such that standard methods of measurement overestimate the corneal power. Following RK, both the anterior and posterior corneal surfaces undergo a relatively proportional flattening, and the relationship between them is not disrupted. The central cornea flattens more than the paracentral cornea, and the midperipheral cornea steepens ( Fig. 27.2A ). The standard keratometer measures close to the paracentral transition (knee) zone after RK, which leads to an overestimate of the curvature of the central flat effective optical zone ( Fig. 27.2B ). The greater the amount of myopic correction, the smaller the effective central optical zone and the greater the magnitude of error. A temporary hyperopic shift in the early course after cataract surgery in eyes that underwent RK is due to mechanical instability of the cornea, which may flatten almost as if refractive keratotomy had just been done. This temporary hyperopic shift may be as high as +4 D to +6 D, giving the false impression of a miscalculated IOL power. Therefore hyperopic shift after RK should not be corrected surgically before corneal stability is ensured after cataract surgery. In contrast, mechanical stability of the cornea is not significantly decreased after PRK and LASIK.


Fig. 27.1


(A) Reflected images from the anterior corneal surface of the projected keratometric mires are analyzed to calculate accurately the anterior corneal radius of curvature. (B) Normal cornea with an average anterior corneal power of +48 D and an average posterior corneal power of −5.6 D. Index of refraction at the air–cornea interface (N c = 1.376) can be used only to assess the anterior corneal power; posterior surface is not measured but compensated for by the use of the modified (effective) index of refraction “n” (e.g., EyeSys videokeratography: 1.3375).



Fig. 27.2


(A) Proportional flattening of the anterior and posterior corneal surfaces after radial keratotomy (RK) associated with peripheral steepening and the formation of a transitional knee zone in an eye that underwent radial keratotomy. (B) Standard keratometer measures close to the paracentral transitional zone (knee) after RK, which is steeper than the central flat effective optical zone.


Following uncomplicated photorefractive surgery (PRS), the R a measurement by current instruments is still accurate because the transition area (knee zone) is far outside the 2.6- to 3-mm zone that is measured, and the irregular astigmatism in the central 3-mm zone is usually minimal. In this instance, the lack of accuracy in the K-reading results from the fact that the normal relationship between the anterior and posterior corneal surface curvature is disrupted as a result of anterior corneal surface flattening while the posterior surface curvature remains unchanged. Therefore the use of an effective index of refraction that was generated in normal corneas does not compensate correctly for the posterior corneal surface power, which results in an inaccurate K-reading. Change in corneal thickness following a photoablative procedure has a minimal effect (estimated to be < 0.1 D) on the parameters used to calculate IOL power, and posterior corneal curvature changes slightly or remains unchanged following uncomplicated refractive surgery.




Present Methods for K-Reading After Corneal Refractive Surgery


To obtain an accurate IOL power calculation following corneal refractive surgery, several methods have been adopted for assessing the K-reading following refractive surgery.


Clinical History Method


The clinical history method (CHM), or calculation method, first published by Holladay in 1989 and later by Hoffer as the CHM for eyes after RK involves subtracting the change in spherical equivalent (SE) refraction at the corneal plane (ΔSEQC) induced by the refractive procedure from the preoperative K-reading (K-reading preop ):


<SPAN role=presentation tabIndex=0 id=MathJax-Element-2-Frame class=MathJax style="POSITION: relative" data-mathml='K-reading after surgery=K-readingpreop−ΔSEQC’>K-reading after surgery=K-readingpreop−?SEQCK-reading after surgery=K-readingpreop−ΔSEQC
K-reading after surgery=K-readingpreop−ΔSEQC
K-reading after surgery=K-readingpreop−ΔSEQC
K-reading after surgery=K-readingpreop−ΔSEQC

<SPAN role=presentation tabIndex=0 id=MathJax-Element-3-Frame class=MathJax style="POSITION: relative" data-mathml='ΔSEQC=SEQCpostop−SEQCpreop​.’>?SEQC=SEQCpostop−SEQCpreop.ΔSEQC=SEQCpostop−SEQCpreop​.
ΔSEQC=SEQCpostop−SEQCpreop​.
ΔSEQC=SEQCpostop−SEQCpreop​.
ΔSEQC=SEQCpostop−SEQCpreop​.
SEQC is the SE refraction at the corneal plane ( Fig. 27.3 ).


Fig. 27.3


The spheroequivalent refraction for refractions at the corneal plane (SEQC) is calculated using the spheroequivalent refractions at the spectacle plane (SEQS) at a given vertex distance (V).


Example


The patient’s preoperative corneal power was 45.0 D and refractive error (SE) was −6.00 D at the spectacle plane (V = 12 mm). At 1 year postoperatively, the eye had an SE refractive error of −1.00 D at the spectacle plane without cataract:


<SPAN role=presentation tabIndex=0 id=MathJax-Element-4-Frame class=MathJax style="POSITION: relative" data-mathml='SEQCpreop=1000/[(1000/−6)−12]=−5.6D’>SEQCpreop=1000/[(1000/−6)−12]=−5.6?SEQCpreop=1000/[(1000/−6)−12]=−5.6D
SEQCpreop=1000/[(1000/−6)−12]=−5.6D
SEQCpreop=1000/[(1000/−6)−12]=−5.6D
SEQCpreop=1000/[(1000/−6)−12]=−5.6D

<SPAN role=presentation tabIndex=0 id=MathJax-Element-5-Frame class=MathJax style="POSITION: relative" data-mathml='SEQCpostop=1000/[(1000/−1)−12]=−0.9D’>SEQCpostop=1000/[(1000/−1)−12]=−0.9?SEQCpostop=1000/[(1000/−1)−12]=−0.9D
SEQCpostop=1000/[(1000/−1)−12]=−0.9D
SEQCpostop=1000/[(1000/−1)−12]=−0.9D
SEQCpostop=1000/[(1000/−1)−12]=−0.9D

<SPAN role=presentation tabIndex=0 id=MathJax-Element-6-Frame class=MathJax style="POSITION: relative" data-mathml='ΔSEQC=(−0.9)−(−5.6)=4.7D’>?SEQC=(−0.9)−(−5.6)=4.7?ΔSEQC=(−0.9)−(−5.6)=4.7D
ΔSEQC=(−0.9)−(−5.6)=4.7D
ΔSEQC=(−0.9)−(−5.6)=4.7D
ΔSEQC=(−0.9)−(−5.6)=4.7D

<SPAN role=presentation tabIndex=0 id=MathJax-Element-7-Frame class=MathJax style="POSITION: relative" data-mathml='K-reading after surgery=45D−4.7D=40.3D’>K-reading after surgery=45?−4.7?=40.3?K-reading after surgery=45D−4.7D=40.3D
K-reading after surgery=45D−4.7D=40.3D
K-reading after surgery=45D−4.7D=40.3D
K-reading after surgery=45D−4.7D=40.3D

<SPAN role=presentation tabIndex=0 id=MathJax-Element-8-Frame class=MathJax style="POSITION: relative" data-mathml='SEQS=sphere+0.5(cylinder)’>SEQS=sphere+0.5(cylinder)SEQS=sphere+0.5(cylinder)
SEQS=sphere+0.5(cylinder)
SEQS=sphere+0.5(cylinder)
SEQS=sphere+0.5(cylinder)

<SPAN role=presentation tabIndex=0 id=MathJax-Element-9-Frame class=MathJax style="POSITION: relative" data-mathml='SEQC=1000/[(1000/SEQS)−V].’>SEQC=1000/[(1000/SEQS)−?].SEQC=1000/[(1000/SEQS)−V].
SEQC=1000/[(1000/SEQS)−V].
SEQC=1000/[(1000/SEQS)−V].
SEQC=1000/[(1000/SEQS)−V].
Recommendation to use the SE change at the spectacle plane rather than the corneal plane has been suggested in order to minimize the amount of possible overestimation of K-reading. The CHM is considered to be accurate and perhaps the most reliable method after RK and photorefractive procedures. It does, however, have limitations because it requires postrefractive surgery refraction before cataract surgery, which may be biased because of lens-induced and AL progression myopia after refractive surgery. Lenticular opacities at the time of cataract surgery may also preclude accurate refraction. Therefore it is important to choose a postoperative refraction at a time point when the cornea is stable and before any myopic shift from nuclear sclerosis. Corneal regression after refractive surgery is not uncommon and may affect the result of K-reading when a “remote” postoperative refraction is used. To avoid the error induced by corneal regression, we suggest comparing the K-reading measured using the conventional methods at the time of cataract surgery to the previous K-reading measured at the same time as the refraction was performed. Any significant change in corneal power should be subtracted from the refraction (at the corneal plane) used to calculate the corneal power.


Hard Contact Lens Method


This method was first described by Soper and Goffman and later recommended for determining the corneal power for IOL calculation after RK and after PRK and LASIK. The concept of the hard contact lens (HCL) method (also known as the contact lens overrefraction method) is based on the principle that if an HCL with plano power and a base curve equal to the corneal power is fitted over the cornea, it will not change the refractive error of the eye. This method can be used with no knowledge of pretreatment data. The patient’s manifest refraction is determined without a contact lens and then repeats the manifest refraction after placement of a plano HCL of known base curve. The difference between the HCL overrefraction and the SE refraction without the contact lens is added to the contact lens base curve measured in diopters to obtain the corneal dioptric power. Three results are possible: (1) If the refraction does not change, the central corneal power is equal to the contact lens base curve; (2) if the SE shifts toward hyperopia after fitting the contact lens, the corneal power is more than the HCL base curve; (3) if the SE shifts toward myopia, then the corneal power is less than the HCL base curve ( Fig. 27.4 ).




Fig. 27.4


Plano hard contact lens (HCL; pink ) of a known base curve is fitted over the cornea (blue) . (A) HCL and anterior cornea have the same base curve. In this case, the tear film meniscus formed between the HCL and the cornea (green) has no dioptric power and the refraction does not change after lens fitting. (B) Anterior cornea is steeper than the HCL base curve. In this case, the formed tear film meniscus has a divergent power and the sphere equivalent of refraction shifts toward hyperopia after HCL fitting. (C) The HCL base curve is steeper than the anterior corneal curvature, and the SE shifts toward hyperopia after fitting of the HCL due to the formation of a convergent tear film meniscus between the HCL and the cornea.


Example


The patient’s refraction (SE) is −1.0 diopter (D). After adding the HCL of base curve 40.0 D, the manifest refraction becomes −2.0 D. This means that the corneal power is less than the HCL base curve and equal to


<SPAN role=presentation tabIndex=0 id=MathJax-Element-10-Frame class=MathJax style="POSITION: relative" data-mathml='40.0D+[(−2.0D)−(−1.0D)]=39.0D.’>40.0?+[(−2.0?)−(−1.0?)]=39.0?.40.0D+[(−2.0D)−(−1.0D)]=39.0D.
40.0D+[(−2.0D)−(−1.0D)]=39.0D.
40.0D+[(−2.0D)−(−1.0D)]=39.0D.
40.0D+[(−2.0D)−(−1.0D)]=39.0D.
This method is widely used after RK but has not been validated for use after photorefractive surgery. Dense cataract may give rise to a false refraction. Thus the accuracy of this method in cataractous eyes is questionable.


Our analysis of this method shows that the difference in SE refraction before and after adding the HCL is the power of the tear film meniscus created between the lens and the anterior corneal surface. Thus adding this power (the difference of SE refraction before and after adding the HCL) to the HCL base curve gives the value of the anterior corneal surface power and not the total corneal power. Many corneas (especially after keratorefractive surgery) have different posterior curvatures and may share the same anterior curvature (with different total corneal power) but give rise to an equal difference in SE refraction after adding the same plano HCL ( Fig. 27.5 ). We conclude that only the anterior corneal power can be assessed by this method, which may be useful after RK surgery in which the current instruments cannot adequately assess the anterior corneal curvature. This measurement must be converted to a total corneal power by appropriate use of the effective index of refraction (e.g., n = 1.3315 if using the Zeiss ophthalmometer, and n = 1.3375 if using EyeSys corneal topography). Since the anterior corneal curvature measurement can still be assessed adequately by current instruments following PRS, use of the HCL method is not meaningful.




Fig. 27.5


The same tear film meniscus (green) , with equal difference in sphere equivalent refraction after adding the same plano hard contact lens (HCL), is formed between the same HCL (pink) and three different corneas (blue) with the same anterior curvature but different posterior curvature and different total dioptric power. (A) The cornea has the flattest posterior curvature, and (C) the cornea has the steepest posterior curvature. The HCL method would erroneously give an equal value of total dioptric power in these three corneas that have different total dioptric power.


Calculation of the Corneal Dioptric Power by Measuring the Anterior Corneal Curvature


Jarade and Tabbarra proposed a new formula ( Fig. 27.6 ) to calculate the K-reading in eyes that underwent myopic LASIK according to the change of R a induced by LASIK surgery. This formula does not use the assumed index of refraction, which might vary between devices. It can also be applicable for eyes after PRK. The theoretical basis of this formula is the fact that change in corneal power following LASIK is proportional to the amount of corneal ablation measured in diopters. This amount of corneal ablation can be subtracted from the K-reading measured before the photorefractive procedure to obtain the K-reading following surgery ( Fig. 27.7 ).


<SPAN role=presentation tabIndex=0 id=MathJax-Element-11-Frame class=MathJax style="POSITION: relative" data-mathml='Kpostop=Kpreop−[(Nc−1)×(Ra−postop−Ra−preop)Ra−postop×Ra−preop]’>?postop=?preop−[(??−1)×(??−postop−??−preop)??−postop×??−preop]Kpostop=Kpreop−[(Nc−1)×(Ra−postop−Ra−preop)Ra−postop×Ra−preop]
Kpostop=Kpreop−[(Nc−1)×(Ra−postop−Ra−preop)Ra−postop×Ra−preop]
Kpostop=Kpreop−[(Nc−1)×(Ra−postop−Ra−preop)Ra−postop×Ra−preop]
Kpostop=Kpreop−[(Nc−1)×(Ra−postop−Ra−preop)Ra−postop×Ra−preop]



Fig. 27.6


Jarade’s formula for the calculation of K-reading following LASIK. K postop = K-reading following LASIK. K preop = K-reading before LASIK. N c = index of refraction of the cornea (air–cornea interface: 1.376). R a-postop = radius of curvature of the anterior corneal surface following LASIK. R a-preop = radius of curvature of the anterior corneal surface before LASIK.



Fig. 27.7


Derivation of the formula. D ablation = total amount of dioptric ablation induced by LASIK. K preop = total corneal dioptric power before LASIK. K postop = total corneal dioptric power after LASIK. K a-preop and K a-postop are the dioptric power of the anterior corneal surface before and after LASIK, respectively. K p-preop and K p-postop are the dioptric power of the posterior corneal surface before and after LASIK, respectively. N c is the corneal index of refraction at the air–cornea interface (1.376).


Example


Before surgery, a patient’s anterior corneal curvature (R a ) is 7.8 mm and the K-reading is 45.0 D. After surgery, R a is 8.5 mm and the K-reading is 42.0 D. Using this formula, the calculated K-reading after surgery is equal to


<SPAN role=presentation tabIndex=0 id=MathJax-Element-12-Frame class=MathJax style="POSITION: relative" data-mathml='45−[(1.376−1)×(0.0085−0.0078)/(0.0085×0.0078)=41.03D.’>45−[(1.376−1)×(0.0085−0.0078)/(0.0085×0.0078)=41.03?.45−[(1.376−1)×(0.0085−0.0078)/(0.0085×0.0078)=41.03D.
45−[(1.376−1)×(0.0085−0.0078)/(0.0085×0.0078)=41.03D.
45−[(1.376−1)×(0.0085−0.0078)/(0.0085×0.0078)=41.03D.
45−[(1.376−1)×(0.0085−0.0078)/(0.0085×0.0078)=41.03D.
Thus the measured K-reading overestimates the corneal power by 0.97 D. This formula has been proven to be simple, objective, nonrefraction dependent, and as accurate as the CHM formula. Also, this formula compensates for corneal regression, which might happen at any time after refractive surgery as a result of the wound-healing process, epithelial hyperplasia, or other factors. This regression will be manifested by a change in the anterior corneal curvature. Axial length progression myopia (not infrequent after refractive surgery, especially in relatively young patients who undergo refractive surgery) and lenticular myopia will not affect the K-reading result obtained by this formula since it is independent of the refractive error of the eye at the time of cataract surgery. The only prerequisite of this formula is to have records of K-reading and anterior radius of curvature before refractive surgery.
<SPAN role=presentation tabIndex=0 id=MathJax-Element-13-Frame class=MathJax style="POSITION: relative" data-mathml='Dablation=Kpreop−KpostopDablation=(Ka-preop+Kp-preop)−(Ka-postop+Kp-postop)=Ka−preop−Ka−postop;(Kp-preop is unchanged following uncomplicated LASIK)=(Nc−1)×(Ra-postop−Ra-preop)/(Ra-postop×Ra-preop)Kpostop=Kpreop−Dablation=Kpreop−[(Nc−1)×(Ra-postop−Ra-preop)/(Ra-postop×Ra-preop)]’>?ablation=?preop−?postop?ablation=(?a-preop+?p-preop)−(?a-postop+?p-postop)=??−preop−??−postop;(?p-preop is unchanged following uncomplicated LASIK)=(??−1)×(?a-postop−?a-preop)/(?a-postop×?a-preop)?postop=?preop−?ablation=?preop−[(??−1)×(?a-postop−?a-preop)/(?a-postop×?a-preop)]Dablation=Kpreop−KpostopDablation=(Ka-preop+Kp-preop)−(Ka-postop+Kp-postop)=Ka−preop−Ka−postop;(Kp-preop is unchanged following uncomplicated LASIK)=(Nc−1)×(Ra-postop−Ra-preop)/(Ra-postop×Ra-preop)Kpostop=Kpreop−Dablation=Kpreop−[(Nc−1)×(Ra-postop−Ra-preop)/(Ra-postop×Ra-preop)]
Dablation=Kpreop−KpostopDablation=(Ka-preop+Kp-preop)−(Ka-postop+Kp-postop)=Ka−preop−Ka−postop;(Kp-preop is unchanged following uncomplicated LASIK)=(Nc−1)×(Ra-postop−Ra-preop)/(Ra-postop×Ra-preop)Kpostop=Kpreop−Dablation=Kpreop−[(Nc−1)×(Ra-postop−Ra-preop)/(Ra-postop×Ra-preop)]
Dablation=Kpreop−KpostopDablation=(Ka-preop+Kp-preop)−(Ka-postop+Kp-postop)=Ka−preop−Ka−postop;(Kp-preop is unchanged following uncomplicated LASIK)=(Nc−1)×(Ra-postop−Ra-preop)/(Ra-postop×Ra-preop)Kpostop=Kpreop−Dablation=Kpreop−[(Nc−1)×(Ra-postop−Ra-preop)/(Ra-postop×Ra-preop)]
Dablation=Kpreop−KpostopDablation=(Ka-preop+Kp-preop)−(Ka-postop+Kp-postop)=Ka−preop−Ka−postop;(Kp-preop is unchanged following uncomplicated LASIK)=(Nc−1)×(Ra-postop−Ra-preop)/(Ra-postop×Ra-preop)Kpostop=Kpreop−Dablation=Kpreop−[(Nc−1)×(Ra-postop−Ra-preop)/(Ra-postop×Ra-preop)]

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Oct 10, 2019 | Posted by in OPHTHALMOLOGY | Comments Off on Intraocular Lens Calculations After Keratorefractive Surgery

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