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Magnification changes in specularmicroscopy after corneal refractivesurgeryPeter Isager, Jesper Ø. Hjortdal and Niels Ehlers

Department of Ophthalmology, Århus University Hospital, Denmark

ABSTRACT.Purpose: To describe the effect of corneal refractive surgery on the magnifi-cation of a contact and a non-contact specular microscope.Method: The magnification of a contact specular microscope (Konan ClinicalSpecular Microscope) and a non-contact specular microscope (Topcon SP-1000) was experimentally and theoretically studied as a function of anteriorcorneal refractive power and central corneal thickness.Results: The magnification of the contact and non-contact specular microscopewas found to decrease slightly with decreasing central corneal thickness. Inaddition, the magnification of the non-contact specular microscope decreasedslightly with decreasing anterior corneal refractive power.Conclusion: As the preoperative and postoperative measuring conditions aredifferent in patients undergoing corneal refractive surgery a correction for mag-nification changes is necessary when small changes in endothelial cell densityare looked for.

Key words: magnification – specular microscope – contact – noncontact – refractive keratectomy –refractive surgery – excimer laser – endothelium – cell density – human – cornea.

Acta Ophthalmol. Scand. 1999: 76: 391–393Copyright c Acta Ophthalmol Scand 1999. ISSN 1395-3907

Currently, an important clinical ques-tion is whether corneal refractive

surgery, especially excimer laser photore-fractive keratectomy (Isager et al. 1998),affect the corneal endothelial cell density.In specular microscopy of the endo-thelium, light is refracted at the anteriorcorneal surface. Refractive surgery formyopia reduces the corneal power and inphotorefractive keratectomy for myopiaalso the central corneal thickness (CCT).The preoperative and postoperativemeasuring conditions for specular micro-scopy are therefore not the same. The aimof this study is to describe the effect ofchanging anterior corneal refractivepower and changing CCT on the magni-fication of a contact and a non-contactspecular microscope.

MethodsIn contact specular microscopy the endo-thelium is imaged after applanation of thecorneal surface. By manual focusing of theKonan Clinical Specular Microscope asharp image of the endothelium can bemade. Without touching the cornea thenon-contact specular microscope TopconSP-1000 automatically takes a picturewhen the endothelium is in focus.

In this study the Konan Clinical Specu-lar Microscope was calibrated at a CCT of520 microns giving a certain magnification(M

æ). The Topcon SP-1000 is standard

calibrated by the company at a CCT of500 microns and an anterior corneal ra-dius of 8.00 mm (M

æ) (Personal communi-

cation with Topcon Europe B.V.).

ResultsMagnification of the contact specularmicroscopeIn a previous study the magnification (M)of the contact specular microscope (Kon-an Clinical Specular Microscope) was ex-perimentally found to decrease linearlyand equally in the horizontal and verticaldimension with decreasing focusing dis-tance. The magnification (M2) of aphotomicrograph therefore decreased asa second order function (Isager et al.1996). The normalized magnification(M2/M

æ2) at different CCT’s was calcu-

lated (Fig. 1 and Table 1).

Magnification of the non-contact specularmicroscopeThe magnification of the non-contactspecular microscope can be calculatedfrom theoretical considerations.

The light reflected from the corneal en-dothelium is refracted at the anterior cor-neal surface (representing a certain an-

Fig. 1. Normalized magnification of the con-tact and non-contact specular microscope ver-sus CCT for different values of anterior cor-neal radius (r).

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Table 1. Normalized magnification.

Specular microscope

Non-contact ContactAnterior corneal radius/mm

CCT/microns 7 8 9 10

300 0.9892 0.9862 0.9840 0.9822 0.9753350 0.9931 0.9897 0.9870 0.9849 0.9809400 0.9970 0.9931 0.9900 0.9876 0.9865410 0.9978 0.9938 0.9906 0.9882 0.9876420 0.9986 0.9945 0.9913 0.9887 0.9888430 0.9994 0.9952 0.9919 0.9892 0.9899440 1.0002 0.9958 0.9925 0.9898 0.9910450 1.0010 0.9965 0.9931 0.9903 0.9921460 1.0018 0.9972 0.9937 0.9909 0.9932470 1.0026 0.9979 0.9943 0.9914 0.9944480 1.0034 0.9986 0.9949 0.9920 0.9955490 1.0042 0.9993 0.9955 0.9925 0.9966500 1.0050 1.0000 0.9961 0.9931 0.9977510 1.0058 1.0007 0.9968 0.9936 0.9989520 1.0066 1.0014 0.9974 0.9942 1.0000530 1.0074 1.0021 0.9980 0.9947 1.0011540 1.0082 1.0028 0.9986 0.9953 1.0023550 1.0090 1.0035 0.9992 0.9958 1.0034560 1.0098 1.0042 0.9998 0.9964 1.0045570 1.0106 1.0049 1.0005 0.9969 1.0056580 1.0114 1.0056 1.0011 0.9975 1.0068590 1.0122 1.0063 1.0017 0.9981 1.0079600 1.0130 1.0070 1.0023 0.9986 1.0090650 1.0171 1.0105 1.0054 1.0014 1.0147700 1.0212 1.0140 1.0085 1.0042 1.0204

terior corneal refractive power (P)) beforebeing imaged by the specular microscope.From fundamental equations of geo-metric optics (Rubin 1993) the followingcalculations can be done:

UπPΩV (1) whereP is the anterior corneal refractive power

Ω(n(cornea) – n(air))/r (2) wheren(cornea) is the refractive index of cor-nea (1.376) (Mandell 1994)n(air) is the refractive index of air (1.0)rΩanterior corneal radius

U is the reduced vergence power of theobject

Ωn(cornea)/object distance (3)

V is the reduced vergence power of theimage

Ωn(air)/image distance

Convergence is defined as positive and di-vergence as negative.The magnification of the image (two di-mensions) is

M2ΩU2/V2 (4)

By substituting (1), (2), and (3) in (4) themagnification can be expressed as

M2Ω(ª1.376/CCT)2/(ª1.376/CCTπ0.376/r)2

For different CCT’s and anterior cornealrefractive powers the magnification (M2)

Fig. 2. A counting area of the endothelium before and after refractive surgery for myopia (largerespectively small hexagons) is illustrated. In this example the preoperative magnification (M(pre))in the vertical and horizontal dimension is two times larger than the postoperative magnification(M(post)) giving the normalized magnification M(post)2/M(pre)2Ω1/4.

of the image was calculated. The normal-ized magnification (M2/M

æ2) at different

CCT’s and anterior corneal radii isshown in Fig. 1 and Table 1.

Correction for magnification changesThe endothelial cell density is normallyestimated by counting the number of en-dothelial cells within a certain area of aphotomicrograph of the endothelium.The size of the endothelial cells is de-pendent on the magnification of thespecular microscope. When the magnifi-cation is low the endothelial cells looksmall. The estimated endothelial cell den-sity will be too large as more cells will becounted within a certain counting area.To obtain the real endothelial cell densitythe apparent endothelial cell density hasto be multiplied by the normalized mag-nification (M2/M

æ2) at a specific value of

anterior corneal refractive power andCCT. See Fig. 2.

Clinical examples of changes inmagnificationRadial keratotomy (RK) and implan-tation of an intracorneal ring segment(ICRS) result in a decrease in anteriorcorneal refractive power without chang-ing CCT. Photorefractive keratectomy(PRK) for myopia reduces anterior cor-neal refractive power as well as CCT. Innonrefractive phototherapeutic keratec-tomy used for treatment of superficialcorneal scars CCT is reduced, prefer-ably without changing the anterior cor-neal refractive power. The endothelial

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Table 2. Examples of overestimation of endothelial cell density after different corneal surgicalprocedures.

Overestimation ofendothelial cell density (per cent)

Corneal Specular microscopesurgical Reduction in Reduction in anteriorprocedure CCT (microns) corneal power (dioptres) Non-contact Contact

PRK 90 10 1.28 1.02RK/ICRS 0 5 0.38 0PTK 90 0 0.64 1.02

PRK: Photorefractive keratectomyRK: Radial keratotomyICRS: Intracorneal ring segmentPTK: Phototherapeutic keratectomy.

cell density will, as shown in Table 2, beoverestimated after these corneal surgi-cal procedures if not corrected for mag-nification changes. The calculations arebased on surgery on an average corneawith an anterior corneal radius of 7.76mm (Borish 1975) and a CCT of 520microns (Hansen 1971).

ConclusionFrom experimental and theoreticalstudies it has been shown that the magni-

fication of the contact and non-contactspecular microscope decreases slightlywith decreasing central corneal thickness.In addition, the magnification of the non-contact specular microscope decreasesslightly with decreasing anterior cornealrefractive power. As the preoperative andpostoperative measuring conditions aredifferent in patients undergoing cornealrefractive surgery a correction for magni-fication changes has to be done whensmall changes in endothelial cell densityare looked for.

ReferencesBorish IM (1975): Clinical refraction, 3rd edi-

tion, Vol 1, p 72.Hansen FK (1971): A clinical study of the nor-

mal human central corneal thickness. ActaOphthalmol (Copenh) 49: 82–89.

Isager P, Hjortdal JØ & Ehlers N (1996): Theeffect of 193 nm excimer laser radiation onthe human corneal endothelial cell density.Acta Ophthalmol Scand 74: 224–227.

Isager P, Guo S, Hjortdal JØ & Ehlers N(1998): Endothelial cell loss after photore-fractive keratectomy for myopia. ActaOphthalmol Scand 76:304–307.

Mandell RB (1994): Corneal power correctionfactor for photorefractive keratectomy. J Re-fract Corneal Surg 10: 125–128.

Rubin ML (1993): Optics for Clinicians: pp67–75 and pp 345–46.

Received on December 6th, 1998.Accepted on March 11th, 1999.

Corresponding author:

Peter IsagerDepartment of OphthalmologyÅrhus University HospitalNorrebrogade 44DK-8000 Århus CDenmark.