the effect of posterior corneal flat meridian and astigmatism amount on the total corneal...

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The effect of posterior corneal flat meridian and astigmatismamount on the total corneal astigmatism estimated from anteriorcorneal measurements

Youngsub Eom & Su-Yeon Kang & Hyo Myung Kim &

Jong Suk Song

Received: 3 April 2014 /Revised: 16 June 2014 /Accepted: 24 June 2014 /Published online: 20 July 2014# Springer-Verlag Berlin Heidelberg 2014

AbstractBackground To evaluate the effects of posterior corneal astig-matism and the absolute flat meridian difference betweenanterior and posterior corneal surfaces (AMDAnt-Post) on theestimation of total corneal astigmatism using anterior cornealmeasurements (simulated keratometry [K]).Methods Ninety-nine eyes of 99 healthy participants wereenrolled. Anterior, posterior, and total mean corneal power,cylinder power, flat meridian, and vector components J0, andJ45 measured by a dual Scheimpflug camera were analyzed.The correlation between the posterior corneal cylinder power,AMDAnt-Post, and the difference in the cylinder power betweensimulated K and total cornea (cylinder power differenceSimK-

Tot) were evaluated.Results The cylinder power differenceSimK-Tot was positivelycorrelated with the posterior corneal cylinder power (rho=0.704 and P<0.001) and negatively correlated withAMDAnt-Post (rho=−0.717 and P<0.001). In the multivariatelinear regression analysis, anterior corneal J0 was stronglyassociated with the posterior corneal cylinder power and theAMDAnt-Post. When corneal J0 had a positive value, thecylinder power of simulated K tended to be larger than thetotal corneal cylinder power. In comparison, the oppositetrend was presented in eyes with negative anterior corneal

J0. When anterior corneal J0 was larger than 1.0 or smallerthan −0.9, the errors from estimating the total corneal cylinderpower using anterior corneal measurements tended to belarger than 0.25 D.Conclusion Posterior corneal astigmatism should be consid-ered for more accurate corneal astigmatism predictions, espe-cially in eyes with anterior corneal astigmatism greater than2.0 D of with-the-rule astigmatism or greater than 1.8 D ofagainst-the-rule astigmatism.

Keywords Anterior corneal astigmatism . Posterior cornealastigmatism . Total corneal astigmatism

Introduction

Corneal astigmatism is composed of the anterior and posteriorcorneal surfaces. However, conventional automatedkeratometers calculate the mean corneal power and cylinderpower from anterior corneal measurements only using a re-fractive index of 1.3375 under the assumption that the curva-ture of the anterior and posterior surfaces of the cornea have aconstant ratio [1]. Koch et al. [2] reported that neglectingposterior corneal astigmatism may lead to incorrect estimationof total corneal astigmatism and 5 % of eyes showed anestimation error of more than 0.50 D.

Scheimpflug tomography is an optical system for anteriorsegment analysis. This device can measure both anterior andposterior corneal surfaces with high precision, and providesthe total corneal power and astigmatism [3]. Previous studieshave reported the relationship between anterior, posterior, andtotal corneal power and astigmatism using Scheimpflug to-mography [2, 4–8]. Total corneal power and astigmatism canbe calculated by Gaussian optics in paraxial approximation [9]or by ray tracing through the anterior and posterior cornealsurfaces using Snell’s law [10]. Between the two, ray tracing is

All the authors have full control of all primary data, and they agree toallow Graefe’s Archive for Clinical and Experimental Ophthalmology toreview the data of the current study if requested.

Y. Eom : S.<Y. Kang :H. M. Kim : J. S. SongDepartment of Ophthalmology, Korea University College ofMedicine, Seoul, South Korea

J. S. Song (*)Department of Ophthalmology, Guro Hospital, Korea UniversityCollege of Medicine, 80, Guro-dong, Guro-gu, Seoul 152-703,South Koreae-mail: [email protected]

Graefes Arch Clin Exp Ophthalmol (2014) 252:1769–1777DOI 10.1007/s00417-014-2737-9

better than Gaussian optics in paraxial approximation forcalculating total corneal power [10].

Errors from estimating total corneal astigmatism usinganterior corneal measurements mainly arise from the mag-nitude of posterior corneal astigmatism and the flat merid-ian difference between anterior and posterior corneal sur-faces. Thus, the purpose of this study was to evaluate theeffect of the magnitude of posterior corneal astigmatismand the absolute flat meridian difference between anteriorand posterior corneal surfaces (AMDAnt-Post) on the esti-mation of total corneal cylinder power using anterior cor-neal measurements.

Material and methods

Study population

This prospective cross-sectional study was conducted at theDepartment of Ophthalmology in the Korea UniversityCollege of Medicine. The study adhered to the tenets of theDeclaration of Helsinki and was approved by the institutionalreview board of Korea University Ansan Hospital. Subjectsfrom our institute were enrolled between September 2013 andOctober 2013. Informed consent was obtained from all sub-jects. Subjects younger than 18 years of age, those who hadpreviously undergone ocular surgery (e.g., cataract surgeryand refractive surgery), those who showed corneal pathologythat could affect the measurements, and those who were usingeye drops or wearing contact lenses within 2 weeks of recruit-ment were excluded.

Subject examination

All participants completed an ophthalmic examination withslit lamp biomicroscopy to observe the corneal pathology

which could affect the measurements. Clinical measurementswere performed on the right eye of all participants in thefollowing order: 1) A double Scheimpflug camera was used(Galilei, Ver 6.02), 2) An IOLMaster was used (Carl ZeissMeditec, Jena, Germany). All measurements were performedby a single trained technician. For the Scheimpflug measure-ment, if one scan had met all minimally required qualitypercentages for overall, motions compensation, Placido,Scheimpflug, and motion distance qualities, the scan wasselected for the analysis of each participant. If the measure-ment did not meet the required quality, the scan was repeatedaccording to the manufacturer’s guideline.

Main outcome measure(s)

The total corneal power was calculated by ray tracingthrough the anterior and posterior corneal surfaces usingSnell’s law over the central 1.0 to 4.0 mm zone from thedual Scheimpflug camera. Corneal cylinder power, whichwas measured according to the conventional keratometermethod using a refractive index of 1.3375, was displayedas the cylinder power of simulated keratometry (K).Anterior corneal cylinder power was calculated using arefractive index of 1.376.

The anterior, posterior, and total corneal astigmatism wereconverted from the “negative-cylinder form” convention to

Table 1 Clinical characteristics of study participants and their eyes in astudy of the effect of posterior corneal surfaces on corneal astigmatism(n=99)

Parameters Mean±SD Range

Age, years 37.9±13.0 18–64

Sex, n

Male (%) 56 (56.6) –

Female (%) 43 (43.4) –

Corneal power, Da 43.45±1.66 37.44–49.56

Anterior Chamber depth, mma 3.48±0.39 2.55–4.33

Axial length, mm* 24.73±1.49 21.30–28.48

SD standard deviation, D dioptersa Corneal power, anterior chamber depth, and axial length measured byIOLMaster

Table 2 The mean corneal power, cylinder power, flat meridian, andcomponent of Jackson cross cylinder at 0 and 90° (J0) and at 45 and 135°(J45) for anterior and posterior corneal surfaces and total cornea

Anteriorcornealsurface(mean±SD)

Posteriorcornealsurface(mean±SD)

Total cornea(mean±SD)

Corneal power, D 48.43±2.05 −6.36±0.29 42.33±1.83

Cylinder power, CD 1.35±0.77 0.38±0.16 1.10±0.66

Flat meridian, Degrees 89±72 105±80 83±67

J0, D 0.46±0.54 0.17±0.07 0.29±0.50

J45, D 0.00±0.31 −0.01±0.08 0.01±0.29

SD standard deviation, D diopters, CD cylinder diopters

Table 3 Pearson correlation coefficients (CC) and P values of thecorrelation analysis for the component of Jackson cross cylinder at 0and 90° (J0), and at 45 and 135° (J45) among anterior and posteriorcorneal surfaces and the total cornea

Anterior vs. Posterior Anterior vs. Total Posterior vs. Total

CC* P value CC* P value CC* P value

J0 0.756 <0.001 0.994 <0.001 0.682 <0.001

J45 0.528 <0.001 0.967 <0.001 0.301 <0.001

1770 Graefes Arch Clin Exp Ophthalmol (2014) 252:1769–1777

the rectangular forms of Fourier notation for the power vectoranalysis using the following equations: [11]

J0 ¼ −C=2 x cos 2α

J45 ¼ −C=2 x sin 2α

where C is the negative-cylinderpower and angle α is thecylinder axis. J0 is the Jackson cross cylinder power at axis0° and 90° and J45 is the Jackson cross cylinder power at axis45° and 135°.

To compare the astigmatism of the simulated K and totalcornea, double-angle plots were drawn and the vector

difference between the astigmatism of the simulated K andtotal cornea was calculated using vector analysis [2, 12].

AMDAnt-Post was defined as the absolute value of the flatmeridian difference between the anterior and posterior cornealsurfaces. The cylinder power differenceSimK-Tot was defined asthe difference in the cylinder power between the simulated Kand total cornea (cylinder power differenceSimK-Tot=cylinderpower of simulated K – total corneal cylinder power).

The optimal partial adjustment of the cylinder power ofsimulated K according to the anterior corneal J0 was analyzedusing the corrective regression formula: Adjusted cylinderpower of simulated K=β x cylinder power of simulated K,where β is a correlation coefficient that is a magnitude of the

Fig. 1 Linear regression anlaysis of the relationship between anterior,posterior, and total corneal J0. a Comparison between anterior and totalcorneal J0. b Comparison between anterior and posterior corneal J0. J0=Jackson cross cylinder power at axis 0 and 90°

Fig. 2 Linear regression anlaysis of the relationship between anterior,posterior, and total corneal cylinder power. a Comparison between ante-rior and total corneal cylinder power. b Comparison between anterior andposterior corneal cylinder power

Graefes Arch Clin Exp Ophthalmol (2014) 252:1769–1777 1771

adjustment of the cylinder power of simulated K to match thetotal corneal cylinder power.

Statistical methods

Descriptive statistics for all patient data were obtained usingthe Statistical Package for the Social Sciences version 12.0(SPSS Inc., Chicago, IL, USA). Wilcoxon signed-rank testswere done to compare the cylinder power of the anteriorcorneal surface, simulated K, and total cornea, and the flatmeridian of the anterior corneal surface and total cornea.Pearson’s correlation analyses for parametric parameters,Spearman’s correlation analyses for non-parametric parame-ters, and linear regression analyses were performed to evaluatethe relationship between the mean cylinder power, vectorcomponents J0 and J45 of the anterior and posterior cornealsurfaces and the total cornea, AMDAnt-Post, and the cylinderpower differenceSimK-Tot. Multivariate linear regression anal-yses were performed to calculate the predictive factors for theposterior corneal cylinder power and the AMDAnt-Post throughseveral parameters which showed significant results fromunivariate linear regression analysis. Results were consideredstatistically significant if the p-valuewas <0.05.

Results

This study evaluated 99 eyes of 99 participants. Of the 99participants, 56 were men. Themean age was 37.9±13.0 years(range, 18–64 years). The mean corneal power, anterior cham-ber depth, and axial length measured by IOLMaster are shownin Table 1.

Table 2 shows the mean corneal power, cylinder power, flatmeridian, and J0 and J45 for anterior and posterior corneal

surfaces, and the total cornea. The mean anterior cornealsurface power was 48.43±2.05 D, mean posterior cornealsurface power was −6.36±0.29 D, and mean total cornealpower was 42.33±1.83 D. The mean anterior corneal cylinderpower (1.35±0.77 CD) was significantly larger than the totalcorneal cylinder power (1.10±0.66 CD) (P<0.001; Wilcoxonsigned-rank test). The cylinder power of simulated K, 1.21±0.70 D, was also significantly larger than the total cornealcylinder power, 1.10±0.66 D (P<0.001; Wilcoxon signed-rank test). However, there was no significant difference in theflat meridian between the anterior corneal surface (89±72°)and the total cornea (83±67°) (P=0.552; Wilcoxon signed-rank test).

Correlation coefficients of the J0, and J45 componentsshowed significant correlations among anterior and poste-rior corneal surfaces, and the total cornea (Table 3).Anterior and total corneal J0 had good correlations andhad either positive or negative values. However, the pos-terior corneal J0, with the exception of one case, all hadpositive values (Fig. 1). Both posterior and total cornealcylinder powers increased as the anterior corneal cylinderpower increased (Fig. 2).

The flat meridian of anterior cornea was horizontallyaligned in 71.7 % and was vertically aligned in 12.1 %. Theflat meridian of posterior cornea was horizontally aligned in94.0% and was vertically aligned in 0.0 % (Fig. 3). This resultindicates that almost all eyes had against-the-rule (ATR) astig-matism on the posterior corneal surface, instead of with-the-rule (WTR) astigmatism because the posterior corneal surfacehad a negative power. The aggregated mean astigmatism ofsimulated K was 0.84±0.74 at 180°, and that of total corneawas 0.58±0.76 at 1° (Fig. 4). The mean vector differencebetween the astigmatism of the simulated K and total corneawas 0.25±0.13 at 179° (Fig. 5).

Fig. 3 Location of anterior andposterior corneal flat meridian


The cylinder power differenceSimK-Tot was significantlypositively correlated with the posterior corneal cylinder power(Spearman’s rho=0.704 and P<0.001) and negatively corre-lated with the AMDAnt-Post (Spearman’s rho=−0.717 andP<0.001). When the posterior corneal cylinder power wassmaller than 0.21 D, the cylinder power differenceSimK-Tottended to be a negative value. In contrast, when the posteriorcorneal cylinder power was larger than 0.21 D, the cylinderpower differenceSimK-Tot tended to be a positive value(Fig. 6a). When the AMDAnt-Post was smaller than 30°, thecylinder power differenceSimK-Tot tended to be a positive val-ue. In comparison, when the AMDAnt-Post was larger than 30°,the cylinder power differenceSimK-Tot tended to be a negativevalue (Fig. 6b).

In the univariate linear regression analyses, age, axiallength, anterior corneal cylinder power, and anterior corneal

J0 were associated with the posterior corneal cylinder power.However, in the multivariate linear regression analysis, ante-rior corneal J0 was only strongly associated with the posteriorcorneal cylinder power (Table 4). Regarding the AMDAnt-Post,

age, anterior chamber depth, axial length, anterior and poste-rior corneal cylinder power, and anterior and posterior cornealJ0 were associated with the AMDAnt-Post in the univariatelinear regression analyses. However, in the multivariate linearregression analysis, anterior corneal J0 was proven to bestrongly associated with the AMDAnt-Post (Table 5). The cyl-inder power differenceSimK-Tot tended to be a positive valuewhen the anterior corneal J0 had a positive value. On the otherhand, when anterior corneal J0 had a negative value, thecylinder power differenceSimK-Tot showed the opposite trend.When the anterior corneal J0 was larger than 1.0 or smallerthan −0.9, the errors in estimating the total corneal cylinderpower from anterior corneal measurement tended to be largerthan 0.25 D (Fig. 6c).

According to the corrective regression formula, the corre-lation coefficient (β) was 0.88 in eyes with anterior corneal J0of larger than 0 and was 1.20 in eyes with anterior corneal J0 ofsmaller than 0 (Fig. 7). This indicated that a 12 % reduction ofcylinder power of simulated K is recommended in eyes withWTR astigmatism, and a 20 % addition of cylinder power ofsimulated K is recommended in eyes with ATR astigmatism.

Discussion

Total corneal astigmatism is mainly composed of anterior andposterior corneal surfaces. Although previous studies [13, 14]have reported satisfactory corneal astigmatism correction re-sults with toric intraocular lens (IOL) using conventionalkeratometers which estimated total corneal astigmatism from

Fig. 5 Double-angle plots of the vector difference between the astigma-tism of the simulated keratometry (K) and total cornea

Fig. 4 Double-angle plots of theastigmatism of the simulatedkeratometry (K) and total cornea.a Corneal astigmatism ofsimulated K. b Total cornealastigmatism


anterior corneal measurements [1], additional studies [2, 15,16] have demonstrated that neglecting posterior corneal astig-matism may lead to some errors in total corneal astigmatism.Therefore, if the errors in estimating total corneal astigmatismfrom anterior corneal measurement could be predicted by theanterior corneal measurement, this could be applied in practiceby many clinicians.

In the present study, we evaluated the effect of the magni-tude of posterior corneal astigmatism and the AMDAnt-Post onthe estimation of total corneal cylinder power using anterior

corneal measurements. We determined that the cylinder powerof simulated K tends to be larger than the total corneal cylinderpower as the AMDAnt-Post decreases or the posterior cornealcylinder power increases. In contrast, the cylinder power ofsimulated K tends to be smaller than the total corneal cylinderpower when the AMDAnt-Post increases or the posterior corne-al cylinder power decreases. As the posterior corneal surfacehas negative power, when anterior and posterior corneal sur-faces have the same flat axes, the steep axis power is reducedbymore than the flat axis power is; therefore, the magnitude of

Fig. 6 Linear regression anlaysis of the relationship between the poste-rior corneal cylinder power, absolute flat meridian difference betweenanterior and posterior corneal surfaces (AMDAnt-Post), anterior corneal J0,and the cylinder power difference between simulated keratometry (K) andtotal cornea (cylinder power differenceSimK-Tot). a Comparison between

the posterior corneal cylinder power and the cylinder powerdifferenceSimK-Tot. b Comparison between the AMDAnt-Post and cylinderpower differenceSimK-Tot. c Comparison between the anterior corneal J0and cylinder power differenceSimK-Tot


astigmatism in the total cornea is smaller. On the other hand,when anterior and posterior corneal surfaces have oppositeaxes, the flat axis power is reduced bymore than the steep axispower is, thus the magnitude of astigmatism in the total corneais larger.

Multivariate linear regression analysis indicated that onlythe anterior corneal J0 was strongly associated with the poste-rior corneal cylinder power and the AMDAnt-Post. Koch et al.[2] reported that 86.6 % of eyes had ATR astigmatism on theposterior corneal surface. However, in this study, 94.0 % ofeyes had ATR astigmatism on the posterior corneal surface.Because most eyes had a positive value of posterior corneal J0,the AMDAnt-Post was more significantly associated with ante-rior corneal J0 than posterior corneal J0. When anterior cornealJ0 has positive value, the cylinder power of simulated Ktended to be larger than total corneal cylinder power. Incomparison, when anterior corneal J0 had a negative value,the opposite trend was apparent. This finding is similar to thereport by Koch et al. [2].

Koch et al. [2] analyzed 715 eyes of 435 patients andreported that anterior corneal astigmatism was 1.20 D,posterior corneal astigmatism was 0.30 D, and total cornealastigmatism was 1.07 D. In the present study, the anteriorcorneal astigmatism was 1.35 D, posterior corneal astig-matism was 0.38 D, and the total corneal astigmatism was1.10 D. These are slightly larger than values from previousstudies [2, 5, 6]. This is likely because the range of agesand race were different in the present study and previousstudies [2, 5, 6].

The main reasons for the errors in estimating total cornealastigmatism from anterior corneal measurements, the magni-tude of posterior corneal astigmatism and the flat meridiandifference between anterior and posterior corneal surfaces,were only correlated with the anterior corneal J0. Thus, ac-cording to the anterior corneal J0, it can be determinedwhetherthe posterior corneal measurement required or not. If estima-tion error of more than 0.25 D for total corneal cylinder powerfrom anterior corneal measurements is thought to be

Table 4 Univariate and multi-variate adjusted predictive factorsfor the magnitude of posteriorcorneal astigmatism

CI confidence interval, J0 Jacksoncross cylinder power at axis 0 and90°, J45 Jackson cross cylinderpower at axis 45 and 135°a Stepwise variable selection onmultivariate linear regressionanalysis

Univariate regression analysis Multivariate regression analysisa

β 95 % CI P value β 95 % CI P value

Age −0.003 −0.005, 0.000 0.021

Anterior chamber depth 0.082 −0.002, 0.165 0.054

Axial length 0.035 0.014, 0.056 0.001

Anterior corneal radius −0.029 −0.129, 0.071 0.567

Anterior corneal cylinder power 0.109 0.073, 0.145 <0.001

Anterior corneal J0 0.202 0.157, 0.246 <0.001 0.202 0.157, 0.246 <0.001

Anterior corneal J45 0.045 −0.070, 0.159 0.438

Table 5 Univariate and multivariate adjusted predictive factors for the absolute flat meridian difference between anterior and posterior corneal surfaces

Univariate regression analysis Multivariate regression analysisa

β 95 % CI P value β 95 % CI P value

Age 0.788 0.493, 1.084 <0.001

Anterior chamber depth −25.264 −35.284, −15.244 <0.001

Axial length −4.852 −7.562, −2.141 0.001

Anterior corneal radius 10.406 −2.635, 23.446 0.117

Anterior corneal cylinder power −12.720 −18.332, −7.107 <0.001

Anterior corneal J0 −31.263 −37.497, −25.029 <0.001 −31.263 −37.497, −25.029 <0.001

Anterior corneal J45 −0.379 −15.550, 14.793 0.961

Posterior corneal radius 10.472 −4.548, 25.492 0.170

Posterior corneal cylinder power −50.803 −75.387, −26.218 0.001

Posterior corneal J0 −137.289 −188.142, −86.437 <0.001

Posterior corneal J45 40.015 −13.501, 93.531 0.141

CI confidence interval, J0 Jackson cross cylinder power at axis 0 and 90°, J45 Jackson cross cylinder power at axis 45 and 135°a Stepwise variable selection on multivariate linear regression analysis


meaningful to make a more precise astigmatism correction bytoric IOL, posterior corneal measurements should be conduct-ed in eyes with anterior corneal J0 larger than 1.0 or smallerthan −0.9. Therefore, in eyes with anterior corneal astigma-tism more than 2.0 D ofWTR astigmatism or more than 1.8 Dof ATR astigmatism, the measurement of posterior cornealsurface is needed.

Ho et al. [4] showed that the total and posterior cornealpowers can be more accurately predicted using theScheimpflug camera-derived keratometric index. Previous

studies have reported different ratios of the radius of theanterior corneal curvature to that of the posterior cornealcurvature [1, 17, 18]. Moreover, because total corneal astig-matism is also affected by the magnitude of posterior cornealastigmatism and the flat meridian difference between anteriorand posterior corneal surfaces, anterior corneal J0, which wasstrongly associated with these factors in this study, could beused to estimate the total corneal cylinder power. If the poste-rior corneal measurements were not available, a correctiveregression formula can be used to adjust the cylinder powerof simulated K, especially in eyes with an anterior corneal J0larger than 1.0 or smaller than −0.9. Based on our regressionformula, a 12 % reduction of cylinder power of simulated K isrecommended in eyes with corneal astigmatism greater than2.0 D ofWTR astigmatism, and 20% addition is recommend-ed in eyes with corneal astigmatism greater than 1.8 D of ATRastigmatism.

There are some limitations to this study. First, the samplesize was relatively small. Second, the mean age of participantsin this study was 38 years old with range from 18 to 64 yearsold. Corneal astigmatism shifts toward ATR from WTR withincreasing age [19, 20]. Therefore, the results of this studymight be more suitable to apply to relatively young patients,though the results of this study were quite similar to those ofKoch et al.’s previous study in which 715 eyes of 435 patientswere analyzed and the mean age was 55 years old with rangefrom 20 to 89 years old [2].

In conclusion, posterior corneal astigmatism should beconsidered for more accurate corneal astigmatism predictions,especially in eyes with an anterior corneal astigmatism greaterthan 2.0 D of WTR astigmatism or greater than 1.8 D of ATRastigmatism.

Conflicts of interest The authors have no financial or proprietaryinterest in any product, method, or material described herein.

Funding/Support This study was supported by the Basic ScienceResearch Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology(2012R1A1A2042054), Seoul, South Korea.

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Fig. 7 Linear regression anlaysis of the relationship between the cylinderpower of simulated keratometry (K) and total corneal cylinder poweraccording to anterior J0. a Comparison between the cylinder power ofsimulated K and total corneal cylinder power in eyes with anterior cornealJ0 larger than 0. bComparison of the cylinder power between simulated Kand total cornea in eyes with an anterior corneal J0 smaller than 0; J0=Jackson cross cylinder power at axis 0 and 90°


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the effect of posterior corneal flat meridian and astigmatism amount on the total corneal...

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