new approach for the calculation of the intraocular lens

Research ArticleNew Approach for the Calculation of the Intraocular Lens PowerBased on the Fictitious Corneal Refractive Index Estimation

Joaquın Fernandez12 Manuel Rodrıguez-Vallejo 1 Javier Martınez1 Ana Tauste1

and David P Pintildeero 34

1Department of Ophthalmology (Qvision) Vithas Virgen Del Mar Hospital 04120 Almerıa Spain2Department of Ophthalmology Torrecardenas Hospital Complex 04009 Almerıa Spain3Department of Optics Pharmacology and Anatomy University of Alicante Alicante Spain4Department of Ophthalmology Vithas Medimar International Hospital Alicante Spain

Correspondence should be addressed to David P Pintildeero davidpinyerouaes

Received 8 February 2019 Revised 4 April 2019 Accepted 28 April 2019 Published 14 May 2019

Guest Editor Damian Siedlecki

Copyright copy 2019 Joaquın Fernandez et al is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Purpose To identify the sources of error in predictability beyond the effective lens position and to develop two new thick lensequations Methods Retrospective observational case series with 43 eyes Information related to the actual lens position cornealradii measured with specular reflection and Scheimpflug-based technologies and the characteristics of the implanted lenses (radiiand thickness) were used for obtaining the fictitious indexes that better predicted the postoperative spherical equivalent (SE) whenthe real effective lens position (ELP) was known ese fictitious indexes were used to develop two thick lens equations that werecompared with the predictability of SRKTand Barrett Universal II Resultse SE relative to the intended target was correlated tothe difference between real ELP and the value estimated by SRKT (ΔELP) (rminus047 p 0002) but this only predicted 22 ofvariability in a linear regression model e fictitious index for the specular reflection (nk) and Scheimpflug-based devices (nc)were significantly correlated with axial length Including both indexes fitted to axial length in the prediction model with the ΔELPincreased the r-square of the model up to 83 and 39 respectively Equations derived from these fictitious indexes reduced themean SE in comparison to SRKT and Barrett Universal II Conclusions e predictability with the trifocal IOL evaluated is notexplained by an error in the ELP An adjustment fitting the fictitious index with the axial length improves the predictabilitywithout false estimations of the ELP

1 Introduction

Intraocular lens (IOL) power calculation formulas haveevolved since the publication of the Fyodorov formula in1967 [1 2] Nowadays there are several methods forcalculating the IOL power that can be classified in one ofthe following groups (1) historicalrefraction based (2)regression (3) vergence (4) artificial intelligence and (5)ray tracing [3] e first two approaches are considered outof date the artificial intelligence is growing in popularitybut not in predictability [4] and the ray tracing [5 6] is thepromising option that has not still replaced the most usedmethods based on the vergence formula An important

reason for the absence of a clear evidence of differencesbetween these previous three approaches is the inclusion ofsome regression components in all of them including raytracing [3] In fact the main difference between vergenceformulas is the number of variables used for estimating theeffective-thin lens position (ELPo) [7] ranging from two inSRKT Hoffer Q and Holladay I formulas to five or sevenin the Barrett Universal II or Holladay II formulas re-spectively [3]

ere are several studies that report the predictability ofvergence formulas for eyes with different axial lengths buthigh discrepancies are found in the percentage of eyeswithin plusmn050 D between studies [4 8ndash13] For instance

HindawiJournal of OphthalmologyVolume 2019 Article ID 2796126 9 pageshttpsdoiorg10115520192796126

Shrivastava et al [14] reported no differences between SRKTand the newer formulas in short eyes but a meta-analysisreported superiority of the Haigis formula [15] e realityis that there are no clinically relevant differences in thestatistics of centrality for the postoperative sphericalequivalent (SE) between equations and special attentionshould be taken in dispersion [10] is dispersion of thedata has been reported to be lower for the Barrett UniversalII which results in a higher percentage of eyes withinplusmn050 D in medium to long eyes [4 8ndash13] e BarrettUniversal II was born from the theoretical universal for-mula which considers the thick lens formula [16] and afteran estimation of the lens factor which is the distance fromthe iris to the second principal plane of the IOL [17]erefore the thin lens formula can be used consideringthe ELPo as the anterior chamber depth (ACD) plus the lensfactor which can be derived from the A-constant [17]Other authors have used the terms surgeon factor [18] oroffset [19] instead of lens factor but the aim of theseconstants was the same to estimate the location of thesecond principle plane of the IOL optic from a relativelyfixed anatomical reference plane and to compute the ELPoby means of this factor [16]

If the intended preoperative spherical equivalent (SE)and the postoperative SE are not equal the constantsimplemented by different formulas can be optimized forimproving refractive results in eyes with different axiallengths [20 21] but this may contribute to an error in theELPo if the lens position is not measured during thepostoperative follow-up e aim of this study was toevaluate if the postoperative SE after implantation of atrifocal IOL was due to an error in the ELPo estimated withthe SRKT formula and if this was not the reason toidentify the possible sources of error For this purpose theactual lens position (ALP) of each eye was measured aftersurgery and the thick lens formula [22] was used to avoidthe optical approximations required by the vergence for-mula [2]

2 Materials and Methods

21 Subjects and Procedures e study was approved by thelocal Ethics Committee and was performed in adherence tothe tenets of the Declaration of Helsinki Data from 43subjects measured at the 3-month follow-up visit wereretrospectively retrieved from our historical database in-cluding only one eye randomly in the analysis e to-mography obtained at this visit with the Pentacam HR(Oculus Wetzlar Germany) was used for collecting dataincluding anterior (r1c) and posterior corneal radii (r2c)corneal thickness (ec) and ALP measured from cornealvertex (anterior corneal surface) to the anterior IOL surfacee axial length (AXL) the preoperative ACD and theanterior corneal radius (rk) were retrieved from the mea-surements obtained with the IOLMaster 500 system (CarlZeiss Meditec AG Germany) e postoperative bestspectacle refraction was also obtained for each eye com-puting the SE e pupil diameter for the conditions forwhich the refraction was performed (around 90 lux) was

estimated as the mean between photopic and mesopic pupilsmeasured with the Keratograph 5M system (Oculus Wet-zlar Germany)

22 Surgery Procedure All surgeries were conducted by thesame surgeon (X) by means of phacoemulsification orfemtosecond laser-assisted cataract surgery (Victus Bauschamp Lomb Inc Dornach Germany) through clear cornealincisions of 22mm for manual incisions or 25mm for laserincisions both at temporal location e implanted IOL atcapsular bag was the Liberty Trifocal (Medicontur MedicalEngineering Ltd Inc Zsambek Hungary) based on theelevated phase shift (EPS) technology which is an aspherichydrophilic IOL with +350D of addition for near and+175D for intermediate at the IOL plane e preoperativecalculation of the IOL power was conducted with the SRKT[19] formula considering the manufacturer recommendedconstant of 1189

231ickLensFormula All the calculations were conductedby means of paraxial optics and coupling the measuredoptical structures with the thick lens formula [22] Someapproaches were conducted depending on the system usedto measure the cornea For the anterior corneal radius (rk)obtained with IOLMaster the corneal power in equation (1)(Pk) should be estimated with a fictitious index (nk) and thecornea was considered as a single dioptric surface thereforecorneal principal planes were approximated to the anteriorcorneal surface (Figure 1(a)) For the measurement of bothcorneal radii (r1c and r2c) and corneal thickness (ec) with thePentacam (Figure 1(b)) the total corneal power was com-puted with equation (2) and corneal principal planes werecalculated since the cornea was considered as a thick lens(Figure 1(b)) [22]

Pk nk minus 1

rk (1)

Pc nc minus 1

r1c+13374minus nc

r2cminus

ec

nc1113888 1113889

nc minus 1r1c

1113888 111388913374minus nc

r2c1113888 1113889

(2)

e characteristics of the IOL implanted in each patientwere provided by the manufacturer including thickness andanterior and posterior radii (these are not detailed in theresults as they were required to be kept as confidential by themanufacturer) erefore the principal planes were alsocalculated for the IOLs (Figure 1) Finally to calculate theequivalent lens for the coupling of the cornea and the IOL itwas required to define the distances between both opticalstructures (ELP) taking the principal planes as the referenceif possible (Figure 1(b)) or the anterior cornea location whenthe cornea was considered as a thin lens (Figure 1(a))Different approximations for the real effective lens positiondepending on the principal planes location were consideredfrom corneal vertex to second IOL principal plane (equation(3) Figure 1(a)) from second corneal principal plane to firstIOL principal plane (equation (4) Figure 1(b)) and from

2 Journal of Ophthalmology

corneal vertex to rst IOL principal plane (equation (5)Figure 1(a))

ELPo ALP +H2l (3)

ELPc ALPminusH2c +H1l (4)

ELPk ALP +H1l (5)

While equation (3) was the real ELPo that should bepredicted for the vergence formula [2] the other two wereused in the thick lens formula depending if both cornealsurfaces radii (ELPc) (equation (4)) or only anterior cornealradius (ELPk) (equation (5)) were used

e SRKT is a vergence formula therefore it predictswhat would be the ELPo (equation (3)) considering thebiometric eye parameters and an A-constant associated to

the IOL As we measured the postoperative ALP and cal-culated the principal planes of the IOL we can calculate thedierence between the ELPo estimated preoperatively by theSRKT formula (hereinafter abbreviated as ELPSRKT) [19]and the real ELPo calculated postoperatively (equation (3))(ΔELPELPSRKTminusELPo) e correlation between ΔELPand the postoperative SE was computed in order to assess theamount of postoperative SE explained by an error in theELPo estimation by the SRKT formula

e predictability obtained with SRKT and the pre-dictability that would have expected if Barrett Universal II(white to white and lens thickness not considered) [23] hadbeen used were compared with those achievable with thetwo thick lens equations for which the corneal power wasderived from the measures of the anterior corneal radiusmeasured with the IOLMaster (equation (1) Figure 1(a))or both corneal surfaces measured with the Pentacam

rkrrnk

ELPk

ELPo

13374 1336

H2lH1l

(a)

nc

ec

13374 1336

H2c H1c

r1c r2c

ALP

ELPc

H2lH1l

(b)

Figure 1 (a) Model for the calculation of the corneal power derived from anterior corneal radius (rk) and ctitious index (nk) e eectivelens positions for vergence thin lens formula (ELPo) and for thick lens formula (ELPk) are shown 13374 and 1336 are the refractive indexesfor the aqueous and vitreous respectively (b) Schema for computing the IOL power based on the thick lens formula both anterior (r1c) andposterior (r2c) corneal radii were measured and total corneal power was obtained estimating refractive index of the cornea (nc) Actual lensposition (ALP) and eective lens position (ELPc) from principal planes are represented H1c H2c H1l and H2l are the rst and secondprincipal planes for the cornea and the IOL

Journal of Ophthalmology 3

(equation (2) Figure 1(b)) For this purpose the post-operative SE refraction was adjusted to the intended targetrefraction computed by each formula for the implantedIOL power [24 25]

24 Fictitious Indexes e fictitious indexes were definedas the refractive indexes used for computing the cornealpower that better predicts the postoperative SE aftersurgery when the real ELP is known Considering that thecorneal radii ELP AXL and the IOL characteristics (radiiand thickness) were known after surgery the only vari-able for predicting the postoperative SE with the thicklens formula was the fictitious index erefore an it-erative process was conducted for obtaining these indexesconsidering two possibilities (1) the corneal power wasderived from a fictitious index (nc) considering anteriorand posterior corneal radii and corneal thickness(Figure 1(a)) and (2) the corneal power was derived froma fictitious index (nk) and the anterior corneal radius(Figure 1(b)) is kind of iterative processes has beenused for finding the best constant that predicts best thedifference between the intended and the actual SE [20]However it should be considered that the purpose ofrefining constants is to correct wrong estimations ofELPo In our study as the real ELPo was known otherunknown sources of error were investigated and adjustedby modifying the corneal power through the fictitiousrefractive indexes

25 Statistical Analysis e normality of data distributionsfor the variables evaluated was tested with the ShapirondashWilktest and parametric statistics were selected for testing hy-pothesis only if the assumptions were met Correlations wereevaluated with the Pearson r test and the paired t-test wasused for testing differences between real ELPo and ELPSRKTe thick lens equation [22] and all the functions required toestimate the fictitious indexes by means of iteration pro-cesses were implemented in MATLAB (Mathworks IncNatick MA) e statistical analyses were performed usingthe IBM SPSS 240 software for Windows (SPSS ChicagoIL) Meanplusmn standard deviation [median (interquartilerange)] is used in Section 3 for reporting central tendencyand data dispersion

3 Results

Mean age of the sample was 68plusmn 8 [70 (7)] years old eΔELP was significantly correlated with the postoperative SErelative to the intended target (rminus047 p 0002)(Figure 2(a)) A linear regression model predicted that the22 of the variability in the postoperative SE was explainedby an error estimation of the ELPo [F(1 41) 11308p 0002 R2 022] No significant correlations of ΔELPwere found with AXL (r 023 p 015) and preoperativeACD (rminus023 p 014) e real ELPo was 505plusmn 029[502 (032)]mm and the ELPSRKT was 536plusmn 031 [539(034)]mm (t 7336 plt 00005) e anterior corneal ra-dius measured by specular reflection (rk) overestimated the

value measured by the Scheimpflug-based devices in003plusmn 005 [003 (005)]mm (t 349 p 0001) and thedifference was correlated with the average of both measures(rminus036 p 002) (Figure 2(b))

Mean fictitious refractive indexes for nk and nc were1336plusmn 0003 [1336 (0004)] and 1339plusmn 0017 [1336(0021)] respectively ese indexes were correlated with theaxial length of the eye for both nc (r 049 p 0001)(Figure 3(a)) and nk (rminus033 p 003) (Figure 3(b)) Amultiple linear regression model for predicting post-operative SE relative to the intended target was conductedincluding ΔELP and nk or nc e r-square increased from022 to 083 after including nk [F(2 40) 99425 plt 00005R2 083] and from 022 to 039 after including nc [F(240) 1278 plt 00005 R2 039] in the regression incombination with ΔELP (Table 1)

Two thick equations were developed considering differentfictitious indexes depending on axial length For the thick lensequation considering anterior corneal radius (nk equation)nk 1339 was used for eyesle 22mm nk 1336 for eyes from22 to 245mm and nk 1333 for eyesge 245mm For thethick lens equation considering anterior and posterior cornealradii nc 1328 was used for eyes le22mm nc 1339 for eyesfrom 22 to 245mm and nc 1350 for eyes ge245mm Amultiple linear regression was conducted for predicting ALPconsidering preoperative ACD and AXL obtaining the fol-lowing equation for ALP 0527middotACD+0102middotAXL+041[F(2 40) 5720 plt 00005 R2 074] e predicted ALPinstead of the real measured ALP was used for computing thepredictability with both thick lens equations since the ALPshould be estimated before surgery

Postoperative SE relative to the intended target wasminus012plusmn 038 [minus011 (050)] D for the SRKT (Figure 4(a))minus020plusmn 033 [minus024 (054)] D for Barrett Universal II(Figure 4(b)) minus001plusmn 041 [minus005 (062)] D for nk equation(Figure 4(c)) and minus002plusmn 040 [001 (057)] D for nc equation(Figure 4(d)) e predictability was significantly correlatedwith pupil diameter for nc equation (rminus050 p 0001)(Figure 4(e)) and for nk equation (rminus051 plt 00005)(Figure 4(f )) A similar correlation but of less strength wasfound for Barrett Universal II (rminus031 p 004) but notfor SRKT (rminus004 p 079)

4 Discussion

Optical biometers use the keratometric index (13375) forcomputing the corneal power from anterior corneal radiusHowever it is well known that this keratometric index isfar from being the one which better predicts the post-operative SE and current formulas use a fictitious re-fractive index from 13315 to 1336 close to the tear filmrefractive index which results in better postoperative SEpredictions [7] e formula used for calculating the IOLpower in this study (SRKT) uses a fictitious index of 1333which is within this range It is well known that SRKTformula as any other formulas reduces the predictabilityin more or less degree depending on the axial length of theeye corneal power and other variables [10] In our studywe found that an estimated error in the ELPo with the


SRKT formula explained 22 of the variability in thepostoperative SE but a higher percentage of errorremained unknown It is important to note that in theregression of Figure 2(a) we maintained an outlier in the

analysis corresponding to the highest postoperativespherical equivalent of minus150 D is value can aect the r-square value due to the small sample For this reason werecomputed the regression equation omitting the outlierand the r-square value decreased to 15 (p 001) ismeans that the variability explained by a wrong estimationof the ELPo might be even lower

Interestingly we found that when real ELPo is knownthe ctitious index can be tted in order to reduce thepredictability error that was not attributed to the ELPo Ourmean refractive index for computing corneal power andderiving from anterior corneal surface was nk 1336 thathas been historically reported by Holladay to be close to thetear lm [7 26] By contrast nc 1339 was found whenanterior and posterior corneal radii were considered e

nc = 0007 lowast AXL + 117R2 = 024 (p = 0001)

1300

1310

1320

1330

1340

1350

1360

1370

1380

Corr

ecte

d co

rnea

l ref

ract

ive i

ndex

(nc)

21 22 23 24 25 26 2720Axial length (mm)

(a)

nk = ndash0001 lowast AXL + 1357R2 = 011 (p = 003)

1328

133

1332

1334

1336

1338

134

1342

Corr

ecte

d ke

rato

met

ric in

dex

(nk)

1344

21 22 23 24 25 26 2720Axial length (mm)

(b)

Figure 3 Correlations between the ctitious index (nc) that minimize the postoperative SE for a known eective lens position consideringboth corneal radii and thickness (a) and the ctitious index (nk) derived from the anterior corneal radius (b)

Table 1 Multiple regression linear models for prediction ofpostoperative SE relative to the intended target

Variable B SEB β t p

Intercept 15455 1273 1214 lt00005ΔELP (mm) minus144 011 minus107 minus1310 lt00005nk minus11545 952 minus099 minus1213 lt00005Intercept minus1410 420 0002ΔELP (mm) minus098 020 minus073 minus499 lt00005nc 1067 316 050 338 0002

SE = ndash062 lowast ∆ELP ndash 008R2 = 022 (p = 0002)

ndash20

ndash15

ndash10

ndash05

0

05

1Po

stope

rativ

e sph

eric

al eq

uiva

lent

(D)

07

08

04

ndash01 0

01

02

03

06

ndash03 05

ndash04

ndash02 09 1

ndash05

∆ELP = ELPSRKT ndash ELPo (mm)

(a)

ndash007

012

003

ndash015

ndash010

ndash005

000

005

010

015

020

025

r kndashr 1

c (m

m)

82

76

80

84

72

74

78

Average rk and r1c (mm)

(b)

Figure 2 (a) Postoperative spherical equivalent relative to the intended target for the SRKTversus the dierence between the eective lensposition estimated by the SRKTformula (ELPSRKT) and the real obtained from themeasurement of the actual lens position and the locationof the second principal plane of the IOL (ELPo) (b) Agreement between anterior corneal radius measured with IOLMaster (rk) andPentacam HR (r1c)


latter nding is also quite important because ray tracing andtotal corneal refractive power have not demonstratedas theoretically expected to provide better predictabilitythan current formulas [27ndash30] From our results it can be

concluded that a ctitious index is required for computingcorneal power derived from anterior corneal radius whereasa dierent ctitious index is required for total corneal powercalculation

0 0 29

3530

19

5 0 0 0

43 eyes3 months postop plusmn100D98

plusmn050D84

0

20

40

60

80

100

of e

yes

ltndash2

00

gt+2

00

ndash20

0 to

ndash1

51

ndash15

0 to

ndash1

01

ndash10

0 to

ndash0

51

ndash05

0 to

ndash0

14

ndash01

3 to

+0

13

+01

4 to

+0

50

+05

1 to

+1

00

+10

1 to

+1

50

+15

1 to

+2

00

Postoperative spherical equivalent refraction (D)

(a)

0 0 212

42

23 21

0 0 0 0

3 months postop43 eyes

plusmn100D98plusmn050D86

0

20

40

60

80

100

o

f eye

s

ltndash2

00

gt+2

00

ndash20

0 to

ndash1

51

ndash15

0 to

ndash1

01

ndash10

0 to

ndash0

51

ndash05

0 to

ndash0

14

ndash01

3 to

+0

13

+01

4 to

+0

50

+05

1 to

+1

00

+10

1 to

+1

50

+15

1 to

+2

00


(b)

0 0 09

28 28 26

90 0 0


plusmn050D82

ltndash2

00

gt+2

00

ndash20

0 to

ndash1

51

ndash15

0 to

ndash1

01

ndash10

0 to

ndash0

51

ndash05

0 to

ndash0

14

ndash01

3 to

+0

13

+01

4 to

+0

50

+05

1 to

+1

00

+10

1 to

+1

50

+15

1 to

+2

00

0

20

40

60

80

100

o

f eye

s


(c)

0 0 010

23

35

1913

0 0 0


plusmn100D100plusmn050D 77

ltndash2

00

gt+2

00

ndash20

0 to

ndash1

51

ndash15

0 to

ndash1

01

ndash10

0 to

ndash0

51

ndash05

0 to

ndash0

14

ndash01

3 to

+0

13

+01

4 to

+0

50

+05

1 to

+1

00

+10

1 to

+1

50

+15

1 to

+2

00

0

20

40

60

80

100

o

f eye

s


(d)

ndash1

ndash075

ndash05

ndash025

0

025

05

075

1

Posto

pera

tive s

pher

ical

equi

vale

nt (D

)

25 3 35 4 452

Pupil diameter (mm)

(e)

ndash1

ndash075

ndash05

ndash025

0

025

05

075

1

Posto

pera

tive s

pher

ical

equi

vale

nt (D

)

25 3 35 4 452

Pupil diameter (mm)

(f )

Figure 4 Postoperative spherical equivalent relative to the intended target for (a) SRKT (b) Barrett Universal II (c) nk equation and (d) ncequation (D) Correlations between the postoperative spherical equivalent relative to the intended target and the pupil diameter for (e) ncequation and (f) nk equation


Fictitious indexes were correlated with AXL suggestingthat fitting these refractive indexes depending on the axiallength the predictability can be increased without over-estimating or underestimating the ELP from its real valuee inclusion of nk with ΔELP in the model of prediction ofpostoperative SE relative to the intended target explained83 of the variability instead of 22 By contrast the in-clusion of nc with ΔELP in the model of prediction ofpostoperative SE after target correction explained 39 ofvariability is means that even though improving theprediction of the real ELP there would be some error in thepostoperative SE that can be corrected by means of modi-fying de fictitious index and then the corneal power Fur-thermore even though both approaches can improve thepredictability the corneal power derived from specularreflection devices would lead to better results [31] Possiblyspecular reflection devices compute the radius over the tearfilm whereas with Scheimpflug devices tear film is ignoredIn fact we found that the difference in the anterior cornealradius measured with Pentacam HR and IOLMaster systemswas correlated with the average from both measures sug-gesting that some caution should be considered when usingequations derived from measurements of different devices

A very important consideration is to evaluate the modeof change of these fictitious indexes between different ap-proaches to compute the corneal power Whereas nk de-creased with the increase of axial length and nc increased inthe opposite direction but with an overestimation of thecorneal power with the increase of AXL in both cases isoverestimation can be corrected by means of decreasing nkor increasing nc with the increment of AXL Our results areconsistent with those reported by Preussner et al [32] whofound an hyperopic outcome in very long eyes (gt28mm)and this was attributed to an overestimation of the cornealpower that can be compensated in normal eyes with asystematically overestimated ELP but not being possible invery long eyes In fact even though our sample does notinclude very long eyes applying our linear regression for aneye of 30mm we obtained the fictitious refractive index(nk 1327) proposed by Preussner et al [32] for very longeyes

emean postoperative SE relative to the intended targetwith the thick lens formulas derived from the study wasreduced in comparison to SRKT or Barrett Universal IIboth showing a myopic shift that can be explained by theoverestimation of ELPo with SRKT e higher was theELPo the lower was the eye power and consequently anoverestimation of ELPo led to an underestimation of eyepower leading to an overestimating of the required IOLpower and resulting in a myopic shift While the percentageof eyes within plusmn050D was higher for SRKT and BarrettUniversal II the percentage of eyes within plusmn100D was 100for both thick formulas with better predictability with nkequation in comparison to nc equation e most interestingfinding is that the percentage of cases with an error higherthan plusmn050D corresponded to eyes with the highest andlowest pupil diameters suggesting that a hyperopic shift canbe estimated by the formula as a consequence of the presenceof small pupils focusing the image in front of the retina with

the opposite trend for large pupils is suggests that usingthese formulas with the trifocal IOL evaluated in our series atrend to plus target should be used in patients with smallerpupils and to a minus target in eyes with larger pupils aschoosing a negative target in small pupils can lead to highermyopic residuals than those predicted by the formula andvice versa is reasoning can be also valid for BarrettUniversal II after constant fitting but not for SRKT forwhich the correlation with pupil diameter was not signifi-cantly manifested

is study is a first approach for the development ofnew thick lens equations that can be used when measuringthe corneal geometry with specular reflection orScheimpflug-based devices but it has some limitations thatshould be considered First the small sample for a par-ticular surgeon supposes that the ALP prediction formulamight not be transferable to other surgeons Highersamples with results obtained from different surgeons arerequired for a general estimation of the ALP Second thesample included eyes with AXL ranging from 2096 to2635mm and therefore with low number of short and longeyes in comparison to medium or medium-long eyesAlthough the tendency of nk and nc is clear with axiallength an improvement in the estimation of the fictitiousindexes would be obtained by increasing the number ofeyes especially for short long and very long eyes Finallythe predictability of these new formulas has been computedin the same sample for which they were developed eperformance of new studies with these formulas in a dif-ferent sample for confirming the results of predictability isneeded In fact in our opinion future crossover studies arerequired assigning different formulas to uniform groupsinstead of predicting what would have happened if differentformulas had been used as the current comparative studiesof formulas are doing

In conclusion in this study we have demonstrated thatthe postoperative SE with some of the current vergenceformulas can be due to the result of an underestimation oroverestimation of the real ELP However even if the real ELPwas perfectly predicted before surgery some postoperativeSE can appear depending on axial length is could becorrected by means of fitting the constant of the formulaleading to a false ELP prediction or by means of optimizingthe fictitious indexes for different axial lengths We have alsodemonstrated that the second option reduces the meanpostoperative SE either for specular reflection devices orScheimpflug-based devices However it is important toconsider that the slopes of correlation between both ap-proaches are of opposite sign Another very interestingfinding is that higher errors of predictability can be due topupil diameter changes during refraction with the usedmultifocal intraocular lens We suggest to include the pupildiameter in predictability studies for exploring this findingwith other multifocal or monofocal IOLs

Data Availability

e data supporting the results of the current article areavailable from the corresponding author upon request


Disclosure

Dr Fernandez is a consultant from Medicontur MedicalEngineering Ltd Inc Zsambek Hungary Remaining au-thors declare nothing to disclose

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e authors thank Medicontur Medical Engineering LtdInc Zsambek Hungary for provide the information re-quired about the Liberty Trifocal in order to conduct thisstudy

References

[1] S N Fyodorov and A Kolinko ldquoEstimation of optical powerof the intraocular lensrdquo Vestnik Oftalmologii vol 80pp 27ndash31 1967

[2] S N Fyodorov M A Galin and A Linksz ldquoCalculation ofthe optical power of intraocular lensesrdquo Investigative Oph-thalmology vol 14 pp 625ndash628 1975

[3] D D Koch W Hill A Abulafia and L Wang ldquoPursuingperfection in intraocular lens calculations I Logical approachfor classifying IOL calculation formulasrdquo Journal of Cataractamp Refractive Surgery vol 43 no 6 pp 717-718 2017

[4] J X Kane A Van Heerden A Atik and C PetsoglouldquoAccuracy of 3 new methods for intraocular lens power se-lectionrdquo Journal of Cataract amp Refractive Surgery vol 43no 3 pp 333ndash339 2017

[5] P-R Preussner J Wahl H Lahdo B Dick and O FindlldquoRay tracing for intraocular lens calculationrdquo Journal ofCataract amp Refractive Surgery vol 28 no 8 pp 1412ndash14192002

[6] H Jin T Rabsilber A Ehmer et al ldquoComparison of ray-tracing method and thin-lens formula in intraocular lenspower calculationsrdquo Journal of Cataract amp Refractive Surgeryvol 35 no 4 pp 650ndash662 2009

[7] J T Holladay ldquoStandardizing constants for ultrasonic bi-ometry keratometry and intraocular lens power calcula-tionsrdquo Journal of Cataract amp Refractive Surgery vol 23 no 9pp 1356ndash1370 1997

[8] S E Gokce I Montes De Oca D L Cooke L WangD D Koch and Z Al-Mohtaseb ldquoAccuracy of 8 intraocularlens calculation formulas in relation to anterior chamberdepth in patients with normal axial lengthsrdquo Journal ofCataract amp Refractive Surgery vol 44 no 3 pp 362ndash3682018

[9] T V Roberts C Hodge G Sutton and M LawlessldquoComparison of hill-radial basis function Barrett Universaland current third generation formulas for the calculation ofintraocular lens power during cataract surgeryrdquo Clinical ampExperimental Ophthalmology vol 46 no 3 pp 240ndash2462018

[10] R B Melles J T Holladay and W J Chang ldquoAccuracy ofintraocular lens calculation formulasrdquo Ophthalmologyvol 125 no 2 pp 288ndash294 2018

[11] Q Wang W Jiang T Lin et al ldquoAccuracy of intraocular lenspower calculation formulas in long eyes a systematic review

and meta-analysisrdquo Clinical amp Experimental Ophthalmologyvol 46 no 7 pp 738ndash749 2018

[12] J X Kane A Van Heerden A Atik and C PetsoglouldquoIntraocular lens power formula accuracy comparison of 7formulasrdquo Journal of Cataract amp Refractive Surgery vol 42no 10 pp 1490ndash1500 2016

[13] D L Cooke and T L Cooke ldquoComparison of 9 intraocularlens power calculation formulasrdquo Journal of Cataract amp Re-fractive Surgery vol 42 no 8 pp 1157ndash1164 2016

[14] A K Shrivastava P Behera B Kumar and S NandaldquoPrecision of intraocular lens power prediction in eyes shorterthan 22 mm an analysis of 6 formulasrdquo Journal of Cataract ampRefractive Surgery vol 44 no 11 pp 1ndash4 2018

[15] Q Wang W Jiang T Lin X Wu H Lin and W ChenldquoMeta-analysis of accuracy of intraocular lens power calcu-lation formulas in short eyesrdquo Clinical amp ExperimentalOphthalmology vol 46 no 4 pp 356ndash363 2018

[16] G D Barrett ldquoIntraocular lens calculation formulas for newintraocular lens implantsrdquo Journal of Cataract amp RefractiveSurgery vol 13 no 4 pp 389ndash396 1987

[17] G D Barrett ldquoAn improved universal theoretical formula forintraocular lens power predictionrdquo Journal of Cataract ampRefractive Surgery vol 19 no 6 pp 713ndash720 1993

[18] J T Holladay K H Musgrove T C Prager J W LewisT Y Chandler and R S Ruiz ldquoA three-part system forrefining intraocular lens power calculationsrdquo Journal ofCataract amp Refractive Surgery vol 14 no 1 pp 17ndash24 1988

[19] J A Retzlaff D R Sanders and M C Kraff ldquoDevelopment ofthe SRKT intraocular lens implant power calculation for-mulardquo Journal of Cataract amp Refractive Surgery vol 16 no 3pp 333ndash340 1990

[20] P Aristodemou N E Knox Cartwright J M Sparrow andR L Johnston ldquoIntraocular lens formula constant optimi-zation and partial coherence interferometry biometry re-fractive outcomes in 8108 eyes after cataract surgeryrdquo Journalof Cataract amp Refractive Surgery vol 37 no 1 pp 50ndash622011

[21] J C Merriam E Nong L Zheng and M Stohl ldquoOptimi-zation of the A constant for the SRKTformulardquoOpen Journalof Ophthalmology vol 5 no 3 pp 108ndash114 2015

[22] S Schwartz ldquoick lensesrdquo in Geometrical and Visual OpticsChapter 6 pp 77ndash88 McGraw Hill Medical (ed) New YorkNY USA 2002

[23] ldquoAPACRS calculator Barrett Universal II formula v1rdquoDecember 2018 httpswwwapacrsorgbarrett_universal2

[24] D Z Reinstein T J Archer S Srinivasan et al ldquoStandard forreporting refractive outcomes of intraocular lens-based re-fractive surgeryrdquo Journal of Cataract amp Refractive Surgeryvol 43 no 4 pp 435ndash439 2017

[25] D Z Reinstein T J Archer S Srinivasan et al ldquoStandard forreporting refractive outcomes of intraocular lens-based re-fractive surgeryrdquo Journal of Refractive Surgery vol 33 no 4pp 218ndash222 2017

[26] J T Holladay and K J Maverick ldquoRelationship of the actualthick intraocular lens optic to the thin lens equivalentrdquoAmerican Journal of Ophthalmology vol 126 no 3pp 339ndash347 1998

[27] G Savini K Negishi K J Hoffer and D Schiano LomorielloldquoRefractive outcomes of intraocular lens power calculationusing different corneal power measurements with a newoptical biometerrdquo Journal of Cataract amp Refractive Surgeryvol 44 no 6 pp 701ndash708 2018


[28] G Savini K J Hoffer D Schiano Lomoriello and P DucolildquoSimulated keratometry versus total corneal power by raytracingrdquo Cornea vol 36 no 11 pp 1368ndash1372 2017

[29] O Reitblat A Levy G Kleinmann A Abulafia andE I Assia ldquoEffect of posterior corneal astigmatism on powercalculation and alignment of toric intraocular lenses com-parison of methodologiesrdquo Journal of Cataract amp RefractiveSurgery vol 42 no 2 pp 217ndash225 2016

[30] T B Ferreira P Ribeiro F J Ribeiro and J G OrsquoNeillldquoComparison of methodologies using estimated or measuredvalues of total corneal astigmatism for toric intraocular lenspower calculationrdquo Journal of Refractive Surgery vol 33no 12 pp 794ndash800 2017

[31] Y Mejıa-Barbosa and D Malacara-Hernandez ldquoA review ofmethods for measuring corneal topographyrdquo Optometry andVision Science vol 78 no 4 pp 240ndash253 2001

[32] P Preussner P Hoffmann and J Wahl ldquoIntraocular lens(IOL) calculation in very long eyesrdquo in Proceedings of the 36thCongress of the ESCRS Wien Austria September 2018


Stem Cells International

Hindawiwwwhindawicom Volume 2018


MEDIATORSINFLAMMATION

of

EndocrinologyInternational Journal of



Disease Markers


BioMed Research International

OncologyJournal of



Oxidative Medicine and Cellular Longevity


PPAR Research

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Immunology ResearchHindawiwwwhindawicom Volume 2018

Journal of

ObesityJournal of



Computational and Mathematical Methods in Medicine


Behavioural Neurology

OphthalmologyJournal of


Diabetes ResearchJournal of



Research and TreatmentAIDS


Gastroenterology Research and Practice


Parkinsonrsquos Disease

Evidence-Based Complementary andAlternative Medicine

Volume 2018Hindawiwwwhindawicom

Submit your manuscripts atwwwhindawicom

Shrivastava et al [14] reported no differences between SRKTand the newer formulas in short eyes but a meta-analysisreported superiority of the Haigis formula [15] e realityis that there are no clinically relevant differences in thestatistics of centrality for the postoperative sphericalequivalent (SE) between equations and special attentionshould be taken in dispersion [10] is dispersion of thedata has been reported to be lower for the Barrett UniversalII which results in a higher percentage of eyes withinplusmn050 D in medium to long eyes [4 8ndash13] e BarrettUniversal II was born from the theoretical universal for-mula which considers the thick lens formula [16] and afteran estimation of the lens factor which is the distance fromthe iris to the second principal plane of the IOL [17]erefore the thin lens formula can be used consideringthe ELPo as the anterior chamber depth (ACD) plus the lensfactor which can be derived from the A-constant [17]Other authors have used the terms surgeon factor [18] oroffset [19] instead of lens factor but the aim of theseconstants was the same to estimate the location of thesecond principle plane of the IOL optic from a relativelyfixed anatomical reference plane and to compute the ELPoby means of this factor [16]

If the intended preoperative spherical equivalent (SE)and the postoperative SE are not equal the constantsimplemented by different formulas can be optimized forimproving refractive results in eyes with different axiallengths [20 21] but this may contribute to an error in theELPo if the lens position is not measured during thepostoperative follow-up e aim of this study was toevaluate if the postoperative SE after implantation of atrifocal IOL was due to an error in the ELPo estimated withthe SRKT formula and if this was not the reason toidentify the possible sources of error For this purpose theactual lens position (ALP) of each eye was measured aftersurgery and the thick lens formula [22] was used to avoidthe optical approximations required by the vergence for-mula [2]

2 Materials and Methods

21 Subjects and Procedures e study was approved by thelocal Ethics Committee and was performed in adherence tothe tenets of the Declaration of Helsinki Data from 43subjects measured at the 3-month follow-up visit wereretrospectively retrieved from our historical database in-cluding only one eye randomly in the analysis e to-mography obtained at this visit with the Pentacam HR(Oculus Wetzlar Germany) was used for collecting dataincluding anterior (r1c) and posterior corneal radii (r2c)corneal thickness (ec) and ALP measured from cornealvertex (anterior corneal surface) to the anterior IOL surfacee axial length (AXL) the preoperative ACD and theanterior corneal radius (rk) were retrieved from the mea-surements obtained with the IOLMaster 500 system (CarlZeiss Meditec AG Germany) e postoperative bestspectacle refraction was also obtained for each eye com-puting the SE e pupil diameter for the conditions forwhich the refraction was performed (around 90 lux) was

estimated as the mean between photopic and mesopic pupilsmeasured with the Keratograph 5M system (Oculus Wet-zlar Germany)

22 Surgery Procedure All surgeries were conducted by thesame surgeon (X) by means of phacoemulsification orfemtosecond laser-assisted cataract surgery (Victus Bauschamp Lomb Inc Dornach Germany) through clear cornealincisions of 22mm for manual incisions or 25mm for laserincisions both at temporal location e implanted IOL atcapsular bag was the Liberty Trifocal (Medicontur MedicalEngineering Ltd Inc Zsambek Hungary) based on theelevated phase shift (EPS) technology which is an aspherichydrophilic IOL with +350D of addition for near and+175D for intermediate at the IOL plane e preoperativecalculation of the IOL power was conducted with the SRKT[19] formula considering the manufacturer recommendedconstant of 1189

231ickLensFormula All the calculations were conductedby means of paraxial optics and coupling the measuredoptical structures with the thick lens formula [22] Someapproaches were conducted depending on the system usedto measure the cornea For the anterior corneal radius (rk)obtained with IOLMaster the corneal power in equation (1)(Pk) should be estimated with a fictitious index (nk) and thecornea was considered as a single dioptric surface thereforecorneal principal planes were approximated to the anteriorcorneal surface (Figure 1(a)) For the measurement of bothcorneal radii (r1c and r2c) and corneal thickness (ec) with thePentacam (Figure 1(b)) the total corneal power was com-puted with equation (2) and corneal principal planes werecalculated since the cornea was considered as a thick lens(Figure 1(b)) [22]

Pk nk minus 1

rk (1)

Pc nc minus 1

r1c+13374minus nc

r2cminus

ec

nc1113888 1113889

nc minus 1r1c

1113888 111388913374minus nc

r2c1113888 1113889

(2)

e characteristics of the IOL implanted in each patientwere provided by the manufacturer including thickness andanterior and posterior radii (these are not detailed in theresults as they were required to be kept as confidential by themanufacturer) erefore the principal planes were alsocalculated for the IOLs (Figure 1) Finally to calculate theequivalent lens for the coupling of the cornea and the IOL itwas required to define the distances between both opticalstructures (ELP) taking the principal planes as the referenceif possible (Figure 1(b)) or the anterior cornea location whenthe cornea was considered as a thin lens (Figure 1(a))Different approximations for the real effective lens positiondepending on the principal planes location were consideredfrom corneal vertex to second IOL principal plane (equation(3) Figure 1(a)) from second corneal principal plane to firstIOL principal plane (equation (4) Figure 1(b)) and from



ELPo ALP +H2l (3)


ELPk ALP +H1l (5)





rkrrnk

ELPk

ELPo

13374 1336

H2lH1l

(a)

nc

ec

13374 1336

H2c H1c

r1c r2c

ALP

ELPc

H2lH1l

(b)






3 Results






4 Discussion






nc = 0007 lowast AXL + 117R2 = 024 (p = 0001)

1300

1310

1320

1330

1340

1350

1360

1370

1380

Corr

ecte

d co

rnea

l ref

ract

ive i

ndex

(nc)

21 22 23 24 25 26 2720Axial length (mm)

(a)


1328

133

1332

1334

1336

1338

134

1342

Corr

ecte

d ke

rato

met

ric in

dex

(nk)

1344

21 22 23 24 25 26 2720Axial length (mm)

(b)






ndash20

ndash15

ndash10

ndash05

0

05

1Po

stope

rativ

e sph

eric

al eq

uiva

lent

(D)

07

08

04

ndash01 0

01

02

03

06

ndash03 05

ndash04

ndash02 09 1

ndash05


(a)

ndash007

012

003

ndash015

ndash010

ndash005

000

005

010

015

020

025

r kndashr 1

c (m

m)

82

76

80

84

72

74

78


(b)





0 0 29

3530

19

5 0 0 0


plusmn050D84

0

20

40

60

80

100

of e

yes

ltndash2

00

gt+2

00

ndash20

0 to

ndash1

51

ndash15

0 to

ndash1

01

ndash10

0 to

ndash0

51

ndash05

0 to

ndash0

14

ndash01

3 to

+0

13

+01

4 to

+0

50

+05

1 to

+1

00

+10

1 to

+1

50

+15

1 to

+2

00


(a)

0 0 212

42

23 21

0 0 0 0



0

20

40

60

80

100

o

f eye

s

ltndash2

00

gt+2

00

ndash20

0 to

ndash1

51

ndash15

0 to

ndash1

01

ndash10

0 to

ndash0

51

ndash05

0 to

ndash0

14

ndash01

3 to

+0

13

+01

4 to

+0

50

+05

1 to

+1

00

+10

1 to

+1

50

+15

1 to

+2

00


(b)

0 0 09

28 28 26

90 0 0


plusmn050D82

ltndash2

00

gt+2

00

ndash20

0 to

ndash1

51

ndash15

0 to

ndash1

01

ndash10

0 to

ndash0

51

ndash05

0 to

ndash0

14

ndash01

3 to

+0

13

+01

4 to

+0

50

+05

1 to

+1

00

+10

1 to

+1

50

+15

1 to

+2

00

0

20

40

60

80

100

o

f eye

s


(c)

0 0 010

23

35

1913

0 0 0



ltndash2

00

gt+2

00

ndash20

0 to

ndash1

51

ndash15

0 to

ndash1

01

ndash10

0 to

ndash0

51

ndash05

0 to

ndash0

14

ndash01

3 to

+0

13

+01

4 to

+0

50

+05

1 to

+1

00

+10

1 to

+1

50

+15

1 to

+2

00

0

20

40

60

80

100

o

f eye

s


(d)

ndash1

ndash075

ndash05

ndash025

0

025

05

075

1

Posto

pera

tive s

pher

ical

equi

vale

nt (D

)

25 3 35 4 452

Pupil diameter (mm)

(e)

ndash1

ndash075

ndash05

ndash025

0

025

05

075

1

Posto

pera

tive s

pher

ical

equi

vale

nt (D

)

25 3 35 4 452

Pupil diameter (mm)

(f )









Data Availability



Disclosure




Acknowledgments


References








































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of




















ELPo ALP +H2l (3)


ELPk ALP +H1l (5)





rkrrnk

ELPk

ELPo

13374 1336

H2lH1l

(a)

nc

ec

13374 1336

H2c H1c

r1c r2c

ALP

ELPc

H2lH1l

(b)






3 Results






4 Discussion






nc = 0007 lowast AXL + 117R2 = 024 (p = 0001)

1300

1310

1320

1330

1340

1350

1360

1370

1380

Corr

ecte

d co

rnea

l ref

ract

ive i

ndex

(nc)

21 22 23 24 25 26 2720Axial length (mm)

(a)


1328

133

1332

1334

1336

1338

134

1342

Corr

ecte

d ke

rato

met

ric in

dex

(nk)

1344

21 22 23 24 25 26 2720Axial length (mm)

(b)






ndash20

ndash15

ndash10

ndash05

0

05

1Po

stope

rativ

e sph

eric

al eq

uiva

lent

(D)

07

08

04

ndash01 0

01

02

03

06

ndash03 05

ndash04

ndash02 09 1

ndash05


(a)

ndash007

012

003

ndash015

ndash010

ndash005

000

005

010

015

020

025

r kndashr 1

c (m

m)

82

76

80

84

72

74

78


(b)





0 0 29

3530

19

5 0 0 0


plusmn050D84

0

20

40

60

80

100

of e

yes

ltndash2

00

gt+2

00

ndash20

0 to

ndash1

51

ndash15

0 to

ndash1

01

ndash10

0 to

ndash0

51

ndash05

0 to

ndash0

14

ndash01

3 to

+0

13

+01

4 to

+0

50

+05

1 to

+1

00

+10

1 to

+1

50

+15

1 to

+2

00


(a)

0 0 212

42

23 21

0 0 0 0



0

20

40

60

80

100

o

f eye

s

ltndash2

00

gt+2

00

ndash20

0 to

ndash1

51

ndash15

0 to

ndash1

01

ndash10

0 to

ndash0

51

ndash05

0 to

ndash0

14

ndash01

3 to

+0

13

+01

4 to

+0

50

+05

1 to

+1

00

+10

1 to

+1

50

+15

1 to

+2

00


(b)

0 0 09

28 28 26

90 0 0


plusmn050D82

ltndash2

00

gt+2

00

ndash20

0 to

ndash1

51

ndash15

0 to

ndash1

01

ndash10

0 to

ndash0

51

ndash05

0 to

ndash0

14

ndash01

3 to

+0

13

+01

4 to

+0

50

+05

1 to

+1

00

+10

1 to

+1

50

+15

1 to

+2

00

0

20

40

60

80

100

o

f eye

s


(c)

0 0 010

23

35

1913

0 0 0



ltndash2

00

gt+2

00

ndash20

0 to

ndash1

51

ndash15

0 to

ndash1

01

ndash10

0 to

ndash0

51

ndash05

0 to

ndash0

14

ndash01

3 to

+0

13

+01

4 to

+0

50

+05

1 to

+1

00

+10

1 to

+1

50

+15

1 to

+2

00

0

20

40

60

80

100

o

f eye

s


(d)

ndash1

ndash075

ndash05

ndash025

0

025

05

075

1

Posto

pera

tive s

pher

ical

equi

vale

nt (D

)

25 3 35 4 452

Pupil diameter (mm)

(e)

ndash1

ndash075

ndash05

ndash025

0

025

05

075

1

Posto

pera

tive s

pher

ical

equi

vale

nt (D

)

25 3 35 4 452

Pupil diameter (mm)

(f )









Data Availability



Disclosure




Acknowledgments


References








































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of






















3 Results






4 Discussion






nc = 0007 lowast AXL + 117R2 = 024 (p = 0001)

1300

1310

1320

1330

1340

1350

1360

1370

1380

Corr

ecte

d co

rnea

l ref

ract

ive i

ndex

(nc)

21 22 23 24 25 26 2720Axial length (mm)

(a)


1328

133

1332

1334

1336

1338

134

1342

Corr

ecte

d ke

rato

met

ric in

dex

(nk)

1344

21 22 23 24 25 26 2720Axial length (mm)

(b)






ndash20

ndash15

ndash10

ndash05

0

05

1Po

stope

rativ

e sph

eric

al eq

uiva

lent

(D)

07

08

04

ndash01 0

01

02

03

06

ndash03 05

ndash04

ndash02 09 1

ndash05


(a)

ndash007

012

003

ndash015

ndash010

ndash005

000

005

010

015

020

025

r kndashr 1

c (m

m)

82

76

80

84

72

74

78


(b)





0 0 29

3530

19

5 0 0 0


plusmn050D84

0

20

40

60

80

100

of e

yes

ltndash2

00

gt+2

00

ndash20

0 to

ndash1

51

ndash15

0 to

ndash1

01

ndash10

0 to

ndash0

51

ndash05

0 to

ndash0

14

ndash01

3 to

+0

13

+01

4 to

+0

50

+05

1 to

+1

00

+10

1 to

+1

50

+15

1 to

+2

00


(a)

0 0 212

42

23 21

0 0 0 0



0

20

40

60

80

100

o

f eye

s

ltndash2

00

gt+2

00

ndash20

0 to

ndash1

51

ndash15

0 to

ndash1

01

ndash10

0 to

ndash0

51

ndash05

0 to

ndash0

14

ndash01

3 to

+0

13

+01

4 to

+0

50

+05

1 to

+1

00

+10

1 to

+1

50

+15

1 to

+2

00


(b)

0 0 09

28 28 26

90 0 0


plusmn050D82

ltndash2

00

gt+2

00

ndash20

0 to

ndash1

51

ndash15

0 to

ndash1

01

ndash10

0 to

ndash0

51

ndash05

0 to

ndash0

14

ndash01

3 to

+0

13

+01

4 to

+0

50

+05

1 to

+1

00

+10

1 to

+1

50

+15

1 to

+2

00

0

20

40

60

80

100

o

f eye

s


(c)

0 0 010

23

35

1913

0 0 0



ltndash2

00

gt+2

00

ndash20

0 to

ndash1

51

ndash15

0 to

ndash1

01

ndash10

0 to

ndash0

51

ndash05

0 to

ndash0

14

ndash01

3 to

+0

13

+01

4 to

+0

50

+05

1 to

+1

00

+10

1 to

+1

50

+15

1 to

+2

00

0

20

40

60

80

100

o

f eye

s


(d)

ndash1

ndash075

ndash05

ndash025

0

025

05

075

1

Posto

pera

tive s

pher

ical

equi

vale

nt (D

)

25 3 35 4 452

Pupil diameter (mm)

(e)

ndash1

ndash075

ndash05

ndash025

0

025

05

075

1

Posto

pera

tive s

pher

ical

equi

vale

nt (D

)

25 3 35 4 452

Pupil diameter (mm)

(f )









Data Availability



Disclosure




Acknowledgments


References








































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of






















nc = 0007 lowast AXL + 117R2 = 024 (p = 0001)

1300

1310

1320

1330

1340

1350

1360

1370

1380

Corr

ecte

d co

rnea

l ref

ract

ive i

ndex

(nc)

21 22 23 24 25 26 2720Axial length (mm)

(a)


1328

133

1332

1334

1336

1338

134

1342

Corr

ecte

d ke

rato

met

ric in

dex

(nk)

1344

21 22 23 24 25 26 2720Axial length (mm)

(b)






ndash20

ndash15

ndash10

ndash05

0

05

1Po

stope

rativ

e sph

eric

al eq

uiva

lent

(D)

07

08

04

ndash01 0

01

02

03

06

ndash03 05

ndash04

ndash02 09 1

ndash05


(a)

ndash007

012

003

ndash015

ndash010

ndash005

000

005

010

015

020

025

r kndashr 1

c (m

m)

82

76

80

84

72

74

78


(b)





0 0 29

3530

19

5 0 0 0


plusmn050D84

0

20

40

60

80

100

of e

yes

ltndash2

00

gt+2

00

ndash20

0 to

ndash1

51

ndash15

0 to

ndash1

01

ndash10

0 to

ndash0

51

ndash05

0 to

ndash0

14

ndash01

3 to

+0

13

+01

4 to

+0

50

+05

1 to

+1

00

+10

1 to

+1

50

+15

1 to

+2

00


(a)

0 0 212

42

23 21

0 0 0 0



0

20

40

60

80

100

o

f eye

s

ltndash2

00

gt+2

00

ndash20

0 to

ndash1

51

ndash15

0 to

ndash1

01

ndash10

0 to

ndash0

51

ndash05

0 to

ndash0

14

ndash01

3 to

+0

13

+01

4 to

+0

50

+05

1 to

+1

00

+10

1 to

+1

50

+15

1 to

+2

00


(b)

0 0 09

28 28 26

90 0 0


plusmn050D82

ltndash2

00

gt+2

00

ndash20

0 to

ndash1

51

ndash15

0 to

ndash1

01

ndash10

0 to

ndash0

51

ndash05

0 to

ndash0

14

ndash01

3 to

+0

13

+01

4 to

+0

50

+05

1 to

+1

00

+10

1 to

+1

50

+15

1 to

+2

00

0

20

40

60

80

100

o

f eye

s


(c)

0 0 010

23

35

1913

0 0 0



ltndash2

00

gt+2

00

ndash20

0 to

ndash1

51

ndash15

0 to

ndash1

01

ndash10

0 to

ndash0

51

ndash05

0 to

ndash0

14

ndash01

3 to

+0

13

+01

4 to

+0

50

+05

1 to

+1

00

+10

1 to

+1

50

+15

1 to

+2

00

0

20

40

60

80

100

o

f eye

s


(d)

ndash1

ndash075

ndash05

ndash025

0

025

05

075

1

Posto

pera

tive s

pher

ical

equi

vale

nt (D

)

25 3 35 4 452

Pupil diameter (mm)

(e)

ndash1

ndash075

ndash05

ndash025

0

025

05

075

1

Posto

pera

tive s

pher

ical

equi

vale

nt (D

)

25 3 35 4 452

Pupil diameter (mm)

(f )









Data Availability



Disclosure




Acknowledgments


References








































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of





















0 0 29

3530

19

5 0 0 0


plusmn050D84

0

20

40

60

80

100

of e

yes

ltndash2

00

gt+2

00

ndash20

0 to

ndash1

51

ndash15

0 to

ndash1

01

ndash10

0 to

ndash0

51

ndash05

0 to

ndash0

14

ndash01

3 to

+0

13

+01

4 to

+0

50

+05

1 to

+1

00

+10

1 to

+1

50

+15

1 to

+2

00


(a)

0 0 212

42

23 21

0 0 0 0



0

20

40

60

80

100

o

f eye

s

ltndash2

00

gt+2

00

ndash20

0 to

ndash1

51

ndash15

0 to

ndash1

01

ndash10

0 to

ndash0

51

ndash05

0 to

ndash0

14

ndash01

3 to

+0

13

+01

4 to

+0

50

+05

1 to

+1

00

+10

1 to

+1

50

+15

1 to

+2

00


(b)

0 0 09

28 28 26

90 0 0


plusmn050D82

ltndash2

00

gt+2

00

ndash20

0 to

ndash1

51

ndash15

0 to

ndash1

01

ndash10

0 to

ndash0

51

ndash05

0 to

ndash0

14

ndash01

3 to

+0

13

+01

4 to

+0

50

+05

1 to

+1

00

+10

1 to

+1

50

+15

1 to

+2

00

0

20

40

60

80

100

o

f eye

s


(c)

0 0 010

23

35

1913

0 0 0



ltndash2

00

gt+2

00

ndash20

0 to

ndash1

51

ndash15

0 to

ndash1

01

ndash10

0 to

ndash0

51

ndash05

0 to

ndash0

14

ndash01

3 to

+0

13

+01

4 to

+0

50

+05

1 to

+1

00

+10

1 to

+1

50

+15

1 to

+2

00

0

20

40

60

80

100

o

f eye

s


(d)

ndash1

ndash075

ndash05

ndash025

0

025

05

075

1

Posto

pera

tive s

pher

ical

equi

vale

nt (D

)

25 3 35 4 452

Pupil diameter (mm)

(e)

ndash1

ndash075

ndash05

ndash025

0

025

05

075

1

Posto

pera

tive s

pher

ical

equi

vale

nt (D

)

25 3 35 4 452

Pupil diameter (mm)

(f )









Data Availability



Disclosure




Acknowledgments


References








































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of

























Data Availability



Disclosure




Acknowledgments


References








































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of



















Disclosure




Acknowledgments


References








































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of





























of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of



















new approach for the calculation of the intraocular lens

Documents