the precise measurement of corneal power after myopic laser refractive surgery is still currently an issue under debate .
several methods have been proposed during the last years which are classified as methods requiring historical clinical data and methods not requiring historical data . among those methods requiring previous clinical data ,
some of them are based on a correction of the corneal power using the refracting change achieved [ 13 ] and others on performing such correction by adjusting the keratometric index [ 47 ] .
the main disadvantage of all these methods is that they are infeasible if previous clinical patient 's data are not available .
for this reason , other methods that do not require patient 's historical data have been developed [ 3 , 5 , 811 ] . in this line
, our research group has recently proposed a new method for estimating with enough accuracy the corneal power using the keratometric approach that has been found to be valid in both healthy   and post - lasik eyes .
this algorithm based on a variable keratometric index was named adjusted keratometric index ( nkadj ) and it has been prevalidated clinically in a sample of 32 eyes that had undergone previously myopic lasik surgery .
the aim of the current study is to validate clinically this algorithm for the estimation of the corneal power in eyes with previous myopic lasik in a larger population including also a larger range of intended refractive corrections .
this retrospective study comprised 62 eyes of 62 patients that had undergone previous correction of a myopic refractive error by means of laser in situ keratomileusis ( lasik ) surgery .
all lasik surgeries had been performed using the pulzar z1 solid - state laser ( customvis laser pty ltd .
, osborne park , australia , currently cv laser pty ltd . ) at the department of ophthalmology ( oftalmar ) of the vithas medimar international hospital ( alicante , spain ) .
all surgeries had been performed by one experienced surgeon ( aa ) between october 2012 and december 2013 . for this study ,
only one eye from each subject was chosen according to a random number sequence ( dichotomic sequence , 0 and 1 ) .
a comprehensive ophthalmologic examination was performed in all cases at least 3 months after surgery , which included refraction , corrected distance visual acuity ( cdva ) , slit lamp biomicroscopy , goldman tonometry , fundus evaluation , and the analysis of the corneal structure by means of a scheimpflug photography - based tomographer , the pentacam system ( oculus optikgerte gmbh , germany , software version 1.14r01 ) .
all patients were informed after surgery about this retrospective study and signed an informed consent document in accordance with the helsinki declaration .
our research group recently proposed the use of a variable keratometric index ( nkadj ) for the estimation of the corneal power ( pc ) using the keratometric approach in patients with previous myopic lasik surgery .
the following expression was defined for nkadj considering the ocular conditions of the gullstrand eye model and the range of anterior and posterior curvature that is commonly found in this kind of patients : ( 1)nkadj=0.0064286r1c+1.37688,where r1c is the postoperative anterior corneal radius .
furthermore , adjusted keratometric corneal power ( pkadj ) was defined as follows : ( 2)pkadj = nkadj1r1c . for comparison purposes ,
the keratometric corneal power was also calculated using the classical keratometric index nk = 1.3375  ( pk(1.3375 ) ) .
the gaussian corneal power was calculated using the following expression:(3)pcgaussp1c+p2cp1cp2c = ncnar1c+nhancr2cecncncnar1cnhancr2c , where pcgauss is the gaussian total corneal power , p1c is the anterior corneal power , p2c is the posterior corneal power , r1c is the anterior corneal radius , r2c is the posterior corneal radius , na is the refractive index of air , nc is the refractive index of the cornea , nha is the refractive index of the aqueous humour , and ec is the central corneal thickness . likewise , the true net power ( tnp ) was also recorded , which is the corneal power provided by the pentacam system ( oculus ) based on the anterior ( r1c ) and posterior ( r2c ) corneal radius and calculated by using the gaussian equation ( pcgauss ) with the gullstrand eye model , but neglecting the corneal thickness ( ec):(4)true  net  power  tnp=1.3761r1c1000 + 1.3361.376r2c1000 .
besides this , corneal power was also estimated by using other methods described previously for such purpose in eyes with previous myopic laser refractive surgery:(1)methods requiring previous clinical data:(a)awwad method : ( 5)pcawwad = pc0.23se;(b)camellin method : ( 6)pccamellin=1.3319 + 0.00113se1r1cpost/1000;(c)clinical history method:(7)pcpost = pcpre+se;(d)jarade method : ( 8)pcjarade=1.3375 + 0.0014se1r1cpost/1000;(e)savini method [ 5 , 6 ] : ( 9)pcsavini=1.338 + 0.0009856se1r1cpost/1000.(2)methods not requiring previous data:(a)haigis - l method:(10)pchaigisl=5.1625r1cpost+82.26030.35;(b)shammas method : ( 11)pcshammas=1.14pc6.8;(c)seitz method : ( 12)pcseitz=1.114pc4.98,where se = sepre  sepost , sepre and sepost being the pre- and postsurgery spherical equivalents , r1cpost is the postsurgery anterior corneal radius , and pcpre is the presurgery keratometric corneal power .
methods requiring previous clinical data : ( a)awwad method : ( 5)pcawwad = pc0.23se;(b)camellin method : ( 6)pccamellin=1.3319 + 0.00113se1r1cpost/1000;(c)clinical history method:(7)pcpost = pcpre+se;(d)jarade method : ( 8)pcjarade=1.3375 + 0.0014se1r1cpost/1000;(e)savini method [ 5 , 6 ] : ( 9)pcsavini=1.338 + 0.0009856se1r1cpost/1000 .
awwad method : ( 5)pcawwad = pc0.23se ; camellin method : ( 6)pccamellin=1.3319 + 0.00113se1r1cpost/1000 ; clinical history method:(7)pcpost = pcpre+se ; jarade method : ( 8)pcjarade=1.3375 + 0.0014se1r1cpost/1000 ; savini method [ 5 , 6 ] : ( 9)pcsavini=1.338 + 0.0009856se1r1cpost/1000 . methods not requiring previous data : ( a)haigis - l method:(10)pchaigisl=5.1625r1cpost+82.26030.35;(b)shammas method : ( 11)pcshammas=1.14pc6.8;(c)seitz method : ( 12)pcseitz=1.114pc4.98 , haigis - l method:(10)pchaigisl=5.1625r1cpost+82.26030.35 ; shammas method : ( 11)pcshammas=1.14pc6.8 ; seitz method : ( 12)pcseitz=1.114pc4.98 , for the clinical validation of pkadj , it was compared with pcgauss and tnp . likewise , the different methods mentioned above were also compared with pkadj and pcgauss in order to demonstrate which was the most accurate approach .
statistical analysis was performed using the software spss version 19.0 for windows ( spss , chicago , illinois , usa ) .
normality of all data distributions was first confirmed by means of the kolmogorov - smirnov test .
specifically , the paired student t - test or wilcoxon test was used for comparing the different methods of pc calculation depending on whether the normality condition could be assumed or not .
the bland - altman analysis   was used for evaluating the agreement and interchangeability of the different methods for obtaining the corneal power .
this study comprised 62 eyes of 62 patients ( 34 women [ 54.8% ] ) , with a mean age of 33.42  7.16 years ( range 21 to 52 years ) and with preoperative myopia between 0.25 and 6.8  d. the sample comprised 31 left eyes ( 50% ) .
mean ocular features of the eyes evaluated in the current study can be seen in table 1 .  
table 2 shows the values of corneal power estimated with the previously published methods ( awwad , camellin , clinical history , haigis - l , jarade , savini , seitz , and shammas methods ) . as shown in table 3 , there were significant differences ( p < 0.01 , paired student 's t - test ) between pkadj and pcgauss , but not ( p = 0.319 , paired student 's t - test ) between pkadj and tnp .
the bland - altman analysis showed that differences between pkadj and pcgauss were barely clinically significant ( mean difference : 0.14  0.24 ; limits of agreement ( loa ) : [ 0.33 , 0.60  d ] ) and that differences between pkadj and tnp were not clinically significant ( mean difference 0.03  0.24 ; loa :
a very strong and statistically significant correlation was found between pkadj and pcgauss ( r = 0.994 , p < 0.01 ) as well as between pkadj and tnp ( r = 0.994 , p < 0.01 ) . as shown also in table 3 ,
differences between pkadj and the rest of the methods for estimation of pc were statistically significant ( p < 0.01 ) , except for the difference between pkadj and pchaigisl ( p = 0.09 ) .
the bland - altman analysis confirmed that all these statistically significant differences were also clinically relevant as the ranges of agreement were quite large ( > 0.5  d ) . only differences between pkadj and pchaigisl (
mean : 0.04  0.17  d ) did not reach clinical significance ( loa : [ 0.37 to 0.29  d ] ) . 

table 4 summarizes the results of the comparison between the corneal power calculated considering the curvature of the two corneal surfaces as well as corneal thickness ( pcgauss ) and those values obtained with the other previously published methods for corneal power estimation in corneas with previous myopic laser refractive surgery . as shown , all differences between pcgauss and pc values obtained with such methods were statistically significant ( p < 0.01 ) .
considering the bland - altman analysis , pkadj and pchaigisl provided the lower mean differences with pcgauss ( 0.14  0.24  d and 0.18  0.21  d , resp . ) and the smaller ranges of agreement ( [ 0.6 to 0.33 ] and [ 0.60 to 0.23 ] , resp . ) .
pccamellin was also close to pcgauss ( mean difference : 0.42  0.14  d ) , but the range of agreement was larger than that found for pkadj and pchaigisl ( [ 0.15 to 0.68  d ] ) .
in the current study , the use of pkadj as a method to estimate the corneal power in corneas with previous myopic laser refractive surgery has been validated clinically .
furthermore , the results show that previously reported methods for this estimation are not better than the calculation of pkadj .
we have confirmed the clinical prevalidation we conducted in 32 eyes that had undergone myopic lasik surgery where no statistically significant differences between pkadj and tnp were found , with a mean difference value of 0.00  d and limits of agreement of 0.45 and + 0.46  d . in the current series , a mean difference of 0.03  0.24  d between tnp and pkadj ( p = 0.319 ) and a range of agreement from 0.50 to 0.44  d have been found . besides this , the comparison of pkadj with pcgauss has been also performed .
it should be considered that pcgauss takes into account neither the curvature of the two corneal surfaces nor the corneal thickness . in this comparison ,
the mean difference between pkadj and pcgauss was 0.14  0.24  d ( p < 0.01 ) , with a range of agreement from 0.33 to 0.60  d. there were only 4 cases out of 66 that showed differences between pkadj and pcgauss of more than 0.5  d. all these results are consistent with the theoretical predictions reported previously that estimated maximum differences between pkadj and pcgauss of 0.7  d . therefore , pkadj is an acceptable method for estimating the corneal power of corneas with previous myopic laser refractive surgery as 100% of estimations were within 0.7  d if pcgauss is taken as reference . when pkadj was compared with other different methods of corneal power estimation , statistically significant differences were found ( p < 0.01 ) , except for the comparison between pkadj and pchaigisl ( p = 0.09 ) .
the comparison between pchaigisl and pkadj showed a mean of difference of 0.04  0.17 and a range of agreement from 0.37 to 0.29  d , confirming that pkadj and pchaigisl were interchangeable . considering that pcgauss is the most exact method of calculation of the central corneal power in paraxial optics and that pkadj , pchaigisl , and pcgauss can be considered interchangeable according to the results of our study , pkadj and pchaigisl
can be considered appropriate methods for estimating the corneal power in corneas with previous myopic laser refractive surgery when posterior corneal surface data are unknown in clinical practice .
the remaining methods ( independently if previous historical data are required or not ) were found to overestimate pcgauss ( table 4 ) .
the classical keratometric approach for corneal power estimation based on calculations performed only considering the anterior corneal radius ( pk(1.3375 ) ) induces significant overestimations , ranging from 1.07 to 1.97  d. however , this was not the method providing the poorest performance .
the clinical history method was the most variable procedure , providing corneal power estimations that differed from pcgauss in a range going from 1.55 to 3.76  d. among methods requiring previous historical clinical data , pccamellin was the method providing lower overestimations of corneal power , with differences compared to pcgauss ranging from 0.04 to 0.78  d. furthermore , this corneal power estimation method could be clinically valid by using a correction factor .
the rest of the methods evaluated led to overestimations of more than 1  d. among methods requiring previous historical clinical data , pccamellin , pcsavini , and pcjarade methods are based on a variation of the keratometric refractive index depending on the induced refractive change ( se ) .
this keratometric approach for corneal power estimation is more appropriate than the use of a single value of keratometric index in all cases , but it is still associated with some level of limitation , as has been shown in the current study . a specific keratometric index value for each cornea must be calculated if the keratometric approach is intended to be used for an estimation of corneal power , as demonstrated by our research group in a previous study . this keratometric index was named as exact keratometric index ( nkexact ) and its calculation requires the measurement of anterior and posterior corneal curvature . as devices measuring the posterior corneal curvature are not available in all clinical settings , our group developed the concept of adjusted keratometric index ( nkadj ) , which is a clinically valid method for estimating an appropriate keratometric index allowing calculation of the corneal power with enough accuracy .
this method only requires the measurement of the anterior corneal radius postoperatively , which can be easily obtained in any clinical setting . among methods not requiring previous historical clinical data , the methods evaluated in the current study led to overestimations of more than 1  d except for pchaigisl , as commented previously .
these findings confirm the relevance of the curvature of the posterior corneal surface in the error associated with the corneal power estimation when the keratometric approach is used .
this is consistent with previous scientific evidence remarking that there is an error in considering the k = r2c / r1c ratio as a constant when corneal power is estimated in eyes after refractive surgery using the keratometric approach .
this is also the reason explaining the inaccuracy of methods of corneal power estimation based on considering the refractive change induced .
our results also confirm that the use of an inappropriate method for corneal power estimation in eyes with previous laser refractive surgery mainly leads to an overestimation of corneal power and consequently to an underestimation of the iol power required when cataract surgery is planned in this type of cases , resulting in hyperopic residual refractive errors postoperatively . in conclusion , the use of the adjusted keratometric index ( nkadj ) is a valid and easy method to estimate the central corneal power in corneas with previous myopic laser refractive surgery , improving the accuracy of methods described previously for such purpose .
only pchaigisl has been found to be comparable to our method and therefore leading to differences compared to the gaussian corneal power which are clinically acceptable .
the advantage of the use of pkadj method is that the estimation of corneal power can be performed with the only requirement of measuring the postoperative anterior corneal radius and with an associated error within 0.7  d and only 6% of cases showing differences with the gaussian power out of the range of 0.5  d.
with this paper , a new method for calculating corneal power after myopic refractive surgery was validated clinically , with the advantage that only postoperative refractive surgery parameters are required .
 
 purpose . to validate clinically a new method for estimating the corneal power ( pc ) using a variable keratometric index ( nkadj ) in eyes with previous laser refractive surgery . setting . 
 university of alicante and medimar international hospital ( oftalmar ) , alicante , ( spain ) . 
 design . 
 retrospective case series . methods . 
 this retrospective study comprised 62 eyes of 62 patients that had undergone myopic lasik surgery . 
 an algorithm for the calculation of nkadj was used for the estimation of the adjusted keratometric corneal power ( pkadj ) . 
 this value was compared with the classical keratometric corneal power ( pk ) , the true net power ( tnp ) , and the gaussian corneal power ( pcgauss ) . 
 likewise , pkadj was compared with other previously described methods . 
 results . 
 differences between pcgauss and pc values obtained with all methods evaluated were statistically significant ( p < 0.01 ) . 
 differences between pkadj and pcgauss were in the limit of clinical significance ( p < 0.01 , loa [ 0.33,0.60 ]  d ) . 
 differences between pkadj and tnp were not statistically and clinically significant ( p = 0.319 , loa [ 0.50,0.44 ]  d ) . 
 differences between pkadj and previously described methods were statistically significant ( p < 0.01 ) , except with pchaigisl ( p = 0.09 , loa [ 0.37,0.29 ]  d ) . 
 conclusion . 
 the use of the adjusted keratometric index ( nkadj ) is a valid method to estimate the central corneal power in corneas with previous myopic laser refractive surgery , providing results comparable to pchaigisl . 
1. Introduction
2. Methods
3. Results
4. Discussion
5. Conclusion