Validity of Novel Microsoft Excel Software for Calculating Surgically Induced Astigmatism

Purpose: To investigate validity and predictability of a new software calculator for surgically induced astigmatism quantification. Techniques and Methods: A new astigmatic calculator was designed, based on Pythagorean principle and trigonometric functions using Microsoft office excel 2007. Astigmatic magnitude was quantified in diopters and axis direction was depicted in degrees. Calculator was applied, investigated and analyzed on 30 pseudophakic eyes that underwent temporal scleral incision surgery with in the bag intraocular lens implantation. Pre and postoperative anterior corneal curvature was measured with Bausch and Lomb keratometer. Similarities and differences were compared with the existing version 1.1 and 2.1 calculators and statistical analysis was performed using Microsoft excel. Results: Mean pre and postoperative astigmatic magnitude was calculated as 62.67 (+/2.40) and Original Research Article Krishnacharya et al.; OR, 5(4): 1-9, 2016; Article no.OR.22108 2 62.83 (+/2.29) diopters. Mean pre and postoperative astigmatic axis was 89.74 (+/1.37) and 89.51 (+/1.37) degrees. Pearson’s coefficient (r) was calculated as 0.91 and 0.83; coefficient of determinations (R) was calculated as 0.82 and 0.68 for astigmatic magnitudes and axes respectively. Student chi-square test was used to calculate T values, which were 0.39 and 0.26 for astigmatic magnitude and axis respectively. P value less than 0.05 was considered as statistically significant (p 0.16). Validity was compared with existing surgically induced astigmatism calculators 1.1 and 2.1 versions and predictability was assessed by y=2.83+0.95x for astigmatic magnitude and y=15.28+0.83x equations for astigmatic axis. Conclusion: Present Microsoft excel calculator application was valid as the values for astigmatic magnitude and axis were comparable with existing SIA calculators and can be used for astigmatic predictability.


INTRODUCTION
Unexpected and post cataract surgical refractive astigmatic surprises are not uncommon in clinical practice. Understanding surgically induced astigmatism enlightens modifications in astigmatic control. Clinical prediction about pre and postoperative astigmatic magnitude and axis after cataract surgery improves acceptable modifications of surgeons' incision techniques that would provide least astigmatic correction to patients. Surgically induced astigmatism (SIA) determination uses subtraction method, vector analysis, vector decomposition, Cravy's vertical vector, Naeser's polar values and algebraic methods for calculations [1][2].
Recently, minimum standard format for reporting astigmatic outcomes and terminology to define astigmatism was formulated by astigmatic project group of the American national standard institute (ANSI) [3]. As astigmatism is manifested in magnitude and direction simultaneously, principles of vector Cartesian coordinate system calculations were adapted in the present study. Research rationale of this novel simple Microsoft (MS) excel 2007 software construction is to validate and correlate with existing SIA calculator 1.1 and 2.1 software. Furthermore, predictability of postoperative SIA vectors was evaluated by means of regression equations.

SUBJECTS AND METHODS
The experimental study was conducted primarily on patients recruited from an ongoing study on manual keratometric analysis of anterior corneal curvature following temporal scleral incision cataract surgery. Informed consent was taken from all patients. This project was approved by the institutional ethical committee and conducted in accordance with the Declarations of Helsinki of 1975. A new, yet a simple MS excel software functions were employed to analyze SIA on the basis of Cartesian coordinate vector system. Thirty eyes of 30 cataract patients were included after three months of surgery as refractive status stabilizes by this time [4]. All patients underwent temporal scleral incision cataract surgery with in the bag intra ocular lens implantation. Eyes with intra operative complications were excluded. Pre and postoperative keratometric horizontal (Kh) and vertical meridians (Kv) were measured by Bausch and Lomb keratometer (Appasamy KMS 6). As Microsoft Excel is easily available and accessible, it can be used similarly on other versions also.

MS EXCEL SIA SOFTWARE-BASIC PRINCIPLES
Formulae were constructed accordingly, as astigmatism abides with power in diopters and axis direction in degrees by vector analysis system. Magnitude and axis of pre and postoperative SIA vectors was expressed in diopters and in degrees respectively. Generally in day-to-day practice, astigmatism involves correction of two principle meridians that are perpendicular to each other; hence resultant vector is the hypotenuse of Pythagorean right angle triangle that was used to calculate magnitude of SIA vector.
Pythagorean principle applies to right angle triangles composed of adjacent and opposite sides with hypotenuse. The formula is adjacent side 2 +opposite side 2 = hypotenuse 2 , hence hypotenuse is equal to sum square root of adjacent and opposite sides that represents net astigmatic magnitude in diopters (Fig. 1

Surgically
induced astigmatism in 30 pseudophakic eyes of 30 patients was studied by applying newly formulated Microsoft Excel software calculator. Mean age was 60.3 (+/-8.66) years with 14 males (46.66%) and 16 (53.34%) females. All cases operated from temporal side and in the bag intraocular lens placement were performed in 30 (100 %) eyes by same surgeon. Linear relationship and line of best fit for magnitude and axis of pre and postoperative magnitude and axis of SIA vectors is shown in Figs. 2 and 3.
Descriptive statistics of pre and postoperative magnitude with resultant magnitude of SIA vector in diopters is shown in Table 1. Descriptive statistics of pre and postoperative axis with resultant axis of SIA vectors in degrees is shown in Table 2. Student t test was performed to find out t values to know difference in the means. Statistical significant levels were set at 0.05 p value. Regression equation was employed to find out predictability of postoperative SIA vectors. This is calculated from the equation y=a+bx, where 'y' is dependant variable, 'a' is intercept and 'b' is slope for SIA vector (Table 3). Validity was tested by comparing with existing SIA calculator version 1.1 and 2.1. Tables 4 and 5 shows pre and postoperative keratometric data of study patients and summarizing similarities and differences between SIA calculator 1.1, SIA calculator 2.1 and new SIA calculators.     No significant difference was perceived on comparing means of magnitude and axis of SIA vectors as the t values calculated from student t test unveiled less than the t critical one tail values (Table 3). Analysis of resultant magnitude between SIA version 2.1 and present calculator was shown with pre and post operative keratometric data. T Values are the values calculated by one tailed and two tailed test to find out any comparative difference between the two means. If t value moves closure to zero then there would probably be not rejecting the null hypothesis on the other hand if it is moving towards greater value then the results more likely is against rejecting null hypothesis. In our study there is no difference between t values SIA calculators were compared and t value is closure to zero signifying that null hypothesis was not rejected means there was no difference between two methods of assessment of SIA (Table 4).
Linear regression analysis demonstrated data point's distribution close to trend line that suggested best fit model line. Predictability was assessed by substituting pre operative magnitude of SIA in place of independent variable 'x' in the regression equation y=2.83+0.95x (Fig. 2). Similarly for axis of SIA vector, predictability was assessed by regression equation y=15.28+0.83x. Data point's distribution was not close to the trend line suggesting axis of SIA vector discrepancy as majority of the data points was scattered widely and sparsely (Fig. 3).
Previous methods of surgically induced astigmatism were calculated from subtraction method, polar methods and vector method. Simple subtraction method involves subtracting the post operative average keratometric reading from preoperative reading that was insufficient to address overall change in anterior corneal curvature. Polar analysis of SIA is complicated and involves diopteric conversion in to plus cylinder form that involves laborious work up. Both polar method and vector analysis was followed for construction of SIA calculator version 1.1 and 2.1. Present calculator construction is only based on vector analysis. Vector analysis of SIA is reliable and acceptable method since it takes into account of astigmatic magnitude expressed in diopters and astigmatic axis direction expressed in degrees.

Similarities and Differences between Calculators
Existing SIA calculator version 1.1 and 2.1 are used to evaluate single case and multiple case analysis respectively however their theoretical aspects of analysis of SIA are similar. Simultaneous representation and measurement of astigmatic magnitude and axis add to the complexity of assessment that can be solved by applying principles of vector-based system. Both of these versions are based on astigmatic vector that assigned a position represented by x and y points.
In  Marek et al. [9] reported 0.63 (+/-0.28) diopters of astigmatic magnitude for temporal phacoemulsification with 2.8 mm corneal incision with statistical significant difference comparable to the present study. Naeser et al. [10] demonstrated univariate and bivariate polar analysis method for SIA calculations and reported astigmatic magnitude of 1.02 diopters for 9 mm incision, 0.71 diopters for 5.5 mm and 0.64 diopters for 4 mm corneal incisions. Polar methods were not analyzed in the present study. Ernest et al. study of SIA following squared posterior limbal and clear corneal incisions during phacoemulsification revealed average 0.25 (+/-0.14) diopters for 2.2 mm incision size. There was no statistical significant difference between two types of incision sites similar to results of present study and SIA calculated from statsoft Inc 'statistica' software [11][12].

Comparative Analysis of New SIA Calculator
Ofir et al. [13] studied SIA by vector analysis for 2.4 mm corneal incision in 70 eyes and compared between three corneal measuring devices (Lenstar LS900, Haag-Streit, Koeniz, Switzerland; IOLMaster 500, Carl Zeiss Meditec, Dublin, CA; and Atlas topographer, Carl Zeiss Meditec) with similar results. Bausch and lamb keratometry was used to assess SIA in the present study. Hala Ali and Sumith Perera reported a mean SIA vector or 0.5-0.7 diopters following small incision cataract surgery and recommended inclusion of measurements variation of biometric devices when interpreting the results, while calculating SIA using the doctor-hill.com online SIA calculator [14].
Derya et al. [15] reported lower SIA values for superior limbal incision group on the basis of vector analysis although the difference was not statistically significant. Yoon et al. [16] reported a mean SIA of 0.81 and 0.92 diopters respectively for temporal and nasal 3.0 mm clear corneal incision in bilateral phacoemulsification with equivocal astigmatic change at three months follow-up.
Kawahara et al. [17] study calculated astigmatism using the Alpins method that showed no statistical difference in mean SIA score between one handed and two handed phacoemulsification techniques however results indicated corneal side port in two handed cataract surgery had a torque effect on astigmatic axis. Denoyer et al. [18] recommended consideration of biomechanical features of cornea such as corneal hysteresis and corneal resistance factor for better predictability of refractive outcomes of cataract surgery.

LIMITATIONS OF STUDY
SIA magnitude and axis quantified irrespective of incision dimensions and configuration was one of the limitations. Small sample size was chosen for new calculator application as a pilot study to corroborate validity and predictability. Strength of new calculator is in determining accurate axis and post operative predictability of magnitude and axis of SIA vector.

CONCLUSION
In conclusion, new SIA calculator provided comparable results with existing calculators in addition to predictability judgment on astigmatic quantification and axis direction. Added value of present new SIA calculator is magnitude and axis separately dealt for ease of understanding and knowledge on predictability on post operative SIA vector was highlighted. Ophthalmic surgeons with fair knowledge concerning Microsoft office excel software 2007 are sufficient to enter their patients pre and post operative keratometric readings for appraising surgically induced astigmatic quantifications and provide maximum post operative visual rehabilitation with prescription of minimum amount of induced astigmatic error.

DISCLAIMER
This manuscript was presented in the conference "24 th Annual Conference of Karnataka Ophthalmic Society" available link is "www.koscon2015.in/images/Final_New.PDF" date Nov 20 -Nov 22, Dr. D Veerendra Heggade Kalakshetra SDM College of Medical Sciences and Hospital, Sattur , Dharwad.

ACKNOWLEDGEMENT
We thank Head of the Institution and head of ophthalmology department for their untiring cooperation.

COMPETING INTERESTS
Authors have declared that no competing interests exist.