Pupil Diameter and Variable Multifocal Zone Sizes Relate to SuccessAuthors: Matthew Lampa, OD, FAAO; Robert Davis, OD, FAAO; P. Douglas Becherer, OD, FAAO; Lindsay McCorkle, MSEd; John Hayes, PhD

Introduction Near-Center Zone Diameter Table 1: This table depicts Standardized Regression Coefficients (beta) Figure 4: This graph depictswe performed a stepwise regression to identify relevant variables in predicting The regression equations from Figures 7 and 8 were used to develop tables

Pupilfactors associated with the size of the Size 7.6 7.7 7.8 7.9 8

Radius8.1 8.2 8.3 8.4 8.5 8.6

near-center zone diameter. Line -1 -0.5 0 0.5 1 1.5

near-center zone diameter (average 1.91 up the pupil size and radius to 3 1.74 1.75 1.77 1.79 1.81 1.82 1.84 1.86 1.88 1.90to assist in determining the near-center and peripheral zone diameternear-center zone diameters. Next, we applied a Wilcoxon non-parametric test linical experience indicates that the success of multifocal contact lenses is infl uenced by multiple 3.2 1.75 1.77 1.79 1.81 1.82 1.84 1.86 1.88 1.89 1.91Pupil Size R2=.79). In regular lighting, pupil 1.93 determine the suggested near-center 3.4 1.78 1.79 1.81 1.83 1.85 1.86 1.88 1.90 1.92 1.93 1.95

3.6 1.81 1.82 1.84 1.86 1.88 1.89 1.91 1.93 1.95size was the primary factor impacting 1.97 1.98 zone diameter. values. The average successful diameter can be identifi ed at the intersection to all near-center and peripheral zone diameter models to determine if there Radius 3.8 1.84 1.86 1.88 1.90 1.91 1.93 1.95 1.97 1.98 2.00 2.02 the size of the near-center zone. factors. These include lens centration, relationship of cornea to contact lens base curve, lens 4 1.89 1.91 1.92 1.94 1.96 1.98 1.99 2.01 2.03 2.05 2.06 4.2 1.94 1.96 1.98 1.99 2.01 2.03 2.05 2.06 2.08 2.10 2.12 When the lighting conditions wereDiameter of the row representing the patient’s pupil size and the column representingwas a signifi cant difference in model residuals (the deviation from the line) 4.4 2.00 2.02 2.03 2.05 2.07 2.09 2.10 2.12 2.14 2.16 2.17

altered, add power also affected the 4.6 2.06 2.08 2.10 2.12 2.13 2.15 2.17 2.19 2.20 2.22 2.24 movement, limbal coverage, optical placement, line of sight, lens orientation, lens dehydration, Power 4.8 2.14 2.15 2.17 2.19 2.21 2.22 2.24 2.26 2.28 2.29 2.31size of the near-center zone. the radius. (Refer to Table 1 for near-center zone diameter and Table 2 for between successful and unsuccessful patients. We expected that the successful 5 2.22 2.23 2.25 2.27 2.29 2.30 2.32 2.34 2.36 2.37 2.39

5.2 2.30 2.32 2.34 2.35 2.37 2.39 2.41 2.42 2.44 2.46 2.48Cylinder

5.4 2.40 2.41 2.43 2.45 2.47 2.48 2.50 2.52 2.54 2.55 2.57 pupil size, lens design, optic-zone sizes, patient adaptation, and accommodation, among others.C peripheral zone diameter.) For example, if the median pupil size is 4.2mm patients would be a better fi t than the unsuccessful patients. The model 5.6 2.50 2.51 2.53 2.55 2.57 2.58 2.60 2.62 2.64 2.65 2.67 5.8 2.60 2.62 2.64 2.66 2.67 2.69 2.71 2.73 2.74 2.76 2.78Axis 6 2.72 2.74 2.75 2.77 2.79 2.81 2.82 2.84 2.86 2.88 2.89and the median radius is 8.1mm, the tables indicate the recommendedpredicted near-center and peripheral zone diameter values at the 8.1mm 6.2 2.84 2.86 2.87 2.89 2.91 2.93 2.94 2.96 2.98 3.00 3.02

Add PowerThis poster will examine pupil size in relation to near-center and peripheral optic-zone diameters as a predictor 6.4 2.97 2.99 3.00 3.02 3.04 3.06 3.07 3.09 3.11 3.13 3.14 6.6 3.10 3.12 3.14 3.16 3.17 3.19 3.21 3.23 3.24 3.26 3.28near-center zone diameter would be 2.03mm and the peripheral zoneradius, which were then used to test the association with values generated by 6.8 3.25 3.26 3.28 3.30 3.32 3.33 3.35 3.37 3.39 3.40 3.42Lighting Other OD n=13 Lighting Other OS n=13 7 3.40 3.41 3.43 3.45 3.47 3.48 3.50 3.52 3.54 3.55 3.57 Regular Lighting OD n=69 Regular Lighting OS n=66of positive patient outcomes when fi nalizing a custom soft multifocal contact lens prescription. Note: All measurements in mm. diameter would be 3.68mm.the SpecialEyes Multifocal Simulator (see Figure 3).

4. There is a strong linear association (see Figure 9) between the values Figure 1A: This image depicts Peripheral Zone Diameter Table 2: This table depictsStandardized Regression Coefficients (beta) Figure 5: This graph depictsSpecialEyes 54 Multifocal – Aspheric Design the multifocal lens design used in Pupilfactors associated with the size of the 8Radius

8.1 8.2 8.3 8.4 8.5 8.6 peripheral zone diameter. The

Size 7.6 7.7 7.8 7.9 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 generated by the SpecialEyes Multifocal Simulator and the model’s predicted Terminology Defi ned this study. peripheral zone diameter (average 3.39 peripheral zone diameter uses the 3 2.95 2.99 3.04 3.08 3.13 3.17 3.21 3.26 3.30 3.35Results 3.2 2.99 3.03 3.08 3.12 3.17 3.21 3.26 3.30 3.34 3.39 3.43Pupil Size R2=.75). In regular lighting, pupil

3.49 near-zone prediction and requires no

3.4 3.05 3.09 3.14 3.18 3.23 3.27 3.31 3.36 3.40 3.45near-center and peripheral zone diameter values from the data set (see 3.6 3.13 3.17 3.21 3.26 3.30 3.35 3.39 3.44 3.48size was the primary factor impacting 3.52 3.57 additional measurements.

Radius 3.8 3.22 3.26 3.31 3.35 3.40 3.44 3.49 3.53 3.57 3.62 3.66the size of the peripheral zone. 4 3.33 3.38 3.42 3.46 3.51 3.55 3.60 3.64 3.69 3.73 3.77 Near-Center Zone: A customizable diameter value in the center of the Table 3), thus validating the simulator’s pupil-size fi tting methodology. 4.2 3.46 3.50 3.55 3.59 3.64 3.68 3.73 3.77 3.81 3.86 3.901. Pupil size had a clinically relevant and statistically signifi cant impact on When the lighting conditions wereDiameter 4.4 3.61 3.65 3.70 3.74 3.78 3.83 3.87 3.92 3.96 4.01 4.05

altered, add power also affected the 4.6 3.77 3.82 3.86 3.91 3.95 3.99 4.04 4.08 4.13 4.17 4.22Nearnear-center SpecialEyes 54 Multifocal lens that is comprised of full near power. Power 4.8 3.96 4.00 4.04 4.09 4.13 4.18 4.22 4.27 4.31 4.35 4.40both near-center and peripheral zone diameter sizes. We used multiple size of the peripheral zone. The black line of identity in Figure 9 shows similarity between the 5 4.16 4.20 4.24 4.29 4.33 4.38 4.42 4.47 4.51 4.55 4.60

5.2 4.37 4.42 4.46 4.51 4.55 4.59 4.64 4.68 4.73 4.77 4.82Cylinder IntermediateSee Figures 1A and 1B.

5.4 4.61 4.65 4.70 4.74 4.79 4.83 4.87 4.92 4.96 5.01 5.05 regression to examine the association between measured variables (pupil SpecialEyes Multifocal Simulator and the Regression Model developed 5.6 4.86 4.91 4.95 5.00 5.04 5.08 5.13 5.17 5.22 5.26 5.30(Progressive)

Axis 5.8 5.13 5.18 5.22 5.27 5.31 5.35 5.40 5.44 5.49 5.53 5.58

6 5.42 5.47 5.51 5.55 5.60 5.64 5.69 5.73 5.78 5.82 5.86size, radius, lens diameter, power, cylinder, axis, and add power) and the from the data. The R2 values are very high (0.9807 and 0.9604). R2 valuesIntermediate Area: Located between the near-center zone and peripheral 6.2 5.73 5.77 5.82 5.86 5.91 5.95 5.99 6.04 6.08 6.13 6.17

Add Power Distance 6.4 6.05 6.10 6.14 6.19 6.23 6.27 6.32 6.36 6.41 6.45 6.49 6.6 6.39 6.44 6.48 6.53 6.57 6.62 6.66 6.70 6.75 6.79 6.84 assigned near-center and peripheral zone sizes. Figures 4 and 5 report the vary from 0 to 1 and represent the proportion of variance shared by thezone, this area contains aspheric intermediate powers. See Figure 1A. 6.8 6.75 6.80 6.84 6.89 6.93 6.97 7.02 7.06 7.11 7.15 7.20 Lighting Other OD Lighting Other OS

7 7.13 7.18 7.22 7.26 7.31 7.35 7.40 7.44 7.48 7.53 7.57 Regular Lighting OD Regular Lighting OS Note: All measurements in mm. beta weights from the regression equations and show pupil size as having two variables. Points share 100% of the variance if they fall directly on Peripheral Zone: This customizable diameter value in the periphery of the

a signifi cant impact on near-center and peripheral zone sizes. a single straight line. The magnitude of deviations from the best-fi t line near-center SpecialEyes 54 Multifocal lens represents the location in the lens at Figure 1B: In this image, the yellow Near-Center Zone Diameter in Relation to Pupil Size Figure 6: This graph predicts Multifocal Simulator and Regression Model Relationship Figure 9: This graph illustrates the(residuals) illustrates variability not shared between the two variables.dashed circle represents the near- near-center zone diameter in relation relationship between the SpecialEyes2. The variables examined in the study did not reveal why some patients werewhich full distance power is reached. The lens remains at full distance power 3.5 6center zone diameter value and the to pupil size. Multifocal Simulator and the

Near Zone R² = 0.9807 There are barely visible dotted lines that are the best-fi t linear lines white dashed circle represents the Regression Model. 5.5successful and others were unsuccessful. However, by using multiple logistic Peripheral Zone R² = 0.9604 from this diameter value to the end of the 8mm optic zone. See Figure 1B. peripheral zone diameter value. Both 5

3 between Model and Simulator. Both lines fall very close to the black line of these parameters are customizable. regression analysis and controlling for all variables, we found the choice

Methods

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Line of Identity 4.5

of identity. This also illustrates the one-to-one comparison between the of peripheral zone diameter size to be a modest predictor of success —signifi cantly for OD (p=.01) and marginally for OS (p=.067).

4

Mo

de

l (m

m)

two computations. The slight curve in the peripheral zones’ comparisonto the line of identity is probably due to the quadratic component of the

2.5 3.5

3

2.5

23. Multiple regression analysis revealed that pupil size and radius were thebest predictors of success (R2 = .92). Some failures were shown to be a

2

This study analyzed data from 48 successful and 39 unsuccessful custom pupil size in the predicted model.

Conclusions 1.5

soft multifocal contact lens patients, with a total of 91 eyes in the successful result of not following the predicted model for near-center and peripheralgroup and 70 eyes in the unsuccessful group. The near-center and peripheral zone size selection (see yellow circles in Figures 7 and 8). We performed a

1.5 13 3.5 4 4.5 5 5.5 6 6.5 1 2 3 4 5 6

Pupil Size (mm) Simulator (mm)

zone diameter values of the SpecialEyes 54 Multifocal contact lenses were Pupil Size Distribution Figure 2: This image depicts Diameter Values Table 3: This table depictsObserved Near-Center Zone Diameters on Predicted Values Figure 7: This graph illustrates theregression of near-center zone diameter values on pupil size for successfulpupil size distribution. The “No relationship between the predicted Regression Model diameter values as determined Simulator ■ Pupil size effectively assisted in determining near-center and peripheral designed from a pupil-size fi tting methodology, where zone sizes were

Peripheral Peripheral 3.5Adjustment” column represents model and the observed near-center No Adjustment Adjusted Pupil Size Near Zone Zone Near Zone Zone

by the Multifocal Simulator andpatients under regular room illumination to build a prediction model for thepupil sizes as measured in regular zone diameter values. It features a the Regression Model. zone diameter values.determined by pupil size. Failure

80- 3.3 3 1.8 3 1.82 3.17

near-center zone diameter values (see Figure 6). The association was strong(R2= .66). However, the deviations from the line appeared systematic.

Success room illumination. The “Adjusted” column represents pupils measured

Jitter plot of all observed near-center zone diameters on predicted values.

3.2 1.8 3 1.84 3.213.1

2.9 ■ The regression models summarize the near-center and peripheral zone We performed a multiple logistic regression analysis to examine the likelihood of success as a function of the measured variables: pupil size, radius, lens

3.4 1.8 3 1.86 3.27 Line of Identity

3.6 1.9 3.2 1.89 3.3560-in photopic or mesopic conditions The Wilcoxon test of success on the 3.8 2 3.4 1.93 3.44

2.7and subsequently adjusted to refl ect effective pupil size in regular roomillumination. All near-center and

absolute value of the residuals was diameter values of successful patients and indicate that peripheral zone 4.2 2 3.5 2.03 3.682.5 signifi cant at p = .002. Absolute residuals were tested because of the

4 2 3.5 1.98 3.55

For further model development, we analyzed separate stepwise regression co

un

t

40-

diameter is related to success. 4.4 2 4 2.09 3.83

diameter, spherical contact lens power, cylinder, axis, add power, near-center zone diameter, and peripheral zone diameter.

2.3 4.6 2.1 4.2 2.15 3.99

peripheral zone diameter valueswere initially chosen based on

distribution of errors above and

equations for each eye (using a sample of the data) to identify relevantvariables in predicting near-center zone diameters. The fi nal model was a polynomial regression with pupil size and radius:

4.8 2.2 4.4 2.22 4.18 2.1

5 2.3 4.6 2.3 4.38below the line of identity, which is 1.9 5.2 2.4 4.8 2.39 4.59

drawn through the center of the ■ The prediction models used pupil size and radius to predict the near-center 1.7 graph. The Wilcoxon test used only

zone diameter. The predicted near-center zone diameter was suffi cient to

20-

pupil-size measurements in regularroom illumination.

5.4 2.4 4.9 2.48

5.6 2.5 5 2.580-

By analyzing the multiple regression, we were able to determine the 1.5

5.83 4 5 6 7 3 4 5 6 7 2.6 5.2 2.69 1.5 2 2.5 3 3.5 samples not included in developing 6 2.8 5.5 2.81

the model. predict the peripheral zone diameter.

Pupil Size (mm)

association between the measured variables and the assigned near-center Predicted Near Center = 1.001435 + (-0.462633 * PupilSize) + (.087728 * PupilSize2)–and peripheral zone diameter values. Using a regression of near-center

+ (0.175540 * Radius)

Predicted Near-Center Zone Diameter Note: All measurements in mm.

■ Though the ability to predict success from the variables included in the study was limited, the fi ndings demonstrated that pupil size and radius could identify successful patients, while those not following the pupil-size

Figure 3: This image displaysa sample screen capture of the

Figure 8: This graph illustrates therelationship between the predicted

Observed Peripheral Zone Diameters on Predicted Values

zone diameter on pupil size for all successful patients under ambient room 7.5SpecialEyes Multifocal Simulator. model and the observed peripheral

zone diameter values. It features a7 Figure 7 illustrates the relationship between the predicted model andillumination conditions, we then built a prediction model for the near-Jitter plot of all observed peripheral

the observed near-center zone diameter values. Figure 8 illustrates thecenter zone diameter.

Failure

Success

fi tting methodology (average successful near-center and peripheral zone diameter selections) were more likely to fail.

6.5 zone diameters on predicted values.Line of Identity The Wilcoxon test of success on the 6

relationship between the predicted model and the observed peripheralDue to the over-sampling of patients with 4mm pupils (see Figure 2), we optedto revise our sample before further developing the model; so we compiled a

non-absolute value of the residuals5.5 was signifi cant at p = .046. Non-

5

absolute residuals were used in thezone diameter values. The predicted near-center zone diameter alone wassuffi cient to fi nd the best-fi tting peripheral zone diameter value using the following equation:

■ Correlation of the data revealed a strong association between the values generated by the SpecialEyes Multifocal Simulator and the model’s

4.5 test because all the outlying residualswere below the line of identity, which

sample of successful patient data consisting of a random selection of 20% ofpatients with pupil diameters of 4mm and all other successful patients with

4

is drawn through the center of the3.5

predicted near-center and peripheral zone diameter values, thus validatingthe simulator’s pupil-size fi tting methodology.

graph. The test used only samples not3

3 4 5 6 7 8 included in developing the model.

pupil measurements based on ambient room illumination. Utilizing this data, Predicted Peripheral = -1.43 + (2.521 * Predicted Near Center) Predicted Peripheral Zone Diameter

4.83

5.08

5.35

5.64