Utility of Theoretical Hirschberg Ratio for Gaze Position Calibration

Application and repeatability of ocular biometric measures for gaze position calibration in children

PURPOSE

The purpose of this study was to investigate the utility of two ocular biometric measurements to obtain Hirschberg ratios (HRs) in a binocularly normal paediatric population, and to assess the repeatability of this approach.

METHODS

Ocular biometry data from 80 participants (aged 5 to 14 years) was obtained using the KM-1 LED manual keratometer and the Tomey Biometer AL-100 A-scan. HRs were calculated from corneal curvature and anterior chamber depth measurements in the horizontal and vertical meridians of each eye using a regression equation based on a geometric optics model. To assess intrasubject variability in the HRs obtained from biometry, measurements were repeated approximately 1 h later.

RESULTS

At the initial measurement, mean (SD, range) HRs were 10.77 (0.79, 9.14-12.73) and 11.02 (0.82, 9.48-13.32) °/mm for the horizontal and vertical meridians, respectively. There was a significant difference between the horizontal and vertical HRs (p < 0.0001). Mean intrasubject variability of HR was 0.06 °/mm (95% Limit of Agreement [LOA]: -0.82 to 0.94 °/mm), and 0.05 °/mm (95% LOA: -1.05 to 1.15 °/mm) for the horizontal and vertical meridians, respectively.

CONCLUSION

The results indicated that HRs obtained through ocular biometry in a binocularly normal paediatric population are consistent with previous studies in both strabismic children and adult cohorts. The HRs obtained with this technique were highly repeatable in this study population. This approach to gaze position calibration could be used in lieu of other empirical techniques in children.

Development and Preliminary Evaluation of a Smartphone App for Measuring Eye Alignment

Purpose

We evaluate a smartphone application (app) performing an automated photographic Hirschberg test for measurement of eye deviations.

Methods

Three evaluation studies were conducted to measure eye deviations in the horizontal direction. First, gaze angles were measured with respect to the ground truth in nonstrabismic subjects (n = 25) as they fixated monocularly on targets of known eccentricity covering an angular range of approximately ±13°. Second, phoria measurements with the app at near fixation (distance = 40 cm) were compared with the modified Thorington (MT) test in normally-sighted subjects (n = 14). Third, eye deviations using the app were compared to a cover test with prism neutralization (CTPN; n = 66) and Synoptophore (n = 34) in strabismic subjects. Regression analyses were used to compare the app and clinical measurements of the magnitude and direction of eye deviations (prism diopters, Δ).

Results

The gaze angles measured by the app closely followed the ground truth (slope = 1.007, R² = 0.97, P < 0.001), with a root mean squared error (RMSE) of 2.4Δ. Phoria measurements with the app were consistent with MT (slope = 0.94, R² = 0.97, P < 0.001, RMSE = 1.7Δ). Overall, the strabismus measurements with the app were higher than with Synoptophore (slope = 1.15, R² = 0.91, P < 0.001), but consistent with CTPN (slope = 0.95, R² = 0.95, P < 0.001). After correction of CTPN values for near fixation, the consistency of the app measurements with CTPN was improved further (slope = 1.01).

Conclusions

The app measurements of manifest and latent eye deviations were consistent with the comparator clinical methods.

Translational Relevance

A smartphone app for measurement of eye alignment can be a convenient clinical tool and has potential to be beneficial in telemedicine.

Quantitative measurement of horizontal strabismus with digital photography

PURPOSE

To develop a method to calculate the gaze angle in photographs and to determine its validity and reliability in real strabismus patients.

METHODS

Photographs of eyes from 15 orthophoric subjects (n = 1,022) with known gaze angle and imaging distance were investigated with the help of a smartphone application developed by the authors. The application provided measurements of the distance from the geometrical center of the cornea to the light reflex (RD) and corneal diameter (CD). The RD/CD ratio of each gaze angle was recorded. To estimate the eyes' gaze angle, an equation to determine the best-fit line for the gaze angle data according to each RD/CD ratio was created. In a second clinical analysis, this equation was applied to photographs of real strabismus patients (n = 72), and the results were compared with measurements taken by a double-masked strabismus specialist. Separately, an equation was created to calculate the imaging distance using the given interpupillary distance.

RESULTS

There was a high correlation between the real and estimated gaze angles (r = 0.990, P < 0.001). The mean error of the estimated gaze angle was found to be 0.03^Δ ± 4.60^Δ. There was a high correlation between the real and estimated imaging distance (r = 0.997, P < 0.001) and a high correlation between the measurements of the application and the specialist (r = 0.966, P < 0.001). The average error was -0.68 ^Δ ± 6.1^Δ, and the reliability was high (Cronbach's α = 0.983).

CONCLUSIONS

The application measured horizontal strabismus in photographs with high reliability.