Mathematical models to describe fixation disparity curves

This study developed mathematical models to describe the four classical types of Fixation Disparity Curves (FDCs), addressing the limitations of existing generalised polynomial fits. These models provide an objective framework for analysing FDCs, with the goal of improving the diagnosis and management of binocular vision disorders.

The study was conducted in two phases. In the first phase, elementary mathematical functions were identified for each type of FDC: a polynomial function for Type I, an exponential function for Types II and III and a trigonometric function for Type IV. The function parameters were optimised using the least squares method in MATLAB. In the second phase, the models were validated using experimental data from 20 participants to ensure representation of all FDC types. The fixation disparity was measured using the Wesson card over a range of seven vergence demands.

The proposed models accurately represented the shape and characteristics of each FDC, achieving 85% classification accuracy across all four types. Agreement between the model and subjective classification by optometrists was 75%. A statistically significant difference was observed in slope calculations between types using the developed model (p = 0.002), but not with a general polynomial fit (p = 0.36).

The newly developed models improve the precision and reliability of FDC analysis, thereby reducing subjective bias. These models have potential applications in both clinical and research settings for more accurate binocular vision assessments.