Abstract
Purpose :
Previous imaging studies have shown that orbital pulleys are subject to limited sideslip but significant longitudinal displacement during eye rotation. Precise longitudinal displacement is required for mechanical implementation of Listing’s Law (LL), but a computational orbit model is needed to simulate realistic pulley positions. We developed a 3D mathematical orbit model that implements realistic pulley positions to examine the resultant biomechanical behaviors of the extraocular muscles (EOMs).
Methods :
The globe is modeled by a rigid sphere that rotates around its center. Each rectus EOM is geometrically modeled by a straight line between origin and its tangent point with the globe, which continues as a curve wrapping around the globe. The model is associated with realistic anatomical characteristics such as EOM origins and insertions as well as published biomechanical properties such as Hill muscle model parameters. An EOM insertion plane is defined in primary gaze, and containing the rectus EOM insertions. A posteriorly-located pulley plane is parallel to the insertion plane and the same distance as the insertion plane to the globe center. Through geometric constraint modeling, four pulleys are constrained to approximate the pulley plane for all eye rotations, and thus maintain equal distance to globe center with the insertions; this criterion implements Listing’s Law. EOM activations are computed through optimization such that the net torque applied on the globe rotates it to follow desired trajectories.
Results :
Horizontal eye rotation from 40o add- to 40o abduction was simulated. For each of the four rectus EOMs, the distance from the globe center to the orbital pulley and that to the EOM insertion are about the same (~7.5 mm), satisfying the equal distance criterion for Listing’s Law. Predicted rectus EOM forces are qualitatively consistent with experimentally measured forces and monotonically related to eye positions.
Conclusions :
We developed a mathematical orbit model that includes actively moving rectus pulleys and implements Listing’s Law with realistic EOM activation and force levels as functions of horizontal eye positions.
This abstract was presented at the 2024 ARVO Annual Meeting, held in Seattle, WA, May 5-9, 2024.