Poster Q8 - Three-dimensional Model for Human Eye Motion

Introduction: The human eye contains an eyeball and six extraocular muscles (EOMs). These muscles are actuators of this system to facilitate eye movement such as fixation and saccades. Some prior computational eye models assumed these six EOMs form three agnostic-antagonistic pairs, and only one of them from each pair gets activated. However, physiological recordings of the oculomotor neurons showed that even during one-dimensional eye movement, both agonist and antagonist EOMs are active. As a result, the human eye is considered a redundant system that has six inputs and three kinematic states of rotation in three dimensions. In this study, we propose an algorithm to determine the activation levels of the six EOMs to generate the required torque for any arbitrary eye movement.

Materials and

Methods: Our computational eye model contains three subsystems, the brain, the controller, and the orbital plant (Fig. A). The brain is responsible for generating the reference trajectory based on the desired eye movement. The orbital plant decides the next kinematic configuration of the eye based on the current configuration and the activation levels of all six EOMs.

The controller is responsible for calculating the EOM activation levels needed to rotate the eye based on the current and desired eye kinematic configurations. The controller itself contains two different components, the high-level controller and the force distributor. The high-level controller calculates the torque needed to change the current state of the eye to the desired configuration employing a sliding-mode controller. To generate such a torque, the six EOMs should be controlled in a coordinated way.

To distribute the responsibility of generating the required torque, an algorithm was designed based on the correlation between the desired torque and the unit vector of the torque that each muscle can generate. In each iteration, the algorithm calculates the image of the desired torque vector on each muscle’s torque unit vector. The algorithm chooses the muscle with the maximum image size. Then, it calculates the required activation to achieve that image and updates the activation level of that muscle. Then, the required torque vector will be replaced by the previous desired torque vector subtracted by the generated torque produced by the last chosen muscle. The algorithm repeats these steps until the residual required torque becomes negligibly small.

Results, Conclusions, and Discussions: We developed a controller based on the force distributor algorithm to determine the EOM activation levels so that the required net torque can be produced. The controller was implemented on the eye model. Simulation results demonstrated that the controller was effective at distributing forces among the EOMs (Fig. C). As shown in Fig. B, the eye was able to perfectly follow the reference trajectory. The controller activated the two vertical extraocular muscles during a vertical eye movement (Fig. C), illustrating its effective function in selecting the appropriate EOM to rotate the eye. As we can see, the activation levels of obliques are considerable and resulted from muscle disability to generate pure vertical motion. Consequently, we can see SR and IR are not the only active muscles. Horizontal eye movement was also simulated which showed consistent results.

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