Simulating Extraocular Muscle Dynamics. A Comparison between Dynamic Implicit and Explicit Finite Element Methods

Jorge Grasa,Begoña Calvo

doi:10.3390/math9091024

Abstract

The finite element method has been widely used to investigate the mechanical behavior of biological tissues. When analyzing these particular materials subjected to dynamic requests, time integration algorithms should be considered to incorporate the inertial effects. These algorithms can be classified as implicit or explicit. Although both algorithms have been used in different scenarios, a comparative study of the outcomes of both methods is important to determine the performance of a model used to simulate the active contraction of the skeletal muscle tissue. In this work, dynamic implicit and dynamic explicit solutions are presented for the movement of the eye ball induced by the extraocular muscles. Aspects such as stability, computational time and the influence of mass-scaling for the explicit formulation were assessed using ABAQUS software. Both strategies produced similar results regarding range of movement of the eye ball, total deformation and kinetic energy. Using the implicit dynamic formulation, an important amount of computational time reduction is achieved. Although mass-scaling can reduce the simulation time, the dynamic contraction of the muscle is drastically altered.

Highlights

The extraocular muscles (EOM) are responsible for the eye movements of the upper eyelid and the eyeball
As the maximum time increment in a dynamic implicit algorithm depends on the typical period of vibration of the system, the natural frequencies and mode shapes were obtained for the model of the right eyeball, the pulleys and the EOMs
The lower natural frequency corresponds to the inferior EOM muscle which is the muscle with the largest volume

Summary

Introduction

The extraocular muscles (EOM) are responsible for the eye movements of the upper eyelid and the eyeball. The group that controls eye movement in the cardinal directions are the superior (responsible for elevation, incyclotorsion and adduction), inferior (responsible for depression, extorsion (outward, rotational movement) and adduction), lateral (responsible for abduction) and medial (responsible for adduction) rectus muscles. The movements of the extraocular muscles take place under the influence of a system of extraocular soft tissue pulleys in the orbit. The extraocular muscle pulley system is fundamental to the movement of the eye muscles, in particular to ensure conformity to Listing’s law. Simulating and analyzing eye movements is useful for assessing the role of these tissues and for exploring the equilibrium of the applied forces that can be impaired and lead to different pathologies [3,4]

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Conclusion