Contractile Force of Human Extraocular Muscle: A Theoretical Analysis

Abstract

Aim. The length-contractile force relationships of six human extraocular muscles (EOMs) in primary innervations should be determined during eye movement modeling and surgery of clinical EOMs. This study aims to investigate these relationships. Method. The proposal is based on the assumption that six EOMs have similar constitutive relationships, with the eye suspended in the primary position. The constitutive relationships of EOMs are obtained by optimizing from previous experimental data and the theory of mechanical equilibrium using traditional model. Further, simulate the existing experiment of resistance force, and then compare the simulated results with the existing experimental results. Finally, the mechanical constitutive relationships of EOMs are obtained. Results. The results show that the simulated resistance forces from the other four EOMs except for the horizontal recti well agree with previous experimental results. Conclusion. The mechanical constitutive relationships of six EOMs in primary innervations are obtained, and the rationality of the constitutive relationships is verified. Whereafter, the active stress-strain relationships of the six EOMs in the primary innervations are obtained. The research results can improve the eye movement model to predict the surgical amounts of EOMs before EOM surgery more precisely.

Figure 1

Schematic of horizontal movement of the left eye, in which only the lateral rectus (LR) and the medial rectus (MR) are plotted. x(x, y, z) is the reference configuration, and x′(x′, y′, z) is the current configuration after the eye rotating by ψ.

Figure 2

Schematic of double eyes only with the lateral rectus (LR) and the medial rectus (MR): not all the six EOMs are plotted.

Figure 3

Total forces of EOMs with eye passively rotated temporalward in the primary innervations.

Figure 4

Comparison of resistance forces from the other four EOMs, except for the horizontal recti, during passive rotation of the eye in the primary innervations (note: the experimental data are adopted from Figure 27 of reference [12]).

Figure 5

Passive forces of EOMs with eye passively rotated temporalward in the primary innervations.

Figure 6

Active forces of EOMs with eye passively rotated temporalward in the primary innervations.