Eye Movement Modeling And Clinical Application Based On Constitutive Model Of Extraocular Muscle

Extraocular muscle(EOM) disorders, such as strabismus, affect the normal life of human beings seriously. About 1%~5% of the population suffers from the strabismus in the world. Recently, EOM disorders induced by pulley(connective tissue of EOM, which can change the path of EOM) heterotopy have been noticed. The treatment of EOM disorders can be divided into non-surgical therapy and surgical therapy, where the surgical therapy accounts for a large proportion. The accuracy of the amounts of EOM surgery is important to the successful EOM surgery. At present, ophthalmologist refers to the empirical value to determine the amounts of EOM surgery. It is theoretically and clinically important to realize the personalized design of amounts of EOM disorders to provide a method to determine the amounts of EOM surgery by establishing a biomechanical eye movement model.Eye movement is controlled by six EOMs and other orbital tissues. Input of mechanical constitutive relationships of six EOMs, the set of the function of pulley, and the set of the stiffness of other orbital tissues resisting eye movement are prerequisite to eye movement modeling. Because of the difficulty of the human EOMs anatomy and the complicated ethics and morals, the constitutive relationships of the six EOMs have not been reported. Biomechanical significance of pulley on the binocular vision is nearly unknown. The contribution of other orbital tissues to eye movement remains to be further determined. The purpose of this paper is to study the constitutive relationships of EOMs, the biomechanical significance of the pulley on binocular vision, and the force of orbital tissues resisting eye movement. Then a corresponding eye movement model is established, and it will provide theoretical guidance for the treatment of clinical EOM disorders.The main work in this paper is as follows:(1) The mechanical constitutive relationships of contractile EOMs were proposed in primary innervations. The one-string EOM eye movement model and three-string EOM eye movement model were established based on the previous experimental data of the length-tension relationship of lateral rectus. An assumption that the length-tension curves of the other five EOMs can be obtained by translating the corresponding curve of lateral muscle along the tension axis was used. Using these two models, the contractile constitutive relationships of EOMs in primary innervations were obtained by the theory of mechanical equilibrium and the optimal function in which the quadratic sum of tensile stress error will be the minimum. The rationality of the constitutive relationships was verified by comparing the simulated results with the existing experimental results. The comparison results of the calculation results between one-string model and three-string model showed that it is simple and valid to derive the contractile constitutive relationships of EOMs based on one-string model.(2) The biological significance of pulley on binocular vision was verified from the perspective of biomechanics first. Three eye movement models, i.e., non-pulley model, passive-pulley model, and active-pulley model, were used to simulate the horizontal movement of both eyes during the normal range of physiology. The forces of six EOMs were calculated by using the equilibrium equations of space force systems and the previous equation of passive force of EOMs, where the innervations of the elongated EOMs were weaken. The results showed that the resultant forces along the y-axis of the left eye for non-pulley model significantly differ from that of the other two pulley models. Compared to the other two pulley models, the differences of resultant forces between two eyes were larger both along x-axis and y-axis. The force results will lead to the different deformations of two eyeballs, which will mislead the judging of two eyes on the visual target. Obviously, the pulley is biomechanically significant to binocular vision.(3) The force of orbital tissues resisting eye movement was tested and analyzed. Fifteen healthy New Zealand white rabbits with body weights of 2.41±0.13 kg were used in the study. The tensile test of orbital tissues was conducted in vivo by Instron5544 tester. The statistical analysis was used to analyze the force of the orbital tissues with and without four EOMs resisting horizontal and vertical eye movement. The stiffness of the orbital tissues resisting eight eye movements was obtained by fitting the experimental data linearly. The results showed that the other four EOMs play little role both in passively horizontal eye movement with the two horizontal recti detached and in passively vertical eye movement with the two vertical recti detached. With the two recti detached, the stiffness of the orbital tissues resisting eye movement with four EOMs statistically differed from that of the orbital tissues without EOMs. The stiffness of the orbital tissues without EOMs cannot be replaced by that of the orbital tissues with four EOMs during resisting horizontal and vertical eye movements. It can provide a reference for the selection of the stiffness of orbital tissues resisting eye movement in eye movement modeling.(4) Provide a method for personalized design of operation plan for clinical strabismus surgery from the perspective of biomechanics. The resection and recession of EOMs were both used to adjust the horizontal exotropia and esotropia by modeling methods. The corrective amounts of eye positions by resection and recession of EOM were both provided. The availability of the corrected methods was verified by comparing the calculation results with the regressive values of the operation data, which verified the obtained constitutive relationships of EOMs further. The regressive formulae of the corrective amounts of EOM surgery can provide a corresponding guidance for clinician before operation. The method can give a personalized prediction to the surgical amounts of different patients before surgery.