Linear and non-linear Modeling of Eye Muscles in Strabismus

Document Type : Original Article

Authors

1 PhD, Department of Biomedical Engineering, Science and Research Branch, Islamic Azad university,Tehran, Iran

2 Department of Biomedical Engineering and physics, shahid beheshti university of medical sciences, Tehran, Iran

3 Department of Ophtalmology,School of Medicine , Tehran University of Medical Sciences, Tehran, Iran

Abstract

Purpose:
Many patients come afoul by the over correction or under correction of the eye muscles after strabismus surgery. This is related to the individual properties of anyone’s distinct eye muscles. Therefore, it is necessary to have accurate information about the living soft tissues in simulations and the proper modeling of the human eye muscles. The aim of this study was to present a three element model which may contribute to more accurate surgery.
Methods:
A three element model consisted of a spring in parallel with a Maxwell element which was composed of a dashpot and a spring in series. The response of the linear and nonlinear three element model was fitted to the obtained creep graphs.
Results:
The results showed a good fitness in both the linear and non-linear models.
Conclusion:
Since the living soft tissues generally exhibit nonlinear behavior, these results may indicate that the experiment have performed in linear range. One of the reasons of non-linear behavior of eye muscle may be related to pulley complex mechanism.

Keywords

Main Subjects


  1. Eugene M. Helveston: Surgical management of strabismus 5th edition Wayenborgh Publishing; 2005: 143-44.
  2. W. Flügge, Viscoelasticity, Blaisdell, United States of America; 1967.
  3. K. Nagayama, S. Yanagihara, T. Matsumoto, A novel micro tensile tester with feed-back control for viscoelastic analysis of single isolated smooth muscle cells, Medical Engineering and Physics 2007; 29 (Issue 5): 620-628.
  4. J. Argyris, I. Stdoltsinis, V.D. Dasilva. Constitutive modeling and computation of nonlinear viscoelastic solids 1 rheological models and numerical integration techniques, Computer Methods in Applied Mechanics and Engineering 1991; 88 (2): 135-163.
  5.  F. Yin, Y.C. Fung, Mechanical properties of isolated mammalian ureteral segments, American Journal of Physiology 1971; 5(221): 1484-1493.
  6. E.H. Sonnenblick, Series elastic and contractile elements in heart muscle: changes in muscle length, American Journal of Physiology 1964; 207 (6): 1330-1338.
  7. B. Fabry, G.N. Maksym, J.P. Butler, M. Glogauer, D. Navajas, J.J. Fredberg. Scaling the microrheology of living cells, Physical Review Letters 2001; 87(14): (148102).
  8. H. Ameri, A. Esteki. Analysis and modeling of viscoelastic properties of eye muscles in strabismus ; thesis 2015.
  9. J. Zhao, D. Liao, P. Chen, P. Kunwald, H. Gregersen, Stomach stress and strain depend on locatiion, direction and layered structure, Journal of Biomechanics 2008; 41(16): 3441-3447.
  10. Y.C. Fung, Biomechanics: Mechanical Properties of Living Tissues, Springer, New York, 1993.
  11. J. Zhao, D. Liao, H. Gregersen, Tension and stress in the rat and rabbit stomach are location-and direction-dependent, Neurogastroenterology & Motility 2005; 17(3): 388-398.
  12.  McMahon ThA: Muscles, Reflexes and Locomotion. Princeton, New Jersey, Princeton University Press 1984; (8): 8-9.
  13. Demer, JL, Miller, JM, Poukens, V, Vinters, HV, Glasgow, BJ. Evidence for fibromuscular pulleys of the recti extraocular muscles. Invest Ophthalmol Vis Sci 1995; 36(6): 1125-36.