Annals of Biomedical Engineering

, Volume 38, Issue 2, pp 247–258 | Cite as

Linear Homeomorphic Models for Muscles in the Head–Neck Region



The linear homeomorphic muscle model proposed by Enderle and coworkers for the rectus eye muscle is fitted to reflect the dynamics of muscles in the head–neck complex, specifically in muscles involved in gaze shifts. This parameterization of the model for different muscles in the neck region will serve to drive a 3D dynamic computer model for the movement of the head–neck complex, including bony structures and soft tissues, and aimed to study the neural control of the complex during fast eye and head movements such as saccades and gaze shifts. Parameter values for the different muscles in the neck region were obtained by optimization using simulated annealing. These linear homeomorphic muscle models provide non-linear force–velocity profiles and linear length tension profiles, which are in agreement with results from the more complex Virtual Muscle model, which is based on Zajac’s non-linear muscle model.


Muscle modeling Linear models Simulated annealing Optimization Muscle tests 


  1. 1.
    Bizzi, E., R. E. Kalil, and V. Tagliasco. Eye-head coordination in monkeys: evidence for centrally patterned organization. Science 173:452–454, 1971.CrossRefPubMedGoogle Scholar
  2. 2.
    Brelin-Fornari, J., P. Shah, and M. El-Sayed. Physically correlated muscle activation for a human head and neck computational model. Comput. Methods Biomech. Biomed. Eng. 8:191–199, 2005.CrossRefGoogle Scholar
  3. 3.
    Brown, I. E., S. H. Scott, and G. E. Loeb. Mechanics of feline soleus: II design and validation of a mathematical model. J. Muscle Res. Cell Motil. 17:221–233, 1996.CrossRefPubMedGoogle Scholar
  4. 4.
    Chang, Y., P. Coddington, and K. Hutchens. The NPAC/OLDA Visible Human Viewer. Adelaide, Australia: Computer Science Department, Adelaide University. Accessed 11 July 2007.
  5. 5.
    Cheng, E. J., I. E. Brown, and G. E. Loeb. Virtual muscle: a computational approach to understanding the effects of muscle properties on motor control. J. Neurosci. Methods 101:117–130, 2000.CrossRefPubMedGoogle Scholar
  6. 6.
    Close, R. I., and A. R. Luff. Dynamic properties of inferior rectus muscle of the rat. J. Physiol. 236:259–270, 1974.PubMedGoogle Scholar
  7. 7.
    Collins, C. C., D. O’Meara, and A. B. Scott. Muscle tension during unrestrained human eye movements. J. Physiol. 245:351–369, 1975.PubMedGoogle Scholar
  8. 8.
    Enderle, J. D. A Physiological Neural Network for Saccadic Eye Movement Control. Report AL/AO-TR-1994-0023 prepared for Armstrong Laboratory AL/AOCFO Brooks AFRB, TX, 1994.Google Scholar
  9. 9.
    Enderle, J. D. Neural control of saccades. Prog. Brain Res. 140:21–49, 2002.CrossRefPubMedGoogle Scholar
  10. 10.
    Enderle, J. D., J. D. Bronzino, and S. M. Blanchard. Introduction to Biomedical Engineering, vol. xxi. Amsterdam: Elsevier Academic Press, 1118 pp., 2005.Google Scholar
  11. 11.
    Enderle, J. D., E. J. Engelken, and R. N. Stiles. A comparison of static and dynamic characteristics between rectus eye muscle and linear muscle model predictions. IEEE Trans. Biomed. Eng. 38:1235–1245, 1991.CrossRefPubMedGoogle Scholar
  12. 12.
    Enderle, J. D., and J. W. Wolfe. Time-optimal control of saccadic eye movements. IEEE Trans. Biomed. Eng. 34:43–55, 1987.CrossRefPubMedGoogle Scholar
  13. 13.
    Farahat, W., and H. Herr. An apparatus for characterization and control of isolated muscle. IEEE Trans. Neural Syst. Rehabil. Eng. 13:473–481, 2005.CrossRefPubMedGoogle Scholar
  14. 14.
    Freedman, E. G. Coordination of the eyes and head during visual orienting. Exp. Brain Res. 190:369–387, 2008.CrossRefPubMedGoogle Scholar
  15. 15.
    Freedman, E. G., and D. L. Sparks. Eye-head coordination during head-unrestrained gaze shifts in rhesus monkeys. J. Neurophysiol. 77:2328–2348, 1997.PubMedGoogle Scholar
  16. 16.
    Hannaford, B. Control of Fast Movement: Human Head Rotation. PhD dissertation, University of California, Berkeley, 1985.Google Scholar
  17. 17.
    Kamibayashi, L. K., and F. J. Richmond. Morphometry of human neck muscles. Spine 23:1314–1323, 1998.CrossRefPubMedGoogle Scholar
  18. 18.
    Kirkpatrick, S., C. D. Gelatt, Jr., and M. P. Vecchi. Optimization by simulated annealing. Science 220:671–680, 1983.CrossRefPubMedGoogle Scholar
  19. 19.
    Lestienne, F., P. P. Vidal, and A. Berthoz. Gaze changing behaviour in head restrained monkey. Exp. Brain Res. 53:349–356, 1984.CrossRefPubMedGoogle Scholar
  20. 20.
    Morasso, P., G. Sandini, V. Tagliasco, and R. Zaccaria. Control strategies in the eye-head coordination system. IEEE Trans. Syst. Man Cybern. 7:639–651, 1977.CrossRefGoogle Scholar
  21. 21.
    Neptune, R. R. Optimization algorithm performance in determining optimal controls in human movement analyses. J. Biomech. Eng. 121:249–252, 1999.CrossRefPubMedGoogle Scholar
  22. 22.
    Quaia, C., H. S. Ying, A. M. Nichols, and L. M. Optican. The viscoelastic properties of passive eye muscle in primates. I. Static and step responses. PLoS One 4:e4850, 2009.Google Scholar
  23. 23.
    Richmond, F. J., K. Singh, and B. D. Corneil. Neck muscles in the rhesus monkey. I. Muscle morphometry and histochemistry. J. Neurophysiol. 86:1717–1728, 2001.PubMedGoogle Scholar
  24. 24.
    Scudder, C. A., C. S. Kaneko, and A. F. Fuchs. The brainstem burst generator for saccadic eye movements: a modern synthesis. Exp. Brain Res. 142:439–462, 2002.CrossRefPubMedGoogle Scholar
  25. 25.
    Song, D., G. Raphael, N. Lan, and G. E. Loeb. Computationally efficient models of neuromuscular recruitment and mechanics. J. Neural Eng. 5:175–184, 2008.CrossRefPubMedGoogle Scholar
  26. 26.
    Sylvestre, P. A., and K. E. Cullen. Premotor correlates of integrated feedback control for eye-head gaze shifts. J. Neurosci. 26:4922–4929, 2006.CrossRefPubMedGoogle Scholar
  27. 27.
    Vandekerckhove, J. General Simulated Annealing Algorithm, 2006. Accessed 14 July 2008.
  28. 28.
    Van Lopik, D. W., and M. Acar. Development of a multi-body computational model of human head and neck. Proc. Inst. Mech. Eng. Part K: J. Multi-body Dyn. 221:175–197, 2007.Google Scholar
  29. 29.
    Vasavada, A. N., S. Li, and S. L. Delp. Influence of muscle morphometry and moment arms on the moment-generating capacity of human neck muscles. Spine 23:412–422, 1998.CrossRefPubMedGoogle Scholar
  30. 30.
    Zajac, F. E. Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. Crit. Rev. Biomed. Eng. 17:359–411, 1989.PubMedGoogle Scholar
  31. 31.
    Zangemeister, W. H., A. C. Arlt, and S. Lehman. Sensitivity functions of a human head movement model. Med. Eng. Phys. 16:163–170, 1994.CrossRefGoogle Scholar
  32. 32.
    Zangemeister, W. H., L. Stark, O. Meienberg, and T. Waite. Neural control of head rotation: electromyographic evidence. J. Neurol. Sci. 55:1–14, 1982.CrossRefPubMedGoogle Scholar

Copyright information

© Biomedical Engineering Society 2009

Authors and Affiliations

  1. 1.Biomedical Engineering ProgramUniversity of ConnecticutStorrsUSA
  2. 2.Electrical and Electronic Engineering SchoolUniversidad Industrial de SantanderBucaramangaColombia

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