Skip to main content
Log in

Linear Homeomorphic Models for Muscles in the Head–Neck Region

  • Published:
Annals of Biomedical Engineering Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11

Similar content being viewed by others

References

  1. Bizzi, E., R. E. Kalil, and V. Tagliasco. Eye-head coordination in monkeys: evidence for centrally patterned organization. Science 173:452–454, 1971.

    Article  PubMed  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  CAS  PubMed  Google Scholar 

  4. Chang, Y., P. Coddington, and K. Hutchens. The NPAC/OLDA Visible Human Viewer. Adelaide, Australia: Computer Science Department, Adelaide University. www.dhpc.adelaide.edu.au/projects/vishuman2/. Accessed 11 July 2007.

  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.

    Article  CAS  PubMed  Google Scholar 

  6. Close, R. I., and A. R. Luff. Dynamic properties of inferior rectus muscle of the rat. J. Physiol. 236:259–270, 1974.

    PubMed  Google Scholar 

  7. Collins, C. C., D. O’Meara, and A. B. Scott. Muscle tension during unrestrained human eye movements. J. Physiol. 245:351–369, 1975.

    CAS  PubMed  Google Scholar 

  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.

  9. Enderle, J. D. Neural control of saccades. Prog. Brain Res. 140:21–49, 2002.

    Article  PubMed  Google Scholar 

  10. Enderle, J. D., J. D. Bronzino, and S. M. Blanchard. Introduction to Biomedical Engineering, vol. xxi. Amsterdam: Elsevier Academic Press, 1118 pp., 2005.

  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.

    Article  CAS  PubMed  Google Scholar 

  12. Enderle, J. D., and J. W. Wolfe. Time-optimal control of saccadic eye movements. IEEE Trans. Biomed. Eng. 34:43–55, 1987.

    Article  CAS  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  14. Freedman, E. G. Coordination of the eyes and head during visual orienting. Exp. Brain Res. 190:369–387, 2008.

    Article  PubMed  Google Scholar 

  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.

    CAS  PubMed  Google Scholar 

  16. Hannaford, B. Control of Fast Movement: Human Head Rotation. PhD dissertation, University of California, Berkeley, 1985.

  17. Kamibayashi, L. K., and F. J. Richmond. Morphometry of human neck muscles. Spine 23:1314–1323, 1998.

    Article  CAS  PubMed  Google Scholar 

  18. Kirkpatrick, S., C. D. Gelatt, Jr., and M. P. Vecchi. Optimization by simulated annealing. Science 220:671–680, 1983.

    Article  PubMed  Google Scholar 

  19. Lestienne, F., P. P. Vidal, and A. Berthoz. Gaze changing behaviour in head restrained monkey. Exp. Brain Res. 53:349–356, 1984.

    Article  CAS  PubMed  Google Scholar 

  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.

    Article  Google Scholar 

  21. Neptune, R. R. Optimization algorithm performance in determining optimal controls in human movement analyses. J. Biomech. Eng. 121:249–252, 1999.

    Article  CAS  PubMed  Google Scholar 

  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. 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.

    CAS  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  CAS  PubMed  Google Scholar 

  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.

    Article  CAS  PubMed  Google Scholar 

  27. Vandekerckhove, J. General Simulated Annealing Algorithm, 2006. http://www.mathworks.com/matlabcentral/fileexchange/10548. Accessed 14 July 2008.

  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. 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.

    Article  CAS  PubMed  Google Scholar 

  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.

    CAS  PubMed  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  CAS  PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to John D. Enderle.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sierra, D.A., Enderle, J.D. Linear Homeomorphic Models for Muscles in the Head–Neck Region. Ann Biomed Eng 38, 247–258 (2010). https://doi.org/10.1007/s10439-009-9851-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10439-009-9851-6

Keywords

Navigation