Skip to main content

In haughton’s footsteps: Mathematical insights into bioengineering and rehabilitation

Abstract

Four attempts are outlined which the author has made to develop mathematical models for topics encountered in bioengineering and rehabilitation. The first isautoregulation in the kidney, for which a nonlinear oscillator model is derived, based on observations of flow noise made by Erol Basar. The second is anonlinear observer based on the theory of automatic control, developed to study patterns of spastic torque in paralysed legs via thependulum test. The third is a design study of a skeletal muscle reflex arc involving the muscle spindle dynamics and invokingprinciple of optimum stability. The final topic is an attempt to lay the groundwork for a mathematical theory of the cross-bridge or sliding filament mechanism of muscular contraction.

This is a preview of subscription content, access via your institution.

References

  1. French, P. Prose, poems and parodies, Talbot Press, Dublin, 1929.

    Google Scholar 

  2. Coakley, D. Irish Masters of Medicine, Town House, Dublin, 1992.

    Google Scholar 

  3. Fox, S. I. Human Physiology. Wm. C. Brown Publishers, Dubuque, Iowa, 1994, (4th edition).

    Google Scholar 

  4. Basar, E. Biophysical and Physiological Systems Analysis, Addison-Wesley, Reading, Mass., 1976.

  5. de Paor, A. M., Timmons, P. A feedback oscillator model for circulatory autoregulation. Int. J. Control. 1986; vol 43: 679–688.

    Article  Google Scholar 

  6. Clynes, M. Unidirectional Rate sensitivity: a biocybernetic law of reflex and humoral systems as physiologic channels of control and communication. Ann. N Y Acad Sci 1961; 92: 946–969.

    PubMed  CAS  Article  Google Scholar 

  7. Øien, A. H., Aukland, K. Mathematical analysis of the myogenic hypothesis, with special reference to autoregulation of renal blood flow. Circ. Res 1983; 52: 241–252.

    PubMed  Google Scholar 

  8. Johnson, P. C., Wayland, H. Regulation of blood flow in single capillaries. Am. J. Physiol. 1967; 212: 1405–1415.

    PubMed  CAS  Google Scholar 

  9. Keane, A. M. Spasticity and Electrical stimulation in the Spinal Cord Injured. M. Med. Sc. thesis, National University of Ireland (UCD), 1994.

  10. de Paor, A. Some contributions to Rehabilitation Engineering in Ireland. Lekar a Technika 1995; 26: 3–8.

    Google Scholar 

  11. McMillan, N. D. Rev. Samuel Haughton and the Age of the earth controversy, pp. 151–161 of Nudds, J., McMillan, N., Weaire, D., McKenna Lawlor, S. (eds). Science in Ireland 1800–1930: tradition and reform, Trinity College Dublin, 1988.

  12. Haughton, S. Principles of Animal Mechanics, Longmans, Green, London, 1873.

    Google Scholar 

  13. Hildebrandt, S., Tromba, A. The Parsimonious Universe: shape and form in the natural world, Copernicus (Springer Verlag), New York, 1996.

    Google Scholar 

  14. Haughton, S. On the forms of the cells made by various wasps and by the honey-bee. Proc. Natural Hist. Soc. Dublin 1863; 3: 128–140.

    Google Scholar 

  15. Maxwell, J. C. On Governors. Proc. Roy. Soc. 1868; 16: 270–283.

    Google Scholar 

  16. Routh, E. J. The advanced part of a treatise on the dynamics of rigid bodies. Macmillan & Co., London, 1884 (4th edition). The stability criterion described on pp. 166–176 was first given by Routh in his Adams Prize essay at Cambridge, 1877.

  17. de Paor, A. Fifty years of Root Locus: some new thoughts, Proceedings of the 2nd IFAC Workshop on New Trends in the Design of Control Systems, Smmolenice, Slovak Republic, September 7-190 1997, pp. 110-115.

  18. Tyldesley, B., Grieve, J. I. Muscles, nerves and movement: Kinesiology in daily living. Blackwell Publications, Oxford, 1989.

    Google Scholar 

  19. Stark, L. Neurologic Control Systems: studies in bioengineering, Plenum Press, New York, 1968.

    Google Scholar 

  20. Granit, R. Receptors and Sensory Perception, Yale University Press, New Haven, Conn., 1955 (5th printing 1967).

    Google Scholar 

  21. Gordon, A. M., Huxley, A. F., Julian, F. J. The variation in isometric tension with sarcoMere length in vertebrate muscle fibres. J. Physiol. 1966; 184: 170–192.

    PubMed  CAS  Google Scholar 

  22. Joyce, G. C., Rack, P. H. M., Westbury, D. R. The mechanical properties of cat soleus muscle during controlled lengthening and shortening movements. J. Physiol. 1969; 204: 461–474.

    PubMed  CAS  Google Scholar 

  23. Murray, C. D., de Paor, A. M. Modelling the force velocity relation of muscle. Proceedings of the 17th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Montreal, Canada, September 20–23, 1995, 2pp. (Not paginated on CD-ROM).

Download references

Author information

Authors and Affiliations

Authors

Additional information

The Fourth Samuel Haughton Lecture presented to the joint meeting of the Section of Bioengineering and the Ulster Biomedical Engineering Society, Dundalk, Co. Louth, 21–22 February, 1998.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

de Paor, A. In haughton’s footsteps: Mathematical insights into bioengineering and rehabilitation. Ir. J. Med. Sc. 167, 170–180 (1998). https://doi.org/10.1007/BF02937932

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02937932

Keywords

  • Characteristic Polynomial
  • Myosin Head
  • Root Locus
  • Optimum Stability
  • Influence Diagram