Advertisement

Simulation of single muscle fibre action potentials

  • S. D. Nandedkar
  • E. St⇘lberg
Article

Abstract

Using the volume conductor model, a single muscle fibre action potential can be expressed as a convolution of the transmembrane current and a weighting function. By simplifying the weighting function, the line source model is derived. We have developed similar expressions to compute the single muscle fibre action potential using simple models and physical considerations without any mathematical complexity. The relationship between the conduction velocity and amplitude is analysed and it is concluded that, for a given fibre, the amplitude is inversely proportional to the conduction velocity. This agrees with the experimental data reported in the literature.

The relation between amplitude and fibre diameter is studied. The amplitude increases with diameter owing to the increase in membrane current, but it is counteracted by the increase in conduction velocity. Because of the opposing effects, a point of inflection in the amplitude/diameter relationship is observed. Squareroot, square and linear dependencies of conduction velocity on fibre diameter were used. The difference in the peak-to-peak amplitude with these relationships is small and a linear relation between amplitude and fibre diameter seems reasonable irrespective of the conduction velocity/fibre diameter relationship.

The effect of lumping the transmembrane current at the axis of the fibre is discussed. This approximation results in an underestimation of the peak-to-peak amplitude near the surface, and the error is close to 50% for very large fibres. This error is accounted for in the model.

The recording distance at which the peak-to-peak amplitude of the signal is 100 μV is found to be 400 μm in the model. This is in good agreement with values obtained from a single-fibre electrode recording. The model is computationally fast and precise. It can easily be used with few modifications to simulate single fibre action potentials recorded using different electrodes.

Keywords

Action potential Models Muscle Simulation Single fibre 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adrian, E. D. andBronk, D. W. (1929) The discharge of impulses in motor nerve fibres. Part II. The frequency of discharge in reflex and voluntary contractions.J. Physiol.,67, 119–151.Google Scholar
  2. Agarwal, G. C. andGottlieb, G. L. (1975) An analysis of electromyogram by fourier, simulation and experimental technique.IEEE Trans.,BME-22, 225–229.Google Scholar
  3. Andreassen, S. andRosenfalck, A. (1981) Relationship of intracellular and extracellular action potential of skeletal muscle fibre. InCritical reviews in bioengineering, CRC Press Inc.6, 267–306.Google Scholar
  4. Boyd, D. C., Lawrence, P. D. andBratty, P. J. A. (1978) On modelling the single motor unit potential.IEEE Trans.,BME-25, 236–243.Google Scholar
  5. Brigham, E. (1974)Fast fourier transform. Prentice Hall, Englewood Cliff, New Jersey.zbMATHGoogle Scholar
  6. Buchthal, F., Guld, C. andRosenfalck, P. (1957) Multielectrode study of the territory of motor unit.Acta Physiol. Scand.,39, 83–104.Google Scholar
  7. Ekstedt, J. (1964) Human single muscle fibre action potentials.Acta Physiol. Scand.,61, Suppl. 226, 1–96.Google Scholar
  8. Geddes, L. A. andBaker, L. E. (1967) The specific resistance of biological material.Med. & Biol. Eng.,5, 271–293.Google Scholar
  9. George, R. E. (1970) Summation of muscle fibre action potential.,8, 357–365.Google Scholar
  10. Griep, P. A. M., Boon, K. L. andStegeman, D. F. (1978) A study of motor unit action potential by means of computer simulation.Biol. Cybernetics,30, 221–230.CrossRefGoogle Scholar
  11. Hakansson, C. H. (1956) conduction velocity and amplitude of action potential as related to circumference in the isolated fibre of frog muscle.Acta Physiol. Scand.,37, 14–34.CrossRefGoogle Scholar
  12. Hodgkin, A. L. (1954) A note on conduction velocity.J. Physiol.,125, 221–224.Google Scholar
  13. Lindström, L. (1973) A model describing the power spectrum of myoelectric signal Part I: Single fibre signal. Technical report 5, 73 Chalmers University, Gothenburg.Google Scholar
  14. Lorente, de No R. (1947) A study of nerve physiology. Studies of the Rockfeller Institute for Medical Research,132, 384–477.Google Scholar
  15. Nygaard, E. (1981) Morfology og funktion i m. Biceps Brachii. (Thesis). Kopenhavns Universitet.Google Scholar
  16. Plonsey, R. (1964) Volume conductor fields of action currents,Biophysics J.,4, 317–328.Google Scholar
  17. Plonsey, R. (1974) The active fibre in a volume conductorIEEE. Trans.,BME-21, 371–381.Google Scholar
  18. Plonsey, R. (1977) Action potential sources and their volume conductor fields.Proc. IEEE.,65, 601–611.CrossRefGoogle Scholar
  19. Rosenfalck, P. (1969) Intra and extracellular potential fields of active nerve and muscle fibres. A physiomathematical analysis of different models.Acta Physiol. Scand., Suppl 321, 1–168.Google Scholar
  20. Rush, S., Abildskov, J. A. andMcFee, R. (1963) Resistivity of the body tissue at low frequencies.Circulation Res.,12, 40–50.Google Scholar
  21. Stalberg, E. (1966) Propagation velocity in human muscle fibre in situ.Acta Physiol. Scand.,70, Suppl. 287.Google Scholar
  22. St⇘lberg, E. andThiele, B. (1975) Motor units fibre density in the extensor digitorum communis muscle.J. Neurol. Neurosurg. & Psych. 38, 874–880.Google Scholar
  23. St⇘lberg, E. andGath, I. E. (1979) Measurement of uptake area of small size electromyographic electrodes,IEEE Trans.,BME-26, 374–376.Google Scholar
  24. St⇘lberg, E. andTrontelj, J. (1979)Single fibre electromyography. Mirvalle Press Ltd., Old Woking, Surrey, England.Google Scholar
  25. St⇘lberg, E. andAntoni, L. (1980) The electrophysiological cross section of a motor unit.J. Neurol. Neurosurg. & Psych.,43, 469–474.Google Scholar
  26. St⇘lberg, E. (1980) Macro EMG, a new recording technique.,43, 475–482.Google Scholar
  27. Wani, A. andGuha, S. (1980) Synthesising of a motor unit potential based on the sequential firing of muscle fibres.Med. & Biol. Eng. & Comput.,18, 719–726.CrossRefGoogle Scholar

Copyright information

© IFMBE 1983

Authors and Affiliations

  • S. D. Nandedkar
    • 1
  • E. St⇘lberg
    • 1
  1. 1.Department of Clinical NeurophysiologyUniversity HospitalUppsalaSweden

Personalised recommendations