Skip to main content
Log in

A mathematical model of the sympathetic-heart period system in the cat

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

Abstract

The dynamic behavior of changes in heart period in response to changes in frequency of supramaximal electrical stimulation of either pre- or postganglionic cardiac sympathetic nerves in five chloralosed cats pretreated with methyl atropine was investigated using time domain techniques. The typical response to step changes in frequency of stimulation (range 1–10 Hz) was found to be a decrease in heart period which reached a steady value after a short delay and was followed, after the stimulus was removed, by a slower return to prestimulus values. No significant difference was found between the responses to pre- and postganglionic stimulation although the strength of the stimuli required to achieve the same response was greater for postganglionic stimulation. Both the observed dynamic and steadystate responses were described to a good approximation by a first-order nonlinear system. The asymmetry in the response was accounted for by including in the model a second-order chemical reaction. The observed delay was accounted for by including a pure time delay. These results suggest that models proposed by previous investigators were unnecessarily complex.

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.

Similar content being viewed by others

References

  • Bezold, A. von.Untersuchungen über die Innervation des Herzens. Leipzig; Engelmann 1863, Pp. 122–129.

    Google Scholar 

  • Chess, G. F., and Calaresu, F. R. Frequency response model of vagal control of heart rate in the cat.American Journal of Physiology 1971,220, 554–557.

    CAS  PubMed  Google Scholar 

  • Chess, G. F., and Calaresu, F. R. A mathematical model of the vagus-heart period system in the cat.IEEE Transactions on Biomedical Engineering 1974,21, 21–27.

    CAS  PubMed  Google Scholar 

  • Draper, N. R., and Smith, H.Applied regression analysis. New York: John Wiley and Sons, 1966, Pp. 26–32.

    Google Scholar 

  • Green, J. H., and Heffron, P. F. The inter-relationship between sympathetic activity and the heart rate.Archives Internationales de Pharmacodynamie et de Thérapie 1967,169, 15–25.

    Google Scholar 

  • Henry, J. L., and Calaresu, F. R. Distribution of cardioacceleratory sites in intermediolateral nucleus of the cat.American Journal of Physiology 1972,222, 700–704.

    CAS  PubMed  Google Scholar 

  • Kuno, M. Quantum aspects of central and ganglionic synaptic transmission in vertebrates.Physiological Review 1971,51, 647–678.

    CAS  Google Scholar 

  • Liddell, E. G. T., and Sherrington, C.Mammalian physiology: A course of practical exercises. Oxford: Clarendon Press, 1929. Pp. 56–62.

    Google Scholar 

  • Randall, W. C., and Kelso, A. F. Dynamic basis for sympathetic cardiac augmentation.American Journal of Physiology 1960,198, 971–974.

    CAS  PubMed  Google Scholar 

  • Randall, W. C., and Rohse, W. G. The augmentor action of the sympathetic cardiac nerves.Circulation Research 1956,4, 470–475.

    CAS  PubMed  Google Scholar 

  • Reid, M. H., and Mackay, R. S. A review and discussion of some methods for system identification and modeling.Medical and Biological Engineering 1968,6, 231–268.

    CAS  Google Scholar 

  • Rosenbleuth, A., and Simeone, F. A. The interrelations of vagal and accelerator effects on the cardiac rate.American Journal of Physiology 1934,110, 42–55.

    Google Scholar 

  • Samaan, A. The antagonistic cardiac nerves and heart rate.Journal of Physiology 1935,83, 332–340.

    Google Scholar 

  • Walpole, R. E., and Myers, R. H.Probability and statistics for engineers and scientists. New York: Macmillan Company, 1972.

    Google Scholar 

  • Warner, H. R., and Cox, A. A mathematical model of heart rate control by sympathetic and vagus efferent information.Journal of Applied Physiology 1962,17, 349–355.

    CAS  PubMed  Google Scholar 

  • Warner, H. R., and Russell, R. O. Effect of combined sympathetic and vagal stimulation on heart rate in the dog.Circulation Research 1969,24, 567–573.

    CAS  PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chess, G.F., Varey, D.W., Henry, J.L. et al. A mathematical model of the sympathetic-heart period system in the cat. Ann Biomed Eng 3, 189–198 (1975). https://doi.org/10.1007/BF02363070

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02363070

Keywords

Navigation