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Limitations of the open loop gain concept in studies of respiratory control

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Abstract

A steady state mathematical model was used to study the limitations of applying the open loop gain concept to the ventilatory control system. Open loop gain is a term used in the study of linear control systems and is an indicator of how well the controlled variable is regulated. The model contained descriptions of the O2 and CO2 control systems as well as their interactions. Disturbances to the system were modelled as occurring via inspired air, metabolic rate and ventilation. The ventilatory response to hypoxia was simulated for (a) hypocapnic hypoxia, (b) normocapnic hypoxia (PaCO2=40 torr) and (c) hypercapnic hypoxia (PaCO2=45 torr). The open loop gains of the O2 and CO2 loops were calculated at each operating point. In addition, the sensitivity of the controlled variable to disturbances to the loop were also compared. It was observed that open loop gain did not completely describe the characteristics of the ventilatory control system. This was due to the fact that the ventilatory system is nonlinear and the regulatory ability of the ventilatory system depends on the route of the disturbance, and (2) open loop gain ignores the interactions of the CO2 and O2 loops, which can be substantial.

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References

  1. Bennett, F.M.; Fordyce, W.E. Gain of the ventilatory exercise stimulus: definition and meaning. J. Appl. Physiol. 65:2011–2017; 1988.

    CAS  PubMed  Google Scholar 

  2. Bennett, F.M.; Fordyce, W.E. Regulation of PaCO2 during rest and exercise: a modelling study. Submitted J. Appl. Physiol.

  3. Cunningham, D.J.C.; Robbins, P.A.; Wolff, C.B. Integration of respiratory responses to changes in alveolar partial pressures of CO2 and O2 and in arterial pH. In: Handbook of physiology. The respiratory system. Vol. II. Control of breathing. Part. 2. Bethesda, Md.; 1986: pp. 475–528.

  4. Gray, J.S.; Grodins, F.S.; Carter, E.T. Alveolar and total ventilation and the dead space problem. J. Appl. Physiol. 9:307–320; 1956.

    PubMed  Google Scholar 

  5. Grodins, F.S.; Gray, J.S.; Schroeder, K.R.; Norins, A.L.; Jones, R.W. Respiratory responses to CO2 inhalation. A theoretical study of a non-linear biological regulator. J. Appl. Physiol. 7:283–308; 1954.

    CAS  PubMed  Google Scholar 

  6. Honda, Y.; Hayashi, F.; Yoshida, A.; Ohyabu, Y.; Nishibayashi, Y.; Kimura, H. Overall “gain” of the respiratory control system in normoxic humans awake and asleep. J. Appl. Physiol. 55:1530–1535; 1983.

    CAS  PubMed  Google Scholar 

  7. Khoo, M.C.K.; Kronauer, R.E.; Strohl, K.P.; Slutsky, A. Factors inducing periodic breathing in humans: a general model. J. Appl. Physiol. 53:644–659, 1982.

    CAS  PubMed  Google Scholar 

  8. Loeschcke, H.H. The respiratory control system: analysis of steady state solutions for metabolic and respiratory acidosis-alkalosis and increased metabolism. Pflugers Arch. 341:23–42; 1973.

    CAS  PubMed  Google Scholar 

  9. Loeschcke, H.H. The effectiveness of the control of pH in the extracellular fluid of the brain by the respiratory control system. Pflugers Arch. 341:43–50; 1973.

    CAS  PubMed  Google Scholar 

  10. Masuyama, H.; Hayashi, F.; Honda, Y. An assessment of overall “gain” of the O2 feedback control system with and without external dead space breathing. Jpn. J. Physiol. 33:699–710; 1983.

    CAS  PubMed  Google Scholar 

  11. Masuyama, H.; Honda, Y. Difference in overall “gain” of CO2 feedback system between dead space and CO2 ventilation in man. Bull. Eur. Physiopathol. Respir. 20:501–506; 1984.

    CAS  PubMed  Google Scholar 

  12. Masuyama, H.; Akiyama, S.; Honda, Y. An assessment of overall open-loop “gain” of CO2 ventilation feedback control system in hypoxia. Jpn. J. Physiol. 35:545–552; 1985.

    CAS  PubMed  Google Scholar 

  13. Milhorn, H.T. Jr.; Guyton, A.C. An analog computer analysis of Cheyne-Stokes breathing. J. Appl. Physiol. 20:328–333; 1965.

    Google Scholar 

  14. Milhorn, H.T., Jr. The application of control theory to physiological systems. Philadelphia, Pa.: Saunders; 1966.

    Google Scholar 

  15. Riggs, D.S. Control theory and physiological feedback mechanisms. Huntington, New York: R.E. Krieger Publishing Co.; 1976.

    Google Scholar 

  16. Stegemann, J.; Seez, P.; Kremer, W.; Boning, D. A mathematical model of the ventilatory control system to carbon dioxide with special reference to athletes and nonathletes. Pflugers Arch. 356:223–236; 1975.

    Article  CAS  PubMed  Google Scholar 

  17. Takano, N.; Sakai, A.; Iida, Y. Analysis of alveolar Pco2 during the menstrual cycle. Pflugers Arch. 390:56–62; 1981.

    Article  CAS  PubMed  Google Scholar 

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  1. Department of Biomedical Engineering, Worcester Polytechnic Institute, 100 Institute Road, 01609, Worcester, MA

    Frederick M. Bennett Ph.D.

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  1. Frederick M. Bennett Ph.D.
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Bennett, F.M. Limitations of the open loop gain concept in studies of respiratory control. Annals of Biomedical Engineering 18, 533–547 (1990). https://doi.org/10.1007/BF02364616

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  • DOI: https://doi.org/10.1007/BF02364616

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