A Computational Model of the Human Respiratory Control System: Responses to Hypoxia and Hypercapnia

Although recent models offer realistic descriptions of the human respiratory system, they do not fulfill all characteristics of a stable, comprehensive model, which would allow us to evaluate a variety of hypotheses on the control of breathing. None of the models offer completely realistic descriptions of the gaseous components of blood, and their description of delays associated with the propagation of changes in partial pressures of respiratory gases between the lungs and brain and tissue compartments have shortcomings. These deficiencies are of particular significance in an analysis of periodic breathing where dynamic alterations in the circulation and in blood chemical stimuli are likely to assume considerable importance. We developed a computational model of the human respiratory control system which is an extension of the model of Grodins et al. (F. S. Grodins, J. Buell, and A. J. Bart. J. Appl. Physiol. 22(2):260–276, 1967). Our model combines an accurate description of a plant with a novel controller design that treats minute ventilation as a sum of central and peripheral components. To ensure that the developed model is stable and sufficiently robust to act as a test platform for hypotheses about control of ventilation, we simulated a series of challenging physiological conditions, specifically, the response to eucapnic hypoxia, the development of periodic breathing during hypocapnic hypoxia, and the open loop response to hypercapnic step. These steady state and transient responses of the model were compared with results from similar physiological experiments. Our simulations suggest that for a particular value of arterial \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $${\text{P}}_{{\text{O}}_2}$$ \end{document}, the steady state difference between brain and arterial \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $${\text{P}}_{{\text{CO}}_2}$$ \end{document} remains approximately constant as a function of arterial \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $${\text{P}}_{{\text{CO}}_2}$$ \end{document}. The model indicates that hypoxia-induced changes in cerebral blood flow contribute significantly to the ventilatory decline observed during eucapnic hypoxia. The model exibits hypoxic-induced periodic breathing, which can be eliminated by small increases in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $${\text{F}}_{{\text{I}}_{{\text{CO}}_2}}$$ \end{document}. The dynamics of the model's open loop hypercapnic ventilatory response approximates experimental data well.