The application of the flow interrupter technique to series and parallel models of the respiratory system is examined theoretically, assuming instantaneous transmission of pressures and incompressible gases in the lung air spaces. The initial pressure change observed immediately after occlusion divided by the preocclusion flow gives an initial resistance (Rinit) equal to that of the airway tree when the model consists of compartments connected in parallel. When the compartments are connected in series, Rinit is the resistance of the most proximal airway only. In general, the initial pressure change is followed by a second slower change, reflecting equilibration of pressures between the compartments. The total postocclusion pressure change divided by the flow gives a steady-state resistance (Rss) whose value depends on the ventilation history before occlusion. When this history consists of a relaxed expiration Rss asymptotes from Rinit to a value higher than the zero-frequency resistance of the model as the expiratory time increases. However, the relative contributions of serial and parallel pendelluft and viscoelasticity to Rss cannot be determined from pressure and flow measurements made at the airway opening. Therefore in disease, the interrupter method does not permit one to say whether ventilation inhomogeneity or alteration in lung tissue properties is the predominant abnormality.

In humans, lung ventilation exhibits breath-to-breath variability and dynamics that are nonlinear, complex, sensitive to initial conditions, unpredictable in the long-term, and chaotic. Hypercapnia, as produced by the inhalation of a CO(2)-enriched gas mixture, stimulates ventilation. Hypocapnia, as produced by mechanical hyperventilation, depresses ventilation in animals and in humans during sleep, but it does not induce apnea in awake humans. This emphasizes the suprapontine influences on ventilatory control. How cortical and subcortical commands interfere thus depend on the prevailing CO(2) levels. However, CO(2) also influences the variability and complexity of ventilation. This study was designed to describe how this occurs and to test the hypothesis that CO(2) chemoreceptors are important determinants of ventilatory dynamics. Spontaneous ventilatory flow was recorded in eight healthy subjects. Breath-by-breath variability was studied through the coefficient of variation of several ventilatory variables. Chaos was assessed with the noise titration method (noise limit) and characterized with numerical indexes [largest Lyapunov exponent (LLE), sensitivity to initial conditions; Kolmogorov-Sinai entropy (KSE), unpredictability; and correlation dimension (CD), irregularity]. In all subjects, under all conditions, a positive noise limit confirmed chaos. Hypercapnia reduced breathing variability, increased LLE (P = 0.0338 vs. normocapnia; P = 0.0018 vs. hypocapnia), increased KSE, and slightly reduced CD. Hypocapnia increased variability, decreased LLE and KSE, and reduced CD. These results suggest that chemoreceptors exert a strong influence on ventilatory variability and complexity. However, complexity persists in the quasi-absence of automatic drive. Ventilatory variability and complexity could be determined by the interaction between the respiratory central pattern generator and suprapontine structures.

We present the current state of the development of the SAPHIR project (a Systems Approach for PHysiological Integration of Renal, cardiac and respiratory function). The aim is to provide an open-source multi-resolution modelling environment that will permit, at a practical level, a plug-and-play construction of integrated systems models using lumped-parameter components at the organ/tissue level while also allowing focus on cellular-or molecular-level detailed sub-models embedded in the larger core model. Thus, an in silico exploration of gene-to-organ-to-organism scenarios will be possible, while keeping computation time manageable. As a first prototype implementation in this environment, we describe a core model of human physiology targeting the short-and long-term regulation of blood pressure, body fluids and homeostasis of the major solutes. In tandem with the development of the core models, the project involves database implementation and ontology development.

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