Patients suffering from chronic obstructive pulmonary diseases, frequently exhibit expiratory airflow limitation. We propose a mathematical model describing the mechanical behavior of the ventilated respiratory system. This model has to simulate applied positive end-expiratory pressure effects during expiration, a process used by clinicians to improve airflow. The proposed model consists of a nonlinear two-compartment system. One of the compartments represents the collapsible airways and mimics its dynamic compression, the other represents the lung and chest wall compartment. For all clinical conditions (...) tested, the mathematical model simulates the removal of expiratory airflow limitation at PEEP lower than 70–80% of intrinsic end-expiratory pressure, i.e. the end-expiratory alveolar pressure without PEEP. It also shows the presence of an optimal PEEP. The optimal PEEP contributes to decrease PAet from 7.4 ± 0.9 to 5.4 ± 0.9 hPa. This simplistic mathematical model gives a plausible explanation of the expiratory airflow limitation removal with PEEP and a rationale to the practice of PEEP application to airflow limited patients. (shrink)

We have measured the change of lung mechanical parameters on isolated rabbit lungs exposed to chlorine gas (Cl{in2}). Experimental results show parallel increase in elastance and resistance of impaired lungs. We tried to determine whether this may be explained by a reduction of the ventilated areas in the lung, consecutive to closure of some airways. We have then tried to simulate these experimental results by studying the effects of various airways occlusions imposed on two concurrent models (symmetrical and dissymmetrical) of (...) the tracheo-bronchial tree. For each model, we successively evaluated the resistance of the normal lung, simulated a partial peripheral airways occlusion and estimated the induced changes in total resistance. Analytical expressions of the "occluded lung" elastance and resistance have been found for the symmetrical model but not for the dissymmetrical model (a graphical approach is proposed). With the symmetrical model, simulated results are comparable to experimental ones when the occlusion level is proximal. Whatever the dissymmetry level (δ) of the fractal tree model, we could not simulate the expected increase in resistance with the observed increase in elastance. We conclude that either the occlusion is non homogeneous or the lung impairment is not only a reduction in ventilated areas. (shrink)

To study the interaction of forces that produce chest wall motion, we propose a model based on the lever system of Hillman and Finucane (J Appl Physiol 63(3):951–961, 1987 ) and introduce some dynamic properties of the respiratory system. The passive elements (rib cage and abdomen) are considered as elastic compartments linked to the open air via a resistive tube, an image of airways. The respiratory muscles (active) force is applied to both compartments. Parameters of the model are identified in (...) using experimental data of airflow signal measured by pneumotachography and rib cage and abdomen signals measured by respiratory inductive plethysmography on eleven healthy volunteers in five conditions: at rest and with four level of added loads. A breath by breath analysis showed, whatever the individual and the condition are, that there are several breaths on which the airflow simulated by our model is well fitted to the airflow measured by pneumotachography as estimated by a determination coefficient R 2 ≥ 0.70. This very simple model may well represent the behaviour of the chest wall and thus may be useful to interpret the relative motion of rib cage and abdomen during quiet breathing. (shrink)

Based on the hypotheses that (1) a physiological organization exists inside each activity of daily life and (2) the pattern of evolution of physiological variables is characteristic of each activity, pattern changes should be detected on daily life physiological recordings. The present study aims at investigating whether a simple segmentation method can be set up to detect pattern changes on physiological recordings carried out during daily life. Heart and breathing rates and skin temperature have been non-invasively recorded in volunteers following (...) scenarios made of “daily life” steps (13 records). An observer, undergoing the scenario, wrote down annotations during the recording time. Two segmentation procedures have been compared to the annotations, a visual inspection of the signals and an automatic program based on a trends detection algorithm applied to one physiological signal (skin temperature). The annotations resulted in a total number of 213 segments defined on the 13 records, the best visual inspection detected less segments (120) than the automatic program (194). If evaluated in terms of the number of correspondences between the times marks given by annotations and those resulting from both physiologically based segmentations, the automatic program was better than the visual inspection. The mean time lags between annotation and program time marks remain <60 s (the precision of annotation times marks). We conclude that physiological variables time series recorded in common life conditions exhibit different successive patterns that can be detected by a simple trends detection algorithm. Theses sequences are coherent with the corresponding annotated activity. (shrink)

Expiratory flow limitation (EFL) can occur in mechanically ventilated patients with chronic obstructive pulmonary disease and other disorders. It leads to dynamic hyperinflation with ensuing deleterious consequences. Detecting EFL is thus clinically relevant. Easily applicable methods however lack this detection being routinely made in intensive care. Using a simple mathematical model, we propose a new method to detect EFL that does not require any intervention or modification of the ongoing therapeutic. The model consists in a monoalveolar representation of the respiratory (...) system, including a collapsible airway that is submitted to periodic changes in pressure at the airway opening: EFL provokes a sharp expiratory increase in the resistance Rc of the collapsible airway. The model parameters were identified via the Levenberg-Marquardt method by fitting simulated data on the airway pressure and the flow signals recorded in 10 mechanically ventilated patients. A sensitivity study demonstrated that only 8/11 parameters needed to be identified, the remaining three being given reasonable physiological values. Flow-volume curves built at different levels of positive expiratory pressure, PEEP, during PEEP trials (stepwise increases in positive end-expiratory pressure to optimize ventilator settings) have shown evidence of EFL in three cases. This was concordant with parameter identification (high Rc during expiration for EFL patients). We conclude from these preliminary results that our model is a potential tool for the non-invasive detection of EFL in mechanically ventilated patients. (shrink)

Misunderstanding of the dynamical behavior of the ventilatory system, especially under assisted ventilation, may explain the problems encountered in ventilatory support monitoring. Proportional assist ventilation (PAV) that theoretically gives a breath by breath assistance presents instability with high levels of assistance. We have constructed a mathematical model of interactions between three objects: the central respiratory pattern generator modelled by a modified Van der Pol oscillator, the mechanical respiratory system which is the passive part of the system and a controlled ventilator (...) that follows its own law. The dynamical study of our model shows the existence of two crucial behaviors, i.e. oscillations and damping, depending on only two parameters, namely the time constant of the mechanical respiratory system and a cumulative interaction index. The same result is observed in simulations of spontaneous breathing as well as of PAV. In this last case, increasing assistance leads first to an increase of the tidal volume (VT), a further increase in assistance inducing a decrease in VT, ending in damping of the whole system to an attractive fixed point. We conclude that instabilities observed in PAV may be explained by the different possible dynamical behaviors of the system rather than changes in mechanical characteristics of the respiratory system. (shrink)