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)

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)