Mathematical and Physical Modelling, Numerical Approximation, Identification Problems and "Space-Time" Model Aggregation in the Human Respiratory System

Abstract

We have analyzed the gases transport in the human lung through a physico-mathematical model. The physical mechanisms that vre have to consider are the diffusion-convection (gas) in the conducting airways and the exchange through the alveolo-capillary barrier.The pulmonary anatomical structure gives a non linear bronchial geometry in space (and eventually time-variant). The contributions of parabolic and hyperbolic terms have different prepondances in space and in time during inspiratory and expiratory phases. The hyperbolic predominates in the first bronchial generations; the parabolic term traduces the controlling phenomena at the ends of the bronchial tree. A mixed finite element method has been retained for the numerical approximation.One of the objectives of the study leads to routine use in Intensive Unit Care for aided monitoring and aid to decision in pathological cases (functions and bronchio alveolar parameters). The implementation which we would like to do necessitates an aggregation of the model. Up to now, the realized aggregation which we have made gives a gain in time by a factor of 8 against the previous computing time.