Section: Application Domains

Respiratory system

Participants : Bertrand Maury, Astrid Decoene.

Comprehensive models to simulate the whole pulmonary system, i.e., the mechanical behavior of the lung and gas exchanges within the pulmonary system, are built upon ODE and PDE approaches. For instance, the mechanical behavior of a lung is often described by single or multi-compartment ODE models, whereas air flow may be determined by the coupling of a 3D PDE system in the proximal part of the bronchial tree with a 0D ODE system in the distal part of the bronchial tree. Gas exchange has so far been investigated using 0D or 1D models in which heterogeneity of gas exchange along the path length may be investigated.

In a mathematical representation of such physiological systems, model parameters can be associated with specific quantities in the real system, such as the resistance and compliance of the pulmonary system. These quantities are time-dependent and nonlinear and are measured by pneumologists in order to characterize chronic obstructive pulmonary diseases (COPD) such as asthma and emphysema. These parameters may be useful in assessing lung conditions.

Although most physiological studies have used averaged deterministic models of the tracheobronchial tree geometry, morphometric studies show that inter-subject and intra-subject variability in the structural components of the human lung is significant. In particular, the resistance of the respiratory tract may be significantly affected as it is directly related to the inner diameter of the bronchi. Feedback from such variability to resistance and, as a consequence efficiency of the gas exchange process, within the framework of a fully coupled model, is unclear. In this situation, the statistical and numerical approaches being developed by Popix are clearly promising estimation methods for respiratory system analysis.