Multiscale and Multiphysics Modelling of the Respiratory System – M3RS

What are the main mechanisms involved in an asthma crisis?
How does a curative aerosol or the dust pollution deposit in the airways?
How emphysema or fibrosis affects the supply of air?
What is the function of the surfactant that covers lung alveoli? …
From the medical, environmental and societal point of view, this kind of questions raises many
challenging issues we would like to contribute to answer. Indeed we think that the mathematical
approach of the problem, in interaction with lung specialists, could provide new elements and improve
the understanding on the topic. In particular, numerical simulations may accurately reproduce
the behaviour of the airflow in the bronchial tree and they may help the clinician to identify the pathology
and cure it.
The present research program thus focuses on the mathematical, numerical and computational modelling
of the respiratory system. The complex fractal geometry of the airway tree makes the airflow
simulation on the whole tree unreachable, not to mention the global simulation of the interaction
between an aerosol and the air. Consequently, it is necessary to find new efficient strategies, including
simple but realistic models.
Depending on the type of applications we want to study (air transport, particle deposition, mechanical
behaviour of the parenchyma, airway closure), we intend to find such adequate and realistic
models by taking into account each physical phenomenon and coupling them one to each other, or
deriving boundary conditions (or reduced model) to describe the part of the lung which is not under
focus.
Then, for each of these models, many questions may be addressed, such as the wellposedness of the
problems, their mathematical properties (regularity of the solution, long time behaviour, controllability
of the system), the design of accurate numerical algorithms, the performing of efficient computational
simulations. At each stage, we shall discuss our results with experts from other fields
(fluid and structure mechanics as well as physiology and medicine). In particular, our computations
will be compared to experimental results or clinical data and it will be used as a feedback until good
agreement is reached and they can serve as a prediction tool.