Multi-scale mathematical modelling of the interplay between mucus dynamics and NO transport in the human lungs. Towards the assessment of bronchial clearance techniques for patients with cystic fibrosis.

17 October 2019

The lung is an organ in which a multitude of transport phenomena take place. Because of the wide spectrum of length scales encountered in this organ, mathematical modelling and numerical simulation are often the only tools for understanding the complexity of these phenomena, especially deep in the lungs.

The bronchial epithelium is covered with a layer of mucus, protecting the body from external pathogens and dust. This mucus is set in motion by cilia beating metachronously, from the distal generations of the lung to the trachea, where it is swallowed. This mucociliary clearance is, however, impaired in many diseases, such as cystic fibrosis. This impairment results in an accumulation of mucus in the bronchi, leading to breathing difficulties and repetitive infections. Many bronchial clearance techniques exist but, currently, there is a lack of quantitative methods to assess their effectiveness. 

Nitric oxide (NO) is a molecule that, like oxygen or carbon dioxide, is exchanged in the lung between the human body and the outside world. More precisely, this molecule is essentially produced in the bronchial epithelium of the pre-acinar generations of the lung. Because of this, several recent studies suggested that the measurement of the NO concentration in the exhaled air could be used to characterize airway calibre changes deep in the lung.

In this work, we propose to demonstrate that measuring the NO concentration in the exhaled air makes it possible to objectively evaluate the quality of various bronchial clearance techniques for patients with cystic fibrosis. To do this, we have developed a multi-scale model of NO production and transport in the lung. This model has been challenged against clinical data obtained in various studies. The results obtained make it possible to highlight the complexity of the interplay between the transport of NO and the mucus dynamics in the distal region of the lungs and offer very interesting perspectives for the characterization of bronchial clearance techniques.

  • Industrial and Applied Mathematics Seminar