Modelling lung deposition of inhaled particles in cystic fibrosis

This project will use mathematical and computational modelling to investigate fundamental physical mechanisms of flow and transport in lung airways, considering in particular features relevant to cystic fibrosis and related aspects of drug delivery. The presence of large quantities of highly viscous mucus in airways is a primary symptom of cystic fibrosis, making it challenging to effectively administer inhaled therapies deep into the lungs. Using the machinery of theoretical continuum mechanics, this project will seek to improve our understanding of how mucus is distributed and transported throughout the lungs, and how this could affect the efficacy of different methods of drug delivery. There will be an initial focus on the impact of the complex rheological properties of diseased mucus (such as its yield stress) on transport within small airways in the lung periphery, regions of the lungs that are difficult to study experimentally and difficult to resolve using medical imaging. In the later stages of the project, multi-scale modelling approaches exploiting tools from discrete calculus will be used to assess how small-airway transport processes impact on drug-delivery at the organ scale, allowing incorporation of the effects of ventilation in the whole airway tree. This will require solution of transport equations on massive discrete networks, which will require relatively intensive computation due to the large number of airways involved. This approach, combined with dimensionality reduction techniques, will allow investigation into the effects of airway geometry on transport in the lungs and on development of disease. Throughout the project, model development will be motivated by the physiological and clinical applications, in particular the effective delivery of inhaled aerosolised pharmaceuticals to damaged or blocked lung regions in cystic fibrosis. To achieve this, the student will be guided by a multidisciplinary team of supervisors, drawn from the Department of Mathematics and the Division of Infection, Immunity & Respiratory Medicine at the University of Manchester. The models emerging from the project are likely to have broader potential application beyond cystic fibrosis (for example, to fundamental fluid mechanics), but this disease-specific approach means that the project will give new capabilities to realistically test and optimise drug-delivery protocols in silico that can make a real difference to patient treatment.