Engineering Approach Offers Hope for Windpipe Swelling
Professor Thomas Pence and Visiting Researcher Kun Gou in the Department of Mechanical Engineering at Michigan State University are using complex mathematical models to study how the human trachea (windpipe) swells in response to an allergic reaction.
Angioedema, the technical term for such tissue swelling, refers to the rapid excess accumulation of fluid in under-skin tissue from blood vessel leakage. When this occurs in the trachea, it can rapidly narrow the airway leading to a life threatening condition. Bringing an engineering perspective to describe this process offers the possibility of developing new methods of treatment.
In order to reflect the altered tissue volume when angioedema is triggered by an allergic attack, Pence and Gou present a continuum mechanics analysis in which conventional large-strain hyperelastic theory is endowed with a swelling-dependent natural configuration – an improvement on traditional mechanical theories of tissue behavior.
The trachea can be visualized as a two layered tube. The inner layer, which is thin, is the soft mucous tissue that lines the airway. The relatively thicker outer layer is mostly cartilage and this provides the main structural support for the windpipe. The swelling is largely confined to the inner layer and this idealization is part of the model analysis. The inner layer also has directional anisotropy associated with a longitudinally aligned fibrous microstructure. The interaction among swelling, anisotropy and large deformation determines the overall airway constriction.
The computation of the modeling is based on a finite element formulation. This effectively breaks up the trachea into a collection of small structures – the finite element mesh. Due to the thin but very long geometry of trachea, extremely fine tetrahedral meshes are needed to obtain an accurate result.
Standard computers bog down or even crash when faced with such a computational task. “Thanks to the powerful computational resources in MSU’s High Performance Computing Center at MSU, we can parallelize our code and run it in various nodes and cores simultaneously,” Pence explains. “The storage of large amounts of data can also be resolved. This vastly shortens the running time and provides us more flexibility to analyze the result.”
Their project is sponsored by the Qatar National Research Foundation in collaboration with Carnegie Mellon University in Qatar.