Professor Thomas Pence and Dr. Kun Gou in the Department of Mechanical Engineering at Michigan State University are working on a research project entitled "New mathematical models for the large strain swelling response of biological tissues." This is an international project sponsored by the Qatar National Research Foundation in collaboration with Carnegie Mellon University in Qatar. Professor Pence is the Principal Investigator in charge of the overall project.
Understanding how the human trachea (windpipe) can swell due to an allergic reaction is part of this research. 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. To analytically describe the swelling process, it is necessary to improve traditional mechanical theories of tissue behavior so as to account for an episode of rapid swelling. To do so, they present a continuum mechanics analysis in which conventional large strain hyperelastic theory is endowed with a swelling dependent natural configuration in order to reflect the altered tissue volume when angioedema is triggered by an allergic attack.
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 an 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 HPCC at MSU, we can parallelize our code and run it in various nodes and cores simultaneously," Gou and Pence commented, "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."