A MULTISCALE MULTIPHYSICS FINITE ELEMENT FOR LUNG

The previously formulated finite element for lung mechanics (MSCL) by the author is extended to include airflow and molecular transport by diffusion. The lung mechanics is analyzed in detail providing an insight into the deformation of the microstructural elements. Also, some refinements are introduced with respect to the previous model. Here, the finite element is extended to incorporate airflow and convective-diffusive particulate (molecular) transport. The smeared concept (the Kojic Transport Model - KTM) is implemented with lung small airway generations considered as subdomains within the KTM. The subdomains refer to a selected number of generations according to the airway diameters. Each domain has its own volumetric fraction and transport tensor specified in terms of the airway size. The computational procedure implemented in the PAK-BIO software consists of three passes within each time step: mechanics, airflow, and diffusion. The current geometry is used for the airflow where the alveolar sacs are considered as the source terms for the last domain, according to the rate of volumetric deformation and volumetric fraction of the sacs. The pressure distribution calculated in the pass 2 is used for the convective term in the diffusion. Here, the alveolar sacs are included as the last subdomain. The new element is now termed the General Lung Finite Element (GLFE). Coupling airflow in large airways, governed by the Navier-Stokes equations, to small airways (with the Hagen-Poiseuille equations) is presented; the same coupling is given for diffusion. Numerical examples illustrate the generality of the formulated finite element.