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A mathematical model of lung fluid secretion and pattern selection in lung branching
Morgan, John Paul
Hong, YoungjoonSant, KarilynZeller, Robert
Mammalian lung development is a complex process that begins at the embryonic stage of development and continues until after birth. During the embryonic stage, the lung begins as an outpouch of the foregut forming the left and right lung buds. Each of the lung buds undergoes a repetitive process of outgrowth and branching to form the future airspaces. Ligands such as Fibroblast Growth Factor-10 (FGF-10) and Sonic hedgehog play important roles in the regulation of lung branching morphogenesis. Other factors such as tissue geometry also regulate lung branching. Laboratory experiments have shown that murine lung explants cultured in microfluidic chest cavities of defined shapes conformed to the shape of the microfluidic chamber, generating cuboidal, cylindrical, triangular or rectangular-prism-shaped organs. How ligands regulates lung branching in the microfluidic chest cavities is not fully understood. In this thesis, we investigate the influence of the shape and size of the region surrounding a lung branch on the distribution of an arbitrary ligand that controls lung branching. In particular, we compare ligand distribution in lung branches surrounded by rectangular-prism tissue with those surrounded by cylindrical tissue. We use an advection-diffusion model to describe the spatiotemporal distribution of ligands. The transport of molecules in lung fluid is modeled using Darcy’s law to capture its transport in the porous lung tissue. Numerical approximation of the model is done using the finite element method. Our findings show that varying the overall size of the region surrounding a lung branch drastically impacts the patterning of ligands, changing bifurcation branching patterns to potential elongation patterns. These findings were consistent in simulations done in rectangular and cylindrical regions and highlights the influence of geometric factors on molecular patterning during lung branching morphogenesis.
Mathematics and Statistics
San Diego State University
Master of Science (M.S.) San Diego State University, 2020
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