Construction and analysis of airway water clearance models
In this dissertation, we focus on the construction and analysis of several nonlinear partial differential equation models of water transport in the lung. The first is a model of airway water clearance in the lungs. We show that there exists a unique solution of the airway water clearance model. To accomplish the proof of the existence and uniqueness of a solution of the nonlinear partial differential equations model of airway water clearance, an explicit form of the solution was derived by the method of characteristics. In this setting, a characteristic curve represents the graph of the position function of a massless particle as it passes through a pulmonary capillary. In addition to existence and uniqueness, model implications of the physical setting are examined. We also show that when a capillary is initially perfused at a flow F0 , assuming water is instilled instantaneously into the airspace, capillary perfusate is flushed and capillary outflow changes, resulting in a vasculature where input and output solute mass flux are momentarily unbalanced. We further show that after a certain length of time, the washout time, the solution of the airway water clearance model system reaches a steady state. We also examine a multicapillary water clearance model using the concept of a distribution of the vascular washout times. We show that the capillary outlet flow and concentration profile can be estimated by the multicapillary airway water clearance model. We also provide an estimate of the permeability-surface area product obtained from experimental data. Finally, we construct and analyze an airway water clearance with radioactive tracer model of the capillary and water-filled airway system. We show that there exists a unique local solution for the airway water clearance with radioactive tracer model using the Banach Fixed Point Theorem. We develop a multicapillary airway water clearance with radioactive tracer model of a capillary network surrounding the water-filled airways and show that the capillary outlet radiolabeled water concentration will increase with time, which is consistent with observations from the experimental data. We also show that the total capillary outflow and radiolabeled water concentration profile can be approximated using the models.
"Construction and analysis of airway water clearance models"
(January 1, 2004).
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