Transport of complex fluids in the human pulmonary airway system

Surfactant Replacement Therapy (SRT), which involves instillation of a liquid-surfactant mixture directly into the lung airway tree, is a major therapeutic treatment in neonatal patients with respiratory distress syndrome (NRDS). This procedure has proved to be remarkably effective in premature newborns, contributing to a five-fold decrease of mortality since the 1980s. Disappointingly, its use in adults for treating acute respiratory distress syndrome (ARDS) experienced initial success followed by failures.In this PhD thesis, we present a mathematical and numerical model for the propagation of a liquid plug into the pulmonary airway system of mammals. To that intent, we first create realistic geometrical models of the tracheobronchial trees of mammals, rat, pig, and human, defined not only by their scaling properties but also by their 3D spatial embedding (i.e., branching and rotation angles), a description necessary for simulating liquid transport. The resulting geometries are compared with the available quantitative morphometric measurements found in the literature.We then introduce the mathematical model describing liquid plug transport. The main feature of this model is to decompose the propagation of liquid plugs in two fundamental elementary steps: (1) liquid deposition onto the airway walls during the propagation of a plug into a single airway, and (2) plug splitting at each bifurcation between two consecutive generations. The equations for the splitting process are derived from momentum conservation considerations, for any type of asymmetric bifurcation and any orientation with respect to gravity. The decomposition of the transport of liquid plugs into these essential steps allows us to compute efficiently and rapidly the propagation of surfactant into the entire airway tree, thus creating a truly biomedical engineering design tool.This mathematical and numerical model is first used to compute surfactant delivery into realistic asymmetric conducting airway trees of rat lung. The roles of dose volume, flow rate, and multiple aliquot deliveries are investigated. We find that our simulations of surfactant delivery in rat lungs are in good agreement with experimental data. In particular, we show that the monopodial architecture of the rat airway trees plays a major role in surfactant delivery, contributing to the poor homogeneity of the end distribution of surfactant. We also observe that increasing the initial dose volume increases in a nonlinear way the amount of surfactant delivered to the acini after losing a portion to coating the involved airways, the coating cost volume. Simulations of delivery in pig lungs exhibit the same general features, but our model demonstrates that SRT is very sensitive to the lung size. Surface tension and gravity effects do not scale similarly, and the end distribution can become highly nonhomogeneous at smaller flow rates or small dose volumes.Finally, in the human lung, our model shows that the failure of SRT in adults could, in fact, have a fluid mechanical origin that is potentially reversible. The coating cost is predicted to increase in adult lungs, enhancing the nonlinearity of the delivery process. This effect can be countered either by instilling the surfactant mixture at a smaller flow rate (but then the distribution is highly nonhomogeneous) or by using a larger dose volume. In addition, our results show that, even if sizes are comparable, the very different geometrical structures of pig and human lungs do not permit a direction translation of experimental results in pigs to humans, and that a reliable mathematical model of the delivery is absolutely crucial if one wants to predict the efficacy of SRT from animal models.In conclusion, this thesis provides a tool for predicting surfactant delivery in animals and humans, for understanding how to build animals models of SRT, and finally for engineering and optimizing patient-specific surfactant delivery in complex situations.