Modeling and numerical simulations of nanometric aerosols in the lower part of the bronchial tree

The classical model of the bronchial tree is divided into several different regions. Between the 8th and 17th tree generations, the air flow can be described through a Poiseuille law. Beyond, till the 23rd generation, the diffusion (Fick's law for instance) is the main phenomenon , and the convection can be neglected. Therapeutic aerosols have to go very low in the bronchial tree (e.g. reach the pulmonary alveola). Several modelings are possible with respect to the mean size of the aerosol particles (statistical description with a kinetic equation, full description with a system of ordinary differential equations). The aerosol metrology is a key point, since the size of an aerosol particle has a strong impact on the location where the aerosol mainly deposits inside the airways. We first aim to give coupled models for the air flow beyond the 8th generation and for an aerosol in which the size of the particles are scaled to the nanometer. Then these models will be coupled to air-aerosols models developed for the proximal part of the bronchial tree and numerically investigated using the solver Freefem++. The project is strongly related with some experimental studies led in the " Aerosols and bronchopneumonic cancer " team of Pr. Patrice Diot, in Tours. The aim of the stage is to operate the coupling between a microscopic model of the molecular pathways involved in the process of tumor angiogenesis and a macroscopic model of tumor growth and treatment efficacy. In particular, a quantitative comparison between the different model dynamics (microscopic and macroscopic) is expected to be achieved through numerical simulations. The process of tumor growth is very complex and not easy to describe, simulate and predict through mathematical modeling tools. Still, with the appearance of innovative treatment strategies such as the targeted therapies, a predictive computer model of tumor growth process may have a significant impact for optimizing the delivery of anti-cancer treatments. The process of tumor-induced angiogenesis is recognized as a key process of tumor growth and cancer development. Anti-angiogenesis drugs have been developed and have shown their efficacy in several cancer diseases. However, these new medicines are always associated with conventional chemotherapy. The framework of this project is the optimization of anti-angiogenesis drug delivery in combination with conventional chemotherapy. The candidate(s) will work on an ongoing development model of tumor growth and treatment. The main objective is to operate the coupling between a macroscopic layer …