The project involves the development of mathematical models and their implementation as software code for high performance computing clusters. The physical problem studied involves two related topics: particle deposition and solute absorption in respiratory airways, and tumour metastasis in arterioles and capillaries. The aim is to couple micro-scale phenomena to large 3D incompressible flow simulations. These topics are chosen for their clinical relevance and complex, coupled nature that requires large-scale computing.The numerical tools to be developed are twofold, namely 1D geometric multi-scale networks and Lagrangian mesh-free schemes. The 1D models will serve as fluid boundary conditions of the main conduit, and represent the vascular bed in the tissue. The 1D models are based on Cosserat director theory. A Lagrangian mesh-free scheme will be used to model the multi-component fluids (whole blood and particle-laden air). This approach will easily cope with multi-body interactions and the deformation of the corpuscles; hence it will model the micro-scales and will interface with existing incompressible solver at the host institution. The Lagrangian mesh-free method is based on radial basis function and point interpolation schemes.The facilities at the host institution are among the best in Europe for high performance scientific computing. The supervisor is experienced in computational mechanics, parallel programming, and biomedical applications. These include simulations of large 3D incompressible flow simulations in the respiratory airways and extensive branching arteries, which are both the applications in this project.The proposed project integrates the candidate's field of expertise in numerical analysis and fluid mechanics in physiology, with high performance computing and large-scale integrated problems. Acquiring these skills will enhance, diversify and strengthen the candidate, and further his inter-disciplinary and inter-sectoral research focuses.