%0 Thesis
%9 Doctoral
%A Sun, Q.
%B Department of Mechanical Engineering
%D 2011
%F discovery:1306876
%I UCL (University College London)
%P 252
%T Numerical simulation of blood flow through permeable vascular network embedded in tumour porous interstitium
%U https://discovery.ucl.ac.uk/id/eprint/1306876/
%X Tumour blood flow plays a critical role in tumour growth and cancer therapies.  Computational fluid dynamics is an efficient method to study blood behaviour  by modelling fluid flow through numerical simulations. A mathematical model  is developed to study the blood flow through a three-dimensional permeable  vascular network embedded in a solid tumour, and its transvascular movement  and spread within tumour interior in context with cancer therapies. The  vasculature is described by the parametric equations in terms of vessel centre  lines. The flow through each tumour vessel is approximated with the leading  component in the longitudinal direction of the vessel, and its governing  equation becomes an ordinary differential equation based on the parameter  of the parametric equation for the vessel centre line. The pressure continuity  and mass conservation conditions are imposed at every junction within tumour  vascular network. The interstitial flow is described by the Darcy’s law which  is converted into the Laplace equation. The coupling effect between the flows  through tumour vasculature and within tumour interstitial due to the vascular  permeability is described by the Starling’s law. A coupling mathematical  model is then developed. Based on mass conservation, a differential equation  for pressures on both sides of vascular surface is obtained. Transforming the  Laplace equation into the boundary-integral form by using the Green’s function  offers another equation linking the pressures inside and outside vessels. The numerical procedure is developed, and the discretised differential and integral  equations are solved by finite difference method and boundary element  method respectively. The model is applied to investigate how different types of  physical parameters and special characters of tumour vasculature affect tumour  blood flow. Finally, an approximation model by ignoring the term with small  value of the fully coupling model is developed, and its validity and simulation  efficiency are examined.