TY  - UNPB
TI  - Numerical simulation of blood flow through permeable vascular network embedded in tumour porous interstitium
Y1  - 2011/03/28/
AV  - public
EP  - 252
N1  - Unpublished
N2  - 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.
ID  - discovery1306876
PB  - UCL (University College London)
UR  - https://discovery.ucl.ac.uk/id/eprint/1306876/
M1  - Doctoral
A1  - Sun, Q.
ER  -