The use of the lattice Boltzmann method in thrombosis modelling.

The effects of thrombosis greatly contribute to the incidence of mortality in the
Western World. Understanding thrombosis is therefore crucial in providing the
correct treatment for the underlying pathologies. Numerical methods have
previously been used to investigate various factors associated with thrombosis,
usually starting from solutions of the Navier-Stokes equations.
This thesis presents the development and implementation of models of
thrombosis using the lattice Boltzmann method, which is a relatively new
technique for simulating fluid dynamics. The advantages and disadvantages of
this methodology are critically reviewed and two major pathologies,
atherosclerosis and deep vein thrombosis have been chosen to demonstrate
principles of the application.
The first part of the work concentrates on the simulation of flow and clotting in
idealised stenotic occlusions representative of the geometry and flow conditions
in a diseased human femoral artery. Simulations of unsteady flow are reported
and comparisons are made to previous flow visualisation studies. Stability
issues regarding the diffusion algorithm are investigated in detail. In the first
instance, clotting is simulated with the use of an aging model with extensions
including proximity and shear stress. Comparisons are made with experimental
results obtained using milk as a blood analogue.
)'he second part of the work focuses on increasing the complexity of the models
to incorporate the representations of the actions and distribution of the platelets,
proteins and enzymes involved in the coagulation cascade. The models are
tested in 2D geometries to demonstrate their functionality. As an example of
this work, a model of deep vein thrombosis was developed, based on a
hypothesis supported by the clinical literature.
The foundations laid in this project allow for future developments, which will
incorporate further details of thrombotic processes, in the hope that a valuable
predictor of thrombosis can be developed.