Simulation of Clotting Processes using Non–Newtonian Blood Models and the Lattice Boltzmann Method

The topic of this thesis is the simulation of blood clotting using the Lattice Boltzmann method and taking into account the non-Newtonian behavior of blood. This kind of simulations could be used for the treatment of diseases like stenosis and aneurysms. Their field of application includes the diagnostic of the diseases, the planning of surgeries and the investigation of new medical treatment strategies. The thesis starts by checking the suitability of the Lattice Boltzmann method based on typical geometries by comparing the results with standard Navier-Stokes solvers. The most interesting quantity for the comparison is the pressure distribution along the centerline of a three-dimensional pipe with different stenosis configurations for different fluid flow velocities. Most important is to see whether or not the Lattice Boltzmann method can capture all the occurring relevant pressure and flow phenomena. The results clearly show that the Lattice Boltzmann method is a suitable alternative to Navier-Stokes solvers. The next chapter investigates the Casson model, one of the most common models for the simulation of the non-Newtonian behavior of blood. This model locally modifies the viscosity of the fluid to simulate the non-Newtonian behavior of blood. Having presented the model, simulation results are compared with the analytical solutions of the problem to check the correct implementation of the Casson model within the Lattice Boltzmann algorithm. Finally, it is demonstrated, using a specially constructed test scenario, why it is important for computer simulations to take into account the effects of the non-Newtonian behavior of blood. Having presented the model for the non-Newtonian behavior of blood, a short introduction into the biological process of blood clotting will be given. It will be discussed why a complete simulation of the hole clotting process is inappropriate and thus why a model for the blood clotting is required. Additionally, the Flekkoy model, a mass transport model for the simulation of additional fluid components, will be introduced. A transport model for additional fluid components is required for both of the latter described blood clotting models. The first of the two models for blood clotting is the Aging model. This model is based on the milk clotting analogous for the blood clotting which is well establish for experimental setups. The process of milk clotting has simpler reaction chains than blood clotting, but shows similar clot formation patterns. The application of this model leads to the tracing of the time a fluid particle has spent within the investigated geometry. Above a certain residence time clotting of the fluid is possible. A number of simulations will be done to check this model and the results will be explained. The investigated geometries are different stenosis geometry configurations and one aneurysm geometry. It will be shown that for a proper choice of simulation parameters a clot formation can be simulated at the biological correct locations. Finally, the second blood clotting model, the shear stress activated platelets model, will be described. This model is based on the observation that platelets, one of the smaller components of the blood mixture, being exposed to high shear stress for a certain time, change into an activated condition. Clotting of blood starts occurring as soon as the concentration of activated platelets is above a certain threshold. This model will be investigated for the case of a single stenosis within a pipe. It will be shown that a realistic clot formation can be simulated with this clotting model and a proper choice of parameters, too. Additionally it will be discussed why this model is not suited to simulate blood clotting for the case of the aneurysm geometry.