My PhD dissertation
This work summarises my investigations about a human pathologic state concerning the circulation of the brain. The cerebral aneurysm is a vessel malformation that manifests itself as a lesion on the vessel wall alongside the Circle of Willis, which is responsible for carrying about 80% of the blood supply of the brain. The formation and development of this disease is in close correlation with the local hemodynamic factors. Therefore, I first select the most appropriate numerical tools for calculating the flow conditions inside the arteries. With these tools I simulate the emerging velocity field inside the geometry of a real aneurysm with a very high numerical resolution. I validate the results using available experimenta results on the same geometry. As a next step, I apply the tested numerical methods on two further problems emerging within the context of aneurysms. In two dimensions I propose a simple numerical model for the haemostasis process in an arteriole that can reproduce the proper platelet density distribution and is able to recover a qualitatively correct thrombus shape compared to the experimental results available in literature. Furthermore, I investigate the properties of particle transport inside the validated flow field of the real aneurysm geometry which turns out to exhibit chaotic behaviour. Using the free-energy formalism I measure several key quantities of the emerging chaotic structure.
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