Modeling, analysis, and simulation of thrombosis and hemostasis [Elektronische Ressource] / vorgelegt von Frédéric Weller

Inaugural-DissertationzurErlangung der DoktorwürdederNaturwissenschaftlich-Mathematischen GesamtfakultätderRuprecht-Karls-UniversitätHeidelbergvorgelegt vonDiplom-Mathematiker Frédéric Welleraus StuttgartTag der mündlichen Prüfung: 14. Juli 2008Modeling, Analysis, and Simulation ofThrombosis and HemostasisGutachter: Prof. Dr. Dr. h.c. mult. Willi JägerProf. Dr. Rolf RannacherAbstractThis thesis investigates the influences of shear stress, saturation-dependent changes in surface reactivity,and thrombus growth on platelet deposition to reactive materials, which is of paramount interestin bioengineering and clinical practice. For this purpose, two mathematical models based on theNavier-Stokes equations and on particle conservation are developed. The first model is formulated on afixed domain (“FD-model”) and describes the initial phase of platelet adhesion, whereas the secondone is a free boundary problem capturing long-term thrombus growth. Several vessel geometries areconsidered: Stagnation point flow, tubular expansion, and t-junction. Model parameters are optimizedto fit the data and their so obtained values are justified on the basis of experimental observations.The FD-model does not match the experimental data at all, when platelet adhesion is assumedindependent of shear stress. In contrast, when adhesion is assumed shear-dependent, at least qualitativeagreement is achieved.