Simulation and Optimization of Vascular Bifurcations by Numerical Solutions of the Navier-Stokes Equations Using Finite Elements

Natural evolution presumably optimizes biological systems, however, the optimality criteria are not explicit and thus unknown to the human observer. Specifically, the vascular system may obey design principles such as volume minimization or power loss minimization, but these assumptions must be verified by examining the technical optima and comparing them to real biological systems. In this thesis we are concerned with the computational aspects of simulation and optimization of vascular bifurcations, which are the basic design elements of the vascular system. We simulate two-dimensional flow in vascular bifurcations by numerically solving stationary Navier-Stokes equations using the method of finite elements. In continuation of previous work we determine optimal bifurcation geometries with respect to biologically motivated cost functions. We compare the results to those found in literature, which are based on simpler flow models.

Master Student


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