Fluid mechanics of abrupt changes : applications to biomedical engineering and free surface flows

Abstract

Abrupt changes in fluid mechanics induce significant consequences. Aneurysm is an example from arterial system which will be catastrophic when ruptured and rogue wave is an example on free surface water waves which threatens ships and offshore facilities. In this thesis, energy loss was tested on intracranial aneurysm treatments and some novel hemodynamics parameters, e.g. helicity, were used to quantify hemodynamics on aortic arch with internally directed side branches. Furthermore, complex pole dynamics were correlated with physical locations of rogue waves.

Intracranial aneurysms: One possible endovascular treatment on intracranial aneurysms is the deployment of flow diverters(FDs), which reduces flow into the sac and promotes thrombosis. Computational fluid dynamics(CFD) simulations were used. The concept of energy loss, as a measure of necessary work done to overcome flow resistance, was utilized to correlate with clinical outcome. If a surgical operation is successful, the flow would be diverted to a shorter path and energy loss should be reduced. Conversely, persistent flow in the sac, associated with treatment failure, would display an increased energy loss as blood is then squeezed through the stent pores. Four clinical cases, involving both bifurcation and sidewall aneurysms, were selected. The simulated results supported this hypothesis. Negative changes in energy loss was found in successful cases and positive changes in failed cases. Here, the FD was simulated explicitly as a virtual stent, which would provide a more accurate description. Quantitative comparisons between the approaches of virtual stenting and a porous medium with typical parameters were conducted by examining the effective flow influx into the aneurysm.

Thoracic aortic aneurysms: Deployment of internally directed side branches provides a feasible alternative to repair aneurysm on the aortic arch, but the hemodynamic implications have not been fully investigated. Quantitative indicators like volume flow rate, wall shear stress (WSS) and helicity index are employed. Changes in volume flow are generally mild unless an antegrade branch is utilized. WSS reveals a fluctuating and complex flow pattern between the brachiocephalic and left subclavian artery after graft implantation. Circumferentially averaged oscillatory shear indices at the left common carotid artery are in the range of (0.18, 0.26). Helical flows are observed both before and after surgical repairs, and are measured by spatially integrated helicity and a “helicity flow index”. In general, aortic blood flow displayed a higher degree of oscillatory and helical features after internal side branches were deployed. Clinically, oscillatory flows may promote blood clot formation. To achieve the goal of side branch patency, proper stent orientation is thus critical.

Pole dynamics: Rogue waves are unexpectedly large deviations from equilibrium or otherwise calm positions in physical systems. The profiles and points of maximum displacements of these rogue waves are correlated with the movement of poles of the exact solutions extended to the complex plane through analytic continuation. Such links are shown to be surprisingly precise for the first order rogue wave of the nonlinear Schrödinger and the derivative NLS equations. A computational study on the second order rogue waves of the NLS equation also displays remarkable agreements.