Applications of continuum mechanics : computational studies in biological and discrete systems

Abstract

This thesis is divided into two parts: part A and part B. Part A mainly focused on the biological systems while part B emphasized on discrete systems. Both studies can be applied readily in the scientific world.

Part A: Computational Fluid Dynamics Study of Biological Systems

Cerebrovascular and cardiovascular diseases are life threatening diseases, and are leading causes of death and disability in the civilized world. Thoracic aortic dissection (TAD), a form of cardiovascular disease, occurs when blood infiltrates into the layers of vascular aortic wall, creating a new artificial channel (the false lumen) alongside with the original channel (the true lumen). The weakened false lumen wall may expand due to the blood pressure, and high mortality rate is resulted upon imminent rupture. A clinical question is to determine the timing of the surgical procedure.

By employing computational fluid dynamics techniques, several biomechanical factors including aneurysm size, blood pressure and tear distance were investigated. Generally speaking, a greater dissecting aneurysm, a higher blood pressure and a partially thrombosed false lumen might lead to undesirable hemodynamics consequences. This analysis may improve the healthcare of patients in the future as it can provide useful information for clinicians to access the risk of aneurysm rupture.

On the other hand, intracranial aneurysm, a dangerous cerebrovascular disorder, occurs when a cerebral artery dilates. Such aneurysm is usually located near the arterial bifurcation in the Circle of Willis, and can lead to massive internal bleeding in the subarachnoid space upon rupture. An endovascular treatment is the implantation of a flow diverting stent which covers the aneurysm orifice. This metallic stent, namely the Pipeline Embolization Device (PED), can restrict the blood flow into the aneurysm, and thus reduces the rupture risk. The clinical question is to determine the factors affecting the stent efficiency. Computational fluid dynamics (CFD) analysis was performed to investigate the flow properties before and after stenting. Several factors including side branch diameter, aneurysm aspect ratio and the stent porosity were tested. Generally speaking, a larger side branch diameter or a higher aspect ratio might provide an undesirable hemodynamic condition, e.g. lower shear stress.

In addition, two patient-specific bifurcation aneurysms reconstructed from Computed Tomography (CT) imaging data were tested, and the results showed good agreements with the idealized geometries. This study can definitely provide physicians with valuable information for treatment planning, therapeutic decision making and for future stent design.

Part B: Discrete Systems

In nonlinear optics and plasmonics, the dissipative spatial solitons are of fundamental importance. Here a discrete dissipative model was introduced, with hot spots (HSs) embedded into it. Symmetric solutions were determined in an implicit analytical form In addition, a two-dimensional discrete dynamical system based on bulk linear lossy lattice was also tested. The analysis of localized modes pinned to the HSs was performed semi-analytically using truncated lattices. These systems can be applied in photonics and plasmonics readily.