Numerical and experimental modeling of atherosclerosis related to MRI
This thesis was motivated by the idea of employing non-invasive investigations of atherosclerosis using Magnetic Resonance Imaging (MRI). MRI has the advantage of being able to detect atheroma in blood vessels with no risk to the patient but is still limited in its application to large blood vessels by the low geometrical resolution obtainable. The capability of MRI to measure velocities as well leads to the idea of correlating atheroma dimensions with measured velocities downstream of the blockage. This thesis makes a first step towards obtaining results that can be applied in investigations of atherosclerosis employing MRI. The fluid dynamics of arterial blood flow, the medical procedure of diagnosing and treating atherosclerotic diseases, and the physical principle of MRI are investigated to find out "if' and "how" the correlation between a blockage and the resulting downstream velocities can contribute to the diagnosis of atheroma. Parallel to this background research, experimental and numerical modeling of atheroma is carried out. These two approaches use identical geometrical and fluid parameters to enable a direct validation of the results. An experimental test-rig is designed. Experiments with different types of blockages are performed. The measured flow parameters are pressure and velocity profiles in a crosssection of the modeled artery. A commercial software package is employed for the numerical simulation of blockages with similar geometries to those used in the experiments. The pressure and absolute velocities are again the derived parameters. Both approaches are validated with analytical results obtainable for flow without any blockages. Blockages are then inserted and the results are compared and analyzed for their potential to contribute to the medical application. The results obtained with the two models give good correspondence. The transitional length of the laminar pipe flow corresponds very well to the expectations. A laminar velocity profile is completely built up before the fluid enters a blockage. Blockages with a small flow area cause a high peak velocity and a large wake. Blockages that slightly reduce the flow area have only a small influence on the flow. The length of a blockage has only a secondary influence on the downstream velocity distribution, while the influence of the surface roughness of the blockage is small. The peak velocities and pressure loss caused by the different blockages give good correlation. The prediction of the diameter of the blockage from peak velocities measured with MRI is an improvement on that which is possible from the theory only. In particular, the results obtained in this thesis show that the true maximum velocities are significantly lower than those obtained with theoretical predictions. The change in the velocity profiles, due to angioplasty, is shown in a simplified form with the models. Typical values of reduced areas before and after such surgery, where the atheroma is squeezed against the arterial walls, are analysed. The influence of the post-surgery blockage on the flow is very small, while the pre-surgery blockage shows a dominant influence. A prominent wake exists downstream of a highly reduced flow area, and high velocities occur. A wake is a potential risk area for atherosclerosis, as low shear rates and high turbulence intensities are possible. The blockage with the less reduced area has almost no influence on the flow, and a wake is hardly formed. The influence of different shapes of atheroma, while having a similar reduced area, is also demonstrated. The perfectly symmetrical blockage has less negative influence on the flow than one which is highly asymmetrical. The asymmetrical blockage causes a larger wake and higher maximum velocities.
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