Hemodynamic analysis based on biofluid models and MRI velocity measurements

Diseases of the cardiovascular system affect the blood flow through the vessels. For example, a narrowing of the aorta changes the blood flow velocity and causes localized jumps in the blood pressure. The heart has to work harder to provide the organs with blood cells and nutrients, reducing its life span and causing numerous related issues. Detecting changes in the blood velocity or pressure
can help to determine the severeness of such a condition and to decide on the required form of therapy or surgery.
However, measuring the blood flow non-invasively in living patients is not an easy task. Several techniques have been introduced to non-invasively measure the blood velocity, for instance, by means of magnetic resonance (MR) imaging. On the other hand, no non-invasive techniques exist for the blood pressure.
The pressure and the flow velocity are strongly related via physical laws. Mathematical methods allow to compute both for ‘well defined’ problems or to deduce the blood pressure from a known (measured) blood velocity. In this thesis, different approaches are investigated for estimating the distribution of blood pressure from noisy MR velocity images. A class of direct methods is compared for phantom and patient data in terms of accuracy and sensitivity to the quality of the image data. Optimization-based methods depend less on the data but rely on accurate physical models. This thesis contributes to the optimization approach by introducing a model that reduces the error caused by inaccurate detection of the blood vessels from the MR images.