Flow pattern analysis for magnetic resonance velocity imaging

Blood flow in the heart is highly complex. Although blood flow patterns have been investigated by both computational modelling and invasive/non-invasive imaging techniques, their evolution and intrinsic connection with cardiovascular disease has yet to be explored. Magnetic resonance (MR) velocity imaging provides a comprehensive distribution of multi-directional in vivo flow distribution so that detailed quantitative analysis of flow patterns is now possible. However, direct visualisation or quantification of vector fields is of little clinical use, especially for inter-subject or serial comparison of changes in flow patterns due to the progression of the disease or in response to therapeutic measures. In order to achieve a comprehensive and integrated description of flow in health and disease, it is necessary to characterise and model both normal and abnormal flows and their effects. To accommodate the diversity of flow patterns in relation to morphological and functional changes, we have described in this thesis an approach of detecting salient topological features prior to analytical assessment of dynamical indices of the flow patterns. To improve the accuracy of quantitative analysis of the evolution of topological flow features, it is essential to restore the original flow fields so that critical points associated with salient flow features can be more reliably detected. We propose a novel framework for the restoration, abstraction, extraction and tracking of flow features such that their dynamic indices can be accurately tracked and quantified. The restoration method is formulated as a constrained optimisation problem to remove the effects of noise and to improve the consistency of the MR velocity data. A computational scheme is derived from the First Order Lagrangian Method for solving the optimisation problem. After restoration, flow abstraction is applied to partition the entire flow field into clusters, each of which is represented by a local linear expansion of its velocity components. This process not only greatly reduces the amount of data required to encode the velocity distribution but also permits an analytical representation of the flow field from which critical points associated with salient flow features can be accurately extracted. After the critical points are extracted, phase portrait theory can be applied to separate them into attracting/repelling focuses, attracting/repelling nodes, planar vortex, or saddle. In this thesis, we have focused on vortical flow features formed in diastole. To track the movement of the vortices within a cardiac cycle, a tracking algorithm based on relaxation labelling is employed. The constraints and parameters used in the tracking algorithm are designed using the characteristics of the vortices. The proposed framework is validated with both simulated and in vivo data acquired from patients with sequential MR examination following myocardial infarction. The main contribution of the thesis is in the new vector field restoration and flow feature abstraction method proposed. They allow the accurate tracking and quantification of dynamic indices associated with salient features so that inter- and intra-subject comparisons can be more easily made. This provides further insight into the evolution of blood flow patterns and permits the establishment of links between blood flow patterns and localised genesis and progression of cardiovascular disease.Open acces

Vector-valued image restoration with applications to magnetic resonance velocity imaging

The analysis of blood flow patterns and the interaction between salient topological flow features and cardiovascular structure plays an important role in the study of cardiovascular function. Flow velocity images acquired by Magnetic Resonance (MR) velocity imaging are generally subject to noise that are intrinsic to system hardware setup and those specific to patient movement in relation to imaging sequence designs. To improve the accuracy of the quantitative analysis of the evolution of topological flow features, it is essential to restore the original flow fields so that the associated critical points can be more reliably detected. In this study, we propose a total variation based variational method for the restoration of flow vector fields. The method is formulated as a constrained optimisation problem by minimizing the total variation energy of the normalized velocity field subject to a constraint that depends on the noise level. The effectiveness of this restoration method greatly depends on the choice of the regularization parameter in the formulation of the optimisation problem. A new computational algorithm based on the First Order Lagrangian method is proposed, which determines the optimal value of the regularization parameter while solving the minimisation problem. The proposed method has been validated with both simulated flow data and MR velocity maps acquired from patients with sequential MR examination following myocardial infarction