A First-Order Lagrangian-based variational approach for 3D flow vector field restoration

Abstract

The analysis of blood flow patterns provides important insight into the health status of the heart. With the ability to acquire multi-dimensional cine flow data, Magnetic Resonance (MR) velocity imaging is widely used to acquire in vivo flow details. The technique, however, is generally subject to a certain amount of noise and this poses a major problem for automatic quantitative analysis of flow features. To tackle this problem, we propose a First-Order Lagrangian-based method for the restoration of flow vector fields. The restoration scheme is formulated as a constrained optimisation problem and a computational algorithm based on the First-Order Lagrangian method is employed to solve the optimisation problem. The proposed method has been proven to be effective for the restoration of both 2D and 3D datasets. To demonstrate the importance of a restoration step prior to the analysis of blood flow pattern, the proposed method is applied to MR velocity maps acquired from patients with sequential MR examination following myocardial infarction and the result shows that critical points are more readily detected in the restored flow field.