Filtering flow measurements in the left ventricle using modal analysis*

Several studies have linked blood flow inside the heart to disease etiology. However, imaging intra-cardiac blood flow remains challenging, limiting our understanding of heart failure and its hemodynamic consequences. Phase-contrast MRI (PC-MRI) is the only non-invasive method that provides velocity information that is 3D, on a 3D grid. However, these fields are noisy and not divergence-free. Color-Doppler ultrasound is inexpensive and readily available, but only provides velocity information in a single direction. We have developed a modal analysis method to de-noise flow data in a 3D domain, producing a divergence-free flow field. The modes are calculated by minimizing the velocity gradient while enforcing a divergence-free condition across the domain. This enables measured velocity fields to be projected onto these modes using a least squares algorithm. The method is tested on the results of a computational fluid dynamics simulation with artificial noise added to the velocity field and on PC-MRI data. Different boundary conditions, mesh sizes, and numbers of modes are tested. The method is also tested as a reconstruction method for 3D color-Doppler ultrasound data by using the CFD and PC-MRI data to construct virtual ultrasound data sets.