Inverse Problem for Color Doppler Ultrasound-Assisted Intracardiac Blood Flow Imaging

For the assessment of the left ventricle (LV), echocardiography has been widely used to visualize and quantify geometrical variations of LV. However, echocardiographic image itself is not sufficient to describe a swirling pattern which is a characteristic blood flow pattern inside LV without any treatment on the image. We propose a mathematical framework based on an inverse problem for three-dimensional (3D) LV blood flow reconstruction. The reconstruction model combines the incompressible Navier-Stokes equations with one-direction velocity component of the synthetic flow data (or color Doppler data) from the forward simulation (or measurement). Moreover, time-varying LV boundaries are extracted from the intensity data to determine boundary conditions of the reconstruction model. Forward simulations of intracardiac blood flow are performed using a fluid-structure interaction model in order to obtain synthetic flow data. The proposed model significantly reduces the local and global errors of the reconstructed flow fields. We demonstrate the feasibility and potential usefulness of the proposed reconstruction model in predicting dynamic swirling patterns inside the LV over a cardiac cycle.