A Doppler-Based Regularization Problem for Intraventricular Vector Flow Mapping

International audienceBackground, Motivation and ObjectiveRecent studies suggest that the analysis of the intracardiac blood flow dynamics via vector imaging can provide relevant evaluation of cardiac dysfunction. In particular, the clinical importance of intraventricular vortex formation has been underlined. Cardiac magnetic resonance and contrast-enhanced ultrasound are commonly used. These approaches, however, cannot be integrated into routine clinical practice. For the purpose of offering robust and clinically-compatible intraventricular vector flow mapping (iVFM), we generalized the Doppler-based algorithm proposed in [10.1109/TMI.2010.2049656] by using a regularized least-squares method with automatic selection of the regularizing parameters.Statement of Contribution/MethodsThe iVFM reconstruction was formulated as an optimization problem based on an l2-norm minimization of a functional composed of a Doppler data-fidelity term and a regularizer. The latter contains three physically interpretable expressions related to mass conservation, Dirichlet boundary conditions, and smoothness. A finite difference discretization of thecontinuous problem was adopted in a polar coordinate system, leading to a sparse symmetric positive-definite system. The three regularization parameters were determined automatically by analyzing the L-hypersurface, a generalization of the L-curve. The performance of the proposed method was evaluated using 1) simulated flow data from a patientspecificCFD (computational fluid dynamics) model of a human left heart, and 2) in vivo echocardiographic data. The main intraventricular vortex was detected by calculating the Okubo-Weiss criterion.Results/DiscussionIn the CFD model, the normalized root-mean-square errors (CFD vs. iVFM) were less than 5% and 15% for the radial and angular velocities, respectively. They reached maxima during left ventricular filling, when the velocities were the largest. The core vorticities were also in good agreement (r2 = 0.91), although the iVFM reconstruction induced someunderestimation (maximum = 130 vs. 160 s-1). The in vivo vector flow maps returned by iVFM made the intraventricular flow patterns and vortex formation well discernible. This 2-D iVFM method will be clinically relevant for assessing the diastolic function in patients. The proposed algorithm will form the framework for three-component volumetric iVFM