Intraventricular vector flow mapping—a Doppler-based regularized problem with automatic model selection. (11th August 2017)

• Record Type: Journal Article
• Authors: Assi, Kondo Claude; Gay, Etienne; Chnafa, Christophe; Mendez, Simon; Nicoud, Franck; Abascal, Juan F P J; Lantelme, Pierre; Tournoux, François; Garcia, Damien
• Is Part Of: Physics in medicine & biology. Volume 62:Number 17(2017:Sep.)
• Page Start: 7131
• Page End: 7147
• Publication Date: 2017-08-11
• Subjects: ultrasound imaging -- color Doppler -- vector flow imaging -- regularized least-squares -- intracardiac flow imaging; Biophysics -- Periodicals; Medical physics -- Periodicals; 610.153
• DOI: 10.1088/1361-6560/aa7fe7
• Languages: English
• ISSNs: 0031-9155

Abstract

Abstract: We propose a regularized least-squares method for reconstructing 2D velocity vector fields within the left ventricular cavity from single-view color Doppler echocardiographic images. Vector flow mapping is formulated as a quadratic optimization problem based on an ℓ 2 -norm minimization of a cost function composed of a Doppler data-fidelity term and a regularizer. The latter contains three physically interpretable expressions related to 2D mass conservation, Dirichlet boundary conditions, and smoothness. A finite difference discretization of the continuous 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 numerically evaluated using (1) a synthetic flow composed of a mixture of divergence-free and curl-free flow fields and (2) simulated flow data from a patient-specific CFD (computational fluid dynamics) model of a human left heart. The numerical evaluations showed that the vector flow fields reconstructed from the Doppler components were in good agreement with the original velocities, with a relative error less than 20%. It was also demonstrated that a perturbation of the domain contour has little effect on the rebuilt velocity fields. The capability of our intraventricular vector flow mapping ( i VFM) algorithm was finally illustrated on in vivo echocardiographic color Doppler data acquired in patients. The vortex that forms during the rapid filling was clearly deciphered. This improved i VFM algorithm is expected to have a significant clinical impact in the assessment of diastolic function.