Physics-constrained intraventricular vector flow mapping by color Doppler

Florian Vixège (1) , Alain Berod (2) , Yunyun Sun (1, 3) , Simon Mendez (2) , Olivier Bernard (1, 3) , Nicolas Ducros (4, 1) , Pierre-Yves Courand (1, 5) , Franck Nicoud (2) , Damien Garcia (1, 6)

1 CREATIS - Centre de Recherche en Acquisition et Traitement de l'Image pour la Santé
2 IMAG - Institut Montpelliérain Alexander Grothendieck
3 MYRIAD - Modeling & analysis for medical imaging and Diagnosis
4 Imagerie Tomographique et Radiothérapie
5 Hôpital de la Croix-Rousse [CHU - HCL]
6 Imagerie Ultrasonore

Color Doppler by transthoracic echocardiography creates two-dimensional fan-shaped maps of blood velocities in the cardiac cavities. It is a one-component velocimetric technique since it only returns the velocity components parallel to the ultrasound beams. Intraventricular vector flow mapping ( i VFM) is a method to recover the blood velocity vectors from the Doppler scalar fields in an echocardiographic three-chamber view. We improved our i VFM numerical scheme by imposing physical constraints. The i VFM consisted in minimizing regularized Doppler residuals subject to the condition that two fluid-dynamics constraints were satisfied, namely planar mass conservation, and free-slip boundary conditions. The optimization problem was solved by using the Lagrange multiplier method. A finite-difference discretization of the optimization problem, written in the polar coordinate system centered on the cardiac ultrasound probe, led to a sparse linear system. The single regularization parameter was determined automatically for non-supervision considerations. The physics-constrained method was validated using realistic intracardiac flow data from a patient-specific computational fluid dynamics (CFD) model. The numerical evaluations showed that the i VFM-derived velocity vectors were in very good agreement with the CFD-based original velocities, with relative errors ranged between 0.3% and 12%. We calculated two macroscopic measures of flow in the cardiac region of interest, the mean vorticity and mean stream function, and observed an excellent concordance between physics-constrained i VFM and CFD. The capability of physics-constrained i VFM was finally tested with in vivo color Doppler data acquired in patients routinely examined in the echocardiographic laboratory. The vortex that forms during the rapid filling was deciphered. The physics-constrained i VFM algorithm is ready for pilot clinical studies and is expected to have a significant clinical impact on the assessment of diastolic function.

Keywords: cardiac flow imaging; color Doppler echocardiography; vector flow mapping

Domains: Computer Science [cs]; Medical Imaging; Life Sciences [q-bio]; Human health and pathology; Cardiology and cardiovascular system; Computer Science [cs]; Signal and Image Processing; Engineering Sciences [physics]; Mechanics [physics.med-ph]; Biomechanics [physics.med-ph]

Florian Vixège, Alain Berod, Yunyun Sun, Simon Mendez, Olivier Bernard, et al.. Physics-constrained intraventricular vector flow mapping by color Doppler. Physics in Medicine and Biology, 2021, 66 (24), pp.245019. ⟨10.1088/1361-6560/ac3ffe⟩. ⟨hal-03538679⟩