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 (iVFM) is a method to recover the blood velocity vectors from the Doppler scalar fields in an echocardiographic three-chamber view. We improved our iVFM numerical scheme by imposing physical constraints. The iVFM 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 CFD (computational fluid dynamics) model. The numerical evaluations showed that the iVFM-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 iVFM and CFD. The capability of physics-constrained iVFM 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 iVFM algorithm is ready for pilot clinical studies and is expected to have a significant clinical impact on the assessment of diastolic function.

Color Doppler imaging is the modality of choice for simultaneous visualization of myocardium and intracavitary flow over a wide scan area. This visualization modality is subject to several sources of error, the main ones being aliasing and clutter. Mitigation of these artifacts is a major concern for better analysis of intracardiac flow. One option to address these issues is through simulations. In this paper, we present a numerical framework for generating clinical-like color Doppler imaging. Synthetic blood vector fields were obtained from a patientspecific computational fluid dynamics CFD model. Realistic texture and clutter artifacts were simulated from real clinical ultrasound cineloops. We simulated several scenarios highlighting the effects of i) flow acceleration, ii) wall clutter, and iii) transmit wavefronts, on Doppler velocities. As a comparison, an "ideal" color Doppler was also simulated, without these harmful effects. This synthetic dataset is made publicly available and can be used to evaluate the quality of Doppler estimation techniques. Besides, this approach can be seen as a first step towards the generation of comprehensive datasets for training neural networks to improve the quality of Doppler imaging.

Objective. Intraventricular vector flow mapping (iVFM) is a velocimetric technique for retrieving two-dimensional velocity vector fields of blood flow in the left ventricular cavity. This method is based on conventional color Doppler imaging, which makes iVFM compatible with the clinical setting. We have generalized the iVFM for a three-dimensional reconstruction (3D-iVFM). Approach. 3D-iVFM is able to recover three-component velocity vector fields in a full intraventricular volume by using a clinical echocardiographic triplane mode. The 3D-iVFM problem was written in the spherical (radial, polar, azimuthal) coordinate system associated to the six half-planes produced by the triplane mode. As with the 2-D version, the method is based on the mass conservation, and free-slip boundary conditions on the endocardial wall. These mechanical constraints were imposed in a least-squares minimization problem that was solved through the method of Lagrange multipliers. We validated 3D-iVFM in silico in a patient-specific CFD (computational fluid dynamics) model of cardiac flow and tested its clinical feasibility in vivo in patients and in one volunteer. Main results. The radial and polar components of the velocity were recovered satisfactorily in the CFD setup (correlation coefficients, r = 0.99 and 0.78). The azimuthal components were estimated with larger errors (r = 0.57) as only six samples were available in this direction. In both in silico and in vivo investigations, the dynamics of the intraventricular vortex that forms during diastole was deciphered by 3D-iVFM. In particular, the CFD results showed that the mean vorticity can be estimated accurately by 3D-iVFM. Significance. Our results tend to indicate that 3D-iVFM could provide full-volume echocardiographic information on left intraventricular hemodynamics from the clinical modality of triplane color Doppler.

We generalized and improved our clinical technique of twodimensional intraventricular vector flow mapping (2D-iVFM) for a full-volume three-component analysis of the intraventricular blood flow (3D-iVFM). While 2D-iVFM uses three-chamber color Doppler images, 3D-iVFM is based on the clinical mode of triplane color Doppler echocardiography. As in the previous twodimensional version, 3D-iVFM relies on mass conservation and free-slip endocardial boundary conditions. For sake of robustness, the optimization problem was written as a constrained least-squares problem. We tested and validated 3D-iVFM in silico through a patient-specific heart-flow CFD (computational fluid dynamics) model, as well as in vivo in one healthy volunteer. The intraventricular vortex that forms during left ventricular filling was deciphered. After further validation, 3D-iVFM could offer clinically compatible 3-D echocardiographic insights into left intraventricular hemodynamics.

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Aortic aneurysm is a common disorder which is due to weakening of the aortic wall [1]. Aneurysm rupture is a potentially life threatening complication [2]. The stent graft implantation is one of the potential alternatives for treating patients at high risk for an open surgical procedure. The short-term outcome for stent implantation is promising; however, as with any medical procedure, this has potential limitations such as side branch occlusion, device malfunctions, dilatation at the proximal portion and the so called ‘endoleak’. An endoleak is the persistent blood flow into and within the aneurysmal sac after endovascular repair (i.e. the blood leaks around the endograft which is supposed to have sealed off the entry of blood around it and can be classified into 5 categories[3]). Type I (inadequate seal) and III (graft mechanical failure) endoleaks, characterized by direct communication between systemic and aneurysm sac compartments, pose higher risk of aneurysm rupture and are therefore aggressively treated [4]. Despite advances in the treatment of aneurysm, we believe that there is a still great need for a medical device that can improve patient outcomes.