Physics-Guided Neural Networks for Intraventricular Vector Flow Mapping.

Intraventricular vector flow mapping (iVFM) seeks to enhance and quantify color Doppler in cardiac imaging. In this study, we propose novel alternatives to the traditional iVFM optimization scheme by utilizing physics-informed neural networks (PINNs) and a physics-guided nnU-Net-based supervised approach. When evaluated on simulated color Doppler images derived from a patient-specific computational fluid dynamics model and in vivo Doppler acquisitions, both approaches demonstrate comparable reconstruction performance to the original iVFM algorithm. The efficiency of PINNs is boosted through dual-stage optimization and pre-optimized weights. On the other hand, the nnU-Net method excels in generalizability and real-time capabilities. Notably, nnU-Net shows superior robustness on sparse and truncated Doppler data while maintaining independence from explicit boundary conditions. Overall, our results highlight the effectiveness of these methods in reconstructing intraventricular vector blood flow. The study also suggests potential applications of PINNs in ultrafast color Doppler imaging and the incorporation of fluid dynamics equations to derive biomarkers for cardiovascular diseases based on blood flow.

Full-volume three-component intraventricular vector flow mapping by triplane color Doppler.

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 makesiVFM compatible with the clinical setting. We have generalized theiVFM 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 2D 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-iVFMin silicoin a patient-specific CFD (computational fluid dynamics) model of cardiac flow and tested its clinical feasibilityin vivoin 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 bothin silicoandin vivoinvestigations, 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.

A Pipeline for the Generation of Synthetic Cardiac Color Doppler.

Color Doppler imaging (CDI) 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 article, we present a numerical framework for generating clinical-like CDI. Synthetic blood vector fields were obtained from a patient-specific 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 1) flow acceleration; 2) wall clutter; and 3) 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 toward the generation of comprehensive datasets for training neural networks to improve the quality of Doppler imaging.

Physics-constrained intraventricular vector flow mapping by color Doppler.

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 ouriVFM numerical scheme by imposing physical constraints. TheiVFM 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 theiVFM-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-constrainediVFM and CFD. The capability of physics-constrainediVFM was finally tested within vivocolor Doppler data acquired in patients routinely examined in the echocardiographic laboratory. The vortex that forms during the rapid filling was deciphered. The physics-constrainediVFM algorithm is ready for pilot clinical studies and is expected to have a significant clinical impact on the assessment of diastolic function.