Bayesian Intraventricular Vector Flow Mapping: Influence of imaging parameters & algorithmic choices on output uncertainty*

Color-Doppler echocardiography remains the workhorse of clinical left ventricular (LV) flow evaluation because of its harmlessness, low cost, portability, and quick acquisition. Offline analysis of Color-Doppler data by vector flow mapping (VFM) allows for reconstructing 2D flow fields, quantifying LV vortex dynamics, and delineating stagnant regions. However, sensitivity to image noise and lack of uncertainty quantification (UQ) limits the clinical translation of VFM­­­.

 

We present a Bayesian VFM (B-VFM) algorithm combining physics-informed priors (mass conservation, endocardial boundary conditions) and input data uncertainty (color-Doppler, endocardial position) to infer LV velocity fields and propagate imaging noise forward.  Maximum a-posteriori estimation locally weighs input noise with priors to automatically handle Doppler artifacts and LV wall segmentation errors. Using synthetic ground-truth data and an ultrasound simulator, we quantify B-VFM's performance vs. imaging parameters and algorithmic choices. Of note, we find that the usual polar-coordinate implementation of VFM augments uncertainty in the LV apex, and offer strategies to avoid this issue by preconditioning the discretized divergence operator.