Echocardiographic particle imaging velocimetry data assimilation with least square finite element methods

Recent developments in the field of echocardiography have introduced various noninvasive methods to image blood flow within the heart chambers. FDA-approved microbubbles can be used for intracardiac blood flow imaging and determining the velocity of the blood based on the displacement of the bubbles and the frame rate of the ultrasound scan. A limitation of this approach is that the velocity field information is only two-dimensional and inevitably contains noise. A weighted least square finite element method (WLSFEM) was developed to assimilate noisy, two-dimensional data from echocardiographic particle imaging velocimetry (echo-PIV) into a three-dimensional Navier–Stokes numerical model so that additional flow properties such as the stress and pressure gradient can be determined from the full velocity and pressure fields. The flexibility of the WLSFEM framework allows for matching the noisy echo-PIV data weakly and using the weighted least square functional as an indicator of how well the echo-PIV data are satisfying the numerical model. Results from the current framework demonstrate the ability of the approach to more closely match the more accurate echo-PIV data and less closely match the noisy data. The positive impact of assimilating the echo-PIV data is demonstrated: compared to a conventional computational fluid dynamic approach, echo-PIV data assimilation potentially enables a more accurate flow model.