Regression analysis for vortex ring characteristics during left ventricular filling

A new technique to determine ventricular function is being developed from non-invasive measurements of centerline mitral flow, using color M-mode (CMM) ultrasound. Based on the hypothesis that vortex rings accompanying mitral flow are significant indicators of ventricular filling, we present a technique to determine characteristics of vortex rings created by mitral inflow, including diameter, position and circulation from the CMM derived centerline velocity data. The rings are modeled as vortex filament loops, which induce axial flow. A quasi-Newtonian regression was performed on the velocity data to determine model ring characteristics. Performance of the technique was determined using a synthetic data set with known vortex ring parameters. The algorithm is shown to be insensitive to initial estimates for ring parameters. However, noise in the data can lead to inaccuracy in the derived ring parameters. Further work to increase the accuracy of the regression algorithm and decrease effect of data uncertainty is ongoing.