Improving the quantification of contrast enhanced ultrasound using a Bayesian approach

Contrast Enhanced Ultrasound (CEUS) is a sensitive imaging technique to assess tissue vascularity, that can be useful in the quantification of different perfusion patterns. This can be particularly important in the early detection and staging of arthritis. In a recent study we have shown that a Gamma-variate can accurately quantify synovial perfusion and it is flexible enough to describe many heterogeneous patterns. Moreover, we have shown that through a pixel-by-pixel analysis the quantitative information gathered characterizes more effectively the perfusion. However, the SNR ratio of the data and the nonlinearity of the model makes the parameter estimation difficult. Using classical non-linear-leastsquares (NLLS) approach the number of unreliable estimates (those with an asymptotic coefficient of variation greater than a user-defined threshold) is significant, thus affecting the overall description of the perfusion kinetics and of its heterogeneity. In this work we propose to solve the parameter estimation at the pixel level within a Bayesian framework using Variational Bayes (VB), and an automatic and data-driven prior initialization. When evaluating the pixels for which both VB and NLLS provided reliable estimates, we demonstrated that the parameter values provided by the two methods are well correlated (Pearson’s correlation between 0.85 and 0.99). Moreover, the mean number of unreliable pixels drastically reduces from 54% (NLLS) to 26% (VB), without increasing the computational time (0.05 s/pixel for NLLS and 0.07 s/pixel for VB). When considering the efficiency of the algorithms as computational time per reliable estimate, VB outperforms NLLS (0.11 versus 0.25 seconds per reliable estimate respectively).