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
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