Because frames with artifacts were excluded from processing, the final datasets contained different numbers of echo frames, potentially affecting the final averaged QUS parameter estimates. We therefore performed a perturbation analysis to determine the minimum number of frames required to obtain stable QUS parameters. The artifact free B-mode images were processed to compute the three QUS parameters (
M,
E, and
P50). Each perturbation,
p, was completed by computing the means of the QUS parameters over
NF randomly selected frames:
\begin{eqnarray}
\mu _Q^p = \frac{1}{{{N_F}}}\mathop \sum \limits_{i \in {R_s}} {Q_i},\quad
\end{eqnarray}
where the notation
i ∈
Rs indicates the randomly selected subset of frames and
Q corresponds to one of the three QUS parameters as defined in the previous section. After each perturbation, the mean,
\(\mu _Q^{{N_P}}\), and standard deviation,
\(\sigma _Q^{{N_p}}\), were found for each QUS parameter and used to compute the coefficient of variation (CV) as
\(CV_Q^{{N_F}} = \mu _Q^{{N_p}}\)/
\(\sigma _Q^{{N_p}}*100\% \). The mean and standard deviation of the CV was then calculated across all perturbations,
Np. As the number of randomly selected frames increases, it is expected that the CV will decrease, and the mean will converge to the “true” mean. A total of 11 perturbation analyses were performed, with
NF ∈ {1, 5, 10, 15, 20, 25, 30, 35, 40, 50, 60} and
Np = 1000. The minimum number of frames was identified as the smallest value of
NF where the CV of all 3 QUS parameters decreased to less than 5%.