## 2 Materials and Methods
### Analysis of Variance (ANOVA)  
A loss function \(\eta\) was defined to capture any deviation between the experimental and desired values, as recommended by [PERSON]. The loss function value was transformed into a signal-to-noise (S/N) ratio. The performance characteristics fell into three (lower-is-better, higher-is-better, and nominal-is-best) categories. Each characteristic was associated with a particularly defined S/N ratio used in the computation of the optimal combination of factors. Larger S/N ratios always correspond to better-quality characteristics, regardless of their category. Restated, the optimal level of operating factors had the highest S/N ratio [15]. In addition, the parameters SSTotal, SSFactor, SSError, and DoF (degrees of freedom) were defined as follows [17]:  
\[SS_{Total}=\left[\sum_{i=1}^{n}\sum_{j=1}^{r}y_{ij}^{2}\right]-n\times r\times \overline{\vec{y}}^{2} \tag{1}\]  
\[SS_{Factor}=\frac{n\times r}{L}\sum_{k=1}^{L}\left(\overline{y_{k}}-\overline {\vec{y}}\right)^{2} \tag{2}\]  
\[SS_{error}=SS_{total}-\sum_{i=1}^{n}SS_{Factor_{i}} \tag{3}\]  
\[DoF_{Total}=n\times r-1;\ DoF_{Factor}=L-1;\ DoF_{error}=n\times(r-1) \tag{4}\]  
where SSTotal is the sum of squares of all variances; SSFactor is the sum of squares that correlates with the particular operating factor; SSerror is the sum of squares of only random errors; \(Y_{\vec{y}}\) is the specific difference between the theoretical calculation and practical survey of the ith group in the \(j\)th trial; \(\overline{\vec{y}}\) is the average of all derived sonography scan data; \(\overline{y_{k}}\) is the average of the obtained difference that is associated with the specific factor; \(L\), \(n\), and \(r\) are the number of assigned levels of the operating factor, number of adopted groups, and number of repeat trials in each group, respectively. The factors are the angle of the probe, water depth, frame rate, amplitude gain, and compress ratio. The corresponding numbers of \(L\) are equal to 2, 3, 3, 3, and 3, respectively, \(n\) = 18, and \(r\) = 3, which ensure reproducibility. Ffactor is defined as an index in the \(F\)_test_ to check the specific factor. It can be expressed as in [18]:  
\[F_{factor}=\frac{SS_{factor}}{DoF_{factor}}/\frac{SS_{error}}{DoF_{error}} \tag{5}\]  
where DoF is the number of degrees of freedom. Its values for the angle of the probe, water depth, frame rate, amplitude gain, compress ratio, random error, and total error are 1 [2 \(-\) 1 = 1], 2, 2, 2, 2 [3 \(-\) 1 = 2], 36 [18 \(\times\) (3 \(-\) 1 = 36], and 54 [(18 \(\times\) 3) \(-\) 1 = 53], respectively. The random error is defined herein as the deviation of the derived data from three independent trials. Thus, the confidence level can be easily derived via the FDIST program run in the Microsoft Excel spreadsheet [19]. The \(F\) test, which was introduced as early as 1925, is a survey that assumes that the variances of two correlated sample cumulations are equal. If the variances are equal, the probability of the value of \(F\) exceeding \(F_{0.05}\) is only 5% (the latter value depends on the number of samples taken from each cumulation). Thus, \(F\) > \(F_{0.05}\) implies that the variance of one cumulation is theoretically larger than that of the other. Since SSerror is the variance due to the random fluctuation, if factor \(A\) is expected to influence parameter \(\eta\), then \(F_{A}\) is most likely to exceed \(F_{0.05}\).