## 2 Materials and Methods
### Orthogonal Arrays  
An experimental design that was based on an orthogonal array was used to examine the five parameters of acquisition in various experiments. One parameter had two levels and the other four had three levels, as presented in Table 1. Accordingly, the total number of possible experiments was 2 \(\times\) 3\({}^{4}\) = 162 listed at Table 2. The most suitable orthogonal array L\({}_{18}\) (2\({}^{1}\)\(\times\) 3\({}^{4}\)) was selected to determine brain CT imaging. The Taguchi design is used to reduce the sensitivity of parameters to causes of variance [14]. Only 18 experiments with different sets of values of the parameters were carried out; the results had the same degree of confidence, as if all of the parameters were considered separately. The five considered parameters were (A) CT slice thickness, (B) milliampere-seconds (mAs), (C) current voltage (kVp), (D) filter type, and (E) field of view (FOV).  
In the Taguchi design, the terms \"signal\" (S) and \"noise\" (N) represent desirable and undesirable output characteristics, respectively. A loss function S/N (\(\eta\)) is defined to quantify the deviation between desirable and undesirable values. [PERSON] recommended the use of S/N to express the deviations of performance characteristics from desirable values [13]. Each experiment is associated with a particular definition of the S/N ratio, which is used in the computation of optimal acquisitions. The optimal acquisitions are those that yield the highest \(\eta\) ratios, which always correspond to better quality [14; 15].  
\begin{table}
\begin{tabular}{l c c c c} \hline
**Parameter** & **Symbol** & **Level 1** & **Level 2** & **Level 3** \\ \hline
**Slice thickness (mm)** & A & 2.5 & 5 & \\
**Milliamperage-seconds (mAs)** & B & 300 & 350 & 400 \\
**Current voltage (kVp)** & C & 80 & 120 & 140 \\
**Filter type** & D & Sharp & Standard & Smooth \\
**Field of View (mm2)** & E & 200 & 250 & 300 \\ \hline \end{tabular}
\end{table}
Table 1: Brain CT parameters and their levels.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Experiment**} & \multicolumn{5}{c}{**Parameter**} \\ \cline{2-5}  & **Thickness** & **mAs** & **kVp** & **Filter** & **FOV** \\ \hline  
\hline \end{tabular}
\end{table}
Table 2: Full Taguchi design with L\({}_{18}\) (2\({}^{1}\)\(\times\) 3\({}^{4}\)) orthogonal array.  
A larger \(\eta\) is considered preferable because the quality of a gauge image is \"the-higher-the-better\". Therefore, the higher-the-better quality characteristic is used as follows.  
\[\eta_{i}=-10\log\frac{1}{m}\left(\sum_{j=1}^{q}\sum_{i=1}^{r}\frac{1}{x_{ij}^{2}}\right) \tag{1}\]  
where \(\eta_{i}\) is the loss function S/N in the \(i\)th experiment and is given in units of dB, for \(x_{ij}\) is the grade of a gauge image that is assessed by the \(i\)th radiologist in the \(j\)th trial. \(r\) is the same image grade by a radiologist for three trials. \(q\) is the number of radiologists. m represents the total number of trial repeats in each experiment. The sensitivity of the average \(\eta_{i}\) for various experiments to each parameter was calculated. In this study, \(q=3\) and \(r=3\) were used in all experiments.  
The average \(\eta\) values from the experiments were calculated to evaluate the sensitivity of each experiment [17]. The total number of trials in each experiment was 9. The same gauge image was graded by three radiologists in three trials, so \(m=3\times 3=9\). [PERSON] recommended the use of the common logarithm of this S/N ratio, multiplied by 10 [6; 7; 14; 15].