## 3 Results and Discussion
### Design of Ink Properties  
#### 3.2.1 Principal Component Analysis  
Principal Component Analysis (PCA) was performed via OriginPro 2018 to reveal and better understand the underlying patterns in material properties and printing behavior. PCA was used to pinpoint the most crucial elements that affect printability when wishing to investigate the material characteristics that are more closely related to printability. The maximum variance method was applied in order to assess each pertinent factor and characterize the hydrogel blends in terms of printability in accordance with parameters based on their rheological properties (viscosity, n_index, m, G\({}^{\prime}\), G\({}^{\prime\prime}\), tan\(\delta\), yield stress, viscosity recovery (Figure 6a)). According to the \"elbow\" of the graph on the scree plot (Figure 6b), for higher accuracy of the conclusions drawn, the study of the ink properties should include the contribution of three Principal Components (PC1, PC2, and PC3) that are retained as significant (cumulative contribution = 95.27) (Figure 6c). Based on the eigenvalues of the correlation matrix, the contribution of PC1 and PC2 was 73.89% and 16.24%, respectively; the cumulative contribution of PC1 and PC2 was 90.13% (Figure 6c), indicating that the majority (>80%) of the data related to the material properties can be explained on the basis of these two components. Figure 5: (**a**) Yield stress results for each of the eleven blends; (**b**) Tan\(\delta\) results for each of the eleven blends. The vectors on the biplot of PC1 and PC2 (Figure 7a) reveal that printability (strand and pore area) is highly positively correlated with viscosity, m, G\({}^{\prime}\), G\({}^{\prime\prime}\), and yield stress. Moreover, the acute angles formed among those variables indicate their strong correlations. Viscosity recovery, n_index, and tan\(\delta\) located on the PC2 axis indicate a non-strong correlation with printing behavior. Specifically, the flow behavior index should be less than 1 to ensure shear thinning behavior, while the different values have no specific effect on the sample's printability. Regarding tan\(\delta\), just a narrow range of values can positively affect printing behavior leading to better printing outcomes, as presented in Table 8. Viscosity recovery exhibits neither a positive correlation with printability nor a strongly negative one, suggesting that this factor could not be included in ink property design. The cosines of the formed vectors on the biplot of PC1 and PC3 (Figure 7b) also pinpoint that the variables strongly affecting printing behavior are viscosity, m, G\({}^{\prime}\), G\({}^{\prime\prime}\), and yield stress. By observing the score plot of either PC1 and PC2 (Figure 7c) or PC1 and PC3 (Figure 7d), it is concluded that the developed candidate inks can be classified into three groups according to their rheological properties (Table 9). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Groups**} & \multicolumn{5}{c}{**Alg\_Gel Composition**} & \multicolumn{5}{c}{**Governing**} \\  & & & **Alg\_Gel Composition** & & & **Properties** & **Printability** \\ \hline Group A & 6.0\_0 & 8.0\_0 & 10.0\_0 & & & & tan\(\delta>1\), viscosity recovery & Non-printable \\ Group B & 0.0\_2.0 & 0.0\_4.0 & 0.0\_6.0 & 2.0\_4.0 & 4.0\_4.0 & 10.0\_4.0 & 8.0\_4.0 & Intermediate region & Poor Printability \\ Group C & 6.0\_4.0 & 8.0\_4.0 & & & & & \(G^{\prime}\), G\({}^{\prime\prime}\), m, viscosity, yield stress & Good to high \\  & & & & & & & stress & printability \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Inks classified into Groups A, B, and C, according to PCA scores. Figure 6: (a) Correlation matrix obtained by PCA; (b) score plot displaying the downward curve of eigenvalues; (c) eigenvalues of the correlation matrix; (d) extracted eigenvectors of each variable. The first class of inks (Group A) shows high viscosity for a low shear rate as well as high G\({}^{\prime}\), m, and yield stress values.