## 3 Results and Discussion
### Some More Simulation Results  
Using the developed model, simulations were further performed to study the influence of penetration on the elastic modulus of scaffolds. For this, the value of penetration was changed from 0.01 mm, to 0.2, 0.3, 0.4, and 0.51, while the values of other parameters were taken the same as the ones listed in Table 2. The simulation results are presented in Figure 5, which shows a larger penetration lead to the higher elastic modulus. Elastic modulus achieved from experiment and model were discussed earlier for 0.2 and 0.51 mm penetration (refer to Section 3.1). More simulations were performed and the model predicted 3.64 KPa, 23.9 KPa, and 25.95 KPa for scaffolds with 0.01, 0.3, and 0.4 mm penetration amongst layers. Additionally, as shown in Figure 5, as the penetration is increased, the model predicts higher elastic modulus and results become closer to the elastic modulus of a bulk gel (experimental elastic modulus = 42.3 KPa). It means that by increasing the penetration, a scaffold with a rigid structure and high mechanical stability is obtained. It should be noted the penetration between layers is an important index to measure the printability of hydrogels (i.e., alginate in the present study) in 3D bioplotting, which is defined as the ability of a hydrogel to form and maintain a 3D structure and characterized by the difference between the printed scaffold structure and the designed one [30; 31]. Lager penetration suggests the bigger difference between the printed structure and designed one, thus poorer printability of the hydrogel. In this study, the measured height of the fabricated scaffolds (2.63 \(\pm\) 0.12 mm) was inputted to the numerical model to predict the elastic modulus of the printed structure (CAD model height was not considered for modeling). Based on the developed model, a numerical analysis was also carried out to study the effect of pore size on the elastic modulus of scaffolds. In these simulations, the pore size value was changed from 0 to 551 \(\upmu\)m, with other parameter values the same as the ones listed in Table 2. The simulation  
Figure 5: Effect of penetration within layers on the elastic modulus of alginate scaffolds with a strand diameter of 0.58 mm and a distance of 1 mm between two adjacent strands. results are shown in Figure 6, showing that a smaller pore size can result in a higher elastic modulus. As such, the pore size of scaffolds can be adjusted in order to obtain the mechanical properties similar to the native tissues. While there are many experimental studies in this regard [19; 21], the use of a finite element method would provide a more effective approach to adjust the pore size or other geometrical parameters to achieve the desired mechanical properties. It should be noted that measured pore sizes in different directions of fabricated scaffolds were not the same as shown in Figure 6. Experimental results were reported in Section 3.1 and here more simulations were performed. Modeling results showed 30.42 KPa, 26.61 KPa, and 24.62 KPa for scaffolds with 300, 400, and 500 \(\upmu\)m pore sizes in the X and Z directions defined in Figure 3.  
The number of layers in the Y direction was investigated to determine the effect of the height of the scaffold on its elastic modulus. The penetration and strand diameter were considered as 0.51 mm and 0.58 mm, respectively. As demonstrated in Figure 7, increasing the number of layers causes a higher elastic modulus numerically and experimentally. This is likely due to having more layers and, consequently, a thicker scaffold with a more mechanically stable structure has a higher elastic modulus. For a scaffold made of 10 layers, the model predicted 22.14 KPa as the elastic modulus of a porous scaffold. As reported in Section 3.1, the model predicted 24.97 KPa, 27.34 KPa, and 28.76 KPa for scaffolds with 16, 24, and 31 layers, respectively.