## 4 Discussion
Generally, elastic fibers confer to tissues the capability to recover from deformation as soon as they are unloaded [63, 69], and the highly cross-linked collagen and the cells would be responsible for the dissipation of the energy stored during the deformation [59, 67, 68], controlling, thus, the time-dependent behaviors of the biological samples. The intricate network formed by the elastic fibers, the highly cross-linked collagen [58], and the cells determined the viscoelastic responses of the biological samples here analyzed. As a matter of fact, the relaxation times \(\tau_{1}\) and \(\tau_{2}\) obtained for the biological samples resulted in significantly different values. However, further studies are required to understand the contribution of the elemental units that composed the tissues and which determined their time-dependent responses. Comparing pig and human native lung tissues, [PERSON] et al. [70] demonstrated consistent differences in the contents of their ECM components. In particular, when compared with pig lung tissue, human lung contains double amount of elastin fibers (30% vs. 15%) and half the amount of glicosaminoglycans (25% vs. 51%), while the percentage of collagen remains quite the same. Moreover, another study conducted by [PERSON] et al. [71], which widely analyzed the composition of lung ECM, highlighted the roles of elastin, collagen, and proteoglycans in providing elasticity, structural support and strength, and stability, respectively. The higher percentages of elastin in human lungs could explain the reduced tissue relaxation and, thus, the inferior load decay of the human lung compared to pig lung illustrated in Figure 7.  
On the other hand, the GelMA samples showed a less-obvious bimodal distribution, and no statistical differences were found between the two time constants. The biggest peak of the violin plot related to the GelMA sample (Figure 9b) could be linked to the contribution of the most present molecular segment, i.e., bovine gelatin, while the contribution of the methacrylic anhydride did not appear to be impactful on the time-dependent response. As reported in the literature, in the context of hydrogels derived from proteins, their viscoelastic behaviors are strongly influenced by the unfolding of the molecular protein chains, which need to overcome friction from other chains [59, 72, 73]. This has led to the hypothesis that a higher concentration of bovine gelatin could control the time-dependent response of a hydrogel. The absence of intravariability in the material parameters (\(p_{1}\) and \(p_{2}\)) and, on the contrary, the intravariability in the time parameters reported in Figure 9 highlighted that the time-dependent characteristics were crucial in defining the mechanical behaviors at the cell-length scale. Furthermore, the GelMA hydrogel was produced in a formulation that conferred greater viscoelastic properties with respect to the analyzed biological samples, and it was characterized by one predominant relaxation mechanism. Despite this, the values of the time parameters found for the GelMA sample were in the same range as the biological samples. Further improvement will be implemented in the formulation of the GelMA hydrogel to obtain a more complex relaxing mechanism that better mimics the mechanical properties of lung tissue. Despite the promising results obtained in this study, there is space for improvement. The implementation of a hyper-elastic model [55, 56], even if this could introduce a higher number of parameters that are difficult to interpret, could better model the behaviors of biological tissues and further improve our approach. However, the Hertz model adopted herein is one of the most common approaches in analogous studies and represents a satisfactory starting point that allowed us to obtain robust and reliable results. Moreover, in the future, the effect of the loading rate of the indentation test and how it could influence a material's response will be further investigated.