## 3 Results  
Mechanical tests were performed to study the different mechanical responses of the tissues composing the LUT, when possible examining the regional and directional tissue variability. From experimental tensile data, the strain was computed as the ratio between the elongation and the initial grip-to-grip length of the specimen, while the stress was computed as the ratio between the force measured by the load cell and the initial cross-sectional area of the sample. Regarding the failure results, for all tested tissues the stress-strain curves were considered up to the inflection point assumed as the failure point of the tissue. At this point, the stress and strain values were extracted as respectively the ultimate tensile stress (UTS) and the strain at UTS to characterize the mechanical tensile response of the different tissues. Median curves and confidence intervals for the tissues tested until failure are shown in Figure 2.  
The elastic modulus \(E\) was extracted from the linear region of the stress-strain curves, which differs among the tissues. This region corresponded to specific strain ranges according to the tissue: for the bladder [19.42-29.99]%, for the Buck's fascia [13.05, 22.91]%, for the prostate [23.63-19.48]% along the longitudinal direction while [52.51-68.32]% along the transversal one and for the tunica albuginea [9.03, 19.04]% along the longitudinal direction and [10.52-19.02]% along the transversal one. \(E\) was then defined as the slope of these regions, computed by means of linear fitting (R\({}^{2}\) > 0.99), as performed in other studies [24; 25]. Median values (25 th, 75 th percentiles) of the UTS, the strain at UTS and the elastic modulus are reported in Table 4. Among all, the highest stiffness of the elastic modulus was exhibited by the tunica albuginea along the transversal direction (median 40.44 MPa, [35.91, 44.97] MPa), followed by its longitudinal direction (12.77 MPa, [10.36, 17.70] MPa), while the lowest one by the prostate along the transversal direction (0.66 MPa, [0.63, 0.86] MPa). In accordance with these results, the tunica albuginea along the transversal direction showed also the highest UTS, while the minimum strain at UTS was recorded by its longitudinal direction. On the opposite, the prostate along the transversal direction exhibited the greater strain at break. Concerning the anisotropy of the prostate tissue, the elastic modulus, the UTS and the strain at UTS along the longitudinal direction resulted, in median terms, respectively, 2.34, 1.37 and 0.30 times the corresponding values along the transversal direction. Data from stress-relaxation tests were processed to analyze the response of each tested tissue during and after the relaxation phases. From stress-time data, the relaxation curves were extracted in response to each step strain and, to compare results at the same strain condition, normalized stress data were obtained as the ratio between stresses at the current time and at the beginning of the relaxation phase. Depending on the strain history assumed for each tissue, the normalized stress-time curves were separately determined and fitted by the following exponential formulations:  
\[\sigma_{norm}\left(t\right)=1-\gamma_{1}-\gamma_{2}+\gamma_{1}\;\mathrm{e}^{ \left(-t/\tau 1\right)}+\gamma_{2}\;\mathrm{e}^{\left(-t/\tau 2\right)} \tag{1}\]  
Equation (1) describes the normalized stress \(\sigma_{norm}\) over time \(t\) and accounts for two viscous branches, whose parameters are \(\gamma_{1}\) and \(\gamma_{2}\) as relative stiffness and \(\tau_{1}\) and \(\tau_{2}\) as the time constants of relaxation. The number of branches was defined by a trade-off between