## 4 Discussion
Narrowed confidence intervals showed a good repeatability of the relaxation phenomenon among the samples. Figure 3e showed the comparison with other tissues, i.e., the bladder and the tunica albuginea (only transversal direction was reported due to sample availability). The tunica albuginea had the lowest percentage of relaxation (65.74%, [53.47, 82.12]%), while bladder behavior appeared similar to those of the urethral tissues (88.55%, [84.00, 91.18]%). Clear anisotropy can be observed between longitudinal and transversal urethral samples when referring to the stress-strain equilibrium curves (Figure 3f). The human urethra exhibited a stiffer response along its axis, while circumferential deformations can be achieved with lower stresses. These insights are also supported by the functional evidence during micturition, where the urine flow applies a radial pressure thus resulting in a predominant radial urethral deformation rather than a longitudinal one. Table 5 reports all the fitting parameters of the different tissues, underlining that, for the equilibrium, the initial stiffness \(k\) for the transversal urethral direction is two orders of magnitude lower than the longitudinal one. As during failure, in the equilibrium response, tunica albuginea was the tissue characterized by the greatest initial stiffness (8.64 MPa). Few other works reported the viscoelastic characterization of human LUT tissues. [PERSON] et al. [4] found that the spongy urethra exhibited more important hysteresis and anisotropy, with a stiffer behavior in the circumferential direction. Contrary to our findings, [PERSON] et al. [5] reported no differences between regional responses for circumferential or longitudinal extension and also in terms of the relaxation or creep parameters defining the response in the two directions, while [PERSON] et al. [8] reported greater stiffness for the proximal specimens of equine urethra along the longitudinal direction, as in the present study. A significant difference in terms of stiffness resulted when comparing the longitudinal proximal specimens to all the other samples. Comparing thickness measurements of human urethral strips, the mean value recorded in the present study (3.73 \(\pm\) 0.78 mm) is within the range outlined by the literature studies mentioned above (2.53 \(\pm\) 0.24 mm [4], 4.44 \(\pm\) 0.64 mm [5]). Stress-relaxation results on porcine bladder samples reported by [PERSON] et al. [9] highlighted a longer relaxation time for animal samples (>600 s) with respect to human samples (after 300 s the relaxation phenomenon lasted). In agreement with the present study, they found no differences among the loading directions in terms of viscosity. Even in humans, the regular spatial distribution of the contractile and support elements hasbeen observed in the various layers of the bladder wall (Figure 5). The bladder can be seen as a three-dimensional multiplanar interweaving structure that allows the forces to be uniformly distributed both in expansion and contraction. This conformation ensures a gradual and coordinated modification of bladder diameters during physiological activity, with greater involvement of the dome and lateral walls. Finally, to investigate LUT biomechanics under additional loading combinations, the compression behavior of the prostate was also analyzed through indentation tests. Figure 4 shows the recorded force between 0 and 1.5 mm of indentation depth and the curves obtained by fitting the experimental data with the elastic Hertz model (Table 6, R2 > 0.85 for all the points with only P3 as an exception). Since the prostate reported some signs of TURP with portions of the gland tissue covered by nodules, points P1, P2 and P7 investigated the stiffness of the nodule surface, then compared with the other points. On average, nodule elastic modulus resulted in 46 \(\pm\) 27 kPa, three times greater with respect to the other regions without repair signs (16 \(\pm\) 5 kPa).