In the last few years, there has been growing interest, in the study of the mechanical behavior of human soft tissues. This research in biomechanics was carried out through experimental characterization and computer-based simulations [1]. This work aims to study the main stages of the mechanical characterization of biological soft tissues, starting from theoretical concepts based on hyperelastic models, followed by the determination of material-dependent parameters. Curve fitting algorithms will be applied to experimental data and ultimately, tissues’ mechanical behavior will be predicted through numerical simulation.

The bladder and rectum of Swifter ewes (virgin, pregnant and parous), n=5 for each group, were collected. The groups considered were virgins (n=5; avg. weight = 45 kg, 9 month old), pregnant (n=5; term = 145 days; avg. weight = 65 kg, 3 years old) after two prior vaginal deliveries (third C-section) and parous (n=5; avg. weight = 60 kg, 4 years old), at least one year after three vaginal deliveries. Excised tissues were divided into samples for biomechanical testing and for histological analyses. 
Histological samples were stained with Miller's Elastica. High-resolution histological images were obtained using image processing techniques (ImageJ software)), making it easier to analyse the full thickness of the tissues’ microstructure and quantify the collagen, elastin, and smooth muscle fractions (%). 
Statistical analysis was performed to study possible variations of pelvic tissues properties, among groups. Using GPower software, statistical power analysis (to compute required sample size) showed that at least 16 samples for mechanical and 6 for morphological analysis were needed to achieve 90% power when alpha error was set to 0.05. Kolmogorov-Smirnov tests showed the data follows a normal distribution, a requirement for ANOVA. One-way ANOVA and post hoc test (Tukey’s correction) were carried out for the intergroup comparisons. The level of significance was set to p<0.05.
Uniaxial tensile tests were performed to obtain mechanical properties of the tissues, using nonlinear constitutive models of fiber-reinforced hyperelastic materials. The tensile testing data presents nonlinear responses while the histological data confirms that the tissues contained collagen and elastin fibers embedded in a matrix of smooth muscle cells (SMCs) and other constituents.  Under these observations, we employed the simpler version of the HGO model [2] which allow the comprehension of tissue mechanics in terms of its structure. The strain-energy (or stored-energy) is postulated as 

ψ=μ/2 (I1-3)+k1/(2k2 )(e^(k2 (I4-1^2 )-1)                                         (1)

where μ, k1, and k2 are the constant parameters that define the mechanical response. While μ is related to the matrix content, k1 and k2 reflect the fibers contribution. These 3 parameters require adjustment to obtain reliable characterization of the tissue. Therefore, a Simple Genetic Algorithm (SGA) is employed for the curve-fitting of the resultant stretch-stress curves (1).

There was a significant difference in mechanical behavior of the bladder during the pregnancy. Pregnant sheep bladder became more rigid compared to virgin (74.6%; p<0.05) and parous sheep (74.9%; p<0.05). The pregnant sheep bladder became less extensible than virgin’s (21.2%; p<0.05) and parous sheep (20.5%; p<0.05). Bladder became significantly thinner during the pregnancy (20.2%; p<0.05). It contained more total collagen (p<0.05), less elastin (p<0.05) and less smooth muscle cells (p<0.05) than virgin and parous sheep (Figure1).
Pregnant sheep rectum became stiffer compared to virgin (44.1%, p<0.05) and to parous sheep (19.9%, p<0.05), respectively. Parous sheep rectum became stiffer than of virgin (30.5%, p<0.05). However, during the pregnancy rectum became less elastic compared to virgin (23.8%, p<0.05) and parous (22.4%, p<0.05). 
There were no significant differences in rectal wall thickness. Pregnant sheep rectum contained more total collagen (p<0.05) than virgin and parous (p<0.05) sheep. It contained less elastin fibers than virgin (p<0.05) and parous (p<0.05) sheep and less smooth muscle cells. Smooth muscle cell content was significantly higher in virgin sheep compared to pregnant (p<0.05) and parous (Figure1).
Fitting results agree with histological data. Soft tissues show nonlinear material behavior (Figure 1), in accordance with higher collagen content while low collagen content is evidenced in softer material parameters.

This research has shown that along the studied reproductive stages, pelvic floor soft tissue undergoes profound histological and mechanical changes, particularly during pregnancy. For both parous and pregnant sheep, the elastin fibres and smooth muscle cell contents of rectum and bladder, were significantly decreased. These changes reduced their flexibility and capacity. As a result, this could be related with frequent urination or urinary incontinence, involuntary defecation and haemorrhoids or POP.
In this study a strategy to correlate tensile testing experiments with a material model capable to capture the nonlinear response over a large strain range is proposed. Based on histological and longitudinal tensile testing of ovine rectum and bladder the results demonstrate high correlation with the constituents’ content where the resultant material parameters reflect the physiological state of the tested samples.

Curve-fitting algorithms were applied to experimental data. Experimental and simulation fittings are in good agreement with histological data. The material parameters reflect the pathophysiological state of the tissues and can be used in complex simulation environments.

Biomedical Engineering Letters, 2016, Volume 6, , pp 181–195.
Journal of Elasticity, 61(1-3):1–48, 2000.