**2. Computational model of the human placenta and its analysis**

The model development and computations were carried out by the finite element analysis software (COMSOL Multiphysics®, 6.1). The computational model of the human placenta, developed in this study, is shown by **Figure 1**. The morphological characteristics and mechanical properties of the components in this model are indicated by **Tables 1** and **2**, respectively. As **Figure 1** shows, the placenta is set as the ellipse (A), whose major and minor axes were based on the radius and thickness of the placenta at the gestational age (40 weeks), respectively [15]. The placenta was covered with the thin area (B2) entirely, composed of the chorion (part of the chorionic plate), marginal zone, and basal plate. The thickness was corresponding to that of the chorion [21]: Because the thickness of the chorionic plate was larger than the sum of those at the amniotic and chorionic layers [21], the difference was evenly added to each layer's

*Histological Properties of the Chorionic and Basal Plates and Maintenance of the Mechanical… DOI: http://dx.doi.org/10.5772/intechopen.112935*

#### **Figure 1.**

*A computational model for the human placenta and its surroundings, developed in this study. A, placenta; B1, amnion (chorionic plate); B2, chorion (chorionic plate), marginal zone, and basal plate; B3, boundary region between the placenta and myometrium; C, myometrium; D, surroundings. The details of the region R1 (broken lines, upper) and R2, part of R1 (broken lines, lower, left), are shown at the lower images (left and right), respectively. F1, F2, and F3 were fixed in all the cases.*

thickness. Also, the region B2 was surrounded by the two thin layers (B1 and B3): B1, amnion (part of the chorionic plate); B3, the boundary region between the placenta and myometrium. The thickness in B1 and B3 was the same as that in amnion [21]. B1 and B2, corresponding to the chorionic plate, were extended to the point, 24 mm from the ellipse A (about 10% of the major axis), keeping parallel with its major axis. Both ends of B1 and B2, F1 and F2 in **Figure 1** were fixed at all the computation. The region C, the myometrium, was put the thin regions (B2 and B3) with the thickness before labor [23]. Every region in the region C, including the side of the region A, and the region under the region A, was connected smoothly, with the radius of curvature, the same as its thickness. Considering that the uterus is constrained in the various ways, including cardinal ligament, broad ligament of the uterus ligament of ovary, and round ligament of uterus [26, 27], the region D (surroundings) under the region C (myometrium)


#### **Table 1.**

*Morphological characteristics in the computational model.*


#### **Table 2.**

*Mechanical properties in the computational model.*

was set. The bottom of the region D, F3 in **Figure 1**, was fixed at all the computation. Assuming that the uterus could move to some degree, the elastic modulus of the region D was set much lower than that of the others. The elastic modulus of the placenta was corresponding to that at compression [22] in order to weaken the influence of the chorionic plate. The elastic modulus at chorion [21] was used for B2. Because the region B3 faces the maternal side, which is composed of the loose fibers and a complex vascular plexus [17], its elastic modulus was set at the same as B1. While Poisson's ratio at myometrium was 0.499 for incompressibility as muscular tissue, that in other parts was 0.3, corresponding to gel [24], because incompressibility was not clear. **Table 3** shows the elongation and contraction of the uterus (Mode 1, Mode 2, and Mode 3). **Figure 2** shows the model with the triangular elements (305,336 elements).

The mechanical environment was evaluated by von Mises stress, the first principal stress, displacement, and the first principal strain. The distribution in each parameter was visualized. Also, the fluctuation of each parameter was evaluated along the lines, depicted by **Figure 3**.

*Histological Properties of the Chorionic and Basal Plates and Maintenance of the Mechanical… DOI: http://dx.doi.org/10.5772/intechopen.112935*


#### **Table 3.**

*Elongation and contraction of the myometrium.*

#### **Figure 2.** *Mesh in the computational model (305,336 elements).*

#### **Figure 3.**

*Lines for evaluation in the mechanical environment of the placenta and surroundings. 7 lines (a–g), parallel with each other, were set 40 mm each along the horizontal direction.*
