**1. Introduction**

The substances in the fetal and maternal blood, such as nutrition and gas, are successfully exchanged so that a fetus grows well. The fetal blood flows into the umbilical artery, circulates the blood vessels in the villous trees of the placenta, and returns to the fetus through the umbilical vein, while the maternal blood in the endometrial spiral artery flows into the intervillous space, corresponding to the space around the villous tree, and after circulating the space, returns to the endometrial vein. The fetal and maternal blood circulations do not share the space, but their substances are exchanged through the villous trees in the placenta. The condition of the fetal and maternal circulations would directly influence the substance exchange. Considering that the mechanical environment around these circulations could change the flow pattern, the environment would be modulated in order to keep the proper conditions of the circulations.

The umbilical cord shows the histological characteristics [1], which would be helpful to keep the mechanical environment suitable for the blood flow [2]. Also, the active contraction of the villous tree [3, 4], the contractile cells around the fetal blood vessels [5–8], expected to cause the contraction, have been reported. The computational models based on these previous reports [3–8] have been developed and indicated that the contractile system would be helpful for the fetal and maternal blood circulations [9, 10]. Moreover, it has been reported that the dilation of the spiral artery, caused by the loss of smooth muscle and elastic lamina, could modulate the maternal blood flow properly [11]. In the meantime, the deformation of the placenta and blood flow caused by the uterus contraction, evaluated by MRI images, has been reported [12, 13]. According to the previous report [14–16], the thickness and diameter of the placenta at the third trimester were about 40 mm and 200 mm, respectively. Comparing the placental size with the resolution of the MRI images (2.4 × 2.4 × 5 or 2.5× 2.5 × 6 [mm3 ]) [12], these quantitative values would be helpful in the evaluation along the circumferential direction of the uterus.

The placenta at term is covered with the chorionic plate, marginal zone, and basal plate [17, 18]. The chorionic plate connects to the umbilical cord while the basal plate is next to the placental bed. The marginal zone is placed between these two plates. These regions, which are continuously connected with each other, show the two types of fibrinoid, the fibrin-type and matrix-type fibrinoid [17–20]. Also, smooth muscle was observed at the chorionic plate [5] and marginal zone [18]. The distribution was expanded to the basal plate [18]. The mechanical properties of the chorionic plate were evaluated by the elastic moduli and thickness in the amniotic and chorionic layers [21]: the amniotic layer, 1.90 MPa and 47 μm; the chorionic layer, 2.2 MPa and 185 μm; the entire layer, 4.7 MPa and 243 μm. The elastic moduli of the placenta were varied by the methods [22]: The elastic moduli at tension and shear were more than twice of those at compression. Considering that the amniotic and chorionic layers could influence the elastic moduli at tension and shear more than that at compression, the elastic modulus of the region surrounded by the layers would be much lower than those in the layers.

In this study, a computational model of the human placenta was developed in order to evaluate changes in the mechanical environment of the human placenta, caused by the elongation and contraction of the uterus. Based on the results, how the histological characteristics of the placenta assist the fetal and maternal blood circulations will be indicated.
