Placental villous tree models for evaluating the mechanical environment in the human placenta

The human placenta has the fetal and maternal blood flows, which are in the villous tree and intervillous space, respectively. The oxygen environment influences the branching of the villous tree. The contraction of the villous tree can directly modulate the intervillous space. The change in the shape and the contraction are necessary to investigate the maternal and fetal circulations from the viewpoint of biomechanics. In this study, the method to construct the villous tree models for evaluating the mechanical environment in the placenta was developed. The two-dimensional diffusion-limited aggregation model was used to make the axis of the villous tree model. The centripetal and centrifugal orders in each branch showed that the axis was unequally dichotomous as well as asymmetric. By changing the range of the centripetal order, 6 types of the axes were made. The size of the axis was modulated to keep the area of its bounding rectangle constant in the models. By curving the axis three-dimensionally, and then dilating it, the villous tree model including blood vessels was made. The component ratio was almost constant in the models. The surface area and volume in the smallest model were less than 30% of those in the largest one.