Is there a exchange of cells between the mother and the fetus through the placenta?

Under normal conditions, there is not a passage of cells across the placenta during gestation. The placenta has a smooth mucosa dividing the richly vascularized region in contact with the mother's endometrium from the umbilical cord in contact with the fetal blood. This barrier is called as placental barrier. Although permeable to some substances (selective permeability) the placental barrier forbids the passage of cells.