As a result of sharing a single placenta, the blood supplies of monochorionic twin fetuses can become connected, so that they share blood circulation: although each fetus uses its own portion of the placenta, the connecting blood vessels within the placenta allow blood to pass from one twin to the other. Depending on the number, type and direction of the interconnecting blood vessels (anastomoses), blood can be transferred disproportionately from one twin (the "donor") to the other (the "recipient"). The transfusion causes the donor twin to have decreased blood volume, retarding the donor's development and growth, and also decreased urinary output, leading to a lower than normal level of amniotic fluid (becoming oligohydramnios). The blood volume of the recipient twin is increased, which can strain the fetus's heart and eventually lead to heart failure, and also higher than normal urinary output, which can lead to excess amniotic fluid (becoming polyhydramnios).
Whether such twins survive usually depends on how early in the pregnancy the syndrome is diagnosed. Minnesotastan also found out who the children in the painting were. Link