The cord stops pulsating when the baby's blood vessels from the cord shut down and fulfill the requirement to switch from fetal circulation to newborn circulation. The cord blood that is carried from the placenta to the baby is rich in stem cells (which is why you have for profit companies wanting to harvest them for a fee! Seems like they could be important for the baby!), iron and blood. The amount of blood the newborn misses out on with 'managed third stage' would be equivalent to major haemorrhage in a newborn if that blood was 'lost' after the cord was clamped. It is interesting to me that timing is everything. If it stays in the placenta because of active management, then that is ok, if it comes from the baby after that, it is not ok.
Sometimes, when the placenta is left attached, the placenta can be born and it is possible to still feel faint pulsation in the cord. The cessation of cord pulsation is not necessarily related to placental release from the uterine wall or the birth of the placenta. There are probably biochemical interrelationships and interactions that we are not sophisticated enough to know about or recognise in this process as yet. Most studies done on placentas after birth are done on placentas which come from actively managed third stages, so the natural process has not even begun to be mapped yet. As with placental implantation, there must be enzymatic and hormonal interactions at the cellular interfaces of the placental surface and the uterine wall when the process is allowed to follow the natural course of events, alongside the space reduction component following the birth of the baby. It is interesting that women who have birthed their placentas naturally and physiologically find that the post partum bleeding is substantially less than when they experienced actively managed third stages of labour.
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