Did placental oxygen transfer support increased brain metabolism as humans evolved?

Cerebral blood flow in relation to age of fossil skulls
from 12 hominin species.
Reproduced from Seymour et al.  R S Open Science (CC-BY) 

There is much interest in how increased brain size impacted on dimensions of the pelvis, birth weight and placentation as humans evolved (here). Increased brain growth in fetal life would seem to demand a greater placental blood flow to ensure an adequate oxygen supply. This may have led to increased invasiveness (discussed here) and indirectly to the risk of preeclampsia (here). 

But what if there was an increase not only in size but in the metabolic rate of the brain?

In a novel approach, Seymour, Bosiocic and Snelling attempted to assess cerebral blood flow in fossil adult hominins as a surrogate for oxygen supply to and consumption by the brain. As their starting point they measured the diameter of the carotid foramen in skulls of fossil hominins ranging from Australopithecus to archaic Homo sapiens (the carotid foramina carry the principal arteries supplying the brain). As can be seen in the figure, their main finding was that during hominin evolution cerebral blood flow increased disproportionately to brain size. The implication was that there was a progressive increase in the metabolic rate of the brain.

Of course this approach required some major assumptions (see below). But if the metabolic rate of the adult brain did increase successively as humans involved, so perhaps did that of the fetal brain. Here more is at play than the rate of blood flow to the brain. In adults the blood becomes fully saturated in the lungs, but that is not the case in fetal life. The oxygen content of the blood reaching the brain is dependent on placental function (reviewed here).

For Neanderthals there is enough data to conclude that brain size at birth did not differ from that of modern humans (here). But if human fetal brain had a higher metabolic rate than Neanderthal fetal brain, it might still have required a more efficient placenta.

Assumptions: The approach adopted by Seymour et al. relied on rearranging an equation for shear stress to isolate one of its determinants, blood flow rate. To accomplish this, shear stress must first be estimated using a scaling model that relates shear stress to body size. This is the weak point in the analysis, but the authors point to a previous study that verified the approach in primates and marsupials