Slowing down blood could increase the oxygen extraction from a given volume of blood but what possible compensatory function could that have? To extract more oxygen over time you want faster flow and return to lungs as quick as possible for new oxygen.
If I'm not mistaken, that may not be the case. I need to read some more but I believe that we actually have more oxygen per unit volume of blood delivered to the brain than it can use in normal circumstances. That is the principle of fMRI and BOLD (blood oxygen level dependent) imaging. Because the brain doesn't have a fuel reserve and increase in demand requires tight neurovascular coupling. So with a lag of 2-6 seconds we see an increase in blood flow in brain regions which is a surrogate of increased neuronal activity. But what we measure is the rise in oxygenated Hb in that brain volume because the neurons can't use it all.
So in fMRI (BOLD) increased oxyHb is a surrogate for increased blood flow which is a surrogate for increased neuronal activity.
Why the O2 overshoot in normal circumstances? I think it's been suggested that the increased neuronal activity produces metabolic waste and that needs to be cleared. So it's not simply about the O2 and glucose inputs, it's also the waste outputs.
A few things might follow, but there are still some holes.
Slowing blood flow to the brain generally — perhaps for the benefit of certain regions in particular — might have the consequence of reducing the clearance of metabolic waste. Then you might have a little more waste needing to be cleared via the glymphatic system, which might explain enlarged perivascular spaces that are commonly seen.
In this model cognitive-induced PEM may relate to further reduced clearance of waste products, leading to increased neuro symptoms; and systemic cardiovascular effects, leading to increased body symptoms.
If it's true that the brain wants slower flow to allow it to extract more O2 than it it would or could in normal circumstances, then the brain could try and influence this by aiming to reduce circulating blood volume and putting us in a near shock state, to try and keep MABP down.
That could explain reduced or undetectable vasopressin levels (aka anti-diuretic hormone, from the hypothalamus).
Could also explain the RAAS (renin-angiotensin-aldosterone) paradox as again the hypothalamus could be adjusting the HPA axis, although I don't have a handle on potential mechanisms.
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One problem though, in me and others, is that my BP is now high. Admittedly a bit of a hand-wave for now, but maybe that results from the contention between brain requests and body requests of the cardiovascular system.
(I don't get brain fog and maybe my brain compensation mechanisms are doing a better job at holding the line, at the cost of body symptoms.)
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PS if this were true then it puts a knife into the TPJ findings in the NIH paper, as BOLD imaging can not be regarded as at all reliable in this scenario.