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I am thinking the mechanism from hyperventilation into brain damage:

  • hyperventilation
  • [CO2] decreases in plasma
  • cerebral vasoconstriction

which then decreases the oxygen supply i.e. [O2] in the brain. The vessels get thinner. Those vessels are not surrounded by muscles so no Laplace law. There should be extensive diffusion. I do not understand how the vasoconstriction lead to decreased [O2] in cerebellum (probably in other parts of the brain too as complications; but primary complication in cerebellum first).

My intuition is that the smaller volume in the vessels can hold less oxygen particles inside (simplifying thinking by ideal gas Law pV = nRT; volume V down so the amount of substance n down too). Since there is continuous diffusion from vessels into brain tissue, the pressure p in the vessels and brain keeps constant. It is important to regulate this for homeostasis.

Concentration is directly proportional to the amount of substance. So vasoconstriction (decreased volume) leads to

  • decreased oxygen and
  • also carbon dioxide supply to the brain.

I think it would be better to say that vasoconstriction leads to decreased circulation of essential molecules. Hypoxia is a decreased oxygen supply so Decreased oxygen supply is NOT causing hypoxia. Carbon dioxide play some role in brain when in little quantities; at least, it is similarly required by the buffer system.

I think it is most correct to say that

Vasoconstriction leads to decreased local circulation of brain and eventually hypoxia.

I think this kind of logical mistake has been done in many books about the subject earlier. Claiming that A is causing A.

How can cerebral vasoconstriction lead to decreased O2 supply?

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First of all, bear in mind that oxygen is not carried as "particles" dissolved in plasma, but as oxygen molecules complexed to hemoglobin tetramers with a well defined stochiometry inside red blood cells. Second, seems like the reason is simply less blood = less oxygen - am I missing something? –  Superbest May 12 at 18:26
    
That is the question. I simplified the binding process of oxygen in blood and used ideal gas law. Question is: Why does the decrease of vessel diameter which leaks decreases the O2 supply to tissues? I should know the flow rate in the brain to answer this - I think it increases. I think Biot-Savart equation and differentials should be used here. What happens to the leakiness under higher flow rate is another thing - I think it stays constant. Smaller diameter, higher flow rate and more blood. If little little leaky, then smaller diameter and less blood. It seems the little leaky dominates. –  Masi May 12 at 18:52
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I don't think your simplifications are appropriate for various reasons. By the way, the critical parameter is number of RBCs going through, and capillaries are already just about wide enough for only a single cell to pass. Also, smaller vessels would mean less blood, not more - since it is hard to push RBCs through a small vessel, pressure in the brain would increase, and more blood would go through the aorta into your torso rather than taking eg. the carotid artery. –  Superbest May 12 at 19:17
    
@Superbest You are completely right. I ignored by accident the squeezing of the red blood cell. Make that an answer and I will accept it. –  Masi May 12 at 19:45

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