Hypothesize as to why would paleness or cyanosis of the skin occur when there is a lack of oxygen

This is because the body, when in need of oxygen, and which is in low supply, will prioritize the sending of whatever oxygenated blood there is available towards what is known as white organs, or the most vital organs, while depriving the skin and shunting the flow towards it.

Explanation:

In general circulation, there are what are known as white organs, which are those the body definitely needs to survive and gives priority to in terms of energy and oxygenation, and those that are not. The brain, the heart, the lungs, the kidneys, are some of these organs whose activities, if they failed, would cause irreversible damage and the damage to them without oxygen is almost always irreversible. The brain, more than any other organ, is a main priority for the body in terms of saving oxygenated blood, and this is why, when there is a lack of oxygen the body shunts flow of oxygenated blood to the skin, which essentially has better reparation properties and is deemed as less vital, causing cyanosis and paleness.

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