wakey,

I have never read anything like "the altitude can, in theory, constrict the flow of blood to the brain" can you help me understand this theory.

The effect of altitude is usually based on the lower amount of oxygen available due to the lower air pressure. People with a history of brain injury often have a decrease capillary capacity leading to a reducing on oxygen perfusion to the brain tissues.

I could understand that as the brain struggles for oxygen, the increased blood flow may cause head aches. Plus, any sensitivities to lower barometric pressures can cause related inflammation discomforts.

Either way, head aches are still head aches.