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That's not written in stone either. Grigg (1987) reviewed patients at a hospital and identified a considerable number whose brainstem was totally destroyed, absolutely brain dead by all medical criteria, (hopeless cases) but scalp EEG recordings were still measuring electrical brain activity, some patients displayed sleep like brain wave patterns, yet their brainstem was just a mess of necrotic tissue. So trying to claim that if the brainstem is down, there can be no other electrical activity in the brain, as if it were some golden rule, just isn't correct.
https://thinkingdeeper.files.wordpress.com/2017/03/brain_death_1987.pdf
Thanks for sticking that up, Max. Unwittingly however you've just demonstrated that you don't understand the crux of the matter here. Those patients with severe damage to their brainstems (that the article refers to) (and therefore able to be predicted brain dead) still have a beating heart. So of course when the heart is still beating there can (sometimes) be some kind of wave patterns on the EEG. All the 56 patients in this paper died without any return of normal cerebral function which also demonstrates (apparently) how good a measure a severely damaged brain stem is of the viability of life.
In cardiac arrest, the brainstem, cortex, the whole brain is taken out of the equation. No blood flow = nothing going on after 10-20 seconds, the patient is dead and will stay dead unless resuscitated
A simple way (for Malf particularly) to envisage this is to think about a house and it's vital services, electric, gas, water supply etc. To make sure that all systems in the house are non functional, all that needs to be done is flip the switch on the RCD, turn the gas lever and close down the stop cock. Everything stops.