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1706, "stoppage of pulse," from Modern Latin, from Greek asphyxia "stopping of the pulse," from a- "not" (see a- (3)) + sphyzein "to throb." The current sense of "suffocation" is from 1778, but it is a "curious infelicity of etymology" [OED] because victims of suffocation have a pulse for some time after breathing has stopped.
asphyxia as·phyx·i·a (ās-fĭk'sē-ə)
A condition in which an extreme decrease in the amount of oxygen in the body accompanied by an increase of carbon dioxide leads to loss of consciousness or death.