'apneustic' originates from Greek via New Latin, specifically the Greek word 'apneustikos', where 'a-' meant 'not' and 'pneustikos' related to 'breathing'.

'apneustic' passed from Greek 'apneustikos' into New Latin/medical Latin (e.g. 'apneusticus') and entered English medical usage to describe the characteristic breathing pattern and related centers in the 19th century.

Initially it literally meant 'not breathing' or 'without breath' (from the Greek roots), but over time it evolved into the specific medical sense of 'relating to a prolonged inspiratory spasm' or to the brain structures that produce that pattern.