Systematic check-up securing most of the oxygen (10)

I believe the answer is:
methodical
'systematic' is the definition.
(similar in meaning)
'check-up securing most of the oxygen' is the wordplay.
'check up' becomes 'medical' (I can't justify this - if you can you should give a lot more credence to this answer).
'securing' means one lot of letters goes inside another.
'most of' means to remove the last letter.
'oxygen' becomes 'O' (atomic symbol for oxygen).
'the' with its last letter taken away is 'th'.
'th'+'o'='tho'
'medical' going around 'tho' is 'METHODICAL'.
Can you help me to learn more?
(Other definitions for methodical that I've seen before include "Systematic" , "following a set pattern" , "Orderly" .)
