Problem with seabird penetrating bone (7)

I believe the answer is:
sternum
'penetrating bone' is the definition.
'sternum' can be an answer for 'bone' (the breastbone). I'm unsure of the 'penetrating' bit.
'problem with seabird' is the wordplay.
'problem' becomes 'sum' (as in a mathematical problem).
'with' indicates putting letters inside.
'seabird' becomes 'tern' (tern is a kind of seabird).
'sum' enclosing 'tern' is 'STERNUM'.
Can you help me to learn more?
(Other definitions for sternum that I've seen before include "front of breast" , "big bone" , "Breastbone" , "Munster (anag.)" , "Chest bone" .)
