In the two years since I was last glued to an O2 tank I’ve learnt we can breathe in one of three ways:-
First and almost universally we breathe by expanding the chest.  Second is abdominal breathing, like new born babies breathe  - extending the belly to lower the diaphragm under the lungs and the third way is reverse abdominal breathing.

That’s still using the diaphragm but where it’s pulled directly down towards the pelvis using internal muscles opposed to pushing the belly out.  It’s promoted in some of the more meditative martial arts such as Tai Chi and I’m told in pilates.
In practice over the past week, once you’ve mastered pulling your diaphragm down, each breath seems more powerful and deeper. 

Whilst I have absolutely no hard evidence that it’s a better way to take O2, my impression is that I’m spending a little less time busting attacks and that’s a good thing.