There's growing evidence that breathing is linked to brain activity in interesting ways [1]. There's also the "4-7-8" breathing technique that is supposed to help you fall asleep faster. [2]
On top of that, concentrating on breathing takes your focus away from other inner monologue and intrusive thoughts; meditation programs typically start you off on that path.
I remember reading a long walk technique from middle east, where they would hold their breath a few seconds on each cycle. Supposed to augment your range significantly.
I also found out while trying to hold my breath above 2 minutes, that slowly swinging my shoulders to massage my lungs would delay the feeling of syncopation. Maybe, mayyyybe, because it would help enforce more gaz movement thus exchange.
On top of that, concentrating on breathing takes your focus away from other inner monologue and intrusive thoughts; meditation programs typically start you off on that path.
[1] https://news.northwestern.edu/stories/2016/12/rhythm-of-brea...
[2] http://www.medicaldaily.com/life-hack-sleep-4-7-8-breathing-...