Hi Georgios, thanks for your message.
Generally speaking, all breathing knowledge is thousands of years old - it's the roots of pranayama and yoga.
You don't need to know any how to practice yoga or all the pranayama exercises though because the breaths is consistent as ever. Just a few can help a lot.
As for the brain - science shows that inhaling activates the left hemisphere and the sympathetic nervous system and exhaling activates the right hemisphere and the parasympathetic nervous system. It's designed to keep us balanced - one breaths stress into the body, the other breathes it out.