This is important to keep in mind whether you are trying to become a more efficient runner or swimmer, or simply clear brain fog by maintaining max oxygen delivery.
Homework: At different times throughout the day today, pause to notice the rhythm of your breath. Do you hold air in or out? Is your exhale shallow (i.e. less than two seconds!!) Is your breath energizing--you know, the kind that feels like it "re-sets" your breathing?
Now apply this awareness to an easy movement pattern--i.e. stretching.
A) Sit in a tall position with legs relaxed. Breathe in for 2 counts, hold the air for 2 counts, exhale for 2 counts and hold empty for 2 more. Increase the count as long as you can keep it even (i.e. all four phases being equal.)
B) Now do the same thing but moving in and out of a simple bridge. Lie on your back with legs bent, feet on floor. Raise hips toward ceiling as you inhale; hold breath at the top of the bridge; lower down for chose number of counts and pause at the bottom for an equal count. Again, choose a count that can remain consistent during all four phases. Build up to ten full cycles.
Once you can apply this method to simple movements, you can eliminate the breath holding and begin to focus on a steady flow of air in/out. When the inhale becomes limited it is because you are tensing your secondary breathing muscles in the upper torso/neck area. Reduce the intensity or range of motion until you can maintain your easy breathing pattern. This takes a lot of concentration and practice but is the key to providing you muscles with much needed oxygen and for reducing overall stress that accumulates during extended training/racing situations.