Your VO2 max is not about the volume of air you breathe into your lungs with every breath or every minute. It is a measure of the oxygen exchange happening at a cellular level between the cardiovascular and musculoskeletal systems – between the blood and the muscle. Generally, this will be limited by either supply or demand. Most commonly, the limiting factor is one of supply which may include diffusion of oxygen at the alveoli in the lungs, the volume of blood your heart can pump in a beat or a minute, or the level of vascularity within the muscle (and therefore the ability to deliver oxygen to as many fibres of the muscle as possible).
So, if you’re running along at a leisurely aerobic pace and I am measuring your VO2 (just VO2, not VO2 max because you’re not at maximum capacity) and I ask you to take a few bigger, deeper breaths, I wouldn’t observe a significant change in the VO2 numbers. This is because the amount of oxygen required by the muscles at that pace has not changed. The intensity has not changed and therefore the oxygen requirements of the muscles to carry out exercise at that pace or intensity is unchanged. Neither the supply to the muscle, nor the demand at the muscle has been altered by a change in breathing. Again, it comes back to the fact that VO2 is a measure of oxygen exchange at a microscopic, cellular level and not a measure of lung volume.
When your breathing becomes laboured and difficult in the later stages of an intense bout of exercise, oxygen exchange at the muscle has probably already begun to reach a plateau or a maximum (i.e. VO2 max). So, while this laboured breathing may – in some cases – affect someone’s ability to plateau or max out at a slightly higher VO2 number, it’s most likely not what is affecting your VO2 output during a time trial.
Dr Timothy Noakes has presented some fascinating research around VO2 max and how it is actually more likely that the brain decides how high we can go. Noakes has aptly titled this the Central Governor Theory.