Let's say a person undertakes a program of high-intensity interval training (HIIT) on an exercise bike, with a heart-rate monitor, in a gym. This program involves 30 min sessions every day. The objective of each session is to reach the maximum achievable heart rate at the end of the 30 min period. By 'maximum achievable' I mean the rate at which a highly motivated individual is able to reach (while being yelled at by a trainer, for instance). I think this limit is effectively determined by the person's ability to tolerate pain/discomfort - it would be around say 85% of a person's 'maximum' heart rate, which is determined using the 220-age_in_years rule-of-thumb. At this limit the person is a 'mess' (lost all inhibition, sweating profusely, short of breath, grunting involuntarily, etc.).
My question is - How would this 'maximum achievable' rate change as the program progresses and as the person (who is already reasonably fit) becomes fitter? Would it increase or decrease? And what determines this discomfort/pain threshold anyway, if it is not heart rate? Furthermore, what is the significance of the 'maximum' heart rate if it is not reachable/achievable in reality?
Thanks in advance for your help.