I don't actually have an answer for this off the top of my head, as I am not sure there is a definite answer yet... might be but I haven't been reading into this area a lot lately.
From my perspective there is two main ways to do HIIT:
-for aerobic improvements - to directly improve ones V02max and all the performance gains that entails.
-to improve anaerobic performance such as lactate threshold and lactate clearance - this is the most important aspect of elite performance once everyone has a sky high vo2max.
I know there are published guidelines for work to rest ratio's but I don't use them, working in the lab means we can measure most things in real time.
Generally for HIIT i just use a HR monitor and base the next interval when we get to a set recovery HR, as you know there max HR and training zones from pre testing it means we get the intervals perfect for how they are feeling for each session, won't work in a group environment.
Doesn't anwer the question your question unfortunately.
MWI, what's the science behind waiting for the HR to return to the same point each interval (which will require longer recovery as you move through the intervals) verse doing intervals on a set time frame eg. every 2 minutes? (making the later intervals progressively harder due to the higher HR). I assumed that the effort to maintain output under increased fatigue would cause the adaptations/progress.