There is a linear relation between hear rate and VO2 max, that is as the intensity increases our HR increases. That said, when exercising below VO2 max, our metabolic fitness and sustainable pace/power- that is our muscles ability to use oxygen to oxidize fat/carbs for fuel, our muscle fatigue resistance, our ability to buffer lactate, etc. all this processes might or might not directly be related to HR responds because it can also be affected by other variables such as heat, hydration, altitude, sleep, diet, etc.
In other words, the work done in our muscles the direct work done
(dose
) and HR is just a response and it might or might not be reflect necessarily to that work done in our muscles. For that reason it is possible to run at 9min/mile
("zone 3"
) with 'x' HR today and tomorrow when is hot, or you had a crappy sleep night or drank too much caffeine your HR might be 'y'.
On the long run, your HR will fall within certain average and might reflect your different paces at different intensities, however on a day to day basis it can be so variable such that it can mislead you in your training decisions
(i.e. run slower because your HR is higher that day for variables other than your work done
). Finally, overtime HR remains fairy constant even though your speed increased, hence you run faster at a same HR level, though HR also decreases as we age or get fitter so it is something you need to adjust.
In the end, IMO if you train with pace and gauge your effort by perceived exertion, then using a HR as well can be redundant or misleading.