It has to do with recovery. That's what a big series of intervals stresses: your recovery system. Another good exercise is "over-unders." Go over threshold (but not sprinting) for a couple minutes, then under threshold for a couple minutes. Continue until you can't. You can also practice hill sprints. Find a hill that you can sprint up in 45 seconds, which isn't a true sprint but never mind. Do 6 of those with 5 minutes of easy spinning between efforts. Always stop an interval set when you do one that's slower. You'll gradually become able to do more of them in a set.

Of course sprinting spikes your HR. The trick is to train yourself to keep going anyway.