Normally you do sprint intervals on a moving treadmill by alternating between rest and running at its fastest setting, but try this advanced twist: leave any treadmill off, and use your own two legs to power the belt for an incredible sprint workout. These "deadmill sprints", as they're called, are a worthy workout challenge because you have to counter the drag of a still treadmill belt from a dead-stop (shout out goes to Kandace Hudspeth, Vice President of Marketing at Bodybuilding.com, for showing me this).
When you begin, make sure the treadmill is off and place both hands on the handle in front of you. No need for a death grip -- you want to keep your arms and shoulders loose, yet have something to brace against. Using the handle for support, push and start digging your toes as if you're trying to run while pushing a heavy object (like a prowler push). It will take some grunting to get the belt moving at first, but once you do the real challenge is in keeping it moving while sustaining decent speed.
You'll soon realise that you can't keep this up for very long, which is normal. Just like you do with a high-intensity interval training-like workout, the idea is to figure out your work-to-rest ratio (work for 10 seconds and rest for 50 seconds, for example) and stick with it. I did this myself the other day, and I can say that repeating five to six times is more than enough!
The video linked above, by Fitness Mentality, demonstrates how the exercise is done.