Not directly related to your question, but I would be careful about passing user health data to the Game Center. I don't have enough details about your product, but here in the States there are strict privacy requirements dictated by HIPAA when it comes to protected health information (PHI). You may not want to tie a user account (in game center) to health activity depending on exactly how it's going to be used and whether it would fall under PHI as defined by HIPAA. Also, as a diabetic myself, the idea sounds pretty cool. If someone could gamify my regular blood sugar testing I'm sure I'd be more compliant with my testing schedule :)

People I look up to and follow when it comes to growth: - Sean Ellis, first marketer @ Dropbox, Eventbrite, Lookout (IPO), LogMeIn (IPO) - Josh Elman, Greylock frmr. Twitter, LinkedIn, Facebook growth - James Currier, Ooga Labs - Gagan Biyani, Lyft, Udemy, Sprig - Stan Chudnovsky, PayPal - Andy Johns, Wealthfront frmr. FB, Twitter, Quora - Saar Gur, Charles River Ventures - Adam Nash, Wealthfront - Elliot Shmukler, Wealthfront frmr. LinkedIn - Ivan Kirgin, frmr. Dropbox - Mike Volpe, Hubspot - Aaron Ginn, StumbleUpon Most are on Twitter, have a blog, Slideshare or appear in YouTube videos. There are many, many more, but that's where I'd start.

Retention–it's the best indicator of product market fit, which is the key to sustainable growth. If you can acquire and activate but not retain, you'll never establish the flywheel of momentum that comes from people who love the product and give lift to your acquisition efforts.