What are the application areas of Pattern formation studies specific to biology?
Ok, I'm not quite sure if we are at the repairing an organ phase, but here are a few interesting examples: 
1. Philip Maini at Oxford has used pattern formation to give insight into jaguar patterning: Paper. He also has a book chapter Pattern formation and wound healing that could of of interest, although I'm not sure if this is a direct application as much as a heuristic understanding of how wound healing happens. 


From the biomedical side, Michael Levin at Tufts is doing amazing work in regenerative medicine, and a lot of what he does is inspired by pattern formation as well, although I am not sure if it explicitly uses the theory - his papers. 
This paper is one of my favorite from Ron Weiss - engineered pattern formation. Will most likely have important biomedical applications some day, although not currently.