Louise Benge's medical problems started when she was 25. Walking became excruciating. Her calves got hard as rocks, and every step was agony. Her hands started hurting too. And the condition, whatever it was, only got worse over the next two decades. Ms. Benge's family doctor in Mount Vernon, Ky., was at a loss, as were a vascular specialist, a hand specialist and a kidney specialist. Her two sisters and two brothers had the problem too, but no doctor could figure out why. Finally, Ms. Benge's family doctor sent her medical history to a detective agency of sorts, the Undiagnosed Diseases Program at the National Institutes of Health. Set up in the spring of 2008, the program relies on teams of specialists who use the most advanced tools of medicine and genomics to try to figure out the causes of diseases that have baffled doctors.