When four-state Mercy broke ground on a four-story, 120,000-square-foot virtual-care center on a patch of green in Chesterfield, Mo., last spring, the blueprint represented a bold and visionary step into American healthcare’s digital future, as the center may be the first of its kind anywhere in the world. The organization estimates that the center will manage more than three million telehealth visits in the first five years following its scheduled 2015 opening.