Two ideas strike me. First, I like the idea of incorporating the mechanical and the anatomical. Perhaps two gears, one above the other and slightly offset with a spine intertwining between the two - possibly something more realistic and recognizable as gears and spine compared to the example below...  Another possibility is separating the two words with a spinal design.... I list the colors of dark red, blue and black only because they are the colors of my existing front-of-store signage. I am not opposed to other creative color choices.

ChiroWorks