It's looking like my new and improved bodily integrity -- now fortified with natural functions! -- doesn't really fly, in that (to take up Tommy's suggested phrase) we can lose the use of a natural function through means that are not really directed against bodily integrity as the term has traditionally been understood.
I'd still say, though, that we can talk about natural functions -- meaning the functions of movement, nutrition, reproduction, thought, and so forth that accord with human nature -- as a consequence of bodily integrity, in that a body with full integrity is capable of all natural functions (or possesses them at least in potency, or some such way of putting it).
Saying it the right way round, bodily integrity is the state of the body being whole and capable of functioning according to its nature. (I had "unwounded" in there, too, but if bruises, stripes, and the like are understood as contrary to wholeness, then I think it's implied by the other two conditions; also, this way bodily integrity is defined entirely in terms of possessing goods rather than lacking evils.)
In which case, acts touching on bodily integrity must touch on the wholeness and capability of natural functions of the body, but -- contrary to my previous suggestion -- acts that touch only on the circumstantial ability of the body to exercise natural functions which it possesses the potential to exercise do not touch on bodily integrity directly, but only by analogy.