Using Integration Tests for profiling memory consumption

I would like to use my integration tests to get an understanding of the memory consumption of my rails application (i.e. does the memory stablize after a number of requests). As the application is a "wizard" of sorts (i.e. screen "B" is dependent on screen "A") I don't think apache benchmark is going to be be much use. How can I use my integration tests to profile memory? How would I call it multiple times? Concurrently?

Cheers, Nicholas