Hi,
I'm a veterinary medicine student and am also interested in regenerative medicine. I worked on a project last summer with an engineering lab. In my experience bioengineering dealt with things such as materials science, designing machines to make a 3-D environment for cell culture, and force analysis. They had very little medicine/life science background (as in one class that lasted a couple weeks), and had trouble with concepts such as maintaining sterility. They just looked at how their structure influenced cells in a basic manner (just microscopy, not even RNA analysis).
Basically, you might want to look into regenerative medicine programs too.