As other posters have said, you'll need classes in fluids, statics, and dynamics to understand the physical forces. You'd also need a materials science class focused on biological materials, or at least compliant materials, to gain a better understanding of how different materials act. Further, you'd probably want a few mechanical design courses and at least one finite element modelling course. That would get you in the ballpark of necessary academic skills. Such a course of study would represent a large part of a mechanical engineering degree.

However, all that said, what you have proposed is a huge, general topic. The question of how a semi-rigid structure interacts with an unknown tortuous, compliant path is probably worth tens of PhD theses and the corresponding years of research. It would be best (probably necessary, really) to get involved in a lab that does this sort of research. You'll need a research group who understands animal models, mechanical design and fab, and simulation to tackle these kinds of questions. You might even be able to get corporate sponsorship from a large cath manufacturer or similar company.

To begin understanding such device behavior, I would recommend trying to answer a question that feels "too small to be useful." I say that because I guarantee that when you go to mathematically model your question, build an experimental setup, or design a repeatable experiment in the first place, you will find that it is far more complicated than you'll initially anticipate, even for something that feels small. That's just the nature of asking questions like these. Through that process, you'll build the experience necessary to ask bigger questions down the road.

Feel free to PM me if you have any more questions. I love talking about stuff like this.

Source: PhD candidate in biomedical engineering, mechanical engineer with patents in steerable endoscopic devices.