I don't think there should be many pain issues with TAVR as it is not open heart surgery as with regular aortic valve replacement. With TAVR the valve is threaded through an artery so they will give pain meds in the area where the artery is, but it shouldn't be much different from other catheter type procedures ?
When it comes to open heart surgery that can be a different matter. I had a lot of pain post surgery, I wonder if it is becuase my sternum is depressed so they would have had to maniputed it and my ribs more during surgery than if I had a regular sternum - I've no idea and I haven't asked. I didn't have any pain when I was in ICU and on morphine, but once I got into high dependency they put me on other pain meds which weren't so effective and had bad side effects so that I ended up not being able to take any pain meds and had bad pain for several weeks….but that wasn't TAVR which you say you are having, that was regular cut through the sternum surgery. Funnily enough the drainage tubes being removed didn't hurt one little bit ! Different type of pain I guess - the sternum pain is bone pain. You won't have drainage tubes anyway with TAVR.