First, find out where your prospects actually spend time. LinkedIn is garbage for a lot of industries. Most doctors don't change jobs much or building "personal brands", so they're not scanning LinkedIn often. Reddit can also be often a better community.
Second, don't cold message people. Put out HELPFUL (not clickbait) content. It can be as simple as a question ("hey, I'm wondering how people solve X?"). Let the community come to you. Then follow up with the people that engaged with your content. They've shown an interest in your topic AND a willingness to engage.
At the end of every call, ask two questions: can you follow up with them with further questions and is there anyone they can think of that would be helpful to learn more? For that second question ask them, IN THE CALL, to write an intro email/message connecting you. Social validation is critical.
Finally, actually follow up. 1-4 weeks later message an update, thank them for their perspective and connection, and again ask if there's anyone they can think of to learn more from.