Best Way To Tell Google That Pages Have Been Permanently Deleted?

My need is pretty simple. The brand direction for my website has changed. I need to tell Google (and other search engines) to stop sending traffic using the word "medical." All the medical-related pages have been removed in a recent site redesign. Now you get a 404 redirect if you try to access one of the pages (and Google has indexed many of them). But this seems to fall short of achieving the SEO goal/don't like what I'm seeing in Google Analytics. It still looks to Analytics like it sent the visitor to the url that was removed (even though the visitor was redirected to the 404 page). How do you tell Google that pages have been permanently removed (not just moved as in 301). Is there a code to put in htaccess? Please advise. Thanks.