The "how" doesn't make as much difference as you imagine. That still sounds like "The exact medical pathway by which I acquired an honest to God brain infection." It really doesn't clear it up.
(I'm only replying because you say you aren't a native speaker. The word doesn't really add clarity in this case.)
"Slight difference" isn't very different from "it doesn't make as much difference as you imagine."
I'm not claiming it makes absolutely no difference to anyone ever.
I've been caught by the fact that HN strips out "how" at the start of a title, stopped and thought about it and, in most cases, concluded it didn't really add anything of value to the title.
(I'm only replying because you say you aren't a native speaker. The word doesn't really add clarity in this case.)