A revolution has taken place in medical science as a result

Dear Mun23,
I'm happy to help with this.

Question #1: what are we "introducing"? We are introducing methods. Presumably, this means, these new method are now taught in med school, and more doctors now are familiar with them. This is not a "surgical introduction" --- (C) is wrong.

Question #2: what is "new"? The methods are definitely new. Does it make sense to call the organs "new"? Obviously, if a doctor is implanting a kidney or liver into my body, that organ is "new" to me, but if someone else dies, and doctors take the liver that person has used for her whole life and insert it into my body, I don't know that it would make sense to call that a "new liver." The word "new" is much more appropriate for the methods. This casts serious suspicions on (C) & (D) & (E).

(D) talks about "implantation methods", which itself makes no sense, and it doesn't mention surgery at all. (D) is completely wrong.

(B) uses a sloppy shortcut. We are taking about methods of surgical implantation, or "methods of surgically implanting ..." Those phrasings are fine. Calling these methods "surgical implantation methods" is sloppy, and in particular, the phrase "surgical implantation methods of human and artificial organs" implies that the poorly named methods belong to the organs --- that the organs are the owners or sources, not the objects of the implantation. (B) is an unholy abomination that should be shot.

Admittedly, (E) is close --- really, the Question #2 problem is the only problem with (E).

Nevertheless, (A) is the best answer --- all modifiers have their proper logical relationship in (A).

Does this make sense?

Mike