This is the 3158th most frequent Russian word.
медицинского
"Медицинского" means "medical" (genitive or adjective form).
Here, 'медицинского' is the genitive form of the adjective 'медицинский', modifying 'университет' in a partitive or possessive sense.
Я живу рядом с медицинского университета.
I live near the medical university.
In this sentence, 'медицинского' agrees in gender, number, and case with 'исследования', indicating possession or relation to medicine.
Нам нужны результаты медицинского исследования.
We need the results of the medical research.
'Медицинского' is used here to describe 'направления', showing the specific area related to medicine.