医界 is read as いかい (ikai) and means medical world.
いかい
ikai
せかいいしかい
World Medical Association
いがく
medical science
いしゃ
doctor
いだい
medical school
いいん
doctor's office
いちょう
medical director
い
いじ
medical practice
ぎょうかい
business world
せかい
realm governed by one Buddha
がっかい
academic world
がいかい
outside world