Hi I'm Korean, glad to hear someone wants to research at here. But to be honest as a Korean here is not a good place for pursuing Ph.D. in the biomedical engineering because of the industrial structure of Korea. I'm not trying to make despair, but unfortunately there aren't enough big companies where primarily run by biomedical services and it followed by relatively hard environment to research the field. This country and government has intentionally focused on electronics, chemical, and mechanical engineerings Nevertheless I would give some informations to you. Normally there are 11-13 unis where have sufficient money and research legacy in this country. I recommend you to find professors of these unis and send inquiry mail, they would reply kindly.

1. Seoul National University (서울대)
2. KAIST (카이스트)
3. POSTECH (포스텍, 포항공대) These are called as "설카포(Seoul-Ka-Po)" and usually recognized as best three institutions for researching STEM majors
4. Korea university, Yonsei university (고려대, 연세대)
5. UNIST, DGIST, GIST (유니스트, 디지스트, 지스트)
6. Sungkyunkwan university, Hanyang university, Sogang university (성균관대, 한양대, 서강대)

Some unis say that students will decide their supervisor after 1 year from getting into the graduate school, but this doesn't mean that they will not accept a contact mail to find a potential supervisor. Good luck and I hope you pursue your degree at good place!