A manga about a skilled surgeon who operates on the president's heart and removes worm-like parasites in the first chapter
After googling to no avail, I tried searching for "surgeon" on mangaupdates and go through the list of result. Among the results, K2 has a similar art style, but the synopsis is a bit different from what I remembered, so I check out the prequels Super Doctor K and Doctor K via Google and found the manga I was looking for in Vietnamese.

The image below is from volume 1 chapter 4 showing parasites on the heart:



Since I still don't know the exact title of the manga, I check the Wikipedia article of Super Doctor K. The manga was serialized from 1988 to 1998. While the series' name stayed unchanged in the magazine, it was changed to Doctor K for tankoubon released after 1996. The synopsis of Doctor K on Wikipedia matches the description in the question:


  アメリカ合衆国大統領ジム・ハミルトンが何者かの手によって瀕死の重傷となる。容疑者はドクターK。犯行の裏には何が?そして一昭の計画とは?KAZUYAの物語に終止符が打たれる。


Translation


  Jim Hamilton, the President of the United States, is suspended between life and death after receiving a serious injury from unknown person. The suspect is Doctor K. What is the motive behind the crime? And what is Kazuaki's plan? Starts the final arc of KAZUYA's story.