Sounds like it could be an entertaining drama. When I read the plot description ("Every time he visits an island in order to treat someone, he falls in love with a local woman. He’s always turned down, though"), it reminds me of Black Jack (from the anime, he's my favorite fictional doctor!) but the complete opposite (in the OVAs, women fall head over heels for Black Jack but he turns them down). I guess there are no actual similarities, though. :)
Most of all, I suddenly remember that I need to start watching the second season of LIAR GAME soon!! Given the relatively short time I've spent in Dramaland, I don't have that much to compare with, but Akiyama is definitely one of my favorite male characters so far! He was so cool and awesome that I even began thinking that Matsuda Shota's hot.