The professor went on with his project ( ) his illness.

D 应该是in spite of
C、B都跟句子

介词后面当然可以直接跟名词
despite [dis'pait]

prep. 不管,尽管
v.憎恨，轻视

例句与用法:
Despite all our efforts we still lost the game.
尽管我们尽了全力，我们还是输掉了比赛。
She managed despite everything to preserve her sense of humour.
她不管遇到什麽情况都竭力保持著幽默感.
Say all you want about her (ie Despite any criticism you can make), she's still a fine singer.
不管你怎麽说, 她唱得还算不错.
Demand for these books is high, despite their high price.
尽管这些书价钱昂贵，对他们的需求仍然很高。
He came to the meeting despite his illness.
尽管生病，他还是来参加会议。